Mathematical Modeling and Numerical Simulation of Atherosclerosis Based on a Novel Surgeon's View

Mechano-chemo-biological model of atherosclerosis formation based on the outside-in theory

Atherosclerosis is a disease in blood vessels that often results in plaque formation and lumen narrowing. It is an inflammatory response of the tissue caused by disruptions in the vessel wall nourishment. Blood vessels are nourished by nutrients originating from the blood of the lumen. In medium-sized and larger vessels, nutrients are additionally provided from outside through a network of capillaries called vasa vasorum. It has recently been hypothesized (Haverich in Circulation 135:205-207, 2017) that the root of atherosclerotic diseases is the malfunction of the vasa vasorum. This, so-called outside-in theory, is supported by a recently developed numerical model (Soleimani et al. in Arch Comput Methods Eng 28:4263-4282, 2021) accounting for the inflammation initiation in the adventitial layer of the blood vessel. Building on the previous findings, this work proposes an extended material model for atherosclerosis formation that is based on the outside-in theory. Beside the description of growth kinematics and nutrient diffusion, the roles of monocytes, macrophages, foam cells, smooth muscle cells and collagen are accounted for in a nonlinear continuum mechanics framework. Cells are activated due to a lack of vessel wall nourishment and proliferate, migrate, differentiate and synthesize collagen, leading to the formation of a plaque. Numerical studies show that the onset of atherosclerosis can qualitatively be reproduced and back the new theory.

Fractals in the Neurosciences: A Translational Geographical Approach

The chapter presents three new fractal indices (fractal fragmentation index, fractal tentacularity index, and fractal anisotropy index) and normalized Kolmogorov complexity with proven applicability in geographic research, developed by the authors, and the possibility of their future use in neuroscience. The research demonstrates the relevance of fractal analysis in different fields and the basic concepts and principles of fractal geometry being sufficient for the development of models relevant to the studied reality. Also, the research highlighted the need to continue interdisciplinary research based on known fractal indicators, as well as the development of new analysis methods with the translational potential between fields.

Mathematical modeling and numerical simulation of arterial dissection based on a novel surgeon's view

This paper presents a mathematical model for arterial dissection based on a novel hypothesis proposed by a surgeon, Axel Haverich, see Haverich (Circulation 135(3):205-207, 2017. https://doi.org/10.1161/circulationaha.116.025407 ). In an attempt and based on clinical observations, he explained how three different arterial diseases, namely atherosclerosis, aneurysm and dissection have the same root in malfunctioning Vasa Vasorums (VVs) which are micro capillaries responsible for artery wall nourishment. The authors already proposed a mathematical framework for the modeling of atherosclerosis which is the thickening of the artery walls due to an inflammatory response to VVs dysfunction. A multiphysics model based on a phase-field approach coupled with mechanical deformation was proposed for this purpose. The kinematics of mechanical deformation was described using finite strain theory. The entire model is three-dimensional and fully based on a macroscopic continuum description. The objective here is to extend that model by incorporating a damage mechanism in order to capture the tearing (rupture) in the artery wall as a result of micro-injuries in VV. Unlike the existing damage-based model of the dissection in the literature, here the damage is driven by the internal bleeding (hematoma) rather than purely mechanical external loading. The numerical implementation is carried out using finite element method (FEM).

A multiphysics-based artificial neural networks model for atherosclerosis

Atherosclerosis is a medical condition involving the hardening and/or thickening of arteries' walls. Mathematical multi-physics models have been developed to predict the development of atherosclerosis under different conditions. However, these models are typically computationally expensive. In this study, we used machine learning techniques, particularly artificial neural networks (ANN), to enhance the computational efficiency of these models. A database of multi-physics Finite Element Method (FEM) simulations was created and used for training and validating an ANN model. The model is capable of quick and accurate prediction of atherosclerosis development. A remarkable computational gain is obtained using the ANN model compared to the original FEM simulations.

Numerical Study on Dynamics of Blood Cell Migration and Deformation in Atherosclerotic Vessels

A phase field model is used to study the effect of atherosclerotic plaque on hemodynamics. The migration of cells in blood flows is described by a set of multiple phase field equations, which incorporate elastic energies and the interacting effects of cells. Several simulations are carried out to reveal the influences of initial velocities of blood cells, cellular elasticity and block rates of hemodynamic vessels. The results show that the cell deformation increases with the growth of the initial active velocity and block rate but with the decrease of the cellular elasticity. The atherosclerotic plaque not only affects the deformation and migration of cells but also can promote the variation in hemodynamic properties. The atherosclerotic plaque causes a burst in cell velocity, and the greater the block rate and cellular elasticity, the more dramatic the variation of instantaneous velocity. The present work demonstrates that the phase field method could be extended to reveal formation atherosclerosis at the microscopic level from the perspective of hemodynamics.