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

This paper deals with the mathematical modeling of atherosclerosis based on a novel hypothesis proposed by a surgeon, Prof. Dr. Axel Haverich (Circulation 135(3):205–207, 2017). Atherosclerosis is referred as the thickening of the artery walls. Currently, there are two schools of thoughts for explaining the root of such phenomenon: thickening due to substance deposition and thickening as a result of inflammatory overgrowth. The hypothesis favored here is the second paradigm stating that the atherosclerosis is nothing else than the inflammatory response of of the wall tissues as a result of disruption in wall nourishment. It is known that a network of capillaries called vasa vasorum (VV) accounts for the nourishment of the wall in addition to the natural diffusion of nutrient from the blood passing through the lumen. Disruption of nutrient flow to the wall tissues may take place due to the occlusion of vasa vasorums with viruses, bacteria and very fine dust particles such as air pollutants referred to as PM 2.5. They can enter the body through the respiratory system at the first place and then reach the circulatory system. Hence in the new hypothesis, the root of atherosclerotic vessel is perceived as the malfunction of microvessels that nourish the vessel. A large number of clinical observation support this hypothesis. Recently and highly related to this work, and after the COVID-19 pandemic, one of the most prevalent disease in the lungs are attributed to the atherosclerotic pulmonary arteries, see Boyle and Haverich (Eur J Cardio Thorac Surg 58(6):1109–1110, 2020). In this work, a general framework is developed based on a multiphysics mathematical model to capture the wall deformation, nutrient availability and the inflammatory response. For the mechanical response an anisotropic constitutive relation is invoked in order to account for the presence of collagen fibers in the artery wall. A diffusion–reaction equation governs the transport of the nutrient within the wall. The inflammation (overgrowth) is described using a phase-field type equation with a double well potential which captures a sharp interface between two regions of the tissues, namely the healthy and the overgrowing part. The kinematics of the growth is treated by classical multiplicative decomposition of the gradient deformation. The inflammation is represented by means of a phase-field variable. A novel driving mechanism for the phase field is proposed for modeling the progression of the pathology. The model is 3D and fully based on the continuum description of the problem. The numerical implementation is carried out using FEM. Predictions of the model are compared with the clinical observations. The versatility and applicability of the model and the numerical tool allow

Polymeric Scaffolds for Bioartificial Cardiovascular Prostheses

The reconstruction or replacement of diseased heart valves, the revascularisation of coronary arteries by coronary artery bypass grafting, the replacement of the central or peripheral blood vessels, and the reconstruction of the irreversibly damaged heart muscle represent the most common fields of application of cardiovascular surgery. In such cases, the diseased tissue is replaced by either a synthetic (metallic or polymeric) or a biological (xenograft, homograft, or autograft) prosthesis, or tissue engineered constructs. The aim of this book chapter is to give an overview over the most frequently used synthetic and biologic polymers as scaffold material in cardiovascular surgery

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)

Characterization of tissue engineered endothelial cell networks in composite collagen-agarose hydrogels

Scaffolds constitute an important element in vascularized tissues and are therefore investigated for providing the desired mechanical stability and enabling vasculogenesis and angiogenesis. In this study, supplementation of hydrogels containing either Matrigel™ and rat tail collagen I (Matrigel™/rCOL) or human collagen (hCOL) with SeaPlaque™ agarose were analyzed with regard to construct thickness and formation and characteristics of endothelial cell (EC) networks compared to constructs without agarose. Additionally, the effect of increased rCOL content in Matrigel™/rCOL constructs was studied. An increase of rCOL content from 1 mg/mL to 3 mg/mL resulted in an increase of construct thickness by approximately 160%. The high rCOL content, however, impaired the formation of an EC network. The supplementation of Matrigel™/rCOL with agarose increased the thickness of the hydrogel construct by approximately 100% while supporting the formation of a stable EC network. The use of hCOL/agarose composite hydrogels led to a slight increase in the thickness of the 3D hydrogel construct and supported the formation of a multi-layered EC network compared to control constructs. Our findings suggest that agarose/collagen-based composite hydrogels are promising candidates for tissue engineering of vascularized constructs as cell viability is maintained and the formation of a stable and multi-layered EC network is supported. © 2020 by the authors. Licensee MDPI, Basel, Switzerland

Cardiovascular Applications of Magnesium Alloys

Therapy in cardiovascular medicine often relies on implantation of prosthetic materials or application of stents. The diseases of many cardiovascular structures require their complete and immediate repair by utilising prosthetic materials. The ideal cardiovascular prosthesis involves good functional properties, capability of regeneration and does not activate the host\u27s immune system. Ideally, the graft can be applied for a temporary use and degrades after a predefined period according to controlled degradation kinetics. Only biological grafts would provide this spectrum of properties by today\u27s level of knowledge. However, biological prostheses exhibit some relevant drawbacks as well, such as insufficient mechanical stability or restricted availability. Implants or supporting structures of magnesium alloys would bridge this gap and would either provide a substrate for innovative and temporary grafts or would—as supporting structures—transiently add some missing properties to regenerative biological prostheses. This chapter reviews the different fields of cardiovascular therapeutic applications of magnesium alloys. The required properties of magnesium alloys and their preparation, fabrication and testing will be discussed under the specific cardiovascular perspective