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lungs following saline instillation at any time point throughout the duration of the experiment (Figures 5C,G), and no significant changes of MRI parameters were detected 24 h after BLM instillation in WT and ST2 −/− mice (data not shown). However, representative axial sections revealed a significant increase of MRI fluid signal at day 7 and 14 in WT ( Figure 5D) and ST2 −/− mice ( Figure 5F). BLM-induced edema was apparent around smaller secondary and tertiary bronchi (slice 2) known as bronchioles, but was more pronounced around larger bronchi (slice 1) indicating inflammation of upper airways (large airways) rather than lower airways (small airways) at these stages ( Figure 5C). In absence of ST2, a prominent the MRI signal was also found in the bronchi and bronchioles. This edema is characterized by augmentation of the MRI signal (in white, as indicated by yellow arrows) (Figure 5E). This difference of signals was quantified as shown in graphs (Figures 5F,G). The signal peaked at day 7 (slice 1 and slice 2) and remained significantly elevated until day 14 in ST2 −/− mice. Importantly, the MRI signal in the lung was significantly increased in ST2 −/− mice in comparison to WT mice, suggesting an earlier edema in ST2 −/− mice (Figures 5E,G). These results suggest that ST2 −/− mice present more severe edema in the inflamed airways when compared with WT mice in accordance with the microscopic data. DiscUssiOn We reported before that BLM induces pulmonary inflammation through the inflammasome-dependent release of IL-1β expression and IL-1R1 signaling (5)(6)(7)(8).
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Here, we focused on the controversial role of another IL-1 cytokine family member IL-33 in BLM-induced lung pathology. Using a clinically approved BLM as a reliable source of the drug, we observed that BLM enhanced the expression of IL-33 during acute inflammation, which remained elevated during chronic inflammation. Moreover, we show for the first time that ST2 deficiency leads to acute exacerbated pulmonary inflammation. Neutrophil influx was associated with enhanced expression of the chemokines CXCL1 and CCL2 and of the remodeling factors MMP-9 and TIMP-1 in the bronchoalveolar space and lung parenchyma, and increased cellular inflammation in lung parenchyma, 24 h after BLM airway instillation. By contrast, the expression of the cytokine IL-6 commonly associated with pro-inflammatory functions was decreased in absence of ST2. Interestingly, an in vitro study reported recently that IL-6 enhances the polarization of alternatively activated macrophages through the upregulation of the IL-4Rα chain of the IL-4 receptor and independently of IL-10 (28). Importantly, our results show that IL-6, which may favor a shift of pro-inflammatory classical macrophages (M1) into anti-inflammatory pro-fibrotic alternative macrophages (M2), is produced very early (day 1 after BLM) and dependent on IL-33/ ST2 signaling. Lung macrophages are important innate immune cells associated with two major distinct phenotypes, a pro-inflammatory subset (or classically activated macrophages) with production of pro-inflammatory cytokine, and an anti-inflammatory subset (or alternatively activated macrophages) linked with wound healing and tissue repair processes (29). At day 11, we observed no difference between WT and ST2-deficient mice, in the number and frequency of total cells, neutrophils, lymphocytes,
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and macrophages infiltrating the airways or lung tissue. Nevertheless, analysis of the infiltrating macrophages revealed reduced numbers and frequency of alternative activated (M2) macrophages in ST2-deficient mice. This was associated with a decreased of M2 macrophages-associated mediators in ST2-deficient mice with reduced expression of the CCL17/TARC chemokine characteristic of M2 macrophage profile, IL-4 and IL-5 cytokines produced by M2 macrophages, and IL-6 cytokine, which was shown to be involved in polarizing the innate immune response toward M2 macrophage activation, 11 days after BLM exposure. Levels of the anti-inflammatory cytokine IL-10 did not change in accordance with an in vitro study showing that IL-6-induced M2 macrophage polarization was independent of IL-10 (28). The expression of the Th1-like cytokine IFN-γ which in association with IL-6 promote the production of IL-1β in vitro (28) was reduced after BLM instillation in both WT and ST2-deficient mice. Levels of IL-13 cytokine known to be produced by ILC2 and/or Th2 cells were not changed, unlike previously shown (26). Our results confirm that the IL-33/ST2 pathway leads to a shift from M1 to M2 macrophage polarization but suggest an important role for early production of The image shows the two selected region of interests (ROIs) used to calculate the signal to noise ratio: the ROI 1 (yellow), corresponding to the reference signal and the ROI 2 (green) of the signal of the lungs. Transverse (axial) thoracic MRI from wild-type (WT) (c) or ST2 −/− mice (e) before (D0) and 2 weeks (D14) following single BLM administration. The arrows indicate the fluid signal detected
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by MRI at the different time point. Signal to noise ratio (lung signal in ROI 2/reference signal in ROI1) at days 0, 1, 7, and 14 before and after instillation with NaCl (light green circles) or BLM (dark green circles), calculated from the MR images from slice 1 (full line) and slice 2 (dotted line) in WT mice (D). Signal to noise ratio at days 0, 1, 7, and 14 before and after instillation with NaCl (light blue squares) or BLM (dark blue squares), calculated from the MR images from slice 1 (full line) and slice 2 (dotted line) in ST2 −/− mice (F). Comparison of the signal to noise ratio in slice 1, at days 0, 1, 7, and 14 before and after instillation with NaCl (light colors) or BLM (dark colors) in WT mice (circles) and ST2 −/− mice (squares) (g). Data are representative of two independent experiments and are expressed as mean values ± SEM [n = 4-6 mice per group, (*) (p < 0.05), ( §) (p < 0.05)]. IL-6 in lung and airways but no role for IL-10 and IL-13 at this stage in our model. In addition, we propose that pulmonary M2 macrophages are the most important cells responsible for lung fibrosis development in this model in comparison to ILC2 or type 2 helper T cells (Th2) producing IL-13, which seem dispensable for promoting inflammation resolution and tissue repair at this stage. Our results show that IL-6 is a pleiotropic cytokine involved in induction but also resolution of inflammation and
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occurrence of wound healing in vivo. These responses were associated with TIMP-1 overexpression, collagen deposit, and pulmonary fibrosis, all being attenuated in ST2-deficient mice confirming the role of IL-33/ST2 pathway in tissue repair and wound scaring driving pulmonary fibrosis as reported before at days 7 and 14 (26). These authors reported reduced cellular inflammation in the bronchoalveolar space, in particular, decreased neutrophils and macrophages in ST2deficient mice. In addition, they observed that IL-33 polarized M2 macrophages to produce IL-13 and induced the expansion of ILC2s to produce IL-13, whereas we report IL-4 and IL-5 but no IL-13 production suggesting a predominant role of M2 macrophages rather than ILC2 in enhancing profibrogenic cytokine production in an ST2-and macrophage-dependent manner and leading to lung fibrosis. The immune cell subsets involved in evolution to pulmonary fibrosis through the IL-33/ST2 pathway is still discussed with studies involving a role of ILC2 (26,30), NK cells (31), and/or M2 macrophages (26,32). By contrast, we report increased extracellular fluid retention in ST2-deficient mice as evaluated by two different methods, histological quantification and in vivo MRI. MRI is a medical imaging technique used in diagnostic medicine and biomedical research to image internal organs and physiological processes in both health and disease. The use of this non-invasive MRI allows analyzing time-dependent development of acute and chronic inflammation in vivo in individual animals during disease progression. MRI analysis demonstrated a rapid development of fluid retention in the airways knows as edema upon BLM administration, which was detectable, but not significant after 1 day, but augmented at
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days 7 and 14. Importantly, the MRI signals were much stronger in the absence of ST2 at day 7 post-BLM, suggesting an increased fluid retention/edema. Interleukin-33 activates various cell types by binding to its receptor complex consisting of ST2 and the IL-1 receptor accessory protein (IL-1RAcP). While we measured a sustained increase of IL-33 in the lung, we could not be detected IL-33 in the bronchoalveolar space. These results might be explained by an increasing availability of the IL-1RAcP chain for interaction with IL-1R1, enhancing pulmonary inflammation induced by IL-1α and IL-1β, which were also induced upon nanoparticle instillation (33). Another possibility is that intracellular IL-33 is involved in the inflammatory processes observed. Indeed, the functional role of nuclear IL-33 in myeloid cell remains poorly studied. Increased IL-33 expression was reported in lungs of patients with IPF disease, as well as in the BLM-induced lung injury in mice but most of the observed IL-33 expression was intracellular and intranuclear (27). IL-33 was shown to have pro-inflammatory and pro-fibrotic effects through its intracellular form, IL-33 remaining predominantly intracellular (27). Using both classical immunologic methods and MRI to analyze inflammation, we observed enhanced early pulmonary inflammation. These results suggest that IL-33 through ST2 interaction promotes anti-inflammatory effects and has profibrotic effect through membrane ST2, suggesting that inflammation resolution is necessary for the development of fibrosis. In addition, MRI allows a rapid, non-invasive detection of lung edema related to inflammation to monitor pulmonary inflammation and predict evolution to lung fibrosis. In addition, ST2 deficiency was associated with delayed resolution
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of fluid retention/edema, reduced shift from classical pro-inflammatory (M1) macrophages to alternative activated (M2) macrophages, which have anti-inflammatory and pro-fibrotic properties. Our data are novel showing early prolonged, unresolved inflammation in absence of ST2 and that IL-33 is an important profibrogenic cytokine that signals through ST2 to promote the initiation and progression of pulmonary fibrosis essentially by recruiting IL-6-dependent alternative activated macrophages and directing pulmonary fibrosis. Even if it appears that M2 macrophages are involved in the aberrant wound-healing cascade during fibrosis, different subtypes were proposed corresponding to activating and produced cytokines (29). However, during the different stage of pulmonary fibrosis, macrophages may coexpress markers of M1/M2 macrophage activation, showing that lung macrophages are highly plastic and may be representative of different activation states during lung fibrosis (34). However, it is not known whether the polarization of lung macrophages observed during pulmonary fibrosis is persistent or reflects transient activation states, or whether it is representative of fibrosisspecific functional heterogeneity. Better understanding of M2 macrophage kinetic and activation, and produced mediators may very important in order to identify new biomarkers and targets to treat pulmonary fibrosis. Treatments Bleomycin sulfate (7.5 and 3 mg/kg for 1 and 11-14 days experiment, respectively; Bellon Laboratories) in saline or saline alone were given through the airways by nasal instillation in a volume of 40 µl under light ketamine-xylasine anesthesia. The mice were monitored daily. Bronchoalveolar lavage (Bal) and cell counts Mice were sacrificed, and BAL was performed as previously described (6). Differential cell counts were performed on cytospin preparation (Cytospin 3,
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Thermo Shandon) after May-Grünwald-Giemsa staining (Sigma-Aldrich, St. Louis, MO, USA) according to the manufacturer's instructions. Differential cell counts were made on at least 200 cells using standard morphological criteria. lung homogenization and analysis After the BAL, the lungs were perfused with isoton to flush the vascular content. Lungs were homogenized by a rotor-stator (Ultra-turrax ® ) in 1 ml of PBS. The extract was centrifuged 10 min at 10,000 rpm, and the supernatant was stored at −80°C before mediator measurements or lung tissue MPO activity as described (36). The MPO activity was evaluated as described (6). Flow cytometry analysis After perfusion, lungs were removed from mice and cut before being digested with DNase (Sigma, 1 mg/ml) and Liberase (Roche, 5 mg/ml) for 1 h at 37°C with stirring. After digestion, cells were filtered on a 40 µM filter, and red bloods cells were lysed with Lysing buffer (BD Pharm Lyse™-BD Pharmingen). Cells were incubated with antibodies ( Table 1) lung histology The left lobe of lung was fixed in 4% buffered formaldehyde, processed, and paraffin embedded under standard conditions. Lung sections of 3 µm were stained with picrosirius red stain specific of collagen (Sigma-Aldrich). The slides were blindly examined by using a Leica microscope at 200× magnification (Leica, Solms, Germany). Inflammatory cell infiltration, edema, and interstitial fibrosis were assessed by a semi-quantitative score (with increasing severity 0-5) by two independent observers. Mediator Measurements For cytokine determination, BALF supernatants and lung homogenates were analyzed by ELISA assay kits for murine IL-33, Total lung collagen Measurements Lung homogenate
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aliquots (50 µl) were assayed for lung collagen levels using the Sircol collagen dye binding assay according to the manufacturer's instructions (Biocolor Ltd., Northern Ireland). Mri Methodology Magnetic resonance imaging was performed on a 9.4 T horizontal ultra-shielded superconducting magnet dedicated to smallanimal imaging (94/20 USR Bruker Biospec, Wissembourg, France) equipped with a 950 mT/m gradient set. A 35-mm Bruker birdcage RF coil was used. The operational software for acquisition and analysis was Paravision PV5 (Bruker). During MRI acquisition, the mouse was placed in supine position in a cradle made of Plexiglas. The head is immobilized by means of a bar teeth. Following a short period of induction in a box, anesthesia was maintained with inhaled isoflurane 1.5-2% in a mixture of air/O2 (1:1) administered with a flow rate of 0.5 l/min via a nose mask. Body temperature was maintained at 37 ± 1°C using a warm-water circulation system. Breathing rate was controlled throughout the experiment using a pressure sensor placed on the abdomen. All images were performed by synchronizing the acquisition on the breath of the animal to suppress artifacts caused by movements of the chest. An intragate flash sequence with the following parameters was used throughout the study for the detection of BLM-induced lung injury in mice: repetition time 6.9 ms, echo time 3.727 ms, field of view 3 cm × 3 cm, matrix size 512*512, flip angle = 20°, bandwidth 75.7 kHz, slice thickness 570 µm. The total acquisition time was 2 min and 58 s for an axial slice. Three resolved images
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(59 μm × 59 μm × 570 μm) were recorded with an inter-slice distance of 1 mm. The first image is located in the bronchi, and the last in the bronchioles. Mri image analysis The area of BLM-induced lesions was quantified on each image from the data set. A region of interest was drawn to manually segment the lungs. It is worthwhile to mention that this procedure includes vasculature in the segmentation since the signal from edema and vessels are of comparable intensities particularly in dosed animals. The background noise was measured from each image. Results were expressed as the ratio of the intensity of pixels in the lungs/background noise on each image. The evolution of the intensity of lungs level signal was then studied at the same time point, before (day 0) and after instillation of NaCl or BLM (days 1, 7, and 14) in control or ST2 −/− mice. statistical Tests Statistical analysis for different groups was done using the parametric one-way ANOVA with Bonferroni's multiple comparison test. The results were considered significant at p < 0.05. aUThOr cOnTriBUTiOns NR made substantial contributions in the analysis and interpretation of data, made the figures, and participated in writing the manuscript. MF made substantial contributions in the conception and design of the study and acquisition of data and participated in writing the manuscript. IM, LB, CS, MA, MLB, MN, and AG made substantial contributions in the conception and design of the study and acquisition of data. VQ and BR made critical revisions of the manuscript. SM
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and WM made substantial contributions in the conception and design of the study and acquisition of data, in the analysis and interpretation of data and participated in writing the manuscript. IC made substantial contributions in the conception and design of the study and acquisition of data, in the analysis and interpretation of data and wrote the manuscript.
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An analogue of Amitsur's property for the ring of pseudo-differential operators Let R be a ring with a derivation \delta. In this paper, we prove that an analogue of Amitsur's property holds for left T-nilpotent radideals of pseudo-differential operator rings R((x^{-1}; \delta)), where R is a delta-compatible ring. As a direct consequence of this fact, we obtain an alternative characterization of the prime radical of R((x^{-1}; \delta)). Introduction In this paper, we study rings of pseudo-differential operators, which can be seen as noncommutative generalizations of commutative Laurent series rings. The idea of using the algebra of pseudo-differential operators R((δ −1 )) is started with Schur (see [13]), later works on these algebras have done by Goodearl [7] and Tuganbaev [16]. In [16], Tuganbaev has studied the ring theoretical properties of pseudo-differential operator rings. Besides being used to construct new examples in ring theory, these rings also have some applications in different fields of mathematics, see [6] and [15] for more information. Throughout this paper, R denotes an associative ring with identity (unless otherwise stated), an ideal means a two-sided ideal and the notation ≤ is used to denote ideals. Let R be a ring equipped with a derivation δ (i.e., δ is an additive map on R satisfying the product rule δ(ab) = δ(a)b + aδ(b), for each a, b ∈ R). The pseudo-differential operator ring over the coefficient ring R formed by formal series n i=−∞ a i x i , where x is a variable, n is an integer (maybe negative), and the coefficients
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a i belong to the ring R and is denoted by the notation R((x −1 ; δ)). In [16,Proposition 7.2], it is verified that R((x −1 ; δ)) satisfies all the ring axioms, where the addition is defined as usual and multiplication is defined with respect to the relations for all a ∈ R. If δ is the zero derivation, then there exists an isomorphism of the ring R((x −1 ; δ)) onto the ordinary Laurent series ring R((x)) (This isomorphism maps x −1 onto x). The Amitsur's property of a radical says that the radical of a polynomial ring is again a polynomial ring. This nomenclature is used since it was Amitsur who initially proved that many classical radicals such as the prime, Levitzki, Jacobson, and BrownMcCoy have this property. Moreover, in [8,Proposition 4.10], it is proved that the left T-nilpotent radideal of a polynomial ring also satisfies the Amitsur's property. It is a natural question to extend the Amitsur's property for other ring extensions. As a generalization of Amitsur's property, in [9], the concept of δ-Amitsur property is introduced for the ring of differential operators. In [4], Ferrero, Kishimoto and Motose have proved that the Jacobson, prime and Wedderburn radicals again possess δ-Amitsur's property. Also, in [9,Theorem 3.3], it is showed that the left Tnilpotent radideal of the ring of differential operators satisfies the δ-Amitsur property. In their seminal papers [8] and [9], the authors have studied how to characterize the left T-nilpotent radideals of skew Laurent polynomial rings and the rings of differential
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operators. Our primary motivation in this paper is to give a description of the left T-nilpotent radideals of pseudo-differential operator rings. Before proceeding the main results, we need to recall some concepts and definitions which will be useful while discussing the left T-nilpotent radideals of pseudo-differential operator rings. Let R be a ring and δ be a derivation of R, we say that a subset S ⊆ R is a δ-subset if δ(S) ⊆ S. Let I be an ideal of R. If I is a δ-subset of R, then I is called a δ-ideal of R. According to [10], an ideal I is called a δ-compatible ideal if for each a, b ∈ R, ab ∈ I implies aδ(b) ∈ I. If the zero ideal is δ-compatible, then the ring R is called δ-compatible. Let R be a ring with a derivation δ and if I is a δ-ideal of R, then δ : R/I −→ R/I is a derivation of R/I induced by the derivation δ. If S is a subset of a ring R, we denote the left annihilator of S in R by the notation(0 : S). For an arbitrary ring R, the ideals R (α) are defined recursively in [5] as follows: Remark 1. It can be seen easily that, by using transfinite induction [3, Proposition 9, Section 1.3], the ideals defined as above are actually δ-ideals, i.e., δ(R (α) ) ⊆ R (α) , for each ordinal α. Main Results In radical theory, it is interesting to characterize the radicals
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of ring extensions in terms of the base rings. In [8] and [9], the authors have proved the analogue of this question for the left T-nilpotent radideals of skew Laurent polynomial rings and the ring of differential operators, by using König's tree lemma. In this section, we investigate the left T-nilpotent radideal of pseudo-differential operator rings R((x −1 ; δ)), where R is a δ-compatible ring. One difficulty with extending the situation for pseudo-differential operator rings is that we no longer have a finite coefficient set. We begin this section by giving the concept of left T-nilpotent set and its properties. Note that right T-nilpotent sets are defined in a similar way and we say that a set is T-nilpotent, if it is both left and right T-nilpotent. The terms are due to Bass [2], but the concepts were introduced by Levitzki [12]. By the very definition, it is easy to see that any subset of a left T-nilpotent set is again left T-nilpotent. Also, if an ideal is left T-nilpotent, then it is nil. Moreover, if an ideal is nilpotent, then it is left T-nilpotent. As one might expect, the ideal I l (R) does not need to be left T-nilpotent itself. Let I((x −1 ; δ)) be the subset of R((x −1 ; δ)) whose coefficients are all contained in I. We begin with the following lemma which gives the relations between the ideals of R((x −1 ; δ)) and R. Lemma 2.5. Let R be a ring and δ be a derivation of
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R. Then the following statements hold: (1) If I is a right ideal of R, then I((x −1 ; δ)) is a right ideal of R((x −1 ; δ)). Proof. The proof can be seen easily, by using [14, Lemma 2.1]. Lemma 2.6. Let R be a ring and δ be a derivation of R. Assume that R is δ-compatible. If aR is left T-nilpotent, then δ i (a)R is left T-nilpotent for each non-negative integer i. Proof. Fix an arbitrary sequence of elements r 1 , r 2 , . . . ∈ R. By the assumption, there exists an integer k ≥ 1 such that ar 1 ar 2 . . . ar k = 0. Since R is δ-compatible, by Lemma 1.1, we have δ i (a)r 1 δ i (a)r 2 . . . δ i (a)r k = 0 for each non-negative integer i. This means that δ i (a)R is left T-nilpotent. The following ring-theoretic characterization of T-nilpotence is obtained by Levitzki [12]. We state this result without the proof (the interested reader is referred to see [12] and [5, Theorem 1.3], for more information). Theorem 2.7. Let R be a ring (maybe without identity). Then R is left Tnilpotent if and only if the upper left annihilator series of R exists. This result enables us to obtain an analogue of Amitsur's property for the left T-nilpotent radideal of pseudo-differential operator rings. −1 ; δ)). By the Remark 1 and Lemma 2.5(2), we have that is a Z-linear combination of
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terms of the form where a i is any coefficient of f (x) for i ≤ n, b j is any coefficient of g(x) for j ≤ m and k is a non-negative integer. Since I is a δ-ideal and a i ∈ I (α+1) for each i ≤ n, by the construction of the upper left annihilator series we obtain a i δ k (b j ) ∈ I (α) for each i ≤ n, j ≤ m and non-negative integer k. This means that f (x)g(x) ∈ I (α) ((x −1 ; δ)). If α is a limit ordinal, then we have −1 ; δ)). We need to show that f (x) ∈ I (α+1) ((x −1 ; δ)). By the assumption, we have f (x)a ∈ I (α) ((x −1 ; δ)) for each a ∈ I. Since the leading term of f (x)a is a n a, we have that a n a ∈ I (α) for each a ∈ I. So, we obtain a n ∈ I (α+1) . Set f ′ (x) = f (x) − a n x n . Then −1 ; δ))) − a n x n I((x −1 ; δ)). By using the assumption and the fact that a n ∈ I (α+1) , we get If we use the same argument as above, we see that the leading coefficient of f ′ (x) belongs to I (α+1) . Continuing this procedure, we get a i ∈ I (α+1) for each i ≤ n. Thus, f
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(x) ∈ I (α+1) ((x −1 ; δ)). Therefore, we obtain is the upper left annihilator series of I((x −1 ; δ)), as desired. Theorem 2.9. Let R be a ring and δ be a derivation of R. Assume that R is δ-compatible. Then 1 ; δ)). Since a i ∈ I l,δ (R) for each i ≤ n, we have that ∞ j=0 δ j (a i )R is a left T-nilpotent δ-ideal of R for each i ≤ n. By Lemma 2.8, we get that a i R((x −1 ; δ)) is a subset of the left T-nilpotent ideal ∞ j=0 δ j (a i )R((x −1 ; δ)) of R((x −1 ; δ)), for each i ≤ n. Therefore, a i x i ∈ I l (R((x −1 ; δ))) for each i ≤ n. Hence, f (x) ∈ I l (R((x −1 ; δ))). Conversely, let f (x) = n i=−∞ a i x i ∈ I l (R((x −1 ; δ))), where a i ∈ R for all i ≤ n. We want to show that a i ∈ I l,δ (R), for all i ≤ n. Fix a sequence of elements r 1 , r 2 , . . . ∈ R and a sequence of non-negative integers i 1 , i 2 , . . . and also let us define the following sequence of elements , where m 1 , m 2 , . . . are integers. Since f (x) ∈ I l (R((x −1 ; δ))),
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there exists an integer k ≥ 1 such that If we expand this product, we see that the leading coefficient is a n r 1 a n r 2 . . . a n r k = 0. Since R is δ-compatible, by using Lemma 1.1, we get δ i1 (a n )r 1 δ i2 (a n )r 2 . . . δ i k (a n )r k = 0 for any non-negative integers i 1 , . . . , i k . Hence, ∞ j=0 δ j (a n )R is left T-nilpotent, and this means that a n ∈ I l,δ (R). By the above discussion, we have a n x n ∈ I l (R((x −1 ; δ))). Set f ′ (x) = f (x)−a n x n . Then we have f ′ (x) ∈ I l (R((x −1 ; δ))). Thus, the leading coefficient of f ′ (x), namely a n−1 , belongs to I l,δ (R). And if we apply the same procedure, then we obtain a i ∈ I l,δ (R) for each i ≤ n. Therefore, f (x) = n i=−∞ a i x i ∈ I l,δ (R)((x −1 ; δ)). In [8, section 5], the higher left T-nilpotent radideals are defined as follows: Set I l (R))}. If α is a limit ordinal, then we define As mentioned in [8], one can define the prime radical of a ring R alternatively as the limit of the left T-nilpotent radideals. Now, our aim is
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to generalize Theorem 2.9 for higher left T-nilpotent radideals by using transfinite induction. Hence, we obtain a new characterization for the prime radical of pseudo-differential operator rings P (R((x −1 ; δ))), where R is δ-compatible. Proof. We will use transfinite induction to prove the statement. For α = 1, the result is clear. Assume that the result is true for every ordinal β < α. If α is not a limit ordinal, then α is a successor of some ordinal β and by the assumption, we have I l,δ (R))((x −1 ;δ)), whereδ is the derivation of the factor ring R/I (α) l,δ (R) induced by δ. By Theorem 2.9, we have that the coefficients of the elements of I l R/I (β) l,δ (R) ((x −1 ;δ)) are determined by the the ideal I l (R/I (β) l,δ (R)). By using the natural isomorphism and the natural surjection, we get the result. If α is a limit ordinal, then by Theorem 2.9 we have l,δ (R) ((x −1 ; δ)).
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Author Correction: MRGPRX2-mediated mast cell response to drugs used in perioperative procedures and anaesthesia The study of anaphylactoid reactions during perioperative procedures and anaesthesia represents a diagnostic challenge for allergists, as many drugs are administered simultaneously, and approximately half of them trigger allergic reactions without a verifiable IgE-mediated mechanism. Recently, mast cell receptor MRGPRX2 has been identified as a cause of pseudo-allergic drug reactions. In this study, we analyse the ability of certain drugs used during perioperative procedures and anaesthesia to induce MRGPRX2-dependent degranulation in human mast cells and sera from patients who experienced an anaphylactoid reaction during the perioperative procedure. Using a β-hexosaminidase release assay, several drugs were seen to cause mast cell degranulation in vitro in comparison with unstimulated cells, but only morphine, vancomycin and cisatracurium specifically triggered this receptor, as assessed by the release of β-hexosaminidase in the control versus the MRGPRX2-silenced cells. The same outcome was seen when measuring degranulation based on the percentage of CD63 expression at identical doses. Unlike that of the healthy controls, the sera of patients who had experienced an anaphylactoid reaction induced mast-cell degranulation. The degranulation ability of these sera decreased when MRGPRX2 was silenced. In conclusion, MRGPRX2 is a candidate for consideration in non-IgE-mediated allergic reactions to some perioperative drugs, reinforcing its role in mast cell responses and their pathophysiology. In this paper we will analyse whether MRGPRX2 may be involved in pseudoallergic reactions associated with drugs used in anaesthesia, in which an IgE-mediated mechanism is not identified. To this end, we intend to test drugs
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used in perioperative procedures and anaesthesia, such as opiates, muscle relaxants, iodinated contrast agents, antibiotics and NSAIDs, based on MRGPRX2 expression in a mast cell line, and to analyse the ability of these drugs to induce a response mediated by this receptor. We hypothesize that the MRGPRX2 receptor may be responsible for allergic reactions occurring during anaesthesia. To confirm this hypothesis, we tested drugs capable of degranulating mast cells in cells where the expression of MRGPRX2 had been selectively silenced, to determine the role of the receptor in such process. Moreover, sera from both patients who had suffered an allergic reaction during anaesthesia and healthy controls were also tested to assess the reactivity in our cell model. Results Analysis of the ability of drugs used during perioperative procedures and anaesthesia to induce degranulation in human mast cells. We first tested the ability of several drugs used in perioperative procedures and anaesthesia (cisatracurium, rocuronium, meglumine amidotrizoate, iohexol, iomeprol, propofol, vancomycin, teicoplanin, amoxicillin-clavulanic acid, diclofenac, remifentanil and morphine) to directly stimulate mast cells. To this end, we incubated LAD2 mast cells with different concentrations of these drugs and analysed their degranulation response using a β-hexosaminidase activity assay. Unstimulated cells (CTL-) were used in all cases as negative controls to evaluate basal degranulation, and cells stimulated with phorbol 12-myristate 13-acetate (PMA) plus ionomycin (I + P) were used as positive controls for degranulation. Our data showed that, among the NMBAs tested, only cisatracurium, at doses over 50 µg/mL, was able to induce cell degranulation (Fig. 1A). Of the three
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iodinated contrasts used (Fig. 1B), meglumine amidotrizoate (at doses over 100 mg/mL) and iomeprol (at doses over 350 mg/mL), but not iohexol, induced cell degranulation. Opiate morphine (but not remifentanil) induced cell degranulation at very low doses (10 μg/mL) (Fig. 1C), whereas, of all antibiotics tested, only vancomycin at a dose of 500 μg/mL induced cell degranulation (Fig. 1E). As an exception, the ability of propofol to induce mast cell degranulation was determined by flow cytometry, because the colour of the compound interfered with the β-hexosaminidase colorimetric assay. Propofol did not induce mast cell degranulation (data not shown). In short, cisatracurium (17.75 ± 2.03, p = 0.022), meglumine amidotrizoate (26 ± 0.73, p = 0.026), iomeprol (26.12 ± 0.52, p-value = 0.025), morphine (56.92 ± 0.14, p < 0.0001) and vancomycin (44.06 ± 1.39, p < 0.0001) caused mast cell degranulation in vitro when examined in comparison with unstimulated cells (6.71 ± 0.62) ( Table 1). Cell viability was measured in all cases in order to discard degranulation due to cell mortality. Cell viability was similar in all cases and over 90% (data not shown). Mast cell degranulation by cisatracurium, morphine and vancomycin depends on MRGPRX2 expression. To test whether the stimulation of mast cells by these drugs is mediated by the MRGPRX2 receptor, we obtained human mast cells with reduced MRGPRX2 receptor expression from the LAD2 line, using a lentiviral knockdown system. Cells transduced with the scramble sequence, which we designated as non-target shRNA, were used as controls and analysed together with the silenced cells
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(MRGPRX2-shRNA). Receptor silencing was confirmed by Western blot and flow cytometry ( Fig. 2A,B). FcεRI and KIT, the most characteristic receptors involved in mast cell degranulation and cell survival, were analysed following the MRGPRX2 knockdown. As shown in Fig. 2C-F, the levels of FcεRI (94.9 ± 1.75 vs. 89.73 ± 1.24, p = 0.08) and KIT (98.68 ± 0.71 vs. 96.28 ± 1.77, p = 0.277) expression were similar in both the control and MRGPRX2-silenced cells. Sera from patients who experienced anaphylactoid reactions induce MRGPRX2-mediated mast cell degranulation. The main problem related to the study of anaphylactoid reactions was the great diversity of drugs that can be administered simultaneously to the same patient during the anaesthetic procedure. Hence, in addition to exposing mast cells separately to different drugs, we decided to analyse the response of our mast cell model to sera collected from patients who had suffered an anaphylactoid reaction during anaesthesia. For this purpose, we obtained several serum samples following the onset of an allergic reaction to perioperative drugs (from time of reaction to 24 h), with a negative skin test (skin prick and intradermal tests). Three of the samples were collected further than 24 hours from the onset of the reaction. Five serum samples from healthy donors (control sera) were also collected. Three of them were from patients after anaesthesia procedure with several drugs showing no adverse reaction. The tryptase and histamine levels of all the allergic patients were also determined ( Table 2). First, we assessed the ability of the sera to induce
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degranulation in mast cells by measuring CD63 expression using flow cytometry. Unlike the control sera (13.78 ± 2.26 and 11.58 ± 3.964), most of the patient sera were activators to some extent. After MRGPRX2 knockdown, we observed a statistically significant reduction in the activation capacity of most of the sera except for sera from patients P3, P4, P8 and P9. The control sera showed no significant differences (Fig. 4A). This indicated that the degranulation ability of mast cells was partly dependent on MRGPRX2 receptor expression. We collected sera from some of our patients at long term time points. As shown in Fig. 4B, all tested sera collected after 24 hours of the time of reaction showed statistically significant less capability to activate mast cell degranulation. Finally, we analysed the sera from patients who went through a perioperative procedure without any anaphylactoid response (C3*, C4*, C5*). We observed that these sera had some ability to induce mast cell degranulation compared to control sera from healthy patients (C1 and C2). This activity was reduced in MRGPRX2-silenced cells (Fig. 4C). Discussion The newly discovered MRGPRX2 receptor is a non-canonical G-protein-coupled receptor expressed on human mast cells that plays a role in host defence and allergic inflammation 4 . Recent findings suggest a role for this receptor in non-IgE-mediated drug-induced pseudoallergic reactions 5 . In vitro studies have demonstrated that this receptor triggers a different type of mast cell degranulation process than the IgE-dependent one. The substance P-dependent activation of the MRGPRX2 receptor induces a quick, and almost immediate, secretion
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of small and relatively spherical granules. On the contrary, FcεRI-dependent degranulation results in a more gradual degranulation, with longer and heterogeneous granules. In vivo, the allergic reaction caused by MRGPRX2 is a faster and more localized reaction compared to the more intense, prolonged and systemic reaction triggered by the FcεRI receptor 7 . In clinical practise, Mertes et al. described that IgE-mediated anaphylaxis are more prone to increase tryptase levels and induce bronchospasm and cardiovascular symptoms while non-IgE mediated reactions frequently show isolated cutaneous symptoms without an increase in tryptase 8 . The purpose of our research was to study the recurring clinical issue of allergic reactions to drugs used during perioperative procedures and anaesthesia, which in many cases may be severe or life-threatening for the patient. Despite their low prevalence, we observed that the frequency of these reactions was higher than expected, up to 1 in every 385 procedures 9 . We focussed in drugs which induce adverse reactions without a verifiable IgE-mediated mechanism. Among the drugs analysed in this study, morphine and vancomycin resulted in mast cell degranulation at administered doses. Both drugs triggered mast cell degranulation through MRGPRX2 since silencing of the receptor significantly reduced degranulation. This result falls in line with the ability of these two drugs to induce non-IgE-mediated reactions according to clinical experience 10 . Skin tests are usually negative in these cases, and the reaction frequently appears during the first administration of the drug, without the possibility of becoming sensitized in a previous contact. We have not a complete
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explanation for the negative result of skin tests in these patients. Skin mast cells have MRGPRX2 receptors in their membrane, and one should wait a positive skin test via MRGPRX2. However, MRGPRX2 is a low-affinity receptor (µg/ml range) 11,12 compared to IgE sensitivity against allergens (ng/ml range) 13,14 . Thus, MRGPRX2 receptor activation in vivo might require to be in close proximity to high local concentrations of the drug 10 . Other possible explanation could be the modification of the drug after binding to skin proteins or the production of a metabolite that modifies the capacity of activation of MRGPRX2. On the other hand, we should also take into consideration that, even if IgE-mediated reactions are usually associated with positive skin tests, some authors claim to be cautious with the interpretation of these tests and propose basophil activation tests (BAT) as a more reliable measurement of specific IgE-mediated anaphylaxis 15 . In this context, it has been reported that the results of the prick test with vancomycin does not correlate with the "red man syndrome" (RMS) elicited after intravenous infusion of vancomycin, suggesting that the route of administration could elicit different responses 16 . The fact that the drug, which did not produce a positive skin test, was able to activate in vitro mast cells via MRGPRX2, could be explained by the different local concentration of the drug in a cell culture in vitro compared show the mean ± SEM. Statistical significance (***p < 0.001) was determined using unpaired t-test with Welch's correction and it is
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relative to non-target shRNA. to the in vivo situation, where mast cells may be more heterogeneous and scattered in the skin and the drug can suffer modifications in its structure and inactive metabolites may be produced. As in previous studies carried out with atracurium 5 , cisatracurium was seen to cause a dose-dependent MRGPRX2-mediated degranulation in LAD2 cells. Interestingly, cases of IgE-mediated allergic reactions to atracurium have also been reported, thus suggesting a dual mechanism of action for this drug 17 . We detected no mast cell degranulation in response to rocuronium. In fact, and according to our data, rocuronium proved to significantly induce degranulation mediated by mouse ortholog receptor MrgprB2 rather than by MRGPRX2, thus proving the existence of differences between the human receptor and its mouse ortholog 5 . Our data showed that all sera collected at the onset of the allergic reaction (<24 h) in patients with a negative skin test to all the suspicious drugs could induce mast cell degranulation. This capacity is not seen in sera collected at a further time from the anaphylactoid reaction (>24 h). Patients who had an anaphylactoid reaction to morphine, cisatracurium and atracurium showed a statistically significant reduction in MRGPRX2-silenced cells compared to non-target cells. Interestingly, patients who had experienced a reaction to remifentanil and rocuronium did not show a significant decrease. This correlates with our data showing that rocuronium and remifentanil did not trigger any mast cell activation in vitro. Additionally, sera from patients who received several drugs also showed a statistically significant reduction of
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the degranulation capacity except for those from patients 8 and 9. Interestingly some of the drugs administered to these latter patients, such as succinylcholine 5 or fentanyl 18 , have been described in the past as non-histamine releasers 14 . Consequently, the ability of sera to induce mast cell degranulation could be explained by the residual presence of drugs or drug metabolites in the serum samples, indicating that some compounds found in patients could trigger a mast cell response 4,6,19 . This hypothesis is supported by the fact that the serum from patients who received several drugs without eliciting an allergic response can also induce some mast cell degranulation in vitro. But the higher degranulation capacity of the sera from patients who suffered an anaphylactoid reaction could suggest that some allergic compounds released by the immune system at the moment of the reaction may also participate, inducing mast cell degranulation. It has been widely reported that iodinated contrast mediums (ICMs) amidotrizoate and iomeprol can induce allergic reactions 6 . However, in our model, the doses needed to induce β-hexosaminidase release in mast cells were also affecting cell viability. For that reason, we consider that the detected β-hexosaminidase activity was due to cell mortality, which causes general release of intracellular components, rather than to a degranulation process. The other ICM tested, iohexol, did not activate mast cells in vitro at any doses assessed. Therefore, these drugs were excluded from the MRGPRX2 analysis and further studies are required to determine the molecular basis and mechanism of ICM-mediated allergic
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reactions. In the near future, it may prove useful to combine drugs and analyse the variable effects of each combination on mast cell degranulation, to collect patient sera at different time points following the anaphylactoid reaction, and to follow up on the kinetics and ability of the sera to induce mast cell degranulation. In short, our results show that the MRGPRX2 receptor is a potential cause of non-IgE-mediated allergic reactions to several drugs commonly used during perioperative procedures and anaesthesia. Supporting our results, a recent study reported that morphine analogues can induce mast cell degranulation mediated by the MRGPRX2 receptor 10 . Our research broadens the scope for the study of non-IgE-mediated reactions. Several conserved polymorphisms for the MRGPRX2 receptor have been described, with 1172 being listed at present in the RefSeq database 20 , of which 152 are missense mutations. An analysis of MRGPRX2 receptor polymorphisms in the genome of allergic patients would enable us to determine whether this receptor has genomic variability, which could explain why only some patients experienced exacerbated reactions to certain drugs. This genomic variability could increase the receptor's affinity to the drugs or induce a stronger intracellular response. One possible explanation for this is the fact that this receptor is differentially expressed in the mast cells of different patients, triggering a greater response in those with increased expression. In this regard, MRGPRX2 has been found to be increased in patients with severe chronic urticaria 21 . The increased expression of this receptor may explain why the injection of neuropeptides, such
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as substance P, enhances wheal reactions in patients with chronic urticaria as compared to healthy controls. Overall, we consider that the knowledge about the different forms, variants, or expression levels of the MRGPRX2 receptor may constitute a powerful diagnostic tool for evaluating the predisposition of patients to suffer adverse reactions in response to certain drugs. Such knowledge would allow professionals to personalize the combination of drugs used based on each patient's genetic profile, so as to reduce the number of anaphylactoid reactions occurring during clinical practice. Materials and Methods This study was approved by the institutional review board of the University of Navarra. Biological samples. The LAD2 human mast cell line was kindly provided by Dr. D. Metcalfe, (NIH Washington) 22 . The HEK 293LTV cell line (Cell Biolabs Inc, San Diego, CA, USA) was used for lentivirus production. The control sera from healthy patients and the sera from patients who had experienced an allergic reaction in response to a muscle relaxant (rocuronium, cisatracurium or atracurium), an opiate (morphine or remifentanil), or after receiving several drugs during the anaesthesia induction, and who had negative allergy tests to these drugs, were collected at the Clínica Universidad de Navarra (Table 2). These patients had already been included in previous studies 1,9 . All serum samples, were extracted during the onset of the allergic reaction, no later than 24 h. We also obtained 3 samples from our patients at a further time from the reaction (48 h, 1 and 2 months). Control sera from healthy individuals and from patients
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that underwent anaesthesia procedure with no anaphylactoid reaction were also collected. All of them are indicated in Table 2. Ethics statement. The study was approved by the State Ethics Committee and the Ethics Research Committee of the University of Navarra. The authors performed these procedures in accordance with the approved guidelines, obtaining informed consent from each subject before conducting the experiments. Mast cell degranulation assays. Degranulation was analyzed based on the levels of β-hexosaminidase activity at the supernatant or on CD63 expression on the cell membrane, assessed by flow cytometry, as described in previous studies 24,26 . β-hexosaminidase is an enzyme found inside mast cell granules and released at the supernatant after cell degranulation. CD63 is a protein found in the granules and expressed on the cell membrane after degranulation. For each type of essay, we briefly incubated 2 × 10 4 -1 × 10 5 cells at 37 °C for 30 minutes with several concentrations of the drugs described earlier. For IgE-stimulation, we sensitized mast cells overnight with biotinylated IgE (Abbiotec, San Diego, CA, USA) (0.1 µg/mL), and stimulated them for 30 minutes at 37 °C with streptavidin (0.4 µg/mL) to induce IgE crosslinking. As a positive control for degranulation, we incubated the samples with ionomycin (200 µg/mL) and PMA (10 ng/mL) for 30 minutes at 37 °C. To carry out the degranulation assays with patient sera, we incubated each serum sample with 1 × 10 5 mast cells in Tyrode's buffer for 30 minutes at 37 °C, at a ratio of 1:1, for a
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total volume of 100 µL. Because of the colour of the serum samples, which interfered with the β-hexosaminidase colorimetric test, only flow cytometry assays with the CD63-APC marker were performed for the sera. To rule out the drugs' toxic effects on the cells, a viability count was also carried out in all cases, using trypan blue in the β-hexosaminidase assays and propidium iodide (PI) in the flow cytometry assays. Statistical analysis of the results. All study data are shown as a mean value ± SEM. Multiple group comparisons were performed using one-way analysis of variance (ANOVA), followed by the Bonferroni post-hoc test. Student's T-test with Welch's correction was used to conduct all analyses between both groups (patients and controls). In addition, the analyses were carried out using GraphPad Prism 6. P-values < 0.05 (two-tailed) were considered statistically significant. The β-hexosaminidase assays were performed in triplicate, and all experiments were carried out at least three times. The CD63 analyses carried out by flow cytometry were also performed at least three times. Data availability. The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request. This degranulation capacity is reduced when MRGPRX2 is downregulated. (A) Percentage of CD63 expression of non-target or MRGPRX2 knockdown mast cells incubated with sera from healthy controls (control sera) or sera from patients (see Table 2). Data show the mean ± SEM. Statistical significance (*p < 0.05, **p < 0.01, ****p < 0.0001; unpaired t-test with Welch's correction) is for non-target shRNA versus MRGPRX2 shRNA.
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(B) Percentage of CD63 expression in mast cells incubated with control sera or patient's sera at different time points (0 h to 24 h versus long term collection). Data show the mean ± SEM. Statistical significance (*p < 0.05, **p < 0.01, ****p < 0.0001; unpaired t-test with Welch's correction) is for 0-24 h versus long term collection. (C) Percentage of CD63 expression of non-target or MRGPRX2 knockdown mast cells incubated with sera from healthy controls and healthy patients who received several drugs. Data show the mean ± SEM. Statistical significance (*p < 0.05, **p < 0.01, ****p < 0.0001; unpaired t-test with Welch's correction) is for non-target shRNA versus MRGPRX2 shRNA. All data is representative of three independent experiments.
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A note on fractional type integrals in the Schr\"{o}dinger setting Assume $\mathcal{L}=-\Delta+V$ is a Schr\"{o}dinger operator on $\mathbb{R}^d$, where $V$ belongs to certain reverse H\"{o}lder class $RH_\sigma$ with $\sigma\geq d/2$. We consider the class of $A_{p,q}$ weights associated to $\mathcal{L}$, denoted by $A_{p,q}^{\mathcal{L}}(\mathbb{R}^d)$, which include the classical Muckenhoupt $A_{p,q}(\mathbb{R}^d)$ weights. We obtain the quantitative $A_{p,q}^{\mathcal{L}}(\mathbb{R}^d)$ estimates for fractional integrals associated to the Schr\"{o}dinger operator. Particularly, the quantitative weighted endpoint bound for fractional integrals associated to the Schr\"{o}dinger operator is first established, which was missing in the literature of Li et al. \cite{LRW}. Moreover, we generalize weighted endpoint inequalities to weighted mixed weak type inequalities for fractional type integrals in the Schr\"{o}dinger setting. Introduction and main results 1.1. Background. In recent years, the problem of quantitative weighted estimates for operators in Laplacian setting have appealed to many mathematician. The initial result was opened by Buckley [5], who proved the following sharp weighted estimates for Hardy-Littlewood maximal operator M M f L p (ω) [ω] 1/(p−1) To resolve an important endpoint result in the theory of quasiconformal mappings that had been conjecture by Astala, Iwaniec and Saksman [1], Petermichl and Volberg [33] settled the quantitative weighted estimates for Beurling transform. Petermichl [31,32] also obtained the sharp bounds for the Hilbert and Riesz transforms. While for general Calderón-Zygmund operators, Hytönen [17] proved the dyadic representation theorem for Calderón-Zygmund operators, this leads to the proof of A 2 conjecture. In 2010, Lacey, Moen, Pérez and Torres [22] obtained sharp bounds for the classical fractional integral operators |x − y| n−α
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dy as follows. Very recently, under the umbrella of "domination by sparse operators", which give a new way to obtain the quantitative weighted estimates for harmonic analysis operators, there is a vast literature concerned with this topic, see [9,10,11,12,13,15,18,21,23,24,26,28] et al., among these, the work of Lerner [23,24] played a center role. Quantitative weighted bounds for operators in the Schrödinger setting began by the work of Li, Rahm and Wick [25]. To state their results, we first recall some necessary definitions. We consider the Schrödinger operator L on R d with d ≥ 3, where ∆ is the standard Laplacian operator in R d and V is a non-negative potential which belongs to certain reverse Hölder class RH σ (σ > d/2), that is, for every ball B ⊂ R d . Define fractional integral L −α/2 and fractional maximal function M ρ,θ α as below. where ψ θ (Q) := (1 + r Q /ρ(x Q )) θ , ρ is the critical radius function (see Section 2 for a precise definition), and x Q , r Q are the center of cube Q and the side-length of Q, respectively. In [25], the authors obtained following quantitative weighted estimates for L −α/2 and M ρ,θ α . Theorem 1.2. (cf. [25]) Suppose that 0 < α < d. Let 1 ≤ p < d/α and that q satisfies Subsequently, Zhang and Yang [38] obtained quantitative weighted strong (p, p) type estimates for Littlewood-Paley operators associated to L. The author and Wu [37] recently investigated quantitative
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endpoint estimates for maximal operators and variation operators associated to L. More generally, Bui et al. [6,7] achieved quantitative weighted strong (p, p) type estimates for square functions and singular integrals associated to general differential operators. On the other hand, to seek a new proof for the qualitative estimate of (1.1), in the case of dimension 1, Sawyer [34] showed that it suffices to establish the following result: if µ, ν ∈ A 1 (R), then It is obvious that (1.2) reduces to the weighted weak (1, 1) type of M when ν = 1. However, the proof of (1.2) is highly non-trivial due to the covering lemmas do not apply for M (f ν)/ν and µν may be very singular. We refer these types of estimates as weighted mixed weak type estimates. Later, Cruz-Uribe, Martell and Pérez [14] extended (1.2) to higher dimension and Calderón-Zygmund with weights µ, ν ∈ A 1 (R d ) or µ ∈ A 1 (R d ) and ν ∈ A ∞ (µ). Li, Ombrosi and Pérez [29] improved the results in [14] by assuming In the case of fractional type integrals, Berra, Carena and Pradolini [2] proved the following weighted mixed weak type inequalities. Theorem 1.3. (cf. [2]) Let 0 < α < d, 1 ≤ p < d/α and q satisfy 1/q = 1/p − α/d. If µ, ν are weights such that µ, ν q/p ∈ A 1 (R d ) or µν −q/p ′ ∈ A 1 (R d ) and ν q ∈ A
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∞ (µν −q/p ′ ), then there exists a positive constant C such that for every t > 0 and every f ∈ L ∞ c (R d ) where T is the fractional maximal operator or I α . Recently, Berra, Pradolini and Quijano [3] first established weighted mixed weak type inequalities for Hardy-Littlewood maximal operator and singular integrals in the Schrödinger setting. For more works on this topic, we refer readers to see [8,9,10,27,28,19] etc. 1.2. Aims and questions. The aim of this paper is to continue the line of Li-Rahm-Wick [25] and Berra-Pradolini-Quijano [3] to study the quantitative weighted estimates and weighted mixed weak type inequalities in the Schrödinger setting. There are several problems of fractional type integrals associated to L remain to resolve. In [25], the authors obtained quantitative weighted strong (p, q) type estimates for L −α/2 . It is very natural to ask the following question. Question 1: Can we establish quantitative weighted endpoint estimates for L −α/2 ? Berra et al. [2] obtained weighted mixed weak type inequalities for fractional maximal operator and fractional integral operators associated to ∆. The proof of Theorem 1.3 relies heavily on extrapolation theorem established in [14] and Coifman type inequality proved in [30]. However, the classes of weights associated to L is larger than classes of classical Muckenhoupt weights. Besides, deficiency of the regularity that −∆ possesses, operator of the form L = −∆ + V present many challenges. Hence, the technique used in [2] may not be applied to fractional integral operators.
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Question 2: How to achieve the weighted mixed weak type inequalities for M ρ,θ α and L −α/2 ? 1.3. Main results. Our first result is concerned with the quantitative weighted estimates for L −α/2 . Remark 1.5. This is a full version of Theorem 1.1 adapted to the Schrödinger setting. Besides, we provide a different method to the quantitative weighted strong (p, q) type estimates for L −α/2 . However, this result is not comparable to the one in Theorem 1.2. For instance, if p ′ > q and 0 ≤ α < d/2, our result is better, while the result in Theorem 1.2 is better provided that p ′ > q and d/2 < α < d. Our next theorems give a positive answer to the second question. We organize the rest of the paper as follows. In Section 2, we will give some preliminaries. In Section 3, we will prove Theorem 1.4 and the proofs of Theorems 1.6, 1.7 will be given in Section 4. Throughout the rest of the paper, we denote f g, f ∼ g if f ≤ Cg and f g f , respectively. For any ball B := B(x B , r B ) ⊂ R d and σ > 0, χ B represents the characteristic function of B and σB means B(x B , σr B ). Preliminaries In this section, we introduce some basic definitions and necessary lemmas. We first recall the definition of critical radius function. A function ρ : R d → (0, ∞)
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is called critical radius function if there exist constants C 0 and N 0 such that for any x, y ∈ R d , In particular, let d ≥ 3, V ∈ RH σ (σ > d/2) be a non-negative function, not identically zero. Shen [35] proved that the function is a critical radius function. The following covering lemma is very useful in our proof. Lemma 2.1. (cf. [16]) There exists a sequence of points x j in R d , so that the family {Q j := Q(x j , ρ(x j ))} j∈Z + satisfies: Next, we introduce new classes of weights, which are extension of A p,q weights associated to critical radius function introduced in [36]. Let Q 0 be a cube. If we replace Q ∈ Q ρ by Q ⊂ Q 0 in Definition 2.3, then we say a weight defined on Q 0 belongs to A p (Q 0 ) (p ≥ 1). We give a remark about these classes of weights. Finally, we recall the following lemma, which is concerned with the extension of weights. where the implicit constants are independent of ω 0 and p. Quantitative weighted estimates for fractional integral operators associated to Schrödinger operator In this section, we give the proof of Theorem 1.4. Before this, we first establish the following quantitative weighted estimates for ρ-localized classical fractional integral operators. Lemma 3.1. Let d ≥ 3, ρ be a critical radius function and B x := B(x, ρ(x)) with x ∈ R d . Suppose that
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0 < α < d, 1 ≤ p < d/α and 1/q = 1/p − α/d. Proof. (i). We only prove the case p = 1 since p > 1 is similar. Let τ = 1 + C 0 2 N 0 N 0 +1 , where C 0 and N 0 are given in (2.1). Let {B j : B(x j , ρ(x j ))} j∈N be the family of balls given by Lemma 2.1. Denote B j = τ B j , then B x ⊂ B j for any j ∈ N and x ∈ B j . To see this, for any y ∈ B x , in virtue of (2.1), we have Now, we claim that for any ω ∈ A ρ,loc 1,q (R d ) and j ∈ N, there holds ω q | B j ∈ A 1 ( B j ) and (3.1) In fact, for any ball B := B(x B , r B ) ⊂ B j , we demonstrate it by considering two cases: which further implies that . This shows (3.1). Case 2. r B > τ ρ(x B ): In this case, it is easy to see that B(x B , τ ρ(x B )) ⊂ B ⊂ B j . Again by (2.1) and |x j − x B | ≤ τ ρ(x j ), we have ρ(x B ) ∼ ρ(x j ). Combing these facts, we deduce that |B| ∼ | B j | and . This also verifies (3.1).
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Now we return to the proof of our lemma. For any j ∈ N, in virtue of Lemma 2.5 and (3.1), ω q | B j admits an extension ω j on R d , which satisfies ω j ∈ A 1 (R d ) and where the implicit constant is independent of j. By making use of Theorem 1.1, we have that for any ω ∈ A 1,q (R d ), Then by Lemma 2.1, we have This completes the proof of (i) of Lemma 3.1. (ii). We still use the notations given in (i). Similar to (3.1), we get . Therefore, in virtue of Theorem 1.1, Lemma 2.1 and p < q, we deduce that To achieve our main results, we also need the following lemma. Lemma 3.2. (cf. [37]) Let d ≥ 3, θ ≥ 0 and ρ be a critical function. Assume that 0 ≤ α < d, 1 ≤ p < d/α and 1/q = 1/p − α/d. Then for ω ∈ A ρ,θ p,q (R d ) and f ∈ L p (ω p ), Now, we are in the position to prove Theorem 1.4. , ρ(x)). It follows that Denote the kernel of e −tL by p t (x, y). It is well known that p t (x, y) ≤ h t (x − y), where h t (x − y) is the classical heat kernel. Then we have the pointwise inequality This together with Lemma 3.1, allows us to get that Next, we consider L −α/2 f 2
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. Given N > 0, recall that there is a constant C N such that for any x, y ∈ R d , see [20]. Thus, where we use e −s s −M/2 for any M > 0 in the last inequality. Let θ ≥ 0, note that for Then we can continue the estimate with In view of Theorem 1.2, we obtain This combines with (3.3), we get f L p (ω p ) , 1 < p < n/α. Weighted mixed weak type inequalities for fractional type integral operators associated to Schrödinger operator In this section, we prove Theorems 1.6 and 1.7. To prove Theorem 1.6, we adapt some ideals in [2]. We need the following lemmas. . Then there exists θ ≥ 0 such that for every positive t, Lemma 4.2. Let 0 < α < d, 1 ≤ p < d/α, 1/q = 1/p − α/d, s = 1 + q/p ′ , ρ be a critical radius function and θ ≥ 0. For each non-negative function ω 0 and f 0 ∈ L p (R d ), there holds Proof. Fix x ∈ R d . Let Q := Q(x Q , r Q ) be a cube and x ∈ Q. Applying Hölder's inequality with exponents d/(d − α) and d/α, we get 1 Taking a supremum over all cubes contained x, we arrive at the first conclusion. To achieve the second result. If s = 1, the second result follows by the first conclusion. If s > 1, by
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using 1 Taking a supremum over all cubes contained x, we get the second conclusion. It follows that Then ν q | B j admits an extension ν q j which satisfies ν q j ∈ A s (µν −q/p ′ ) ⊂ A ∞ (µν −q/p ′ ). Denote ω = µν −q/p ′ . Similarly, ω| B j admits an extension ω j which satisfies ω j ∈ A 1 (R d ). Therefore, by Theorem 1.3, µν q/p x ∈ B j : From this and Lemma 2.1, we have j∈N µν q/p x ∈ B j : This, together with (4.1) and (4.2), allows us to get the desired result.
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The training of Albanian Public Administration : An Analysis of Training Policies and Their Impact in the Professional Development of Civil Servants Teuta Nunaj This study does analyse the training policies that apply for civil servants in the Public Administration and how this training process has an impact in the professional development of civil services in Albania. The research question is: What effects does the training have in the development of Human Resources in the public administration in Albania? The data are obtained from sevent elite interviews and four ministries randomly selected through questionnaires, with n=179 civil servants. By using qualitative and quantitative method is found that the training has directly a significant and positive impact in the professional development of Albanian civil servants. Doing the training is a condition for the development of civil servants on public administration. The civil servants do have a growing request for effective and appropriate training. However, there are the responsible institutions for the training (ASPA and the ministries) that should increase also the level of collaboration, to obtain better results from training. Introduction In the frame of the reform, the public administration has made a lot of changes.One of the main element is the development of the Human Resources (HR).One of the European challenges of Albania is the reform in public administration, but, that cannot be successful without the development of HR.The civil servants are a key resource and a capital in public administration, and their professionalism has a direct impact in the success of the reform.To be more
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professional, the HR need to be trained and for this reason the public investment for the development of HR for training, should be a priority. This study is divided in three parts.The first part of the study will explain various authors" points of view in connection with the importance and the role that the training has in the professional development of HR.The second part, will explicate the training policies that do apply in Albania and the collaboration between the responsable institution for the training of civil servants.The thrid part will be followed by the analysis of the data which is collected through elite interviews and questionnaires obtained from civil servants in the Ministry of Education and Sports (MES), in the Ministry of Transport and Infrastructure (MTI), in the Ministry of Youth and Social Welfare (MYSW) and in the Ministry of Agriculture, Rural Development and Water (MARDW).The hypothesis intended to be supported is the following: The training is a necessary neccesity for development of civil servants in the Albanian public administration. Objectives of the research: 1. To explicate the planning process of the training from responsible institutions.2. To analyze the collaboration between Albanian School of Public Administration (ASPA) and ministries for the development of the trainings of civil servants.3. To address the connection between the criteria that the institution establishes for training and the needs that civil servants have for the training.4. To evaluate the impact of the training programmes in the professional development of civil servants.5. To analyze the feedback of public servants for the effectiveness
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of the training that they have done. 1.1 Study importance Nowadays, the impact of the training in the development of Human Resources (HR) makes an important study field in the Albanian public administration.However, such studies are not easily found in Albania, so the study is important to help to fill the gap.Albania does have 103 years that has created its public administration; it has a university and a public administration school, but it does not have a scientific collaboration between the Public Administration and universities. Methodology The methodology applied in this study is analytical and based on primary and secondary resources.As first resource are the empirical data and surveys.As far as empirical data is concerned, they are obtained through elite interviews, as part of semi-structured interviews with purposeful sample, and as far as structured interviews through surveys is concerened with civil servants as random sample in fourth ministries cited.The secondary research deals with theoretical studies on the training and the interior documents that are used from the public administration for training. The interpretivist approach is applied through the datas taken from elite interviews coming from middle and higher officials from ASPA, from the HR sector in ministries cited and with the chiefs of the departments of public administration in two public universities in Albania.These officials are identified on the basis of their position they have in their institutions. From 9 elite interviews, 3 were conducted between e-mails, 1 was done by writing and 5 one were done face to face. The period that is analyzed is
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January -December 2014.The data is obtained from May until October 2015.179 questionnaires were filled and hard copies are available.Qualitative methods and SPSS Statistics are used for data processing.The population is this study includes the factice civil servants that are employees from four representative ministries randomly selected and they are: MES 84 civil servants, MTI 70 civil servants, MYSW 72 civil servants and MARDW 85 civil servants, in total there are 311 civil servants.The sample of 179 civil servants gives us a confidence level of 95% with a margin of error of 5%. Literature Review Albania has still a need to examine and take new scientific knowledge on how the public administration should function in order to be effective.Irwin L. Goldstein said that training is " the acquisition of skills, concepts, or attitudes that results in improved performance in an on-the-job environment" (Goldstein, 1980:229).According to Robins DeCenzo, "The training of the employers is an education experience, and the goal is to realise a relative change of the employers, to improving their performance skills at work" (DeCenzo, 2011:267).Training is important for the organisation, be it private or public.So, "at the organizational level, a traditional training program designed to teach a skill that has direct and current applications in the organization often can be evaluated in terms of measures of an increase in operating efficiency" (Olslzfski, Crrtchirz, 2001:499).And "the traditional training format is excellent for teaching or improving technical skills, as well as for informing participants about current thinking in a discipline" (Same source, p. 449). In order for
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employers to be professionally developed, the criteria are necessary: to be provided during training with the necessary competencies that it needs to grow professionally; to be encouraged to develop individual skills and teamwork, in order to achieve the objectives; to affect the growth and strengthening of his intellectual capacity with modern knowledge, to prepare for the challenges and demands of the continuous market; and to be helped directly to increase motivation and productivity at work of the civil servants.Director of ASPA, F. Demneri (personal communication, 30 December 2014) confirms that "the training is directly related to the development of human resources.Training is directly related to improving performance at work, professional development as well as career development [the civil servants]".So, is important that "an individual's education and training must necessarily transcend experience as a primary promotional consideration" (Daniello, Laubsch, 2008:6) In the report "Public Service Training System in OECD Countries -SIGMA [Support for Improvement in Governance and Management] papers no.16 that OECD has published in 1997, it emphasizes the importance of training for the public administration employees: "A good training system is crucial for any organization to develop and retain high professional standards of conduct and performance for its staff" (OECD, 1997:3). A The Development of Training in Albania At the end of the 90's, which is the first decade of the democracy in Albania, the management of HR is almost unknown and so is the training of civil servants in the Albanian public administration.In the beginning of the new Millenium, when the development of the country
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has received news dynamism, when the technology was spreading significantly to public functions, when the trade was looking for quality public services, when the criteria to work in civil service was growing and after the counseling from European experts to the public, it came as the institutional needs administration the development of the training for civil servants. The realisation of public administration reform in Albania can not be understood without the capacity building and the development of HR.But, if the civil servants want to increase professionally, it is necessary to continue to be qualified and to be prepared for their duties.The civil servants do have a need to be trained in continuity and for this reason The Albanian government "have given a special attention to the increase of capacity of civil servants of public administration, by their training" (Albanian Government, 2008:12).But, after 3 years that TIPA was created, it "began operation regularly and to organise training for the civil servants of public administration" (Same source, p.12).At the beginning the principal problem for TIPA is the need for the qualified staff, bur after some years it appeared as another important problem, that was the collaboration between TIP and the ministries.In the annual report in 2006 that was prepared from DoPA, is emphasized the demand of TIPA that "ministries should be more active in the training process of civil servants and in the end of the training it is necessary to evaluate the effects of training at public servants.Ministries should exercise more control and to be more demanding
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to them, in term of active attendance at different training" (Council of Ministers,n.d.:14)In difference with TIPA that was limited at civil servants and at training schedule that was approved by DoPA, "ASPA have administrative autonomy and autonomy in determination in curriculum and training schedule.Its aim is to contribute in professional formation of civil servants of public administration… (Albanian Parliament, 2013:.2347)and at the same time, "ASPA offers programs for profound and continuing formation, in this base the civil servants from all categories of work have the possibility to continue the training, and every native or foreign individual that is out of public service" (Council of Ministers, 2014:2347).As a conclusion, it can be said that between training, ASPA have an important role for raising public administration capacities.Training, not only in theory or in level of round-table discussion, but practically, it is needed to see and after to function as a necessary and basic instrument for raising Albanian professional public administration capacities. ASPA for the first time stated "Action Plan includes the digitalization of its education material, putting it on a digital platform and setting up an eLearning system.The use of the Information technology in the training system is likely to facilitate the sustainability as ASPA's training" (ASPA, 2014, paragraph 3).After that, ASPA "on the 29 th of October present the new platform [of electronic learning] and [the first group of] developers of training were provided with necessary technical methods/instructions for the preparation of these training" (ASPA, 2015, paragraph 3). Analysis of Empirical Data In this third part of
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the essay, will be continued by the elaboration in SPSS Statistics of the data collected in the field by survey. The questionnaire addressed to complement civil servants and heads of low and medium executive category levels.Graph 1 provides data on the respondent to share in percentage by gender for the three ministries taken for analysis.In total, 32% of the respondents were males and 68% females.Figure 1 provides data on the respondent to share the percentage by gender and in Figure 2 by age groups.In table 1 provides data on civil servants according to their status at work for every ministry.The data in the field we can see that we have 86% civil servants confirmed and 14% civil servants on probation period.And about the position in the work, there are 136 executive civil servants or 76% of total and 43 managers or 24% of total.The correlation between Ages and the Status at work is significant and weak negative.Pearson correlation coefficient r is -.249 and this is statistically significant p<0.05 (0.01<0.05).The correlation between Level of Education and the Status at work is significant and weak positive.Pearson correlation coefficient r is .160and this is statistically significant p<0.05 (0.032< 0.05).To take the opinion from respondents for the question: Which are the indicator to determines the need for training, in the question there were some ready alternatives.The respondents had the possibility to choose only one answer.At the some time, they had the possibility to choose the alternative "Other" and give their opinions.The data that was collected in the field are reflected
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in table 2: In this question it is not set that the needs for training was determined by the evaluation of the work of civil servants throughout the evaluation reports.This was chosen on mood to test their knowledge.Only one of the respondents has determined "the evaluation of work" as a element that determined the need for training.This indicates two things: the first, the employers have insufficient information and secondly, their supervisor do not inform them for this.But, for this reason, with a lot of probability this part of the law has a little chance to be implemented.Disturbing is the fact that for 26% of respondents in the training are "simple on base of plan".All these results tell that there is a lot of work to be done for the effectivity of the training. The value of training Before analyzing directly the opinion of respondents for the value of the training, in two different figures will be presented the data for the valuation before and after training.While from the results from figures 74% declare that at the end of training do the evalutation, but 4% of respondents declaration that in the end of training they do the evaluation of the process, but, not in every case.19% of respondents declared that at the end of training they did not do the evaluation of the process.Failure to carry out the evaluation is not only a lawlessness, but is something bad for the civil servants because it does not measure the knowledge of the trained civil servans, if they have
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benefited from the training that was done.This brings the reduction of the value of the training, the responsibility of trainers, the motivation and the predisposition of the civil servants to benefit on maximum lore and knowledge from the training. Meanwhile 55% of the respondents declared that they did not do the measuring of performance before the training, and 19% of respondents declared that in the end of the training, they did not do the evaluation of the process.This tells in direct link a lack of seriousness and professional commitment in the training process.We can prove this from the feedback of the respondents, when 26% of respondents declared that the training are "simple on the basis of the plan".The correlation between the indicator to determine the need for training and Training efficiency is significant and average positive.The Pearson correlation coefficient r is .403and this is statistically significant p<0.0005 (0.000<0.0005). The research hypothesis is: there is a relation between the presence in training and the perception of training as an indicator for the professional development of civil servants. The null hypothesis is: there is not a relation between the presence in training and the perception of training as an indicator for the professional development of civil servants.As we can see here Chi-square (2) = 32.234,p = .000,less than the alpha level of significance of 0.05.The null hypothesis is not accepted.So, there is a statistically significant relation between the presence in training and the perception of training as an indicator for the professional development of civil servants. Chi-Square Tests,
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Phi and Cramer's Vare both tests And we can see that the strength of relation between the variables is moderate (.424).The research hypothesis is: there is a relation between the participation in training and the effectiveness of training as an indicator for the professional development of civil servants. The null hypothesis is: there is not a relation between the participation in training and the effectiveness of training as an indicator for the professional development of civil servants.As we can see here Chi-square (2) = 55.014,p = .000,less than the alpha level of significance of 0.05.The null hypothesis is not accepted.So, there is a statistically significant relation between the participation in training and the effectiveness of training as an indicator for the professional development of civil servants. Chi-Square Tests, Phi and Cramer's Vare both tests And we can see that the strength of the relation between the variables is moderate (.554). To answer the research question, now we will say that the training has significant and important effects in the development of HR in the public administration in Albania. The research hypothesis that the training is necessary for the development of civil servants in the Albanian Public Administration is supported by this analysis. Conclusion Meanwhile Albania has 12 years that has began the training of civil servants in the public administration, and it has managed to create its experience and to do this process by the institutions created for training.However, there is a lot of work to be done, so that we can have the possibility to
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take proper results, that training will be efficient, helpful for the growth of the capacity of HR and for the development of administration. During the empirical analysis, important problems came out that do have a need for improvement.For the training criterias the results are: before the training the evaluation of their performance is not done every time in order to see the need they have for training; meanwhile the law establishes that the news for training are established, only one of respondents have determined "the evaluation of the work" as a element that determined the need for training.Disturbing is the fact that for 26% of respondents the training are "simple on the basis of the plan".All these results do demonstrate that a lot of work needs to be done for the effctiveness of the training. For the value that the training has, the results are: 19% of respondents declare that in the end of the training did not do the evaluation of the process.Meanwhile, for the law it is a duty to do this process.This brings the reduction of the value of the training, the responsibility of the trainers, the motivation and the predisposition of the civil servants to benefit on maximum lore and knowledge from the training; the respondents value the training as a valuable element for the profesional development. The correlation between Opinions for trainings program and Training efficiency is significant and strongly positive.The correlation between the indicator to determine the need for training and Training efficiency is significant and average positive.So, if institutions
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can collaborate with civil servants can help to project necessary programs for them and in this mood can help civil servants in their professional development. In the conclusion, the preceding analysis gives the answer of the research question that was submitted in the beginning of the study and at the same time has proven the hypothesis that the training has a basic role in the development of professional capacity of HR.Doing the training is a condition for the development of civil servants on public administration and they have a growing request for effective and appropriate training.But, it is the responsible institutions for the training (ASPA and the ministries) which should grow the level of collaboration not only between them, but and with the universities, to enable better results from training. Final Report establishes several important elements that should be included in the training programs: "The program or training curriculum shall enhance the student's competencies, values, knowledge, and skills to act ethically, equitably, effectively and with efficiency: Subject to the mission of the program, they should include: (i) The Management of Public Service Organizations; (ii) Improvement of Public Sector Processes; (iii) Leadership in the Public Sector; (iv) The Application of Quantitative and Qualitative Techniques of Analysis; (v) Understanding Public Policy and the Organizational Environment" (United Nations Department of Economic and Social Affairs /International Association of Schools and Institutes of Administration [UNDESA/IASIA] 2008:9,10).According to The European Commission and SIGMA "the training and development of civil servants as key instruments for the development of administrative capacity in pre-accession states
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[as Albania].Civil service training is directly linked to effectiveness as a central European principle of administration" (Meyer-Sahling, 2012:60). , the government has decided to create the Training Institute of Public Administration by the Decree of the Council of Ministers No 315, dated 23.03.2000.This decree states: "Establishment of the Training Institute of Public Administration (the Institute), as an institution under the supervision of the Council of Ministers" (Center of the Official Publishing [COP], 2000:883).The mission of TIPA was: "To support the improvement and reform of a sustainable and professional civil service through qualitative and comprehensive training and development" (Cited from Mitrushi, n.d.:4). The Council of Ministers by Decree No. 138, dated 23.03.2014 in "The rules of organisation and the function of Albanian School of Public Administration and the training of civil servants" decided that the civil servants have the possibility to do training in ASPA "... with order of direct superior, on base of the evaluation of the results at work" (Council of Ministers, 2014:5).For the year 2014, head of Human Resource Office on MTI, E. Fusha (personal communication, 23 July 2015) was able to confim: "as the new status of civil servants entered in aplication on 26 February 2014, ASPA [for the year 2014] has done the obligatory training for all civil servants that were on probation period".So, for the year 2014, 122 civil servents or 68% of total have doing at least one training and 57 civil servents or 32% of total, or one in three civil servents haven't doing any training for all the
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year.General Director of Support Services on MTI, A. Kaja (personal communication, 27 July 2015) declares on the basis of law that "the needs for training arised during the process of evalutation of employers and defined from the reporting officer on collaboration with the servants".While the Specialist of Human Resource on MYSW, A. Kodra (personal communication, 23 July 2015) declaration is that the "Head [of sector] that decides which of the civil servants need training.The civil servants did the request for training, after that they take the notification for the training from HR".But, do they respect the law? Figure 4 : Figure 4: The indicators of the need for training (%) In the alternative "Other" the indicators that they have given as a need for training are: a) Understanding/Decision on supervisor.b) The profile of the work and the evaluation on their work.In this question it is not set that the needs for training was determined by the evaluation of the work of civil servants throughout the evaluation reports.This was chosen on mood to test their knowledge.Only one of the respondents has determined "the evaluation of work" as a element that determined the need for training.This indicates two things: the first, the employers have insufficient information and secondly, their supervisor do not inform them for this.But, for this reason, with a lot of probability this part of the law has a little chance to be implemented.Disturbing is the fact that for 26% of respondents in the training are "simple on base of plan".All these results tell that there
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is a lot of work to be done for the effectivity of the training. Figure 5 :Figure 6 : Figure 5: The evaluation before training (%) . The Council of Ministers by Decree No. 220, dated 23.06.2013 decided: "to create and to function the Albanian School of Public Administration (ASPA)" (COP, 2013:2347)."Since April 2013, the ASPA is carrying out several trainings according to the training schedule.In this regard and in terms of training of civil servants, the ASPA has carried out and continued the training activities during the period September 2013 -April 2014, in accordance with its training schedule supported by the foreseen budget and in cooperation with the projects supported by the European Union (PPF and SMEI III), etc." (Ministry of the European of Integration [MEI], 2014:19).But in 2014 "ASPA is responsible for civil servants training.The quality and quantity of training has increased, but ASPA's budget is insufficient for the increased number of civil servants in need of training.The new performance appraisal system is not yet used widely."(European Commission, 2015:10). Table 1 : The status at work of employees Correlation is significant at the 0.01 level (2-tailed).As we can see, the correlation between Gender and the Position in work (Executive civil servants or managers) is significant and weak negative. The correlation between Opinions for trainings program and Training efficiency is significant and strong positive.The Pearson correlation coefficient r is .724and this is statistically significant p<0.0005 (0.000<0.0005). The sample size requirement for the chi-square test of independence is satisfied. The sample size requirement for the chi-square
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test of independence is satisfied.
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Elucidation on the Physicochemical Properties of Potential and Clinically Approved Antiviral Drugs: A Search for Effective Therapies against SARS-CoV-2 Infection COVID-19 has been confirmed in millions of individuals worldwide, rendering it a global medical emergency. In the absence of vaccines and the unavailability of effective drugs for the SARS-CoV-2 infection, vaccine development is being continuously explored and several antiviral compounds and immunotherapies are currently being investigated. Given the high similarity in genetic identity between SARS-CoV and SARS-CoV-2, the present investigation identified the interaction between the physicochemical properties and the antiviral activity of different potential and clinically approved antiviral drugs against SARS-CoV using hierarchically weighted principal component analysis. Representative drugs from the classes of neuraminidase inhibitors, reverse transcriptase inhibitors, protease inhibitors, nucleoside analogues, and other compounds with potential antiviral activity were examined. The pharmacologic classification and the biological activity of the different antiviral drugs were described using indices, namely, rotatable bond count, molecular weight, heavy atom count, and molecular complexity (92.32% contribution rate). The physicochemical properties and inhibitory action against SARS-CoV-2 of lopinavir, chloroquine, ivermectin, and ciclesonide validated the adequacy of the current computational approach. The findings of the present study provide additional information, although further investigation is warranted to identify potential targets and establish exact mechanisms, in the emergent search and design of antiviral drug candidates and their subsequent synthesis as effective therapies for COVID-19. INTRODUCTION SARS-CoV-2, a novel severe acute respiratory syndrome coronavirus 2, has been identified to cause coronavirus disease 2019 (COVID-19) 1 . COVID-19 is a recent medical emergency worldwide with more than
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3.5 million confirmed cases and more than a quarter of a million deaths as of May 4, 2020 2 . Among infected patients, supportive care to help alleviate the symptoms has been recommended 3 . At present, neither effective drugs exist nor vaccines are available for COVID-19; however, vaccines are being developed and several antiviral agents, chemotherapeutics, and immunotherapies are being investigated as pharmacologic interventions. Despite the very complex process, the search for effective therapies for COVID-19 continues. As SARS-CoV and SARS-CoV-2 have high similarity in genetic identity 4,5 , drugs with inhibitory action against SARS-CoV would exhibit similar degrees of inhibition against SARS-CoV-2. In the present investigation, representative drugs from the classes of neuraminidase inhibitors (NAIs), reverse transcriptase inhibitors (RTIs), protease inhibitors, nucleoside analogues, and other compounds with potential antiviral activity were examined. The chemical and physical properties of drugs such as hydrogen bond donor and acceptor counts, topological polar surface area, heavy atom and rotatable bond counts, complexity, and molecular weight were identified to influence their biological activities 6,7 . Hence, the present study identified the relationship between the physicochemical properties and the antiviral activity against SARS-CoV of the available potential and clinically approved antiviral drugs using hierarchically weighted principal component analysis. Identifying the relationship between the properties of a compound and its biological activity has always been considered important in drug design 8 . The generated relationship will identify significant chemical and physical properties of these antiviral drugs explaining inhibition variations against SARS-CoV-2. The findings of the present investigation offer additional insights relevant
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to the search for potential antiviral drug candidates and their subsequent synthesis as effective therapies for COVID-19. MATERIAlS AND METHODS Chemical and physical properties of drugs with antiviral activity Information on the potential and clinically approved antiviral drugs against SARS-CoV was retrieved from the literature. These are representative drugs from the classes of NAIs, RTIs, protease inhibitors, nucleoside analogues, and compounds with potential antiviral activity. In the class of nucleoside analogues, representative drugs such as acyclovir, foscavir, and ganciclovir were identified. Another major antiviral pharmacologic class examined was the human immunodeficiency virus (HIV) antiretroviral drugs, including indinavir, nelfinavir, and saquinavir as protease inhibitors. For the HIV antiretroviral drugs classified as RTIs, selected HIV nucleoside RTIs included in this study were lamivudine and zidovudine. The fourth pharmacologic class of the antivirals examined was the NAIs with oseltamivir and zanamivir as representative drugs. In addition to these clinically approved antiviral drugs, 10 other commercially available drugs with potential antiviral activity were also included. The drugs which exhibited in vitro antiviral activity against SARS-CoV were amantadine 9 , calpain inhibitor III 10 , calpain inhibitor VI 11 , chloroquine 12 , cinanserin 13 , glycyrrhizin 14 , mizoribine 15 , niclosamide 16 , ribavirin 9,10,15 , and valinomycin 17 . The chemical and physical properties of these compounds, namely topological polar surface area, heavy atom count, hydrogen bond acceptor count, hydrogen bond donor count, complexity, rotatable bond count, and molecular weight were retrieved from online databases 18-37 (Table 1). Principal component analysis and computational validation Similarity in the biological
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activity and pharmacologic classification of the different potential and clinically approved antiviral drugs were determined, and the presence of correlations among the various chemical and physical properties of these antiviral drugs was identified using principal component analysis. A principal component contains uncorrelated linear combinations of the drug indices with maximum variance, which suggests that a linear transformation must be performed among correlated variables, and the linearly transformed variables are subsequently arranged in order of decreasing variances 38 . A principal component is considered for inclusion when it has a loading eigenvalue of at least 1.0. For the retention of the drug property within a principal component, a minimum of 0.30 in absolute value is required as the correlation coefficient between the variable and its principal component. Sampling adequacy was assessed using Kaiser-Meyer-Olkin measure. Numerical calculations and data analysis were performed using STATA ® V12.0 software. After obtaining the principal components and identifying the significant indices within the components, additional clinically approved antiviral drugs including abacavir 39 , darunavir 40 , didanosine 41 , galidesivir 42 , stavudine 43 , and zalcitabine 44 for pharmacologic classification and some drugs that inhibited SARS-CoV-2 such as chloroquine 45 , lopinavir 45 , ivermectin 46 , and ciclesonide 45 were utilized to validate the results of the multivariate computational approach. RESUlTS Twenty different compounds with potential and clinically approved antiviral activity against SARS-CoV were classified using principal component analysis. Two principal components were obtained with eigenvalues 5.41 and 1.05. Within a component, the loading values of each drug index were
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computed ( Table 2). The important indices included in the first principal component were complexity (r = 0.4202), heavy atom count (r = 0.4123), and molecular weight (r = 0.4118) with a 77.35% contribution rate. The number of rotatable bond count (r = 0.7441) was the main index in the second principal component, with 14.97% contribution rate. The rotatable bond count, complexity, heavy atom count, and molecular weight indices primarily defined the pharmacologic classification of the compounds with potential and clinically approved antiviral activity (92.32% total contribution rate, 0.7620 Kaiser-Meyer-Olkin sampling adequacy). The main indices in the first principal component, namely complexity, heavy atom count, and Journal of Pure and Applied Microbiology molecular weight were positively correlated with the rest of the chemical and physical properties of the antiviral drugs (Table 3). Rotatable bond count, the leading index in the second principal component, was positively correlated with heavy atom count, complexity, and molecular weight ( Table 3). The comprehensive scores for the different antiviral drugs were calculated using hierarchical weighted principal component analysis (range: 117.41-1087.30, Table 4). Interestingly, higher comprehensive scores (497.74-644.64) were identified among protease inhibitors (indinavir, nelfinavir, and saquinavir). In the validation of the computational approach for pharmacologic classification (Table 5), compounds such as abacavir, didanosine, galidesivir, stavudine, and zalcitabine obtained the lowest comprehensive scores (201.12-259.92). The comprehensive scores of these compounds were within the range of the comprehensive scores for nucleoside analogues and the RTIs (Table 4). Darunavir and lopinavir obtained comprehensive scores similar to those of other protease inhibitors examined in this
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study. The comprehensive score of ciclesonide was within the range of protease inhibitors, whereas ivermectin scored higher than any of the examined protease inhibitors but was inferior to glycyrrhizin and valinomycin. Moreover, DISCUSSION Among the chemical and physical properties of the potential and clinically approved antiviral drugs evaluated in this study, a positive correlation was identified in all drug properties, including complexity, heavy atom count, and molecular weight. Molecular weight has been considered an important compound property in small drug discovery 50 and is closely examined in drug optimization steps 51 . In addition to the Journal of Pure and Applied Microbiology molecular weight in the first principal component, the main index complexity was positively correlated with hydrogen bond acceptor and rotatable bond counts. Molecular complexity, which includes the cardinality of rings, stereocenters, and sp 3hybridized carbons, has been related to biological activity 52 . A compound with at least four aromatic rings has high toxicity risks and low compound developability 53 which justifies the preference for moderately complex structures as lead compounds 54 . Compounds classified as NAIs, RTIs, protease inhibitors, nucleoside analogues, and some drugs with potential antiviral activity were examined. Among the nucleoside analogues, when acyclovir, foscavir, and ganciclovir were compared, there was an inverse relationship between the calculated comprehensive score and the biological activity (IC 50 ) of the antiviral drugs. For instance, when foscavir and acyclovir were examined against herpes simplex virus, acyclovir (IC 50 : 0.06 μmol/mL) was more potent than foscavir (IC 50 : 0.44 μmol/mL) 9 . The
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comprehensive score of acyclovir and foscavir was 207.22 and 124.11, respectively. Similarly, ganciclovir (IC 50 : 0.014 μmol/mL) was more potent than foscavir (IC 50 : 0.80 μmol/mL) against cytomegalovirus 9 . Ganciclovir had a higher comprehensive score (235.11) than foscavir (124.11). These observations led to the examination of a possible relationship between the comprehensive score based on physicochemical properties and the potency of the nucleoside analogues against viruses. The higher the comprehensive score of the nucleoside analogue, the more potent was the antiviral drug (lower IC 50 ). A nucleoside analogue inhibits viral polymerase and interferes with nucleic acid synthesis 18,24,25 . Acyclovir 18 , foscavir 24 , and ganciclovir 25 target DNA viruses such as varicellazoster virus and herpes simplex virus. However, acyclovir is more potent than foscavir (Foscarnet) as the former targets herpesvirus and varicellazoster virus polymerases 18 , whereas the latter selectively blocks the pyrophosphate binding site of herpes virus-specific DNA polymerases 24 . Among the nucleoside analogues examined in the present study, ganciclovir was the most potent (the lowest IC 50 and the highest comprehensive score). Ganciclovir inhibits replication of several viruses including varicella zoster virus, herpes simplex virus-1 and -2, Epstein-Barr virus, and cytomegalovirus 25 . The fourth pharmacologic class of the antivirals examined was the NAIs. Representative drugs included were oseltamivir and zanamivir. Zanamivir had a higher comprehensive score than oseltamivir (334.50 vs. 267.02), suggesting that zanamivir is more potent than oseltamivir, and this comparison was supported by previous studies. When the two NAIs were tested against influenza virus,
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zanamivir (Relenza) had a lower inhibitory concentration value than oseltamivir (Tamiflu) 9 . In addition, zanamivir (IC 50 : 2.7 nM) was significantly more potent than oseltamivir (IC 50 : 8.5 nM) when tested against influenza B virus isolates 57 . Of the ten compounds utilized for validation, six were investigated for the pharmacologic classification and the remaining four for inhibitory potency. Validation of the computational approach for pharmacologic classification revealed low comprehensive scores among abacavir, didanosine, galidesivir, stavudine, and zalcitabine. These comprehensive scores were within the established ranges for nucleoside analogues and RTIs. Interestingly, abacavir, didanosine, and stavudine are nucleoside RTIs 39,41,43 . Abacavir has activity against HIV-1 (HIV-1IIIB EC 50 : 3.7-5.8 μM and HIV-1BaL EC 50 : 0.07-1.0 μM) 39 . Moreover, darunavir and lopinavir, both protease inhibitors 40,47 , had comprehensive scores similar to those of other protease inhibitors (indinavir, nelfinavir, and saquinavir). Similar to darunavir, lopinavir also inhibits the activity of an enzyme critical for the HIV viral lifecycle but has a high likelihood of drug interactions 47 . CONClUSION The chemical and physical properties of potential and clinically approved antiviral drugs explained their pharmacologic classification and biological activity. Hierarchically weighted principal component analysis elucidated the interaction between the physicochemical properties and SARS-CoV inhibition of these antiviral drugs. The physicochemical properties and inhibitory action against SARS-CoV-2 of lopinavir, chloroquine, ivermectin, and ciclesonide validated the adequacy of the current computational approach. The findings of the present study provide additional information, although further investigation is warranted to identify potential targets and establish exact
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mechanisms, in the emergent search and design of potential antiviral drug candidates and their subsequent synthesis as effective treatment against SARS-CoV-2 infection.
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“Dignity as a Small Candle Flame That Doesn’t Go Out!”: An Interpretative Phenomenological Study with Patients Living with Advanced Chronic Obstructive Pulmonary Disease Long-term illness, such as chronic obstructive pulmonary disease (COPD), can expose people to existential suffering that threatens their dignity. This qualitative study explored the lived experiences of patients with advanced COPD in relation to dignity. An interpretative phenomenological approach based on lifeworld existentials was conducted to explore and understand the world of the lived experience. Twenty individuals with advanced COPD (GOLD [Global Initiative for Chronic Obstructive Lung Disease] stages III and IV) were selected using a purposive sampling strategy. In-depth interviews were used to collect data, which were then analysed using Van Manen’s phenomenology of practice. The existential experience of dignity was understood, in essence, as “a small candle flame that doesn’t go out!”. Four intertwined constituents illuminated the phenomenon: “Lived body–balancing between sick body and willingness to continue”; “Lived relations–balancing between self-control and belongingness”; “Lived Time–balancing between past, present and a limited future”; and “Lived space–balancing between safe places and non-compassionate places”. This study explains how existential life phenomena are experienced during the final phases of the COPD trajectory and provides ethical awareness of how dignity is lived. More research is needed to investigate innovative approaches to manage complex care in advanced COPD, in order to assist patients in discovering their inner resources to develop and promote dignity. Introduction Chronic obstructive pulmonary disease (COPD) is a progressive lung disease that is a major source of morbidity and mortality and is expected to
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be the third highest cause of death globally by 2030 [1]. COPD has a significant economic and social impact, which varies greatly depending on socioeconomic status and geographic location [2]. Several risk factors for COPD have been recognized, including accelerated ageing, individual predisposition, and environmental or occupational exposure (e.g., cigarette smoke, air pollution, dust, gases and other irritants) [3,4]. In the early stages, COPD is characterized by the presence of respiratory symptoms such as breathlessness, wheezing, chest tightness and chronic (productive) cough, which worsens during physical activity [5]. Comorbidities arise at more advanced stages of the disease trajectory and include weight loss, which is occasionally associated with cachexia and heart failure, resulting in increased dyspnoea [6]. Depression, psychosocial distress and sleep difficulties are also prevalent and are linked to a lower quality of life and premature death [7,8]. Over the last two decades, there has been an increasing interest in the need and provision of palliative care for COPD patients [9]. One source of concern is whether endof-life (EoL) care is effectively implemented [8]. According to Braço Forte and Sousa [10], "the EoL of patients with COPD is associated with progressive deterioration, worse quality of life, social isolation and absence of symptom control. The main barriers to a correct and appropriate approach at this stage of the disease are: lack of resources, deficient identification of patients at the end stage and absence of robust studies in the area" (p. e84). Living with unmet care demands due to COPD disrupts an individual's existential state, often leading to
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existential suffering [11]. A growing body of research suggests that existential suffering has a substantial impact on the daily lives of individuals who experience it. COPD care raises challenges, as the disease's unpredictable trajectory affects patients physically and emotionally, demanding the provision of multiprofessional care to grant comprehensive care [12]. Furthermore, respecting human beings' rights and preserving dignity are defined as ethical purposes of COPD care. The Universal Declaration of Human Rights asserts, "all human beings are born free and equal in dignity and rights" [13] (p. 1). Dignity is essential in all human interactions, and is, therefore, a key concept in ethics [14] and the foundation for good EoL care [15]. Dignity is associated with a human being's ontological and rational nature and corresponds to a universal value that extends to the intrinsic condition of every human being, from conception to death. Human dignity is the anthropological basis for the human rights of every human being. In this sense, dignity is an ethical concept associated with the purpose and intrinsic value of each person, making each person worthy of respect [16]. However, each person's perception of their own dignity may fluctuate throughout their life cycle. It is through the condition of being rational that autonomy emerges, which, in turn, is the basis of dignity. According to most scholars, one form of dignity is inherent/inborn and cannot be lessened or changed, but another type of dignity is subjective and changeable and is frequently influenced by external influences [17]. This latter type of dignity is especially important
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in the context of healthcare, since care delivery can either foster or harm dignity [18,19]. Understanding caring ethics and dignity encourages healthcare workers to take moral responsibility, to be aware of what they see, hear and feel, and to follow an ethical compass [20]. According to Chochinov et al. [21], sustaining a sense of dignity is important for all people in need of care, and upholding these people's dignity becomes a critical issue for healthcare professionals [22]. Similarly, the sense of dignity has a profound impact on people's lives and may be a source of personal health and well-being [23]. Several researchers have used qualitative approaches to explore the lived experiences of COPD patients; however, their work focused mostly on physical symptoms and self-care [12,[24][25][26] and not on existential difficulties, despite the detrimental impact of existential distress on quality of life [11]. For example, a meta-analysis revealed that people with advanced COPD frequently resort to healthcare, but seldomly engage in dialogues about social and existential concerns [25]. Although dignity has been widely discussed in the literature, there is limited examination of dignity from a first-person perspective. This gap should compel us to consider the depths and details of people's experiences and their values when elaborating guidelines for care. In this sense, we need to recover the essence of care and discussions of the human experience of suffering and dignity, which are connected to all aspects of an individual's life [27]. To the best of our knowledge, there is no prior research in Portugal about what patients
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with COPD think about the concept of dignity. Therefore, there is no information on whether they believe dignity may enhance their care and, if so, how. Because expressions of dignity are influenced by culture [14], the aim of this study was to explore the lived experiences of Portuguese patients with advanced COPD in relation to dignity. The research question guiding this study was as follows: How do lifeworld constituents intertwine with the dignity experience of people who suffer from advanced COPD? From an inner perspective, we hope to understand personal experiences in relation to dignity and how dignity can be fostered. Knowing how existential experiences (such as dignity) are lived in the latter stages of COPD would allow for more holistic approaches to care in this phase, and thereby, help improve COPD patients' care. Study Design A lifeworld-theory-led, interpretive, phenomenological study was conducted to illustrate that an individual's reality is always impacted by their surrounding world and cannot be isolated from it [27][28][29]. In this sense, we wanted to investigate the phenomenon by being open to the participant's life and its significance, in order to improve the practice of professional practitioners. The four existentials that give meaning to the lifeworld and that guided this phenomenological study are: relationality (lived relations), corporeality (lived body), spatiality (lived space) and temporality (lived time) [29]. We advocate that a sensitive and humanized care is grounded in the lifeworld, allowing for the creation of new insights into the human dimensions of care [27]. To "understand the actual character of the object",
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this type of inquiry requires the suspension of taken-for-granted beliefs and a scientific attitude, as described by the founder of phenomenology, Edmund Husserl [29]. Although Van Manen provides a systematic framework, he contends that there is no established technique for phenomenology. As suggested by Van Manen [28], we studied participant experiences through a dynamic combination of research activities, such as examining the phenomenon, interviewing, thinking on key themes, and interpreting and developing a description of the event. The identification of themes through data analysis resulted in phenomenological descriptions. The study was conducted and reported according to the Standards for Reporting Qualitative Research [30]. Participants and Recruitment Participants in a phenomenological research study are often chosen because they have a lived experience with the phenomenon, are eager to share their experience, and can enrich or add to the understanding of a phenomenon's rich and meaningful experience [31]. Potential participants were identified through electronic records of the pneumology service at a hospital in the central region of Portugal. Purposive sampling was used, ensuring participants had a notable experience with the phenomenon under investigation. Participants met the following inclusion criteria: (a) adult patients (aged ≥ 18 years); (b) diagnosed with advanced COPD (stage III and IV) according to the Global Initiative for Chronic Obstructive Lung Disease (GOLD) criteria [32], namely, the presence of "clinical symptoms such as increased dyspnoea, acute exacerbations requiring frequent hospitalization, the use of a non-invasive ventilator, and/or long-term oxygen reliance" [33] (p. 3); (c) currently followed in outpatient care; and (d) speak the Portuguese language.
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Patients who were cognitively impaired, unaware of their medical condition, and unable to communicate or not keen to participate were excluded. Cognitive screening was completed with the Short Portable Mental Status Questionnaire, which assesses short-and long-term memory and orientation. Each correct answer received 1 point and the global score was the sum of the 10 items, yielding a range from 0 to 10. All participants with ≥ 6 incorrect answers were excluded (moderate cognitive deterioration) [34]. Patients who matched the criteria were sent a letter of invitation with study details and contacted one week later by a telephone call from a nurse. If a participant was interested, an interview was scheduled. Written consent was secured on the day of the interview. None of the patients who were invited to participate in the research declined. Data Collection Data were collected between June 2021 and December 2021. The participants chose the venue of the interview. To minimize interruption to their routine, the majority of participants preferred to be interviewed in their own homes. Each patient was given the option of having relatives present. The in-person phenomenological interviews, covering a wide number of subjects, evolved over the study. Sociodemographic information about the patients was acquired during the interviews. These aspects aided in understanding and contextualizing each patient's experience. The main researcher also collected field notes to support the information in the recordings (including aspects such as tone of voice, gestures and body position) and noted his reflections about his role during the interview. The aim during the interviews was
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to listen to participants' narratives and allow them to talk freely before asking any additional questions, thus demonstrating respect for their experiences rather than imposing the researcher's preunderstandings. Initially, the participants were somewhat nervous, but throughout the interviews they became more relaxed, making the conversations more fluid. Twenty patients were interviewed, with an average interview length of 40 min. The first author (C.L.) conducted all interviews. The interviewer had no prior interaction with patients, and interviews were conducted in Portuguese and audio recorded. The interview guide had an approach based on existential experiences. The interviewer sought experientially rich descriptions, emphasized first-person experiences, requested specifics and avoided theoretically loaded questions. To encourage narration, open-ended questions were used, such as "Please tell me what dignity meant to you." and "How may your dignity be preserved or threatened (related to body, space, time and relational)?" Probing and clarifying questions were asked when needed, such as "Could you please clarify this?", "What do you mean by that?", and "Could you please supply me with an example to help us understand your point of view?" The interviews were halted after themes were identified and data saturation was reached. Each patient was interviewed once. Data collection and analysis happened concurrently. Data Analysis A phenomenological approach inspired by van Manen's philosophy [28] was used to analyse the interview texts. Van Manen's analytical six steps [29] guided the analysis and interpretation of the interviews: "(a) turning to the nature of the lived experience; (b) investigating the experience as we live it; (c) reflecting on
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the essential themes that illustrate the phenomenon; (d) using the art of writing to truthfully describe the phenomenon; (e) maintaining a reliable and oriented relation to the phenomenon; and (f) balancing the research context by considering parts and whole" [35] (p. 5). After assembling the findings of the interviews and observations, analytic techniques were applied to discover patterns in the data. Data were coded using an inductive coding approach [36] to produce several codes. Next, codes were grouped. resulting in the development and identification of major themes [36,37]. Lastly, data were used to create a narrative discussion that highlighted the data analysis [37]. At this stage, themes and quotations were translated into English to check for inconsistencies. WebQDA qualitative data analysis software was used to organize the data. Trustworthiness The data's trustworthiness was partly ensured by building trust between the researcher and participants, which allowed the participants to contribute confidential, honest, in-depth information that mirrored their lived experiences of dignity. This study's trustworthiness is backed by four criteria: credibility, dependability, confirmability and transferability [38]. A study is credible when the researcher's interpretations correctly represent reality. Evidence is dependable when constant and stable. This was sought through member checks and peer debriefing to guarantee that the interviewer had understood the participant's meaning. To ensure the dependability of participant experiences, we recorded an audit trail, themes and descriptions. Confirmability is the extent to which data are derived from participant characteristics without researcher bias. This was ensured by documenting all actions, selecting interview quotes to describe findings and generating
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a study report. To ensure data transferability, study materials were maintained safely, and efforts were made to explain research methods thoroughly, fostering the feasible transferal of findings to other contexts. The purposeful sample, research setting and recruitment methods were explained, and variations in patient experiences were achieved to improve transferability. The data yielded a wealth of information that shed light on the study's goal, but no new information emerged during the three final interviews. According to Van Manen [28,29], the preunderstanding should never be overlooked, but rather made explicit. Thus, the research team consisted of an RN working with patients with long-term illnesses (C.L.) and a physician (M.D.), both with extensive experience in palliative care and qualitative research. Ethical Considerations The Local Ethics Review Board (approval nº04/2021) approved the study in accordance with the Declaration of Helsinki's principles. The purpose of the study was explained to all participants, and they were assured of anonymity and an anonymous presentation of the findings. Informed consent was given by all patients. They were told that they might exit the conversation at any time and that there were no right or wrong replies. Recalling vivid memories during the interviews can be unsettling for participants; thus, our main priority was the comfort and well-being of the participants. At the start of the interview, participants were told that the interview might be paused or terminated at any point without explanation. Sample Description A total of 20 participants were interviewed. Most of them were male (n = 15), with an age range between
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58-82 years (M = 66.85; SD = 7.21). The time since CPOD diagnosis ranged from 4 to 11 years (M = 5.9; SD = 2.04), and the majority were in stage III (n = 14). Fifteen participants were retired. More than half of the participants were married (n = 15) and had received a secondary education (n = 12). All the participants used noninvasive ventilation, nebulisers and oxygen therapy as a means of treating COPD and stated that dyspnoea was disabling and one of the main struggles of having COPD. Most participants had a history of smoking (n = 16) and, of these, only 6 had stopped smoking. The majority reported being retired or unemployed due to limits imposed by their illness. No participants accessed specialist palliative care at the time of the interview, receiving only support from community-based services. Details about participants are depicted in Table 1. Findings from Interviews The existential experience of dignity was understood, in essence, as "a small candle flame that doesn't go out!". In the following, we elaborate on how the lived experience of dignity comprised four interrelated themes: "Lived body-balancing between sick body and willingness to continue"; "Lived relations-balancing between self-control and belongingness"; "Lived Time-balancing between past, present and a limited future" and "Lived space-balancing between safe places and non-compassionate places". These four themes were described in the present time, clarifying the phenomenon's fluctuation in time and space, body, and relational experience (see Figure 1). The study themes and quotations from participants are described below. As their illness took
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over their daily lives, some individuals felt more distanced from their own selves, occasionally responding in unexpected and unpleasant ways. They recounted being emotionally and existentially disturbed, as serenity and harmony were replaced with sorrow and doubt: "I feel a lot . . . not exactly anxiety, but something like that . . . it's a whirlwind of feelings that threatens what I am, my dignity. The problem with showing this is that I feel guilty and frustrated . . . I cry a lot, and I have no problem with it . . . but I feel like I'm doing something wrong . . . " (P10); "In moments of greater instability, I feel that I am no longer me, but then when I calm down, everything becomes easier . . . dignity is like a small candle flame that despite the strong wind doesn't go out . . . it can get weaker, but it continues to shine" (P5). Lived Body-Balancing between Sick Body and Willingness to Continue The term "lived body" refers to our physical body or bodily presence in our daily lives, which includes all we experience, expose, hide and communicate through our lived body. When breathing occurs smoothly, it generates a pre-reflective essence of embodiment. Breathing as a finite number of breaths and breath-taking moments is defined as an often unconscious and forgotten truth of existence. Only when breathing becomes difficult, and one gasps for oxygen, does one realize that breathing is a necessary requirement for any action and for life
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in general. Breathing was an ever-present and explicit activity for the participants in this study. Breathing assumed a core action around which daily life was organized. The unpredictability of dyspnoea was clearly one of the greatest burdens for several participants. P3: "Shortness of breath is unpredictable, it appears every three or four weeks-it feels like I'm drowning, it's horrible. The tiredness and anxiety are terrible... my body is exhausted, and in those moments, I think I'm going to die." For some participants, dignity becomes difficult to achieve in ways each patient recognizes themselves, due to the limitations the sick body imposes. In daily care, participants perceived the unpredictability of symptoms and their inability to manage daily activities. Patients described suffering because their bodies are unable to respond to daily requests. The body has no strength anymore, and surrenders itself to the disease. Lived Body-Balancing between Sick Body and Willingness to Continue The term "lived body" refers to our physical body or bodily presence in our daily lives, which includes all we experience, expose, hide and communicate through our lived body. When breathing occurs smoothly, it generates a pre-reflective essence of embodiment. Breathing as a finite number of breaths and breath-taking moments is defined as an often unconscious and forgotten truth of existence. Only when breathing becomes difficult, and one gasps for oxygen, does one realize that breathing is a necessary requirement for any action and for life in general. Breathing was an ever-present and explicit activity for the participants in this study. Breathing assumed a core
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action around which daily life was organized. The unpredictability of dyspnoea was clearly one of the greatest burdens for several participants. P3: "Shortness of breath is unpredictable, it appears every three or four weeks-it feels like I'm drowning, it's horrible. The tiredness and anxiety are terrible . . . my body is exhausted, and in those moments, I think I'm going to die." For some participants, dignity becomes difficult to achieve in ways each patient recognizes themselves, due to the limitations the sick body imposes. In daily care, participants perceived the unpredictability of symptoms and their inability to manage daily activities. Patients described suffering because their bodies are unable to respond to daily requests. The body has no strength anymore, and surrenders itself to the disease. P1: "The despair of being able to breathe and not being able to, generates a frustration that limits me. I think about what I was, the energetic person who did everything independently. And now [pause] . . . I feel trapped in my body, it doesn't obey my will!" P1 revealed that he is familiar with his body, as he realizes that maintaining his previous active life can put him at risk, given his intolerance to exertion and propensity to develop a dyspnoea crisis. Losses and limitations are felt as progressively worsening. The participants are aware that their bodies are failing. They also understand that if they are inactive, the downturn will accelerate. Participants strive hard to keep their bodies in shape and avoid losing muscle mass out of need
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and self-protection. Participants' lives are dominated by their concern for their own bodies. Rather than viewing this as negative, some see it as giving them a purpose in life and contributing to their well-being, as it allows them to organize their day and generates a nice feeling in the short term, even though the entire endeavour is perceived as a losing struggle. An unavoidable relapse or hospitalization that prohibits or restricts moving for an extended period may mean the hard-fought physical condition is soon lost. The deterioration in lung function is overwhelming, since COPD is stronger than the body and the will. The participants understood that no amount of excellent behaviour would make a difference. Even if their body failed them, their motivation and confidence continued. P15 said: "My body breaks, my legs are weak and that limits me a lot, but having kept my strength and motivation, I can't give up". P18 said: "Every time the symptoms reappear, I feel that my body weakens, it is harder for me to recover . . . but I maintain confidence that I will make it". Lived Relations-Balancing between Self-Control and Belongingness The human interactions with others within a shared interpersonal space are referred to as lived human relations. Participants reported feeling "labelled" by their illness, which challenges their sense of "self" and "identity": "From the beginning of the disease I knew that it was a chronic situation . . . In fact, I was making plans for my life, hoping to get better, but now I know
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that death is near, so I . . . I want to understand what is going on, but there is a part of me that is terrified. I'm afraid of feeling an agonizing pain that robs me of who I am" (P2). The participants strongly desired to make choices and have control over crucial decisions in their life, as this helped them retain their self-esteem and autonomy. Feelings of control were heightened when others boosted their perceptions of independence and autonomy. This was perceived as courteous, helpful and compassionate-an acknowledgement of their right to choose while confronting their EoL: "I already told my daughter that . . . when I can no longer speak, I want to let myself die. Having dignity is just that, being able to choose what I want and what I don't want. And feel that those around me understand this and accept my decision" (P1). While the hospital setting generally offered a secure and supportive environment, when transitioning to home care some patients felt "alone" and less supported: " . . . when you go home, you're very much on your own . . . now I need a little aid and support . . . I have the impression that I am receiving a poor . . . well, not a poor service, but a restricted service" (P8). The most common fear was that they would become a burden to others, particularly family members, resulting in a loss of dignity as a result of their incapacity to care for themselves.
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P14 states that: "My biggest fear is overloading my children, life is not easy . . . my pension is small, and I can't cover all the expenses, my children help me, but that's really hard for me". P11 also stated: "With my illness, I had to retire at the age of 50, since then my wife has had to work hard so that we don't lack anything at home. I get angry about it and sometimes we even argue about it, but she understands me." Some participants described feelings of grief when deprived of a sense of control over life, due to physical weakness and their psychological needs. Feeling vulnerable, patients described some situations created by health professionals where their autonomy was threatened and they experienced a loss of power and independence. As P2 said, "The professionals are very kind . . . and always available. But sometimes I feel like they pity me . . . when I'm most incapacitated and I need help bathing, they do everything. I even tell them that I want to help, but they [professionals] won't let me. In these moments I feel that I am worthless, my privacy is disrespected . . . it is not worth living like this"; and P19: "They mean no harm, I know! But sometimes, I feel that I can do it for myself, it may take longer, but I can . . . it's just that the nurses, as they have a lot to do in a short time, end up doing
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it for me. This happens during meals, in the shower or when getting up to the highchair". P13 described feeling ashamed and stigmatised by healthcare professionals: "They look at me like there's something wrong with me. Coughing, shortness of breath and oxygen equipment make me feel like a stranger. The doctor told me that I'm like this because I smoked two packs a day. I've always been a smoker, but I don't think it was just that . . . maybe I'm just unlucky. Others also smoke and do not have this problem." Respect for others was essential throughout the decision-making process. During interactions with professionals, some participants mentioned the importance of feeling respected and valued, and of being treated as a human being. Having fruitful relationships is essential for creating meaning. Positive communication focused on the sick person's needs seemed to contribute to promoting dignity and positive relationships between professionals and patients. In this regard, P2 said: "In moments of greater difficulty, it is so good to be able to count on the support of those who take care of us, we feel supported and above all respected"; and P7: "I think that dignity depends a lot on the recognition that others have of me, that I still have value after all." When explaining the impact of their illness, all individuals seemed to echo similar opinions. Most thoughts were of loss: loss of employment due to early medical retirement, loss of family and social contacts and, for P9, loss of intimacy. Nonetheless, patients sought to
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devise coping strategies that took their limitations into account. Feeling loved appears to have had healing effects, being capable of transforming feelings of devastation into strength and hope. Love was important to the participants' existence. They realized deep love within themselves, which enabled them to withstand hardship. P16 and P20 both stated that expressing love gave them the strength to stay alive. P16: "the disease allowed me to strengthen ties in my family! I had an older brother with whom I didn't have much connection, in fact, we had been apart for years, and since he found out I was worse he came to see me! I'm very happy . . . " P20: "there is one thing that the disease brought, it was family unity, my grandchildren see my condition and are always available for whatever I need. Just last week they took me for a walk, I went to see the sea . . . (crying), I couldn't remember that feeling anymore." Lived Time-Balancing between Past, Present and a Limited Future The notion of lived time differs from our experience of clock time or objective time and is related to our temporal manner of being in the world. Participants felt the walls of time closing in and, eventually, the sense of lived time reducing from big and expansive to small and constrained, akin to the "matryoshka doll," which depicts a multilayered person. P2: "I feel like a matryoshka, as time passes, I feel smaller, more compressed with the clear certainty that many of my
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desires will not be possible to come true . . . in the most difficult moments I resort to prayer to find some strength to carry on!" Their approach regarding time was different, having learned to focus on the spiritual element of their life. Spirituality, as an act of expressing and seeking meaning and connecting to a higher force, can be of valuable assistance in adjusting to one's own EoL situation. After deepening spiritual issues, people reported a higher feeling of well-being and self-determination, allowing them to accept death into their life. In this sense, some participants declared a transcendent horizon of time, where death was not an end but the beginning of a new life without worries. P10: "If I die today, I will have the opportunity to live again . . . I have the impression that God is around me . . . I know I may confess my transgressions to him, and that he will forgive me. I can tell you everything since he's a terrific buddy I can rely on." P18: "God . . . give me strength . . . I have no fears." The sense of struggle was central to many patient accounts, as they sought to find meaning and hope in their lives in the face of an unclear and shifting future with a lifelimiting illness. Wishes and expectations were portrayed via feelings of hope and resilience when vulnerable. "When you don't know what's ahead of you . . . I want to gain the strength to get
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through it. This is important to me . . . and to those around me. I want to be able to die in peace . . . with dignity!" (P20). P10: "I'm never alone, I have faith and hope . . . I think that tomorrow I'll be a little better." Patients perceived their past as more dominant compared to their future, arguing that this is so because they have limited life remaining. They preferred to reminisce about happy memories from their past. The analysis also revealed that being anchored in the present while, at the same time, rescuing memories of the past made it possible to dream and sustain hope, creating some sense of time. "The future will bring death . . . after all, it comes to everyone. But I just don't know how it's going to be, how . . . ? You know, I had a good life, I was loved, my children are raised, so right now I hold on to the memories that remain. It's these memories that keep me fighting, and dreaming that even if I'm not there, they'll be fine!" (P12). Lived Space-Balancing between Safe Places and Non-Compassionate Places The lived space is where humans move and feel at ease. Having a location to call home and a safe space to escape to and return to symbolizes human mobility in the world. Having a safe place expands the lived space. On the contrary, being robbed of one's own protected zone disrupts the illusion of living in free space.
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Most participants recognized the relevance of the home space, which they described as a safe place to be and a space of companionship and support, and "natural" settings, where there should be caring, dedication, warmth and attention. However, several aspects can influence the experience at home, particularly the progression of the disease and the need for support from close relatives. All participants emphasized the importance of spending their last days at home, naming it as a place for a "good death", surrounded by love and, above all, good memories. Thus, the findings suggest a strong relationship between the participants' lived space experience and their need to retain feelings of belonging, purpose, security and autonomy. These were some of the qualities that contributed to the capacity to maintain a sense of self-identity, preservation and attachment to a place. P6: "My house is all I have, I helped build it and that makes it a part of me. So, when I die, I want to be here . . . surrounded by those who love me; P9: When I get up in the morning, I look out my window and I see my backyard, the trees I've planted, and I think how good it is to be here." They experienced "home" as promoting autonomy, allowing them to care for themselves and use resources such as assistive technology (e.g., ventilator and oxygen therapy). They expected to use assistive technology because it plays a vital role in adapting to a new life situation. The loss of previous and valued activities,
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such as the ability to drive, was connected to existential aspects and grief over lost activities and roles. When an individual's body becomes practically immobile owing to fatigue and a loss of muscle mass, their reality becomes confined and altered. This new reality is characterized by a tighter living room and space, both perceptually and symbolically, which will stay constrained for the rest of the individual's life. Contact with nature was also mentioned as relevant, although this contact was limited by fatigue. The use of support equipment, such as a wheelchair, can minimize this impact. "Walking in the garden at home" (P13), "feeling the fresh air"(P4) and "sunbathing on the balcony" (P9) are examples that helped patients maintain a sense of well-being when facing their current status, and thus, promoted personal dignity. In turn, being "disconnected" from home could undermine patient identity, as the home is a deep component of identity and a location where identities are expressed. At this point, paying attention to the various meanings of home becomes critical, since it represents an environment where the patient may express their particular identity. Several participants in this study shared similar stories. Whether at home or in healthcare facilities, some participants reported being cared for with compassionate care versus non-compassionate attitudes and limited support from professionals. Such attitudes were reflected in pleasant and stimulating contextual experiences or, on the contrary, in mechanized environments, decentred from individual needs. They wanted to be seen as a whole person, rather than feeling like their healthcare professionals were focusing on
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medical matters alone. P5: "In the hospital, everything is different, when I'm worse and I go to the emergency room, I get even worse. The noise, the closed environment, the lights on all night. Anyway, I get very anxious and that doesn't help me at all . . . When they send me to the pulmonology inpatient ward, things get a little better. Nurses are concerned with creating a more pleasant environment"; and P15: "When I was hospitalized, they [professionals] did what they could . . . there's a lot of work, but the lack of staff doesn't help either. They do a lot!" The patients also expressed ambivalence associated with the home when this environment took on hospital-like characteristics. One participant (P17) said: "My house is different from what it used to be, my room looks like a medical ward, it is the ventilator, the oxygen bottle, the articulated bed, the wheelchair . . . My wife works hard to make the environment pleasant, but when I look around, everything is different . . . but then I think what matters is having the people I care about with me, that's being at home!" As this participant explained, when he requires care, his perception of home and his feelings change. However, the home's value is in "having the right people around you", not its physical constituents, because being at home is being connected with loved ones. Discussion Anchored in Van Manen's phenomenology of practice, this study explored the lived experiences of patients suffering from advanced
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COPD in terms of dignity, providing novel insights into the priority topic of end-of-life care. Our findings are consistent with those outlined in the literature, namely, a universal sense of a vulnerable and disrupted body determining a patient's entire life [39,40]. The disruption of the lived body was felt as a breakdown in the biological body's mechanical functioning, expressed by breathlessness and exhaustion, but also as a disruption of everyday activities around which life is organised [40]. The loss of autonomy or control over the body was frequently perceived as a loss of one's own identity, with profound effects upon the critical sense of dignity [41]. Despite this, paradoxically, individuals tried to maintain motivation as a reaction of the embodied subject to retain their wholeness and dignity. The relationships along the body-others-world axis are profoundly impaired by the patient's physical incapacity. Qualitative studies show that any shift in the lived body can affect the individual perception of dignity [19,[41][42][43]. However, as Rodríguez-Prat and Escribano [41] highlight, "while the loss of functionality may be one factor that leads patients to experience their illness from the viewpoint of the objective, biological, or functional body, the recognition of personal resources (e.g., confidence and motivation) and understanding by others of their symptoms and suffering could help to generate new attitudes and strategies for coping with illness from a more positive perspective" [41] (p. 293). The patient's experience may also be improved if they feel others have a better understanding of what it means to live with an advanced illness [44].
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An active sense of motivation fosters patients to adjust to the trajectory of the illness and helps them to feel secure [45]. As a counterpoint, evidence supports the notion that patients who experience a loss of sense of continuity, as well as diminished motivation and confidence in projecting themselves into the future, are more likely to relive previous unsuccessful or frustrating experiences and, as a result, are more vulnerable to suffering from demoralization syndrome (defined clinically as feelings of hopelessness and helplessness induced by a loss of purpose and meaning in life, and identified by a lack of drive or motivation to cope) [46,47]. Furthermore, evidence shows that demoralization is common in progressive illnesses and is strongly linked with persistent physical issues, a lower quality of life, and psychological problems such as depression, anxiety and a wish to die sooner [47]. Another crucial element is the perception of dignity mediated by the experience of autonomy or control [41] in terms of relations with others. As a result, depending on the nature of the relationships, one's sense of dignity might be violated, reconciled or even increased. Likewise, interpersonal connections can either produce or endanger existential significance. As current studies demonstrate, patient preferences and autonomy must be respected, as patients are the experts in their own lives. Gómez-Vserda et al. [48] underlined the relational character of human beings and our fundamental need for support from others in order to exist. Inasmuch as COPD, in many circumstances, leads to full dependency on others, it threatens the sense of control
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and autonomy. Despite the distressing experience of illness, some studies report that an awareness of vulnerability represented an opportunity to re-establish ties with loved ones, promote union with others through reconciliation and forgiveness [49,50], and see one's final moments as an opportunity to transmit values (legacy) to other family members [49,51]. This evidence is similar to our findings, as some patients recognized family ties as indispensable for their functioning. The ongoing nature of chronic illness imposes a significant strain on both patients and family members. Responsibilities within the family can change because of the illness, which can cause problems and disrupt the peace of family connections. Some participants had to retire early due to their deteriorating health, having to rely on their spouses and family members to help with domestic chores and shopping. A loss of income may cause financial difficulties and place more anxiety and pressure on the family [52]. These shifting responsibilities and changing circumstances may cause misunderstandings or even conflict within the family [53]. Our findings also suggest that illness affects how participants see themselves and others (family, friends, healthcare professionals and the immediate social environment), as well as how social and professional responsibilities shift [54]. The "clinical gaze can sometimes become 'objectifying', in the sense that it is unable to comprehend this subjective, personal world, which needs a human and humanizing attitude to help mitigate the feeling of vulnerability" [41] (p. 290). A previous study found that good communication is an important component of a patient-centred model of care for helping patients
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become active agents in their own healthcare [55,56]. Nevertheless, if the connection is strained, it may be difficult for professionals to provide individualized care. A diagnosis in medical culture can also imply judgment on one's way of life. Studies indicate that some COPD patients feel embarrassed and stigmatized about their diagnosis since healthcare personnel state that they are to blame for their condition [57,58]. As the participants' lived experiences demonstrate, the illness changed their meaning of past, present and future, and their sense of time and rhythm [59], regarding their period of illness and their overall biographical time ("life"). This affected their acceptance of the condition as a "way of life" rather than an "illness" [59]. Some studies have begun to explore the sense of time for the chronically ill and its effects upon the roles they perform [60], how they approach daily activities, and how they constantly renegotiate their identity and illness' influence on how time is experienced [60,61]. Our analysis also demonstrates how participants reflected on the meanings attributed to past memories, bringing them into the present and projecting them into the future, while sometimes rooting themselves in the past to help maintain their personhood. Spiritual beliefs were deeply ingrained in their lives and were obviously part of how they described themselves (personal identity) and their reasons for feeling hopeful and comforted. Their faith undoubtedly provided them with the fortitude to deal with what was happening to them [62]. Respect, spiritual peace and hope have been identified as key attributes of dignity in the
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context of dying [63], and actions that can conserve dignity in this context include seeking spiritual comfort, finding solace within one's religious or spiritual beliefs, and fostering feelings of hopefulness [22]. The findings show a clear link between lived space experience and the need to maintain experiences of belonging, meaningfulness, safety and security, and autonomy in people with advanced COPD [22]. Participants described the home environment as a place for safety and security, an arena where they assert control of their bodies and emotions, avoid stress, do things at their own pace, and where the abilities of caregivers can be improved to meet their needs and wishes [64]. Interestingly, and in keeping with the findings from our study, some studies describe how being outdoors in nature or a garden might have positive consequences, including by fostering emotional well-being and feelings of freedom, and by preventing loneliness. Exposure to nature, particularly green and blue spaces, has been linked to a variety of health advantages, including mental health benefits [65], better psychological well-being [66] and the regulation of body rhythms [67]. In our study, the home appeared as "a place for a good death", which in the literature represents a common measure of quality of EoL care [68]. Dying at home is, therefore, envisioned as a reply to the growing imperative to preserve patient dignity and autonomy, while also addressing the need of healthcare systems to save money and lessen their load on secondary care supplies [69]. Similarly, compassionate spaces in healthcare are regarded as a standard of
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care and a critical component of a patient's healthcare experience, but availability is insufficient. As per the latest studies, compassion is built into healthcare settings, but it can be altered by life events and can change over time [70]. A recent scoping assessment confirmed the limitations of compassionate care as mentioned by participants, highlighting a range of barriers to compassion within practice settings, such as time constraints, workloads and staff shortages [71]. The fragmentation of healthcare settings or the lack of compassion, mentioned during interviews, can be overcome with a more structured care network, including palliative care services and multiprofessional care that properly manages the multiple dimensions of complex care for patients with advanced COPD [71]. Although COPD is recognized as a life-limiting illness requiring palliative care, such care for this group is lacking in Portugal [1]. In this sense, our study confirms this scenario, since none of the participants benefited from an integrated palliative care plan. Besides the scarcity of home-based palliative care services, other reasons could explain this reality, namely, the unpredictable trajectory of COPD and the misunderstanding of palliative care as being exclusively for patients with cancer and only useful in the latter days of life [72][73][74][75][76]. Maintaining patient dignity is the duty of the healthcare provider, but also of the patient's family and the patient themself. Additionally, policymakers and leaders in healthcare play an important role in promoting healthcare that respects people's dignity. From the stories and our interpretations, there is an appeal to the ethics of the face proposed by Emmanuel
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