Biased three-dimensional cell migration and collagen matrix modification

Spatial scaling in multiscale models: methods for coupling agent-based and finite-element models of wound healing

Multiscale models that couple agent-based modeling (ABM) and finite-element modeling (FEM) allow the dynamic simulation of tissue remodeling and wound healing, with mechanical environment influencing cellular behaviors even as tissue remodeling modifies mechanics. One of the challenges in coupling ABM to FEM is that these two domains typically employ grid or element sizes that differ by several orders of magnitude. Here, we develop and demonstrate an interpolation-based method for mapping between ABM and FEM domains of different resolutions that is suitable for linear and nonlinear FEM meshes and balances accuracy with computational demands. We then explore the effects of refining the FEM mesh and the ABM grid in the setting of a fully coupled model. ABM grid refinement studies showed unexpected effects of grid size whenever cells were present at a high enough density for crowding to affect proliferation and migration. In contrast to an FE-only model, refining the FE mesh in the coupled model increased strain differences between adjacent finite elements. Allowing strain-dependent feedback on collagen turnover magnified the effects of regional heterogeneity, producing highly nonlinear spatial and temporal responses. Our results suggest that the choice of both ABM grid and FEM mesh density in coupled models must be guided by experimental data and accompanied by careful grid and mesh refinement studies in the individual domains as well as the fully coupled model.

A novel computational remodelling algorithm for the probabilistic evolution of collagen fibre dispersion in biaxially strained vascular tissue

In this work, we constructed a novel collagen fibre remodelling algorithm that incorporates the complex nature of random evolution acting on single fibres causing macroscopic fibre dispersion. The proposed framework is different from the existing remodelling algorithms, in that the microscopic random force on cellular scales causing a rotational-type Brownian motion alone is considered as an aspect of vascular tissue remodelling. A continuum mechanical framework for the evolution of local dispersion and how it could be used for modeling the evolution of internal radius of biaxially strained artery structures under constant internal blood pressure are presented. A linear evolution form for the statistical fibre dispersion is employed in the model. The random force component of the evolution, which depends on the mechanical stress stimuli, is described by a single parameter. Although the mathematical form of the proposed model is simple, there is a strong link between the microscopic evolution of collagen dispersion on the cellular level and its effects on the macroscopic visible world through mechanical variables. We believe that the proposed algorithm utilizes a better understanding of the relationship between the evolution rates of mean fibre direction and fibre dispersion. The predictive capability of the algorithm is presented using experimental data. The model has been simulated by solving a single-layered axisymmetric artery (adventitia) deformation problem. The algorithm performed well for estimating the quantitative features of experimental anisotropy, the mean fibre direction vector and the dispersion (κ) measurements under strain-dependent evolution assumptions.

Mechanical regulation of fibroblast migration and collagen remodelling in healing myocardial infarcts

Effective management of healing and remodelling after myocardial infarction is an important problem in modern cardiology practice. We have recently shown that the level of infarct anisotropy is a critical determinant of heart function following a large anterior infarction, which suggests that therapeutic gains may be realized by controlling infarct anisotropy. However, factors regulating infarct anisotropy are not well understood. Mechanical, structural and chemical guidance cues have all been shown to regulate alignment of fibroblasts and collagen in vitro, and prior studies have proposed that each of these cues could regulate anisotropy of infarct scar tissue, but understanding of fibroblast behaviour in the complex environment of a healing infarct is lacking. We developed an agent-based model of infarct healing that accounted for the combined influence of these cues on fibroblast alignment, collagen deposition and collagen remodelling. We pooled published experimental data from several sources in order to determine parameter values, then used the model to test the importance of each cue for predicting collagen alignment measurements from a set of recent cryoinfarction experiments. We found that although chemokine gradients and pre-existing matrix structures had important effects on collagen organization, a response of fibroblasts to mechanical cues was critical for correctly predicting collagen alignment in infarct scar. Many proposed therapies for myocardial infarction, such as injection of cells or polymers, alter the mechanics of the infarct region. Our modelling results suggest that such therapies could change the anisotropy of the healing infarct, which could have important functional consequences. This model is therefore a potentially important tool for predicting how such interventions change healing outcomes.