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Multiscale modeling is a promising tool for the study of coronary hemodynamics. A key strength of this approach is that it accounts for microvascular properties and extravascular forces that differ regionally and transmurally, as well as wave propagation effects in the conduit arteries. However, little validation of such models has been reported and no models of the newborn coronary circulation have been described. We therefore validated a multiscale model of the left coronary circulation using high-fidelity data from nine adult sheep and nine newborn lambs and investigated whether wave propagation effects are more prominent in adults, whose body size (and hence wave transit distance) is greater. The model consisted of a one-dimensional (1D) network of the major conduit arteries and a lumped parameter model of microvascular beds. Intramyocardial pressure was considered to arise via contraction-related myocyte thickening and transmission of ventricular cavity pressure into the heart wall. 1D network geometry from published human anatomical data was scaled using myocardial weights, while subject-specific aortic pressure/flow and ventricular pressure formed model inputs. Total vascular resistance was determined iteratively from measured mean circumflex coronary flow (CxQ), but no fitting of phasic aspects of the waveform was performed. Excellent agreement was obtained between simulated and measured CxQ waveforms in most cases. Detailed flow waveform analysis did not clearly reveal a greater prominence of wave propagation effects in adults compared with newborns. This multiscale model is likely to be useful for investigating wave phenomena and phasic aspects of coronary flow in adults and during development.
- coronary arteries
- wave propagation
- allometric scaling
- computer model
- hemodynamics
- newborn
mathematical modeling, in concert with experimental studies, has played an important role in building our current understanding of coronary hemodynamics, providing insights into the role of intramyocardial pressure, large microvascular compliance, and transmural differences of vascular impedance and flow patterns (4, 9–12, 18, 64, 67, 70). Many models of the coronary circulation have been of the lumped parameter [or zero-dimensional (0D)] type, where the resistive and capacitive properties of all coronary vessels are combined into a small number of elements. For example, the main conduit coronary arteries lying on the epicardium (or traversing the ventricular septum) have generally been represented by a single compliance (10, 12, 64) or windkessel compartment (4, 9, 18).
One limitation of an exclusively 0D modeling approach is that wave propagation effects are neglected. That these effects play a role in shaping the coronary arterial flow waveform was first suggested by Rumberger et al. (54, 55) on the basis of flow transients ("oscillations") observed in early systole and diastole in the left anterior descending artery of horses, features that are also evident in published waveforms from humans and other species (5, 14, 38, 76). More recently, therefore, a number of one-dimensional (1D) or multiscale (i.e., combined 0D/1D) models of the coronary circulation, which are best suited to the study of wave propagation effects, have been described (25, 45, 52, 57, 58, 71). Validation of such models requires direct comparison of simulated and experimental waveform shapes, including any high-frequency flow transients. However, although this has been performed for systemic large arteries (53), very little validation of 1D/multiscale coronary arterial models has been presented, a void that has been recognized in recent reviews (34, 73).
Moreover, to our knowledge no models (multiscale or otherwise) of the newborn coronary circulation have been described or validated. Indeed, aside from a few published Doppler velocity recordings (47, 48), relatively little information about phasic coronary hemodynamics in the newborn is available. Of particular relevance to the design of a newborn coronary circulation model is the hypothesis of Rumberger et al. (54, 55) that the prominence of the early systolic and diastolic flow transients (and hence the importance of wave propagation) increases with body size due to longer wave transit distances. While this suggests coronary flow waveforms (along with modeling requirements) may differ between newborns and adults, no qualitative or quantitative comparison of development-related flow waveform changes has ever been made.
In this study, we describe a multiscale coronary circulation model in which an anatomically-based 1D network accounts for wave propagation effects in the main conduit arteries, and numerous 0D compartments inserted throughout the network represent microvascular impedance and established sources of intramyocardial pressure. Allometric scaling is used to generate models of the adult and newborn sheep coronary circulation. These models are validated on two levels: a general validation of microcirculatory flow patterns against published data, and a subject-specific validation utilizing high-fidelity in vivo measurements of proximal circumflex (Cx) coronary arterial flow. A sensitivity analysis is used to reveal the effects of model parameters on the flow waveform. Finally, a detailed analysis of the Cx flow waveform is performed to establish whether wave propagation effects increase in prominence with normal growth.
1D model of conduit coronary arteries.
Most sheep (8, 20) display a left dominant coronary anatomy in which the Cx supplies the posterior portion of the ventricular septum. Based on the gross similarity between left dominant anatomies in humans and sheep (20), the 1D conduit artery model shown in Fig. 1 was adapted from measurements in humans by Dodge et al. (16). Segment lengths were calculated from reported proximal and distal segmental coordinates, and vessel diameters were chosen to be within the reported range, taking care to avoid nonphysiological wave reflections at bifurcations (see Supplemental Data File for parameter values of the 1D network; Supplemental Material for this article is available online at the Am J Physiol Heart Circ Physiol web site). Following Olufsen (46), stiffness of the 1D segments was determined by a prescribed reference wave speed (c0), calculated as a function of reference radius (r0), (1) where values for the coefficients k1 = 2 × 107 g·s−2·cm−1, k2 = −22.53 cm−1 and k3 = 8.65 × 105 g·s−2·cm−1 were taken from (46) and then all wave speed values were uniformly scaled to achieve a target wave speed in the proximal Cx where experimental measurements were taken.
The 1D modeling methodology has been described in detail elsewhere (43–45). Briefly, the nonlinear 1D equations governing pressure (p), cross-sectional mean velocity (u) and cross-sectional area (A) are (2) (3)where ρ is blood density and μ is blood viscosity (1.06 g/cm3 and 0.035 poise, respectively). The viscous term incorporates the constant ξ; for a Poiseuille velocity profile ξ = 8 but, following (58), we use ξ = 22, which better reflects the physiological velocity profile. The following physiologically relevant pressure-area relation was used: (4)where A0 and p0 are reference area and pressure and b is a constant governing the shape of the pressure-area relation, estimated via a nominal zero-area pressure of −10 mmHg (44); note that although all equations in this article assume a centimeters-grams-seconds units system, with a pressure unit of dyn/cm2, pressures values are quoted in mmHg (1 mmHg = 1,333.22 dyn/cm2). The viscoelasticity constant Γ is difficult to estimate and is assumed to be zero for the main results; however, we investigated the effect of viscoelasticity in the sensitivity analysis, where we assumed Γ = 1,792 r0 + 1,522 g/s, as approximated from Eq. 32 in Alastruey et al. (1), wall viscosity data (7), and wall thickness-diameter ratios (42). Note that although we have chosen a simple Voigt model, more sophisticated viscoelasticity models are available (see for example, Refs. 66, 69). External pressure (pext) was set to zero for epicardial conduit arteries, but for septal conduit arteries that lie within the contracting ventricular septum, pext was set to the average of left ventricular (LV) and right ventricular (RV) cavity pressures (pLV and pRV), with an assumed pRV of 0.2 pLV (42, 43). The 1D governing equations were solved using a finite element method (45), with continuity of total pressure (p + ½ ρu2) applied at vessel bifurcations. The viscoelastic term in Eq. 4 was treated with an operator splitting technique as described elsewhere (19, 39).
Lumped parameter model of intramyocardial vascular beds.
The 0D model of the coronary microvasculature (Fig. 2) was based on the models of Bruinsma et al. (11) and Spaan et al. (65). Whereas in those studies a single instance of the model was used to represent the entire left coronary arterial system, in the current study numerous 0D instances each represented a small region of myocardium.
In the coronary circulation, blood flow is delivered to the microvasculature via penetrating arteries that branch off the main conduit arteries, as shown in Fig. 2 of Wüsten et al. (77). The interface between 1D and 0D in our model was at the level of these penetrating arteries. Short 1D penetrating artery segments were inserted throughout the 1D model and were coupled to the 0D model instances (depicted as boxes in Fig. 1) via a penetrating artery characteristic impedance and compliance (Zpa and Cpa, Fig. 2). On the venous side, a penetrating vein characteristic impedance and compliance (Zpv and Cpv) were connected to an assumed constant right atrial pressure (pRA = 5 mmHg).
The microvascular model was divided into subepicardial, midwall, and subendocardial layers (Fig. 2). Following Spaan et al. (65), each layer consisted of two compartments, whose volume varied according to the compliances C1 and C2. The compartments each contained a resistance (R1 and R2), while a "middle" resistance Rm was shared by both compartments, keeping in mind that the physical portion of the microvasculature represented by the two compartments is uncertain and probably changes with perfusion pressure (65). Note that Cpa represents the total compliance of all medium-sized intramyocardial vessels that nominally lie proximal to R1.
Instantaneous compartment volume was given by (5)where i = {1,2} and transmural pressure (ptm) is equal to intravascular pressure (p) minus intramyocardial pressure (pim, Fig. 2). Based on Poiseuille's law, the assumed volume-resistance relationship (11) was (6)where R0,i is a reference resistance corresponding to a reference volume V0,i. The middle resistance shares volume from the two compartments as follows, (7)where γ is a constant between 0 and 1.
Intramyocardial pressure is high during systole and low during diastole, giving rise to systolic flow impediment. A number of mechanisms have been proposed to explain the generation and transmural distribution of pim, and we refer to reviews by Spaan et al. (61) and Westerhof et al. (75) for comprehensive discussion of this complex subject. In the current work, we utilize the recent finding of Algranati et al. (2) that pim can be best accounted for by a combination of two mechanisms. The first is cavity-induced extracellular pressure (CEP), which arises from transmission of ventricular cavity pressure into the heart muscle. Solid mechanics theory predicts CEP will be equal to cavity pressure in the subendocardium, with an approximately linear decline to pericardial pressure in the subepicardium (63); this has been confirmed by computational and in vivo studies (23, 57). The second mechanism is shortening-induced intracellular pressure (SIP). Rabbany et al. (50) hypothesized that when myofibrils shorten, they also thicken to maintain a constant volume, leading to an increased intracellular pressure and radial thickening of the cell that would be felt by adjacent blood vessels (and pressure sensors), thus contributing to pim and systolic flow impediment. Note that, as discussed in Algranati et al. (2), a third mechanism that has been proposed is related to myocardial elastance (Emyo, i.e., stiffness) (32); however, the increasing Emyo that accompanies heart contraction has been shown to reduce transmission of cavity pressure transmurally and may therefore dampen rather than contribute to systolic flow impediment (2, 31). We therefore assumed that pim is given by (8)where α ∝ 1/Emyo and represents the damping effect of Emyo on transmission of cavity pressure into the heart wall. Given the findings of Algranati et al. (2) that the combination of CEP and SIP are best able to account for current experimental data, in the present study we assume α = 1. As in previous modeling studies (4, 11), CEP for the LV free wall was assumed to vary linearly from cavity pressure at the endocardium to pericardial pressure (here assumed to be atmospheric pressure) at the epicardium. Hence, for the three transmural layers, average CEP in the subendocardium, midwall, and subepicardium was therefore 5/6, 1/2, and 1/6 of pLV, respectively. CEP for the ventricular septum was distributed between pLV and pRV in a similar manner.
Algranati et al. (2) calculated SIP from sarcomere stretch ratio, which was assumed to be directly related to ventricular volume and wall thickening. Consistent with measurements by Rabbany et al. (50), the resulting SIP was remarkably similar in shape to the chamber elastance waveform, which attains its maximum in late systole; this is not surprising given that myocardial contractility is responsible for both SIP and chamber elastance variations. Thus as a first approximation, we assumed that SIP is directly proportional to ventricular chamber elastance, or SIP = φELV. Prior experimental measurements (41, 50) have shown that peak pim generally exceeds peak pLV by 10–30% in the subendocardium; hence φ was chosen to result in a peak SIP equal to 20% of peak pLV; in the sensitivity analysis 0 and 40% were also tested.
Reference resistances were obtained as follows. Based on Fig. 13 in Spaan et al. (65), we assumed R1 = 1.2 Rm and R2 = 0.5 Rm, and γ = 0.75, i.e., 75% of Rm is dependent on the volume of chamber 1 and the remainder is dependent on the volume of chamber 2. Assuming subendocardial-to-subepicardial flow ratios (or left-to-right septal flow ratios) reported by Fisher et al. in adult sheep (17), total resistance (i.e., R1, Rm, and R2) was then determined iteratively to achieve a target mean flow.
The compliances C1 and C2 were 0.013 and 0.254 ml·mmHg−1·100 g−1, respectively, while V0,1 and V0,2 were 2.5 and 8.0 ml/100 g (62, 65), with a subendocardial-to-subepicardial ratio of 1.14 for both parameters (11, 74). In preliminary simulations, we found that accounting for the volume-dependence of compliance using the method described by Bruinsma et al. (11) had a negligible effect on coronary flow waveforms (as in Ref. 65), and we therefore used constant compliances. Cpa and Cpv were arbitrarily assumed to be 10% of total C1 and total C2, respectively; however, the influence of Cpa was investigated in the sensitivity analysis. Absolute values of compliance and volume were calculated by distributing myocardial weights according to the inverse cube of 1D penetrating artery radii (i.e., Murray's law) and then equally to the three transmural layers.
Experimental studies.
Experimental data were obtained from our laboratory data repository. Experiments were approved by the institutional animal ethics committee and conformed to guidelines of the National Health and Medical Research Council of Australia. The surgical preparation has been described in detail previously (49, 59). Briefly, nine Border-Leicester cross ewes (47.3 ± 3.8 kg, means ± SD) and lambs (7–10 days old, 6.7 ± 0.7 kg) were anesthetized with intramuscular ketamine (5 mg/kg) and intramuscular xylazine (0.1 mg/kg) followed by intravenous α-chloralose (25–50 mg/kg). Anesthesia was maintained with iv α-chloralose infused at a rate of 12–25 mg·kg−1·h−1. Following tracheal intubation, animals were ventilated to maintain arterial blood gases within the normal physiological range. High-fidelity pressures were measured in the ascending aorta and LV cavity with 5-Fr Millar micromanometer-tipped catheters inserted via the right common carotid artery and left atrium, respectively. Offset calibration of these pressures was performed with a separate pressure obtained from a fluid-filled catheter inserted into the aorta via a purse-string suture and connected to an external manometer. High-fidelity flow signals were measured in the ascending aorta and proximal Cx with Transonic flow probes. At the end of each study, the flow probes were removed, the animal was killed with sodium pentobarbitone, and India ink solution was injected into the Cx to demarcate the anatomical limits of its perfusion territory. The ventricles, atria, and septum were later dissected and weighed, with the weight of the stained portion of myocardium used to normalize Cx blood flows.
Validation procedure.
Validation of the multiscale coronary model was performed with minimal data fitting. In both adults and newborns, we assumed a proximal Cx wave speed of 9.0 m/s in all animals, based on the reported value of 8.6 m/s in the similarly-sized left anterior descending artery in dogs (3) and the observation that, allometrically, wave speed displays negligible dependence on body size (22). Allometric scaling of 1D segment lengths and diameters for a given animal was performed on the basis of reference human myocardial weights (LV, 104 g; septum 54 g) reported in Lorenz et al. (37) and measured individual myocardial weight, using a scaling power of 0.35 (56). An overview of the procedure used for obtaining subject-specific model inputs is shown in Fig. 3. Measured subject-specific aortic pressure was prescribed at the inlet of the left main coronary artery, having applied a delay of 15 ms (in adults) and 8 ms (in newborns) to account for the estimated delay between pressure generation in the myocardium and pLV sensing just below the mitral valve, caused by a ventricular wave speed of ∼4 m/s (72).
Individually measured pLV was used directly for CEP. To estimate SIP, LV cavity volume was derived by integrating measured aortic flow and assuming an ejection fraction of 0.68 (24) and then calculating chamber elastance as the ratio of cavity pressure and volume. Only one free (i.e., fitting) parameter was considered in the validation procedure, namely total intramyocardial resistance, which was uniformly adjusted using an iterative beat-to-beat algorithm to achieve measured mean flow in the proximal Cx. All other parameters described in previous sections were treated as subject generic.
Waveform analysis.
Proximal Cx flow waveforms of adult and newborn sheep (along with corresponding simulated waveforms) were compared after normalization to mean flow and heart period. Four time epochs were defined for analysis: the early systolic flow transient (S1), the remainder of systole (S2), the early diastolic flow transient (D1), and the remainder of diastole (D2). In addition, specific waveform feature points (labeled S1a–S1c and D1d–D1f) were identified, as shown in Fig. 4.
Statistical analysis.
Comparisons of adult vs. lamb data were performed using one-way ANOVA, while comparisons of experiment vs. simulation data were performed with repeated measures ANOVA. Significance was defined as P < 0.05.
Global and regional coronary hemodynamics.
Basic experimental data pertaining to both study groups is provided in Table 1. Weight-corrected mean Cx flow in newborns was almost twice that in adults, and the heart-to-body weight ratio was smaller in adults than newborns. Total effective vascular resistance in the left main coronary artery (LM) of adults and newborns, calculated as p̄LM − pRA/q̄LM, was 0.72 ± 0.35 and 0.34 ± 0.09 mmHg·min·(100 g LV)/ml, respectively.
Simulated total microvascular arterial and venous flow waveforms (Fig. 5A), calculated as ∑Qima and ∑Qimv over all microvascular compartments, were antiphase, demonstrating the intramyocardial pump effect (64) whereby cardiac contraction decreases and even reverses flow on the arterial side, but at the same time increases venous flow. Conversely, cardiac relaxation caused a surge in arterial flow but reduced venous flow.
Figure 5B compares simulated total left coronary flow in the three transmural layers on the arterial side. Subendocardial flow was the most pulsatile and exhibited substantial retrograde flow during systole. Almost all midwall flow occurred during diastole, while subepicardial flow had a similar (antegrade) magnitude in systole and diastole. Transmural flow patterns on the venous side were all systolic-dominant, with notable forward diastolic flow in the subepicardial layer only (Fig. 5C). Vascular volume varied most in the subendocardium (arterial 17%; venous 7%) and least in the subepicardium (arterial 1.6%, venous 2.3%; Fig. 5D, data shown only for arterial side). The reduction in microvascular volume caused by high-systolic pim increased resistance as in Bruinsma et al. (11) and was responsible for 40 ± 8 and 42 ± 8% of total effective resistance in adults and newborns, respectively.
Flow waveforms in different territories.
Figure 6 compares mean normalized flow waveforms in different territories of the left coronary arterial network for a representative adult sheep and newborn lamb. There were no major differences between territories in terms of late systolic or late diastolic flow. The early systolic and diastolic flow transients were of similar prominence in the Cx, left anterior descending (LAD), diagonal and marginal arteries; were less prominent in the left posterior descending artery and were nearly absent in the septal artery.
In vivo validation.
Figures 7 and 8 compare model and experimental flow waveforms in the proximal Cx of adult sheep and newborn lambs, respectively. The waveforms were grossly similar to the diastolic-dominant microvascular arterial waveform (Fig. 5A) but with superimposed oscillatory flow transients during early systole and early diastole (arrows in Fig. 7). Visual agreement between model and experimental waveforms was excellent in most cases, with the model generally performing well in capturing both the flow transients and the levels of systolic and diastolic flow. The root mean square error, normalized to maximal flow, was 16.7 ± 4.9% (range 12.4 to 27.0%) for the adults and 14.5 ± 4.9% (8.0 to 22.6%) for the newborns, with no difference between groups (P > 0.3). In some cases, late systolic flow was underestimated (Figs. 7, E-G, and 8, C, E, and H) or the amplitude of the early systolic flow transient was underestimated (Figs. 7, D and F, and 8, F and I). On the other hand, in some cases the model captured qualitative intersubject differences in Cx waveform shape (e.g., compare Figs. 7, A-C, and 8, A-C).
Table 2 presents the Cx flow waveform analysis, comparing adults and newborns, experiments, and simulations. There was no difference in the duration of the key phases of the flow waveform (S1, S2, D1, and D2) between model and experiment, but S1 and D1 flow transients lasted slightly longer (as a proportion of heart period) in newborns than adults (14 ± 2 vs. 11 ± 2% and 13 ± 4 vs. 9 ± 2%, respectively, both P < 0.05). Conversely, there was a trend for shorter S2 and D2 in newborns (P < 0.15, model and experiment). Mean average-normalized flow during S2 and diastole (i.e., D1 + D2) was the same in adults and newborns; however, the model underestimated S2 flow for adults (P < 0.05) and hence predicted a higher value in newborns than adults; the model also predicted an 8 ± 6% lower diastolic flow in newborns compared with adults (P < 0.05). There was no difference between adults and newborns for the feature points S1a, S1b, S1c, D1d, D1e, or D1f (experiment), but the model incorrectly predicted smaller S1a, S1c, and D1f values in newborns than adults. Conversely, both the simulations and experiments revealed higher D1e values in newborns compared with adults.
Sensitivity analysis.
Figure 9 shows the sensitivity of the Cx flow waveform to a number of key input parameters. Increasing wave speed of all 1D segments by 22% reduced the amplitude of the systolic and diastolic flow transients, whereas decreasing wave speed augmented them (Fig. 9A). If aortic pressure was applied at the model inlet without applying the delay to account for finite ventricular wave speed, a transient negative flow peak was observed in late systole that was either not present or of lower magnitude in the experimental data; the flow waveform shape was otherwise relatively unaffected (Fig. 9B). Removing SIP entirely reduced pim during systole and hence increased systolic flow (via decreased systolic flow impediment); conversely, doubling SIP enhanced systolic flow impediment (Fig. 9C). Increasing C1 reduced diastolic flow, whereas decreasing C1 led to a small increase in systolic flow (Fig. 9D). Increasing Cpa increased the amplitude of the early systolic flow spike and dampened the early diastolic oscillations (Fig. 9E). Increasing/decreasing reference intramyocardial volumes increased/decreased diastolic flow but did not alter systolic flow (Fig. 9F). Incorporating conduit arterial viscoelasticity produced hysteresis in the pressure-area relation (Fig. 10A, representative adult), dampened the early diastolic flow oscillations and led to a small increase in the duration of the early systolic flow transient (Fig. 10B); similar effects were evident in the newborns.
This study has validated a multiscale model of the left coronary circulation using high-fidelity measurements in adult sheep and newborn lambs. Agreement between simulated and measured Cx flow waveforms was excellent in most cases, suggesting that the model adequately captured the most important mechanisms underlying the coronary flow waveform. Moreover, the scalability of the model was validated, supporting its future use for studying coronary hemodynamics in newborns and adults, as well as the intervening growth period. Despite marked differences in weight-corrected coronary flow and heart size, detailed flow waveform analysis suggested that adult and newborn coronary flow waveforms, when normalized, are broadly similar.
Model validation.
While experimental validation is an essential step in establishing the relevance, accuracy, and predictive ability of a mathematical model, only limited validation of 1D coronary models has been performed previously. Huo and Kassab (25, 26) validated pulsatile flow simulations from a 1D coronary network model against measurements in isolated, arrested, and vasodilated pig hearts, but the waveforms were not representative of the in situ beating heart and did not contain high-frequency transients. Rumberger and Nerem (54) and Guiot et al. (21) compared measured flow waveforms with those simulated in a single 1D segment model. Recently, van der Horst et al. (71) compared measured and 1D model-simulated flow waveforms in a single patient; however, the focus was on gross changes to the flow waveform that could likely also be predicted by a 0D model.
Employing minimal data fitting, we validated our multiscale model on two levels, general and subject specific. For a general validation, we showed that characteristic flow patterns throughout the model were representative of published in vivo data. Thus simulated small artery flow exhibited some retrograde flow during early systole, near zero flow during the remainder of systole, and a dominance of forward flow in diastole; conversely, venous flow was predominantly systolic (compare our Fig. 5A with Fig. 1 in Ref. 29). Sustained retrograde flow occurred during systole in the subendocardium (Fig. 5B) as has been observed in vivo (Fig. 4 in Ref. 68 and Fig. 3 in Ref. 27); in some cases, experimentally measured subendocardial flow has been near zero during the latter part of systole (Fig. 3 in Ref. 68) as in the midwall layer of our model (Fig. 5B). Forward flow occurred during systole and diastole in subepicardial vessels (Fig. 5B), in agreement with Kajiya et al. (28) and Toyota et al. (68), although simulated data did not predict the early systolic retrograde flow evident in some (but not all) in vivo waveforms. Vascular volume varied over the cardiac cycle by 17% in the subendocardial arterial compartment but only 1.6% in the subepicardial arterial compartment, consistent with measured diameter variations of these vessels (68).
The difference between predicted LAD and septal flow waveforms (Fig. 6) followed a similar trend to that in canine data, reported by Chilian and Marcus (14), in which the early systolic flow transient (called "mid-systole" in Ref. 14) accounted for 3.5 vs. −7.2% of the total area under the flow-velocity curve in the LAD and septal artery, respectively. This compares with 3.2 vs. −1.4% for our simulated adult group data and 4.3 vs. −0.7% for the newborn group data (both groups P < 0.001, LAD vs. septal). By contrast, the flow integral percentage during late systole was not different between these sites in Chilian and Marcus (14) or in our simulated adult group data; however, in the newborn group, LAD and septal arteries accounted for 7.9 and 4.9%, respectively (P < 0.001).
For subject-specific validation, measured LV pressure, aortic pressure and flow, and LV weight from a particular subject were used as model inputs. Mean Cx flow was matched to the subject by adjusting total coronary resistance, but no other data fitting were employed; importantly, no fitting of phasic waveform features was performed. In 18 subjects (9 adult sheep and 9 newborn lambs), the agreement between simulated and in vivo flow waveforms was excellent in most cases. Overall levels of systolic and diastolic flow were similar in the model and experiments, although late systolic flow was underestimated in some cases, suggesting possible overestimation of SIP (cf. Fig. 9C) or α in Eq. 8. The model generally performed well in predicting the amplitude and duration of the early systolic and early diastolic flow transients arising from wave propagation effects, with the exception that minimum early systolic flow (S1a) and maximum early diastolic flow (D1e) were underestimated in lambs (Table 2). In several cases, the model clearly distinguished qualitative intersubject differences in the coronary flow waveform.
Closer agreement between simulated and in vivo waveforms could undoubtedly have been achieved if more extensive data fitting had been employed. However, as is typically the goal with complex models containing many parameters, we chose a predictive modeling approach in which model performance was assessed with no or minimal data fitting. This contrasts with descriptive modeling, where the aim is to maximize agreement but minimize the number of model parameters. Performing data fitting to maximize agreement in a complex model (such as ours) can be problematic because uniqueness is generally not guaranteed.
Model scalability.
The model described herein, along with our recent study of congenital coronary abnormalities (44), represents the first modeling effort in relation to the newborn coronary circulation. In the absence of subject-specific vascular geometry, this was made possible by using allometric scaling, a powerful technique for predicting physiological parameters over a wide range of body sizes across species (22) or during maturation (56). Our results suggest this approach can be used for developmental coronary models, even when based on data from a different species (albeit with similar gross vascular anatomy) (16). To validate the scalability of the model, we compared simulated and in vivo flow waveforms in adults and newborns (Figs. 7 and 8) and performed a detailed flow waveform analysis that revealed comparable accuracy in both age groups (Table 2); in most respects there was no statistical difference in quantified waveform features between simulated and in vivo data.
Considerable care is required when applying allometric scaling during maturation, which involves physiological changes that are independent of body size per se (43). As a case in point, scaling of coronary artery dimensions must be performed using myocardial weight rather than body weight (normally used for allometric scaling) because, consistent with prior reports (35), the ventricular myocardium/body weight ratio decreased from 5.3 g/kg in newborns to 3.2 g/kg in adults (compared with ∼2.7 g/kg for adult humans). Adopting the scaling power of 0.35 (56) resulted in Cx diameters that were close to those seen in the experiments (∼4 mm and ∼2 mm in adults and newborns, respectively).
Weight-corrected myocardial blood flow in newborn lambs was approximately double that of adult sheep, as has also been reported by Fisher et al. (17). Vascular resistances were correspondingly lower in newborn lambs. Given the general principle that compliance is higher in vascular beds with lower resistance, one might therefore expect weight-corrected intramyocardial compliance to be higher in newborn lambs. However, if we assume that the similar capillary density and luminal area in the LV of newborn and adult sheep (60) implies similar overall vascularity, it follows that weight-corrected vascular volume should be similar in both groups (62). Assuming similar volume distensibility, then in the absence of more firm data it is also reasonable to assume similar vascular compliance in both groups. Despite this and other assumed similarities between adults and newborns (relating to CEP, SIP, resistance, compliance and volume values, and distributions), acceptable agreement between simulated and measured flow waveforms was achieved in both groups.
Wave propagation effects and growth.
In the first investigation of wave propagation effects on the coronary arterial flow waveform, Rumberger and Nerem (54) stated that "there is evidence that the nature of (the early systolic and early diastolic) oscillations may be size (or species) dependent," with comparison of published data across a range of adult species suggesting an apparent trend for more prominent oscillations in larger species. However, as no such comparison has been made during normal growth within a single species, we therefore compared the oscillations (i.e., flow transients) in adult sheep and newborn lambs, whose heart weights differ by a factor of four. Having quantified the main characteristics of the flow transients in both groups (Table 2), we did not find clear evidence that wave propagation effects are less prominent in lambs. On the one hand, there was no difference between S1a, S1b, S1c, D1d, or D1e features. However, the flow transients (S1 and D1) were slightly wider in lambs, suggesting greater wave propagation effects. Conversely, the main negative excursion of both transients (i.e., S1b-S1c and D1e-D1f) was lower in lambs, suggesting less prominent wave effects. We conclude that evidence of wave propagation is apparent in the waveforms of both adult and newborn sheep but that better metrics of "windkesselness" (30) may be required to establish whether these effects are different in small hearts.
It is noteworthy that the importance of wave propagation depends on the ratio λ/L, where L is the length over which waves travel and λ is the wavelength, equal to wave speed multiplied by wave frequency. The importance of wave effects is therefore influenced by body/heart size and vascular anatomy (determinants of L), heart rate and contractility (determinants of wave frequency), and vessel diameter and stiffness (determinants of wave speed). The similar prominence of the flow transients and hence wave effects in adults and newborns is thus likely due to the higher heart rate in newborns (newborn/adult ratio = 1.9) offsetting the effect of smaller body size (adult/newborn ratio of mean 1D segment length = 1.7). Considering other clinically relevant situations, increased coronary wave speed related to vascular aging or disease (15) or increased heart rate accompanying exercise (6) may, respectively, decrease and increase the influence of wave propagation effects on the coronary flow waveform. Note, however, that it is unclear whether the size of the flow transients per se reliably quantifies the importance of wave effects, given the complex combination of phenomena contributing to the coronary flow waveform during early systole and diastole, such as the intramyocardial pump effect and aortic pressure changes.
Sensitivity analysis.
Due to the large number of model parameters, a comprehensive sensitivity analysis was not possible. We therefore included only those global parameters whose values were approximated on the basis of relatively loose constraints (Fig. 9). Other parameters determined by strong constraints (such as total resistance, constrained by measured pressures and mean flow) were not included. Wave speed appeared to be the most important parameter governing the early systolic and early diastolic flow transients, which supports the view that these features mainly arise from wave propagation effects; hence, 1D segment lengths would also be expected to influence these features. Unsurprisingly, the magnitude of SIP had a substantial influence on overall systolic flow; although not included in the analysis, CEP would clearly also have a large influence on systolic flow. The aortic pressure shift, wave speed and Cpa were all important determinants of a late systolic negative flow spike. Other parameters evaluated in Fig. 9 (C1, V0), along with C2, γ, the R1:Rm and R2:Rm ratios (not shown in Fig. 9) had a relatively minor effect on the flow waveform.
Comparison with previous models.
In constructing our model, gross anatomical measurements of only the largest conduit arteries were combined with a lumped parameter representation of the small intramyocardial vessels, with extravascular compression effects applied via a time-varying pressure source and variable resistance. This approach, also adopted by others (52, 71), allows the model to be easily adapted to differing normal or pathological anatomies via anatomical studies (16), known common vascular abnormalities (44), or angiography from specific subjects. An alternative approach is to use stochastic vascular networks based on morphometric data, which allows many more vessels generations to be included in the 1D part of the model (25, 58) but increases computational demands. Our data suggest that representing only the largest conduit arteries in 1D is sufficient when studying the proximal coronary flow waveform. A geometrically idealized model could have been used, through the use of "equivalent" vessels (45); however, such models generally contain parameters with uncertain anatomical significance (such as "effective" length) and more data fitting would have been compulsory given a lack of constraints from the true anatomy.
Use of Eq. 8 enables all three mechanisms of myocardium-vessel interaction evaluated by Algranati et al. (2) to be represented in a straightforward manner, with parameterization guided by in vivo data. Since this approach assumes these mechanisms a priori, study of the mechanisms per se (rather than simply their haemodynamic effects) requires more sophisticated finite deformation mechanics and myocyte-vessel interaction models (2, 57). Table 3 summarizes previous coronary models and shows the historical context in which our model lies.
Study limitations.
In designing our study, we sought to represent the most important aspects of coronary physiology, but inevitably a number of simplifying assumptions were necessary. The geometry of the 1D conduit arterial network was based on human data (16) with similar gross coronary anatomy to sheep (20), and we therefore did not account for any anatomical differences between species or subjects. The 1D model also did not account for the effects of vessel constraint, tethering or translational motion (36, 51). In using a lumped parameter model for the microcirculation, wave propagation effects in the small vessels (21) were neglected and myocardium-vessel interactions were represented in a phenomenological manner without the use of a ventricular structural mechanics model (2, 57). Intramyocardial pressure calculation did not account for the effect of varying myocardial stiffness (elastance) on transmission of LV cavity pressure into the heart wall (2, 31), although this could be incorporated in future studies via α in Eq. 8. Validation was limited to a single location (the proximal Cx), although general agreement with published data was noted for microvascular volumes and flows (Fig. 5), as well as flow in the septal artery (Fig. 6). In addition, while our study focused on baseline conditions in normal adult and newborn sheep, further validation may be required when applying the model in other contexts, for example, congenital coronary abnormalities, coronary stenosis, maximal hyperemia, exercise, or right dominant or balanced coronary anatomies.
We have validated a multiscale model of the coronary circulation in adult sheep and newborn lambs using high-fidelity in vivo measurements. Although no fitting of the phasic aspects of the coronary flow waveform was performed, excellent agreement was obtained between simulated and experimental data. Allometric scaling of the coronary model using ventricular weights enables investigation of coronary hemodynamics during development. Early systolic and early diastolic flow transients are similarly prominent in both adult and newborn sheep. A model sensitivity analysis suggested that 1) early systolic/diastolic flow transients are primarily governed by wave speed of the main conduit arteries, and 2) SIP provides a substantial contribution to systolic flow impediment and should be combined with CEP in modeling studies.
J. P. Mynard is supported by a CJ Martin Biomedical Fellowship from the National Health and Medical Research Council of Australia. This work was supported by funds from the Murdoch Childrens Research Institute and the Victorian Government's Operational Infrastructure Support Program.
No conflicts of interest, financial or otherwise, are declared by the author(s).
Author contributions: J.P.M. conception and design of research; D.J.P. and J.J.S. performed experiments; J.P.M. analyzed data; J.P.M. and J.J.S. interpreted results of experiments; J.P.M. prepared figures; J.P.M. drafted manuscript; J.P.M., D.J.P., and J.J.S. edited and revised manuscript; J.P.M., D.J.P., and J.J.S. approved final version of manuscript.
Present address of D. J. Penny: Dept. of Cardiology, Texas Children's Hospital, Houston, TX.
- Copyright © 2014 the American Physiological Society
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GraphicRiver Multiple Level Background 9377563
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Dear lord. In Jesus name I pray. Let her forgive me. Please restore everything I tore down. Let me forgive myself. The fear and guilt are heavy. Please take this from me lord. Turn my son to the right path lord. Touch his heart towards the mother of his child. Teach him to be a godly man lord for I failed him. Give me guidance lord on the matter of my marriage. I love you lord. Please be with me and my family. Never leave us.
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I work for an organization that collaborates with the Lighthouse in various ways. This experience has also led me to volunteer with the Lighthouse on various occassions. To be very honest, the Lighthouse never ceases to amaze me. The compassion and dedication of the staff seems virtually unending and it is clear that everybody truly believes in the mission of the organization and will do all they can to carry that mission out. In my opinion, the Lighthouse exemplifies what it is to work in the field of human services.
I will be interning at the Lighthouse Foundation this summer. I have also been involved with the Lighthouse a few times in the past through different youth group activities. In my short time there so far, I have seen employees work passionately toward goals and treat each and every person with respect, compassion, and understanding.
I was around when this non profit was formed. I am passionate about this ministry. I have seen many people's lives changed because of this non profit. It was formed at a time when the steel mills were on the decline in Pittsburgh and people who never thought they would need help suddenly needed a Food Bank! The Lighthouse was therre to stand in the gap for them. I have seen homeless kids have a place to live....and a place to set goals and see dreams fulfilled. I
The Lighthouse has been an active and collaborative community partner in Butler County for many years. I have had the privilege of working with The Lighthouse for the past four years in such areas as disaster response and recovery (Hurricane Ivan) through the local Voluntary Organizations Active in Disaster (VOAD), transitional and interim housing through the Local Housing Options Team (LHOT) and with the Utilty Single Point of Contact (USPOC). In each of the above activities and in many more, The Lighthouse has acted with dedication, integrity and admirable commitment to those in need.
I grew up at the Lighthouse since my family has been very actively involved since it's first day of operation. My mother was an employee while I was in middle school. While I was in college, I interned at The Lighthouse- then went on to serve through AmeriCorps after I graduated. I now am the Director of Transitional Housing. I am inspired by the vision of the ministry, Vern- our fearless leader, and seeing people change for the better once you invest in them. It is an amazing thing to be a part of- I feel very blessed!
The Lighthouse Foundation has been an inspiration to our community. I first became aware of the agency in 1994 while working for a health and human service agency. What amazed me about the agency was it's willingness to give to those in need with nothing expected in return. The agency has wonderful staff and volunteers that were always willing to take an extra step and make something positive happen. It has been a pleasure working with the agency over the past 18 years. You won't find a more devoted agency, staff, or volunteer base anywhere.
Awesome organization! Very mission driven, and willing to help any and all people in need of basic life skills and resources.


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Your gift is magnificent - and you embody it with such warmth and compassion. I feel very touched and have received great benefit from connecting. Thank you. I am also so delighted to have someone to refer people to that I trust implicitly - you are my go-to for people looking for intuitive guidance!
Psychologist, Dream Interpreter
Author of "Dream Sight"
Karen is the only psychic I consult. She works with the highest integrity, tells you when she doesn't know, and truly connects with the Divine and your guides to tell you what you need to know at that moment for the highest good of all concerned. She's the real deal, with a big heart!
Master Healer
As a psychic and an empath, I am cautious about whom I receive readings from. Karen is one of the top psychics I've ever worked with -- she continually astounds me with the things she knows and she is nurturing, super-professional and comes from such a clean and clear energy. I always feel better after talking to her. She brings the utmost integrity to the field and every single call we do. I highly, highly recommend her!
I got so, so much out of our reading and really truly feel like things have shifted for me and put in complete perspective. Amazing. The reading was also like an energy clearing for me as well. I feel so much lighter and stronger -- and that dark energy and worry are not there. I'm so glad you are there to call when needed. I'm very grateful to you and your guides!
Thank you so much for your extra time today. Our conversation was incredibly helpful, and I'm excited to move forward with these ideas and intentions. As you must know, you are truly gifted because I feel like you immediately understand me so well, and were able hit on so many points that I needed to address and are sometimes challenging to verbalize. I'm so happy I found you! Many thanks for everything and I will surely be in touch in the future!
Thank you for the timely intuitive wisdom you shared with me. It provided the clarity and direction I need to take my life to the next level! Not only did your guidance completely resonate with where I am, you delivered it in such a compassionate and caring way. Thank you, Karen!
I was impressed at how quickly and accurately you were able to connect with my energy, without asking for any personal details about me prior. I am blown away actually! You are amazing! I will definitely be spreading the word to my friends.
I just wanted to take a moment to thank you again and to let you know how extraordinary I find your gift to be. Since we had our session, I have sent 4 of my friends to you. Each one of them was blown away with your abilities. Not only was the information you were able to tap into spot-on in every instance, but the delivery of your messages is filled with kindness and compassion. Thank you for doing what you do to help guide others and offer them support.
Thank you. Thank you. Thank you. This was an amazing session full of many, many insights for me. I am fascinated by your work and look forward to speaking to you again soon. Love, blessings and much gratitude.
Thank you so much Karen. You've given me a lot to think about and helped me figure out how to approach things. I appreciate your time and energy!
Thank you for an amazing reading Karen! It was just what I needed.
Thank you SO much, Karen. You've been such an integral part of my support system in our sessions and beyond. I continue to sing your praises to anyone who is open to this kind of work. I truly can't thank you enough.
you so much Karen for your great guidance. I feel very blessed to
receive this powerful message from you. ... Not enough to words to
use to show my gratitude. Thank you and thank you!
so much! Largely due to our session ... I have a much shinier
outlook on this change than I would have thought possible. You and
your gang of guides are amazing rock gods/goddesses!
Thank you SO MUCH for this. It really helped, you've really helped! I so appreciate you going the extra mile with your generosity and love.
Thank you so much for the session! The reading was really helpful to me. You sounded like you know me very well, and your advices helped me to make a choice. Relistening to the audio makes me feel I can change my life for the better. I'm going to open a new door and move forward! Thank you for sharing your gift and love with me! You are wonderful!
You are amazing!!!! After our reading, I took what you shared with me and reflected on what you shared. One key note was my question about my health. ... Very empowering to help guide individuals upon their "true" path. THANK YOU so so much. I am so blessed that you share your gift with the world.
Thanks so much for your kindness, clarity and love! It was a great reading and great info, thanks again so much!
Karen is a uniquely gifted intuitive adviser! Not only is she insightful, I truly appreciate how caring she is and how funny she is--a great combination when I'm hurting. I feel she truly listens with her heart and inserts humor appropriately without dismissing my feelings. Her insights are always right on, including pointing things out to me that are true that I may not be conscious of while my heart is hurting. It gives me comfort to know that I can consult Karen when my human challenges prevent me from tuning into my own inner wisdom. Thank you for the blessing that you are, Karen!
Thank you so much for the read! I really enjoyed it, and I'm still digesting its contents. As you have heard before from many others, you most definitely have a HUGE gift for helping people. The talk was SO healing and empowering for me. The information is tremendously useful ... I'm just feeling very uplifted and ready to take care of business!
Thank you SO MUCH again for your Heart Service. You are Amazing! I will definitely pass on your info and I will keep you posted on what's up in my world :)) I hope our paths meet in person one day. I just re-listened to our call and you certainly are right on :)
A million thanks for the reading you gave me. It is tremendously helpful to have somebody who puts things into perspective for me and on top of that you have those wonderful insights. I was able to instantly let go of the feeling "things have to happen instantly" which is one of my weaknesses (being an Aries). I am very grateful to know you.
Thanks Karen. Our session helped me to clarify lots and I'm ready to move forward without fear.
with Karen has been an absolute pleasure. Karen is kind, thoughtful,
and has the most amazing energy. She holds a space of the purest
love, light, and intention for clients.
I have spoken with Karen for intuitive guidance on a couple occasions, and I have always found her thoughts to be spot on. Not only that, but after our sessions, I continue to receive messages from different sources that affirm and validate what we discussed in our session.
I can't describe how valuable these insights have been. They have helped me to stay on course when I was tempted to veer off. They have helped me to remind myself of my priorities, of what's most important to me in a situation.
I also participated in Karen's Breathe Love Live program, which was a gift and a blessing. The calls were so heartfelt and always seemed to touch on exactly what was going on in my life. I felt tremendous relief after each call. I also started to feel a lot more hope and my faith beginning to restore.
The exercises Karen teaches and the channel she opens up to connect with higher guidance and divine will are invaluable. I am so grateful to Karen for her guidance, her wisdom, and her gift, and most especially, her willingness to share that gift with the rest of us.
Shannon Lagasse
I want to thank you for the recent reading. It helped SO much, more than I would have ever thought. This past week has been so peaceful, I don't even know what to do with myself! :)
Hager did a reading for me, and I also got in on a gallery reading.
I just listened to the recordings to both, and wow! I heard her the
first time, but it really helped to listen to it again. If you're
feeling stuck, need some insight on a situation, or just want a peek
into your future, then do sign up for a reading. You will be so glad
you did!
Thank you so much, Karen! The reading was full of information and love!!
Karen is AMAZING! I have have several readings from her and I always come away inspired and ready to move forward. She is the one who got me out of my "bed of grief and fear" last April; otherwise, I really don't know where I would be right now. Thank you, Karen!
Thank you so much for your insights today! I feel renewed in my purpose ... it was a bit of a wake-up call. ... I already feel happier, more optimistic, and ready to take on the challenges. Thank you so much for sharing your gift with me today!
I just wanted to say thank you. It was great to have a reading with you and to see first-hand that you really are as good as I thought you were from listening to your show on iTunes :) I will, without a doubt, recommend you to anyone who is looking for guidance. Thanks again - you are wonderful,
I was stuck in a state of confusion for months. I found Karen by coincidence. It was definitely my Angels & Guides leading me to the help I needed. I hemmed and hawed to myself about having a reading, because (with everything in my head), I never thought I could come up with 1 solid question, I was jumbled/frazzled!! Finally I thought, I will just listen to what she has to say to me, and then maybe a question will come, so I booked a session Well, we could not stop talking (mostly Karen with these amazing insights)!! Karen is as accurate and intuitive as any person can be. Karen is truly Gifted and you will end up with so many questions answered and lots of other amazing information about you that is very helpful to your life; you will gain so much clarity and the confusion, doubt, fear or whatever is in your way...will be gone.
Thank you for your clarity and kind delivery. I appreciate your relationship with your guides and the way that translated into information that I can implement right away. The appreciation I am feeling is also for your sense of humor. You must be told this often. It's a kind of funny that tickles softly but paints a big graphic. I hope for opportunity to meet in person one day.
Thank you so very much for the session today. You are most gifted and I was blown away by your insight, clarity and guidance. My heart is full of gratitude.
What can you get out of a short 10 minute session with Karen? A whole new perspective on life that's what! Karen"s gentle way helped me see that I already have all the answers within, and that if I can be bold enough to keep TRUSTING my OWN intuition, then it will lead me exactly to where I need to go...even if it doesn't always feel that way at first. Give yourself the gift of connecting with this gifted, caring and compassionate teacher. I am in awe of her gift!
Thanks Karen! I'm so glad we had the chance to speak. Our session was incredibly helpful. I feel very at peace with where I'm at and where I'm headed now.
Karen is wonderful. Though I had a short session with her, she answered all of my questions, offered deep insights and advice on how to handle my situation. Karen is very pleasant, delivers accurate messages and encourages feedback. I like that she started and ended my session with a prayer. Also she provided me with a recording to keep. My experience with Karen was wonderful and the message was helpful.
It was such a pleasure speaking with you! I was very happy with how quickly you were able to connect and all the information you were able to give in such a short time. You truly have a great talent and I'm happy you're sharing it with the world. I know I will be in touch on an as-needed basis from here on out.
I can't believe I am starting to feel so much better ... you know you are a miracle, right?
I listened to our session and you are so spot-on as usual. You've helped me immensely over the past however long we've known each other, so thank you! I feel I am back to my good place and that is the best feeling ever!!
I just finished listening to the recording of our session and I wanted to tell you how much I appreciate your work. I have consulted four other psychics in my life and you, by far, have given me clearer, more precise information that makes perfect sense. This new knowledge is allowing me to make a few needed shifts in my perceptions and actions. I feel lighter. I know that is a sign of validation that I am on the right track. Thank You!
I just re-listened to the reading you did for me back in October and was blown away by how much I got from it this time around which was different from what I got when you did the reading. You do amazing work !
I can't thank you enough for your focus and insight. What I really appreciate about your style is that it wasn't all "hocus pocus, here's your future." The [creative project] idea stuck with me and the fact that the success of this project is in my hands. I took an extra week with it, deepened what I had written and [made some changes]. ... The feedback so far has been exactly what I wanted, and more. ... This is the year for this shift and our conversation put the train on the tracks.
I absolutely love my conversations with you, I always have so much fun and feel so loved when I come out
of them.
Karen�s intuition is SPOT ON. Seriously, she could tell me with absolute clarity that I would be volunteering at Heifer International�s Learning Center at Overlook Farm, my �dream job� if you will. She also told me that I would have success sharing my story of an eating disorder and helping women to heal their relationship with food- also something that I�ve made a reality. Not only is she incredibly gifted at her chosen profession, but she�s also a very generous woman in her own right. After hearing about my business and my mission, she graciously offered me the opportunity to speak on her radio show and then later extended the invitation to a show she was guest hosting. I applaud Karen for tapping into her potential and sharing her wisdom and resources with her clients. I can�t recommend her enough.
My reading helped me focus on areas that I need to in my life. You always see into me and help me understand myself so much better. Right before you pulled our energies back into our bodies and closed the session with your prayer I felt your sparkly energy. It was pure and sparkly like a silver streak of water when the sunlight hits it.
You have been my highlight of the week! Thank you for sharing your time and talent with me. It was so confirming of what has been going on.
I took your Facing Fear class, and used one of your Protection prayers for my current situation. It helped! Things are beginning to clear up (in my view), and my vibration shifting upward steadily. I also consistently see angelic numbers around me, almost on a daily basis.
Thanks again for such a lovely reading! The amazing thing is that you were answering questions that I was wondering in the back of my mind but didn't say out loud.
You really helped me to see some things so clearly. I had a huge week last week with people trying to push my boundaries. But I recognized it and put myself first. I am following my intuition more and amazing people have shown up in my life. Thank you so much.
I want to thank you for this great gift, you have confirmed a lot to me and I am still reeling from the Energy download that came through. I stand in infinite Love and Gratitude.
Karen, thank you for changing my perspective about the situation. You have a knack for telling me the truth in a loving way, in a way that helps me move forward.
Thank you -- you are gifted. No one outside of you can give you that acknowledgement, like the fulfillment of your gift feeding you from the inside.
I just wanted to let you know how much our call meant to me. It has restored my faith in my guides, who I "know" are always present but who I forget to call on. You helped me realize that I'm not alone and have plenty of support, if only I will reach out for it. Thank you for helping me to see the big picture.
Thank you so much for inspiring me to use my gifts of service to assist myself and others. And thank you for helping lift this fog of stress and confusion that I've been feeling. Your insight, warmth and compassion are very healing and such a blessing!
I wanted to thank you for my reading the other day. I appreciate your empathy, humor, patience, and encouragement while talking to you. The recording will be useful for me later on to play back if I ever feel lost. Wish there were more people like you in my life, great energy and fun!
It was a joy to speak with you this morning! talk about good energy...I was smiling while I was talking to you and even afterward! The information that you shared with me was so helpful in many ways.
My unruly brainwaves are re-orchestrating themselves into a more harmonious symphony after speaking with you. I was ... afraid of hearing something I felt ill equipped to handle ... . As it turns out, any fear was unfounded. I am feeling lighter and more positive since our conversation. Thank you again for your excellent, insightful and accurate reading. Everything--and I mean 100% of what you said--made total sense and was on the mark.
Thank you Karen! Our call this morning was super helpful. Thank you for sharing your gift with me.
I just wanted to say thank you again for all of your help. It truly takes a special person to deal with the emotional/energetic storm cloud I was in 30 minutes ago and make some sort of sense of it (especially over the phone!) I feel MUCH clearer now that you confirmed a lot of what I've been feeling but was having trouble expressing. I will definitely seek your guidance again.
I cannot thank you enough for the powerful session. Since we spoke, I feel like I reconnected with my spiritual self. I have been calm and mindful. The problems which seemed so intense for the past few months have become less significant with your insight and foresight. Thank you.
Karen, THANK YOU SOOO MUCH for the reading. You are so easy to "be with" and talk to!!! I feel like we've known each other for a long time !! Thank you for ALL of the things that you said -- each and every one makes complete sense to me ... Your gift is priceless to me -- thank you again.
Karen, I know you know how real and true your readings are. WOW ... they just keep giving! So many things you said, which I couldn't confirm because I wasn't yet aware ... and now ... WOW, going all the way back to the first one by phone. Karen, your readings are invaluable and your price is nothing compared to their worth. I hope to have another one very soon. Thank you!
Karen was great! Our session was short, but thorough-- and I appreciate her straight-forward approach. She cuts to the hearts of matters, and helps you to see how things 'might' go depending on where YOU choose to go with them. She believes in free will, and that nothing is 'set in stone'-- which I appreciate.
Karen's prices per session are reasonable, and I really felt she read for me well, and gave me some great insights. I feel better equipped to tackle some upcoming events in my life because of her perspective.
Highly recommended-- give her a call when you can! She definitely got me out of a rut in under 30 minutes :D
Over the years I have had a number of readings from a couple of different psychics. None has been as helpful, insightful and clear as the one I had with Karen. She quickly located the centers of the 2 issues I brought to her. Several months later I still find myself chewing on main elements from the reading in a very productive way. The way she began and ended the session, with prayer and reestablishing boundaries, made our time feel very safe and comfortable. Oh, yeah. She's really funny too! A joyful way to get some clarity and guidance.
I have seen a few "psychics" in the past, but no one came close to Karen. She was not only precise but provided guidance and enlightenment. She is incredible. At first, she told things that made me a bit apprehensive and worry. For example, I was desperate to buy my own house and started looking in May 2009. She told me I will get it in December. I did! She even described to me what it will look like.
There were things she told me that was not happening yet, but, as days went by, I realized "This is what exactly she was telling me after all!"Amazing!
I will keep coming back to her. There is no harm to light another candle to guide your way; and just believing to yourself (inner light) that everything will be fine no matter how dark it is from the outside.
You gave me the most accurate, in-depth, and clear information that I've heard in two and a half years of searching for the root cause of the debilitating fatigue I've been experiencing. I've been doing self healing work around the issues you pinpointed since we spoke and feel more optimistic about my health than I have in a very long time. You truly are highly gifted, and I wish you prosperous blessings and abundant love in all you do.
Just wanted to say thanks again for the reading last week. I really enjoyed it, and it all made a lot of sense. I was worried about the future, but now I have more clarity and feel better about it. I will definitely be getting another reading in the future!
�I first heard about Karen while listening to her on a radio interview. I instantly felt a connection with her and was compelled to contact her. During our first reading together, I knew she was the real deal. She knew things about me she could not have possibly known without me telling her. Her perceptive abilities were most impressive and I truly appreciated her insights. After our session, I felt a new sense of determination and inspiration. I look forward to our next session together and I highly recommend The Fog City Psychic!�
I really can't begin to express how much your readings mean. You remind me that I am supported, especially in tough times when I feel so much anxiety, your readings are like a big warm hug, they give me hope and remind me there IS a light at the end of the tunnel. I thank the universe for bringing you (and your awesome readings) into my life!
"I felt completely safe, supported and connected during my reading. I am happy to recommend you to anyone interested in experiencing a psychic reading."
"You're blowing my mind!" That's what I kept saying throughout the entire reading. I've never called a psychic before but my friend, Missie kept pushing me so I fianally caved and went through with it (expecting a hack). Wow. I was intrigued, guided, and I had fun! I'm not sure how she does it...I wonder if she'll let me attach electrodes to her head so I can figure this out ;-)
There are a lot of capable psychics out there, however Karen is particularly skilled at really reading the energy of how it is - not how you may think it is or want it to be or even how the present moment seems - but really how it is, especially so with relationships either with yourself or with others. I have benefited from and enjoyed Karen's work immensely. You will be getting your insight's worth from every minute with her.
MBA/Psychic/Clairvoyant Healer/Reiki Master
Her professionalism both business-wise and energetically were appreciated as well. I liked the way the reading did not begin until she did an opening prayer and after we ended it and I was given back all my own "energy and bits" it felt totally done and non-invasive. Nice psychic boundaries, that is. I'll be back for more...
Karen Hager is not only a delightful person, but a gifted psychic. I had a reading with her the other day, and let's just say that I got some some answers and perspectives on a situation in my life - just when I needed it! She also has an amazing radio show.
However, I thought about it and realized I had nothing to lose if I called in for a free read on her psychic radio show. I must say I was astounded by her accuracy and that encouraged me to hire Karen for a full indepth reading.
Her readings are very cheap compared to other psychics and she always ensures her client is satisfied with the read;before closing the session (that way you get your money's worth)!
Accuracy is indeed the number one thing a person looks for in a psychic and although there is no such thing as 100% accuracy, Karen comes close at hitting most of the marks. (Sorry to burst your bubbles guys/gals, but the truth is you make your reality and real authentic psychics will reassert that.)
Karen will give you lengthy details about your current situation without needing much information. She told me things about how I viewed myself, and the people around me, and to my surprise she said I was extremely intuitive. (Okay so it was not much a surprise since I already knew.) One of the most surprising thing Karen has said to me was about my room and my fear of people intruding. She spoke about it in a way where I knew nobody except close family members would know.
Okay, to wrap it up, I know many of you want the lowdown on the flaws ... which is not many. I'm thinking really hard right now and the only flaw I can think of is that she picked up on a man who would be by my side who is also in the acting world. I'm not very close to people in general so I couldn't think of a person who fit that character. Perhaps it was a prediction that has yet to come and not one that has past.
Overall, I'd highly recommend Karen to anyone.
More and more of my business associates are turning to intuitive readers to assist them in making critical personnel hires or decisions about their business that could have a huge financial impact. If you have a low tolerance threshold for the woo-woo factor and could use another stream of business advice that you won't get from an MBA-laced consultant, I strongly recommend you contact Karen Hager. Her grounded, practical focus allows you to look at a situation free from your own or anyone else's filters and is invaluable in confirming your intuition or providing the insight you need to make a decision with confidence.
I came across Karen and instantly after only speaking a few minutes with her, I felt a calmness come over me like the "Weight of the World" had been lifted. I could feel in her voice that she genuinely cared about me as a person. In other words, I didn't just seem like another client.
She intuitively picked up on what was troubling me and offered suggestions on how to move forward with the situation at hand that would benefit ME. Throughout the session she allowed me to ask questions thus taking the time to explain, in detail, what her guides were showing her, also giving me constructive feedback.
She pointed out that yes indeed I was on the right path but that this choice needed to be for ME on my TERMS. This wasn't exactly what I wanted to hear but what it taught me was to "Believe In Myself, that I am in charge of creating and manifesting my Destiny"
I have since purchased a few readings from Karen, each time she has been consistent and continues to bring peace and clarity to my heart and my mind.
Her guidance has empowered me to move forward with Strength and Confidence. She has also made me realize that yes, indeed, My Dreams can come to Fruition.
If you want someone that is truly gifted, speaks from the heart and NOT what you want to hear, I suggest you give her a call. You won't be disappointed.
Thank you for sharing this gift Karen.


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The best technology solutions for electrified vehicles are the ones that deliver ∼80% of the performance of 'ideal' systems, at ∼60% of their cost.
Newcomers to hybrid-vehicle development are bypassing the Prius-proven powersplit system for lower-cost and moderately less capable single-motor solutions.
Experts reveal efforts to find lower cost, more strategically stable solutions that can match or improve system performance.


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Mention the name "Eigen" to someone who does imaging in the medical industry and chances are they know the name. Eigen has been a pioneer in the medical imaging industry for decades. They are pushing the limits of technology yet again with their Artemis line of 4D imaging units.
Eigen came to Page Design for a brand identity but stayed for a whole revamp of their Artemis ei•4d software interface. I was fortunate enough to get the job of designing the new user interface. It was a unique challenge for me because it was the first touch screen UI that I had the pleasure of creating.
I love it when people contact me. I really do. If you have a question or comment about... well anything... feel free to ask me. You can also find me on twitter @visual28 and on my mini design blog snipppet.tumblr.com
Contact form disabled due to influx in spam. Please contact me via twitter or Behance in the meantime.


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Anonymous1: Damn. Fucking nice. Love the position. Jack and/or Miranda in the same = Heaven.
Monkeyman79: aids incoming
WhitePrideWW: Only black dick can handle that booty
Anonymous2: @WhitePrideWW: lol can't even take care of yourselfs.
PragueBob: @WhitePrideWW: fuck off
Anonymous3: LOL at the asshurt 1 inchers on this post haha


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Ikea is taking over all homewares-related news at the moment.
Affordable art and two huge collab announcements (with Byredo and Off-White) only scratch the surface when it comes to the Swedish giant's projects.
The Stunsig collection is the latest to come out of Ikea-land.
Designed to make a statement, the collection sees a collaboration between a dream team of designers and artists – including illustrator Frédérique Vernillet, visual artist Malcolm Stuart, avant-garde image creators Pinar & Viola, psychedelic pop artist Steven Harrington, Stockholm-based duo Team Hawaii and digital and photographic artist Tilde Bay.
As a result, cushions, quilt covers, boxes, porcelain and other everyday items have been covered in bold prints and colourful patterns.
You can check out every single piece here.


text: We are a water feature installation company in Michigan and we have been installing for 11 years and we are looking to network with other landscape companies to install your water features. Services we provide. Pond and water garden installation pondless water feature installation bog filtration Rain water harvesting ( Certified by Aquascape for Rainxchange) water feature expansions Indoor water features Outdoor mist cooling systems Seasonal maintenance Thank You Jeff Michaels Pondering Water, LLC Saint Clair Shores,MI Office 586-552-8822 www.ponderingwaters.com


text: Some of my works were featured on one of the latest issues of Advanced Photoshop Magazine (issue 61). This is an European Magazine and it seems this issue finally made its way to Canada. Many thanks to Adam for giving me the opportunity to showcase my work on the magazine! Thanks for stopping by!


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Linux Pandora Box Goes into Mass Production
Around $330 gets you a Linux-based Pandora handheld by shopping online, although the first buyers had to hurry.
The Pandora looks like a Nintendo DS with a built-in keypad. It is the successor to the GP2X released around three years ago. The manufacturer, OpenPandora, hopes to produce 3,000 devices during this year -- assuming enough paid orders come in. Mass production should start 2009.
Visitors started besieging the OpenPandora website soon after the announcement and within six hours 2,000 orders had come in, bringing down the site for a short while. The forum was so overloaded that a temporary one had to be put in its place. The first batch of devices was orderable until Sunday, October 5 (even if they have to raise the batch to 4,000 units), and the first Pandoras should be entering the mail by end of November if all goes according to plan. The website will be updated on Tuesday with the final sales figures and the week after the very first of the mass production PCBs should be seen. The second batch orderable after October 5 should be available next year.
The diminutive Pandora handheld comes with an ARM Cortex-A8 CPU, 128MB active and 156 flash storage, and an OpenGL 2.0 ES-compliant PowerVR SGX 3D graphics processor. The 4.3" touchscreen LCD displays 800x480 pixels in 16 million colors. Input devices include the tiny gaming controls reminiscent of Gamepads and a 43-button QWERTY keyboard. Little treats include Wifi 802.11b/g, Bluetooth, a USB 2.0 port and an S-Video connection for TV output. The batteries should provide at least 10 hours of gaming pleasure. To see the Pandora in action, see the video on OpenPandora's Developer Blog page.
While all the possible tools for gamemakers are available for free on the developer wiki, older console emulators will probably keep the game supply coming, much as they did for the GP2X predecessor.
Issue 205/2017
Buy this issue as a PDF
Linux Kernel 4.14 Released
Torvalds lashes out at a Canonical developer who introduced a regression.
Fedora 27 Is Released
Developers can now access Red Hat Enterprise Linux Developer subscriptions on Fedora 27 at no cost.
Samsung to Bring Linux to the Galaxy Phone
Samsung is testing Linux desktop for its DeX experience.
System76 Releases Pop!_OS
An Ubuntu-based operating system designed for professionals.
News and views on the GPU revolution in HPC and Big Data:
HIP: CUDA Integration with ROCm
Exploring AMD's Ambitious ROCm Initiative
Crypto-Currency Mining Drives a Surge in GPU Sales
New Platform for GPU-Enabled HPC and Ultra-Scale Computing
Radeon Instinct: Evolving, Adapting & Learning Evolving, Adapting & Learning
Linux Comes to Windows
Run multiple Linux distributions in Windows 10.
Docker Embraces Kubernetes
Docker is now offering Kubernetes as an orchestration platform.
Kubernetes 1.8 Announced
The new release comes with two new features for better security.
Final Ubuntu Desktop 17.10 Beta Arrives
Ubuntu completes the cycle of life and goes back to letter A and Gnome.
Linus Torvalds Invites Attackers to Join the Kernel Community
He wants attackers to join the community instead of attacking the code.


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Netball in St. Lucia
Bring your school team to St Lucia where the netball scene is thriving. There are many schools and clubs which promote the sport allowing for the right kind of opposition to be arranged.
When not playing matches, take your group to the Sulphur Springs Park in the Soufriere volcano, or get involved in the water sports besides the beautiful beaches.


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Classes & Workshops
Homebuyer Orientation
This free, 60-minute orientation will teach you the basic steps to becoming a successful homeowner, explain the products and services available through the Home Ownership Center and Home HeadQuarters, and give you an overview of the 8-hour Homebuyer Education Course. This is a pre-requisite to the Homebuyer Education Course.
Homebuyer Education Course
In this 8-hour course, you will learn all of the ins and outs of buying a home and becoming a successful homeowner. This is a great class for first-time buyers or anyone looking to learn more about homeownership. Cost: $49/person or $75/couple for weekday classes and $75/person and $99/couple for Saturday classes.
The Freddie Mac CreditSmart® Workshop
CreditSmart® is designed to help you build and maintain better credit, make sound financial decisions, and understand the steps to sustainable homeownership. Contact us today to learn how CreditSmart workshops can help you reach your financial and homeownership goals.
To learn more, call 315.474.1939 x 6682.
eHome America
The Homeownership Center partners with eHome America to provide an online homebuyer education course that is based on the NeighborWorks America's Realizing the American Dream curriculum and meets the National Industry Standards for homebuyer education. In order to receive a certificate of completion from the Home Ownership Center at Home HeadQuarters, you are required to attend a one-on-one counseling session after you have completed the online Homebuyer Education Course.To schedule your one-on-one session, please call (315)474-1939. Go to ehome America for more information…
If you would like to take the course in Spanish, click here.
General System Requirements
In order to navigate the eHome America online course, it is recommended that you have:
- A broadband Internet connection (dial-up users can navigate the course but will have a difficult time watching videos)
- An Internet Browser (Internet Explorer 6 or newer, Firefox, Safari; mobile browsers are OK)
- 512 MB of RAM (to ensure smooth playback of video)
- Adobe Flash Player which can be downloaded here.
- Java. Java can be downloaded here if you need it.
- Access to a printer (for printing of any page you may want to save for future reference)
Thanks to a May 2016 update, all eHome America course content is accessible on mobile devices, and all videos are in full HD that will work on both computers and phones/tablets.
Understanding & Preventing Foreclosure Workshops
This free, 2-hour workshop is the first step for homeowners who are at risk of losing their home as it provides a general overview of the foreclosure process and explains the steps you need to take to save your home. This is a pre-requisite to participating in the Foreclosure Prevention Program. Classes are offered in the following counties:
Onondaga County
Cayuga County
Cortland County
Jefferson County
Madison County
Oswego County


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iconic images
Iconic Images Recreated With Star Wars Figures
In photographer David Eger's "Cloned Photos" project, he has recreated historical photographs, movie posters, and imagery using Clone Troopers and other Star Wars figures. This project is a "spin-off" of Eger's also awesome 365 Days of Clones series. (via lostateminor.com)
Peculiar Factors That Turn Images Into Icons
Jesus Christ was originally depicted without a beard, the heart symbol didn't get its two round lobes until the 1400s, and the Coca-Cola bottle hasn't changed in almost a century. How did these and eight other iconic images become as recognizable as they are?