Volume 34, Issue 5

Hemostasis is one of the most important protective mechanisms that functions to maintain vascular integrity and prevent bleeding. In arterial and microvascular circulation, where the near-wall shear stress is relatively high, the hemostatic response begins with aggregation of platelets on the injured endothelium or collagen. Regulation of hemostasis and thrombosis is immensely complex, as it depends on the blood cell adhesion and fluid dynamics. A possible regulatory mechanism relies on the coil-stretch transitions in a plasma protein — von Willebrand factor — that serves as a ligand to platelet adhesive membrane receptors. In this work, the initial stages of thrombus growth are studied using a 3D computer model that explicitly accounts for the shear-dependent vWf conformation.

In this work we formulate a hybrid multiscale model for describing the fundamental immune processes in human immunodeficiency type 1 (HIV) infection. These include (i) the T cell migration in the lymphoid tissue, (ii) the replication cycle of HIV within an infected cell, (iii) the type I interferon (IFN) response of the target cells, and (iv) the spatiotemporal dynamics of the HIV and type I IFN fields. Computational implementation of the hybrid multiscale model is presented. It is based on the use of semi-implicit first-order symplectic Euler method for solving the equations of the second Newton’s law for cell migration and the alternating direction method for the initial-boundary value problem for reaction–diffusion equations governing the spatial evolution of the virus and IFN fields in 2D domain representing the lymph node (LN) tissue. Both, the stochastic and deterministic descriptions of the intracellular HIV infection and the IFN reaction are developed. The potential of the calibrated multiscale hybrid model is illustrated by predicting the dynamics of the local HIV infection bursts in LN tissue.

A model of lymph flow in the human lymphatic system in the quasi-one-dimensional approach has been created and investigated under different conditions. The model includes an implementation of contractions and valve influence on lymph flow. We consider contractions of lymphatic vessels and their influence on resulting flow in the whole network of lymphatic vessels and lymph nodes. We have investigated flow with zero pressure gradient and have found parameters, which influence the efficiency of contractions most significantly.

The method of constructing a stability indicatrix of a nonnegative matrix having the form of a polynomial of its coefficients is presented. The algorithm of construction and conditions of its applicability are specified. The applicability of the algorithm is illustrated on examples of constructing the stability indicatrix for a series of functions widely used in simulation of the dynamics of discrete biological communities, for solving evolutionary optimality problems arising in biological problems of evolutionary selection, for identification of the conditions of the pandemic in a distributed host population.

Aortic valve disease accounts for 45% of deaths from heart valve diseases.% \cite{Coffey2015}. An appealing approach to treat aortic valve disease is surgical replacement of the valve leaflets based on chemically treated autologous pericardium. This procedure is attractive due to its low cost and high effectiveness. We aim to develop a computational technology for patient-specific assessment of reconstructed aortic valve function that can be used by surgeons at the preoperative stage. The framework includes automatic computer tomography image segmentation, mesh generation, simulation of valve leaflet deformation. The final decision will be based on uncertainty analysis and leaflet shape optimization. This paper gives a proof of concept of our methodology: simulation methods are presented and studied numerically.

In this work, the lumped parameter model of the left heart is presented. It is based on the concept of the time-varying elastance of myocardium and includes the model of the heart valve dynamics. Comparison of the models with instant and smooth valve opening and closing is given, as well as simulations of pathologies such as mitral valve stenosis and aortic valve insufficiency are addressed.