Presentation_1_Simulation of Multispecies Desmoplastic Cancer Growth via a Fully Adaptive Non-linear Full Multigrid Algorithm.pdf

<p>A fully adaptive non-linear full multigrid (FMG) algorithm is implemented to computationally simulate a model of multispecies desmoplastic tumor growth in three spatial dimensions. The algorithm solves a thermodynamic mixture model employing a diffuse interface approach with Cahn-Hilliard-type fourth-order equations that are coupled, non-linear, and numerically stiff. The tumor model includes extracellular matrix (ECM) as a major component with elastic energy contribution in its chemical potential term. Blood and lymphatic vasculatures are simulated via continuum representations. The model employs advection-reaction-diffusion partial differential equations (PDEs) for the cell, ECM, and vascular components, and reaction-diffusion PDEs for the elements diffusing from the vessels. This study provides the details of the numerical solution obtained by applying the fully adaptive non-linear FMG algorithm with finite difference method to solve this complex system of PDEs. The results indicate that this type of computational model can simulate the extracellular matrix-rich desmoplastic tumor microenvironment typical of fibrotic tumors, such as pancreatic adenocarcinoma.</p

Overview of program workflow.

<p>Overview of program workflow.</p

Comparison of results of the ROI analysis between the manual method and the program in terms of Ki-67 to CD31 stain ratio.

<p>Comparison of results of the ROI analysis between the manual method and the program in terms of Ki-67 to CD31 stain ratio.</p

Epithelial (Ki-67) and stromal (CD31) protein expression in ROI and whole tissue blocks.

<p>Asterisk signifies statistical significance between the two Gleason score categories.</p

Automated analysis of co-localized protein expression in histologic sections of prostate cancer - Fig 4

<p><b>Representative whole tissue block images for (A Column) low grade (Gleason score 6) and (B Column) high grade (Gleason score 9) prostate cancer.</b> Staining is shown for CD31 (vascularization), Ki-67 (cell proliferation), and H&E (cell morphology) for consecutive slides. Bar, 6 mm.</p

Ratio of epithelial (Ki-67) to stromal (CD31) protein expression in ROI and whole tissue blocks.

<p>Asterisk signifies statistical significance between the two Gleason score categories.</p

Pairwise scatterplots of PCA decomposition components.

<p>Pairwise scatterplots of PCA decomposition components.</p

Comparison of results of the ROI analysis between the manual method and the program in terms of Ki-67 stain.

<p>Comparison of results of the ROI analysis between the manual method and the program in terms of Ki-67 stain.</p

Patient demographics of the samples evaluated in this study.

<p>Patient demographics of the samples evaluated in this study.</p

Epithelial (Ki-67) and stromal (CD31) protein expression, and the ratio between these two values in TMAs.

<p>Asterisk signifies statistical significance between the two Gleason score categories. Note that the TMA samples were not used to determine the Gleason categories.</p