cell line and tissue based in - vitro cell culture systems are tools to emulate in - vivo cell behavior and cellular interactions . with 3d cell culture assays , the physiological relevance of in - vivo cell proliferation can be mimicked while preserving cell viability and pathway activity . cell viability , proliferation and morphology in 3d microenvironment depend on administered drug in addition to the cell line , matrix used to coat chamber slides and the structure of assay . viability of incubated cells under the impact of anti - cancer drugs and their morphology changes can be observed via digitized microscopic images from cell cultures captured during in - vitro experiments . poisson point process , a statistical tool for spatial analysis , can be applied to captured images to characterize the patterns . with distance - based techniques relying on the spacing of the points and area - based methods evaluating the intensity of observed numbers of points in predetermined subregions ( e.g. , quadrats ) , the variability in the point locations can be analyzed to decide whether a complete spatial randomness , a clustering or a regularity exists . a homogenous process is observed in the case of a complete spatial randomness , whereas the distribution characteristic of points deviating from a homogenous pattern is formed when an attraction or an inhibition is present among points . ripley s k - function and its derived versions can be used to test the consistency of observed patterns with a homogeneous poisson process . voronoi tessellation is another spatial analysis tool for partitioning an euclidian space into subregions based on node locations , where an association of subregions of a given plane to the closest nodes results in a tessellation diagram containing information specific to a specific plane . as part of our continuing research , we study growth and shrinkage behavior of tumor mass in human body and in xenograft models based on patient specific information such as gene expressions and morphological features of tumor tissue . we compute tumor growth and shrinkage for breast cancer patients using their mri images of tumor tissue and gene expression data . to extract morphological features using spatial pattern analysis , we analyze the digitized images of hematoxylin & eosin ( h&e ) slide samples taken from mice models implanted with tumor specimen of kidney cancer patients . in this paper , we examine the relationship between cell viability and morphological features of 3d microenvironment using spatial analysis methods , namely poisson point process and voronoi tessellations . as case studies , we set up in - vitro experiments using human colon carcinoma cell lines of hct-116 , sw-480 and sw-640 . the cells cultured in in - vitro microenvironment were divided into control and folfox - administered groups for each experiment . with our artificial intelligence based cell tracking and data acquisition system , the bright field and fluorescent images of predetermined locations of regions of interest ( roi ) are captured at certain time points to identify cell positions in microenvironment and to evaluate viability . the morphological features are extracted for live and dead cell positions separately to evaluate the heterogeneity of cell viability and apoptosis , respectively . using spatial point process and voronoi tessellations , we compute heterogeneity of the locations of cells administered with anti - cancer drugs . we observe in all case studies that , due to the impact of folfox solution , while cell viability decreases in time , the heterogeneity of live cell positions increases , whereas a decrease is noted for the dead cell positions . the relationship between cell viability and spatial heterogeneity among cell positions suggest that they can be used for drug efficacy measurements and utilized as a biomarker for 3d in - vitro microenvironment assays . preliminary versions of this work have been reported in   and , where the morphological features of live and dead cell positions were examined to evaluate the heterogeneity of cell viability and apoptosis . iii . spatial analysis tools to compute morphological features of colorectal cells are formulated in sec . the results for cell lines hct-116 , sw-480 and sw-620 are presented with three case studies in sec . v. concluding remarks are in sec . in our in - vitro experiments , human colorectal cancer cell lines of hct-116 , sw-620 and sw-480 were incubated on \documentclass[12pt]{minimal } 
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 } { } $ 75~cm^{2}$ 
 \end{document } cell culture flask using the process described in . a matrigel matrix were used to incubate colorectal cells since various signaling pathways controling cell motility and drug sensitivity in cancer cells are activated by the components of matrigel . in this process , a matrigel basement membrane matrix with a density of \documentclass[12pt]{minimal } 
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 } { } $ 2~mg / ml$ 
 \end{document } were used to coat chamber slides . to provide the environment for matrigel polymerization the cells were collected with trypsin and counted by hemacytometer to add into chamber slides at a density of \documentclass[12pt]{minimal } 
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 } { } $ 500,000~cell / ml$ 
 \end{document } for the in - vitro experiments . the cell suspension was combined with a media of fluorobrite dmem to incubate with 10% of fetal bovine serum , 5% of penicillin and 5% co2 at 37c for one day period to allow their recovery from stress . for prolonged cultured assays , cell viability reduces in time due to the lack of oxygen and nutrients , and the accumulation of waste . in evaluation of the drug impact on cell viability , for the cancer cells which are under treatment , a folfox solution was prepared as a mixture of a concentration of \documentclass[12pt]{minimal } 
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 } { } $ 500~\mu m~5 $ 
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 } { } $ 100~\mu m$ 
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 } { } $ 20~\mu m$ 
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 } { } $ 535/617~nm$ 
 \end{document } excitation level to detect cell apoptosis with its location . the experimental set up was put into special portable incubator to keep the cells under required conditions of 5% of co2 and 37c . in our study , using our 3d cell tracking and data acquisition system , which is built based on bio - inspired computation methods from our previous research , , we observe the morphological changes in interest regions with colorectal cancer cells and anti - cancer drugs . our data acquisition tool guides an imaging system of an inverted microscope and a digital camera to record the bright field and fluorescent images of the regions of interest at the desired level of magnification during multi - day long experiments in 3d microenvironment . to quantify the dependency between cell locations and viability , we present three case studies , each set up as a 48-hour experiment , where the images of colorectal cancer cell lines hct-116 , sw-620 and sw-480 were captured at every three hours . in fig . 1 , sample bright field and gray - scaled fluorescent images which are captured for colorectal cell line of hct-116 at hours 0 , 24 and 48 are shown . in fig . 1a , bright field images of control and treatment groups are presented , where the morphological changes can be observed as time progresses . 1b illustrate the locations of dead cells , which are marked with fluorescent dyes . for each case study , time course of cell viability are determined by calculating the number of incubated cells from fig . figure 1.bright field and gray - scaled fluorescent images of colorectal cell line hct-116 from sample rois of control and folfox treated groups captured by an inverted microscope with 20x magnification at hour-0 , hour-24 , and hour-48 ( case study-1 ) . . bright field and gray - scaled fluorescent images of colorectal cell line hct-116 from sample rois of control and folfox treated groups captured by an inverted microscope with 20x magnification at hour-0 , hour-24 , and hour-48 ( case study-1 ) . administering feature extraction methods on biological images and their transforms , spatial properties of underlying biological processes can be identified . as part of our ongoing research , we apply voronoi tessellations to pathology slide samples from kidney cancer xenograft mice models to determine the features based on the nuclei locations on slides . in another study , we have extracted spatial randomness features from h&e slides to plug into our personalized relevance parameterization method to compute tumor growth parameters . in this paper , we analyze the changes of the morphological features in in - vitro 3d microenvironment using the images captured by our data acquisition system at certain time intervals . the relationship among the locations of incubated cells administered with folfox treatment is evaluated with spatial analysis tools of poisson point process and voronoi tessellations . in addition to heterogeneity analysis , these images are also evaluated to calculate cell viability based on the ratio of the number of live cells to the number of all incubated cells . spatial poisson process describes the randomness and heterogeneity of points ( i.e. , events ) statistically based on distances as a similarity measurement among point locations . spatial randomness in point patterns can be interpreted with the first and second order properties of poisson point process , where the former is calculated to evaluate the variation among point locations in large scale and the latter is to identify the deviation tendency from a complete randomness of neighboring points in a local scale . quadrat count and kernel estimation can be categorized as the first order properties , while nearest neighbor functions can be defined as second order properties . the randomness in the distribution of biological cells can be examined in terms of underlying poisson process based on their locations . in this study , to evaluate the heterogeneity among neighboring cell positions , we compute the functions of the second order properties using their spatial proximity . the distance between a cell pair of \documentclass[12pt]{minimal } 
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 } { } $ \rho _ { i}$ 
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 } { } $ \delta _ { k}(\rho _ { i } , \rho _ { j})$ 
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 } { } \begin{equation * } \delta _ { k}(\rho _ { i } , \rho _ { j } ) = \left [ { \sum _ { d=1}^{d } | \rho _ { i , d } - \rho _ { j , d } |^{k } } \right ] ^{1/k } \end{equation*}\end{document } where \documentclass[12pt]{minimal } 
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 } { } $ k = 2 $ 
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 } { } $ \upsilon $ 
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 } { } \begin{equation * } k(\upsilon ) = \frac { a}{n^{2 } } \cdot \sum _ { i = 1}^{n } \sum _ { \substack { j = 1\\ { j \neq i}}}^{n } { w(\rho _ { i } , \rho _ { j})}^{-1 } \cdot 1_{\left [ { \delta _ { k}(\rho _ { i } , \rho _ { j } ) \le \upsilon } \right ] } \end{equation*}\end{document } where \documentclass[12pt]{minimal } 
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 . since the images captured from in - vitro microenvironment have straight boundaries , k - function is calculated with the assumption of \documentclass[12pt]{minimal } 
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 } { } $ { \left [ { \delta _ { k}(\rho _ { i } , \rho _ { j } ) \le \upsilon } \right ] } $ 
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 . to determine how clustered or regular the point pattern is , the standardized version of \documentclass[12pt]{minimal } 
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 } { } $ l(\upsilon ) $ 
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 } { } $ d_{l}(r)$ 
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 \end{document } pixels . using the results from both spatial analysis methods , we quantify the relationship between cell viability and spatial heterogeneity for the cell lines hct-116 , sw-620 and sw-480 , as presented in sec . v. to study the relationship between cell viability and spatial heterogeneity in the positions of cancer cells , we present three case studies using colorectal cancer cell lines of hct-116 , sw-620 and sw480 . for each case study , the cells are divided into drug - free control and anti - cancer treatment groups . control group of colorectal cancer cells are cultured in metragel , whereas the cells of the treatment group are in folfox solution , and both are provided with nutrition and gas supplies at an ideal temperature of 37c for 48 hours . for cell viability evaluation in our 48 hour long experiments , eight regions of interest rois are randomly selected for each group . our data acquisition system tracks the positions of these selected rois to capture their bright field and fluorescence dyed images at predetermined intervals ( every three hours for this study ) . our system is capable of automatically identifying the rois at each time point and placing the microscope lens at their central positions , and therefore , maintaining visual focus and tracking the cell clusters in 3d microenvironment throughout the experiments . the roi size is determined based on the number of cells located in a selected region . in our experiments , we obtain statistically meaningful results when the images are captured with 20x magnification . for example , with a higher level of magnification ( e.g. , 40x ) , the average number of cells observed in selected rois was less than 10 . the cells within the selected roi can be seen in the bright field images of figs . 1 and 2 . at each time point , the number of cells are calculated using the images captured from control and folfox - treated groups . the spatial heterogeneity is computed based on the locations of live and dead cells , which are identified from the bright field and fluorescent images , respectively . in fig . 5 , cell viability is presented for the colorectal cancer cell lines of hct-116 , sw-620 and sw480 . for each case study , left vertical axis is scaled to present the total number of live and dead cells for the folfox - treated groups with green and pink bars , respectively . the normalized values of cell viability for the control groups are given with gray - colored bars , which are scaled with respect to the right vertical axis of fig . 5 . for all experiments , since the rois were randomly identified at the beginning of each experiment , a high value of standard deviation in the number of live cells is observed in fig . 5 , implying that the number of cells in the selected regions vary significantly with respect to each other . figure 5.number of cells and normalized cell viability from experimental measurements for colorectal cell lines hct-116 in ( a ) , sw-620 in ( b ) and sw-480 in ( c ) . number of cells and normalized cell viability from experimental measurements for colorectal cell lines hct-116 in ( a ) , sw-620 in ( b ) and sw-480 in ( c ) . in our case studies , we have examined spatial heterogeneity for the locations of live and dead cells from the drug administered groups . for live cell positions , heterogeneity is evaluated for the normalized viability levels of \documentclass[12pt]{minimal } 
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 } { } $ \nu = 0.9 $ 
 \end{document } , 0.8 and 0.7 , corresponding to the time points at which 90% , 80% and 70% of the cells are alive , respectively , as the impact of folfox solution increases . in fig . 6 , the results of spatial point process and voronoi tessellations are given for the live cell positions . for the morphology analysis of in - vitro cell - based assays with respect to the dead cell locations , the viability levels are selected as \documentclass[12pt]{minimal } 
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 figure 6.normalized heterogeneity results among live cell positions : ( a ) , ( b ) and ( c ) are from spatial point process , for colorectal cell lines hct-116 , sw-620 and sw-480 , respectively , all are under folfox treatment ; ( d ) , ( e ) and ( f ) are from deviation results among voronoi polygon areas for colorectal cell lines hct-116 , sw-620 and sw-480 , respectively ; all are under folfox treatment . 
 figure 7.normalized heterogeneity results among dead cell positions : ( a ) , ( b ) and ( c ) are from spatial point process , for colorectal cell lines hct-116 , sw-620 and sw-480 , respectively , all are under folfox treatment ; ( d ) , ( e ) and ( f ) are from deviation results among voronoi polygon areas for colorectal cell lines hct-116 , sw-620 and sw-480 , respectively , all are under folfox treatment . normalized heterogeneity results among live cell positions : ( a ) , ( b ) and ( c ) are from spatial point process , for colorectal cell lines hct-116 , sw-620 and sw-480 , respectively , all are under folfox treatment ; ( d ) , ( e ) and ( f ) are from deviation results among voronoi polygon areas for colorectal cell lines hct-116 , sw-620 and sw-480 , respectively ; all are under folfox treatment . normalized heterogeneity results among dead cell positions : ( a ) , ( b ) and ( c ) are from spatial point process , for colorectal cell lines hct-116 , sw-620 and sw-480 , respectively , all are under folfox treatment ; ( d ) , ( e ) and ( f ) are from deviation results among voronoi polygon areas for colorectal cell lines hct-116 , sw-620 and sw-480 , respectively , all are under folfox treatment . in this case study , cancer cells from colorectal cell line of hct-116 were cultured in in - vitro microenvironment . cell viability and the number of cells were evaluated at every three hours during the 48-hour long experiment . as can be seen in fig . 5a , the number of live cells start decreasing at hour 15 with the impact of the anti - cancer drug . at hour 48 , we have measured that the number of dead and live cells are almost equal to each other , implying that approximately 50% of cells were dead at the end of the experiment . for colorectal cell line of hct-116 , we compute spatial heterogeneity among live cell positions at hours 18 , 24 and 30 , corresponding to the viability of 0.9 , 0.8 and 0.7 , respectively . for the same selected rois , the deviation among the voronoi polygon areas is presented in fig . an increasing trend is observed for the heterogeneity among live cell positions in eight rois . using spatial point process and voronoi tessellations , the heterogeneity among dead cell locations is evaluated as shown in figs . , we have analyze the results for the images captured at hours 24 ( \documentclass[12pt]{minimal } 
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 } { } $ \nu = 0.6 $ 
 \end{document } ) . similar to the results obtained for live cells , a relationship between the morphological features of dead cells and cell viability is observed such that heterogeneity of the dead cell positions has a decreasing behaviour with the decrease in viability . the characteristic of cell line sw-620 obtained from human colon lymph node tissue were evaluated in a 48-hour experiment . in fig . 5b , we observe that the cells are more resistant to anti - cancer agents as a high value of viability remains until hour 24 , after which point the viability starts decreasing gradually . at the end of the 48 hour long experiment , the heterogeneity of the cell positions is computed for hours 27 , 36 , 42 and 48 corresponding to the viability levels of \documentclass[12pt]{minimal } 
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 \end{document } , 0.8 , 0.7 and 0.6 , respectively . for the live cells of the folfox treated group , non - randomness values similar to the case of cell line hct-116 , we observe an increase in the heterogeneity of live cells as the viability decreases . 7b and 7e show the results of spatial analysis methods for the dead cell locations . even though the impact of anti - cancer drug for cell line sw-620 is not as strong as it is for the cell line hct-116 , a similar relationship as in case study i is observed between spatial heterogeneity of dead cells and cell viability . the colorectal cell line sw-480 of adenocarcinoma cells are incubated in 3d microenvironment for this case study . the number of live and dead cells from the treatment group and the viability measured for the control group are illustrated in fig . different than the observations for the cell lines hct-116 and sw-620 , the anti - cancer solution has a quick impact on the viability for cell line sw-480 . however , drug impact on live cells saturates at a certain time point when the viability was measured as \documentclass[12pt]{minimal } 
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 } { } $ \nu = 0.6 $ 
 \end{document } ) . an increasing trend is observed for the heterogeneity of the live cell positions with a decrease in cell viability , whereas both spatial point process and voronoi tessellations generate heterogeneity results decreasing with smaller cell viability values for dead cells . in this paper , we examine a relationship between cell viability and the spatial heterogeneity of the locations of live and dead cells incubated in 3d in - vitro cell - based assays under the impact of anti - cancer agents we set up three 48-hour long experiments using human colorectal cancer cell lines of hct-116 , sw-620 and sw-480 . with our 3d cell tracking and data acquisition system guiding an inverted microscope with a digital camera , were able to capture bright field and fluorescent images of colorectal cancer cells at pre - determined intervals during the experiments . after the locations of live and dead cells in captured images are identified , poisson point process and voronoi tessellation methods are applied to extract their morphological features . the spatial analysis results obtained in all case studies for both live and dead cells points out that there is a relationship between cell viability and heterogeneity among cell positions . we observe that heterogeneity of live cell locations increases as the number of live cells in microenvironment decreases under the impact of anti - cancer drugs . for cell apoptosis , our analysis indicate that the randomness in dead cell locations increases as the cell viability in in - vitro cell cultures decreases . similarly , a decrease in deviation of voronoi polygon areas for the dead cells is observed as the experiments progress under the impact of anti - cancer drugs . this relationship between morphological features of in - vitro cell based assays and cell viability can be used for drug efficacy measurements and utilized as a biomarker for 3d in - vitro microenvironment assays . as future direction , we plan to extend this study to include different human carcinoma including breast and kidney cancers with additional clinical measurements such as blood serum samples and genetic information .
in evaluation of cell viability and apoptosis , spatial heterogeneity is quantified for cancerous cells cultured in 3-d in vitro cell - based assays under the impact of anti - cancer agents . in 48-h experiments using human colorectal cancer cell lines of hct-116 , sw-620 , and sw-480 , 
 incubated cells are divided into control and drug administered groups , to be grown in matrigel and folfox solution , respectively . 
 our 3-d cell tracking and data acquisition system guiding an inverted microscope with a digital camera is utilized to capture bright field and fluorescent images of colorectal cancer cells at multiple time points . identifying the locations of live and dead cells in captured images , 
 spatial point process and voronoi tessellation methods are applied to extract morphological features of in vitro cell - based assays . for the former method , spatial heterogeneity 
 is quantified with the second - order functions of poisson point process , whereas the deviation in the area of voronoi polygons is computed for the latter . with both techniques , 
 the results indicate that the spatial heterogeneity of live cell locations increases as the viability of in in vitro cell cultures decreases . on the other hand , 
 a decrease is observed for the heterogeneity of dead cell locations with the decrease in cell viability . 
 this relationship between morphological features of in vitro cell - based assays and cell viability can be used for drug efficacy measurements and utilized as a biomarker for 3-d in vitro microenvironment assays .