Computer simulation of three-dimensional plaque formation and progression in the carotid artery

Abstract

Atherosclerosis is becoming the number one cause of death worldwide. In this study, three-dimensional computer model of plaque formation and development for human carotid artery is developed. The three-dimensional blood flow is described by the Navier-Stokes equation, together with the continuity equation. Mass transfer within the blood lumen and through the arterial wall is coupled with the blood flow and is modeled by a convection-diffusion equation. The low-density lipoproteins transports in lumen of the vessel and through the vessel tissue are coupled by Kedem-Katchalsky equations. The inflammatory process is modeled using three additional reaction-diffusion partial differential equations. Fluid-structure interaction is used to estimate effective wall stress analysis. Plaque growth functions for volume progression are correlated with shear stress and effective wall stress distribution. We choose two specific patients from MRI study with significant plaque progression. Plaque volume progression using three time points for baseline, 3- and 12-month follow up is fitted. Our results for plaque localization correspond to low shear stress zone and we fitted parameters from our model using nonlinear least-square method. Determination of plaque location and composition, and computer simulation of progression in time for a specific patient shows a potential benefit for the prediction of disease progression. The proof of validity of three-dimensional computer modeling in the evaluation of atherosclerotic plaque burden may shift the clinical information of MRI from morphological assessment toward a functional tool. Understanding and prediction of the evolution of atherosclerotic plaques either into vulnerable or stable plaques are major tasks for the medical community.

A summary of results in modeling plaque formation and development, cochlea mechanics and vestibular disorders

“…The inflammatory process was solved using three additional reaction-diffusion partial differential equations Filipovic et al 2013):…”

“…(4); M and S are concentrations in the intima of macrophages and cytokines, respectively; d1, d2, d3 are the corresponding diffusion coefficients; λ and γ are degradation and LDL oxidized detection coefficients; and vw is the inflammatory velocity of plaque growth, which satisfies Darcy's law and continuity equation Filipovic et al 2013):…”

“…This model relies on a matter incompressibility assumption. Some examples of our simulation for plaque formation and progression are given in the results section Filipovic et al 2013). …”

Computational modeling of plaque development in the coronary arteries

“…We are using the incremental-iterative procedure to treat the convective diffusion terms for LDL transport. The inflammatory process was solved using three additional reaction-diffusion partial differential equations (Filipovic et al 2013): …”

Structural biology response of a collagen hydrogel synthetic extracellular matrix with embedded human fibroblast: computational and experimental analysis

“…Despite the existence of previous computational models aiming to simulate the cell-induced ECM contraction process [8,11,24,25,29], to date, no reports exist that combine the effect of the three above-mentioned parameters (proliferation, migration and cytoskeleton exerted forces) and its cross-linking in a 3D model. Moreover, many questions regarding this contraction process remain unsolved.…”