Hybrid models of chemotaxis with application to leukocyte migration

Bridging hemodynamics, tissue mechanics, and pathophysiology in coronary artery disease: A new agent-based model with tetrahedral mesh integration

We introduce a new multi-physics, multi-scale modeling approach to understand plaque progression during coronary artery disease. Prior works have coupled agent-based models (ABMs) with finite element analysis (FEA) or computational fluid dynamics (CFD) to study the individual contributions of tissue mechanics or hemodynamics to plaque growth. However, these approaches could not simultaneously capture the dynamic interplay between all three domains that drive plaque development. This study aims to present a novel method that merges hemodynamics via CFD, biological processes via ABM, and biomechanics via FEA into a single multi-scale, multi-physics simulation (CAFe). A description of the mechanisms and modeling approaches utilized in the CAFe model is provided, as well as preliminary exploration of the model's capabilities in idealized healthy and stenosed coronary artery models. A volumetric 3D tetrahedral mesh of the artery is shared between CFD, ABM, and FEA to simulate geometrical and biological changes with continuity and consistency. The CFD and FEA modules, implemented with FEBio, calculate the wall shear stress and structural stress and strain, respectively. These biomechanical values are passed to the ABM, implemented in MATLAB, which simulates vascular remodeling using molecular diffusion, cell migration, equations for cellular processes, and volumetric growth to update the geometry. Initial results using CAFe suggest atherosclerotic arteries seek to maintain a hemodynamic threshold through preferential growth and remodeling downstream of a stenosis. The innovative approach described herein marks a significant step forward in predictive modeling of CAD progression and paves the way for powerful coupling of the spatiotemporal-dependent remodeling paradigms exhibited by the disease.

A mathematical modeling technique to understand the role of decoy receptors in ligand-receptor interaction

The ligand-receptor interaction is fundamental to many cellular processes in eukaryotic cells such as cell migration, proliferation, adhesion, signaling and so on. Cell migration is a central process in the development of organisms. Receptor induced chemo-tactic sensitivity plays an important role in cell migration. However, recently some receptors identified as decoy receptors, obstruct some mechanisms of certain regular receptors. DcR3 is one such important decoy receptor, generally found in glioma cell, RCC cell and many various malignant cells which obstruct some mechanism including apoptosis cell-signaling, cell inflammation, cell migration. The goal of our work is to mathematically formulate ligand-receptor interaction induced cell migration in the presence of decoy receptors. We develop here a novel mathematical model, consisting of four coupled partial differential equations which predict the movement of glioma cells due to the reaction-kinetic mechanism between regular receptors CD95, its ligand CD95L and decoy receptors DcR3 as obtained in experimental results. The aim is to measure the number of cells in the chamber's filter for different concentrations of ligand in presence of decoy receptors and compute the distance travelled by the cells inside filter due to cell migration. Using experimental results, we validate our model which suggests that the concentration of ligands plays an important role in cell migration.