Volume 40, Issue 5

Self-similar solutions play an important role in the study of complex natural phenomena. In this work, self-similar regimes of the functioning of the blood coagulation system are studied. A review of the main mechanisms and theoretical models describing thrombin generation is presented. These models depend on a large number of kinetic coefficients, the estimation of which can present significant difficulties. We demonstrate that thrombin production is described by self-similar solutions that are controlled by only a small number of parameters, which can be measured experimentally. Analytical expressions for such solutions, including initial power-law regimes and blow up regime, are found using numerical methods for a reduced model describing the initial stage of thrombin generation. The self-similar regimes are also found in the analysis of experimental data.

One of the most important structural and functional elements of lymph nodes (LNs) is the fibroblasts reticular network (RN). Placed in vivo in the LN space, lymphocytes can move directionally, in fact, just along the RN, which acts as a central immune highway. However, despite the multiple experimental studies, mechanisms regulating the lymphocytes motion are not fully understood. In this paper, we propose a modelling study of the basic mechanisms of the lymphocyte migration along the reticulum linear part at the subcellular level. Model simulations were performed in order to test several possibilities of the stochastic T cells motion along the RN driven by chemotaxis. The main goal of the work is to answer the question, what mechanisms are required to provide persistent and non-detached T cells gliding along whole length of the fibronectin fiber, maintaining the T cell integrity, using free energy minimization technique – Cellular Potts Modeling. As a result, a wide range of possible hypotheses and various CPM Hamiltonians were tested. The spatial chemokine gradient is not a universal solution to the problem. The linear chemokine gradient (haptotaxis) of the concentration distributed along the fiber does not solve the problem. Additionally, the production of chemokines by FRC fibers and their diffusion from the fiber into the lymph are not sufficient for a satisfactory solution as well. According to the proposed model, biologically relevant description of immune cells gliding along the RN can be achieved via a combination of haptotaxis and a spatially distributed gradient without a component normal to the fiber. The spatially distributed chemokine gradient becomes a successful solution in combination with the active type of cell motion and fibronectin fibers defined as spatial corridors, which in fact is in line with various experimental evidence.

Mathematical modelling in personalized medicine requires the identification of model parameters characterizing the clinical picture. Simplification and acceleration of this process will make it possible to implement modelling in routine clinical practice with greater efficiency. We have conducted a study of the dependencies between identified parameter (myocardial conductivity) and the activation time of 95% of the myocardium or the width of the QRS complex within a collection of personalized models of ventricles of patients with chronic heart failure and left bundle branch block, as well as varying degrees of structural and functional damage to the myocardium. A simplified algorithm for determining individual myocardial conductivity based on clinical features of a patient’s electrocardiogram using regression models has been proposed. The results show high accuracy in predicting QRSd values using the proposed algorithm, which demonstrates the possibility to facilitate significantly the personalization of model parameters for their wide application.

This work introduces a data-driven approach for modelling the hyperelastic deformation of membranes using inflation tests. To ensure data sufficiency, we employ membranes with a non-homogeneous thickness profile, which expands significantly the experimental data range. An explicit interpolation method is used to define the data-driven constitutive relation, leveraging the Laplace stretch as a strain measure and its corresponding stress response function. The model recovers accurately inflated membrane profiles, with displacement field predictions exhibiting a relative error less than 1%. For stress fields, the error is below 5–6% across most of the membrane.

A continuously discrete stochastic model describing the proliferation process of naive T-lymphocytes during their contact with dendritic cells in a single lymph node is presented. Contact interaction is carried out between antigen-specific naive T-lymphocytes and antigen-presenting dendritic cells. The model is defined in terms of a random process whose components contain populations of different cells and families of unique cell types located in separate phases of the cell cycle. Model assumptions, recurrence relations for model variables, and a numerical simulation algorithm based on the Monte Carlo method are presented. The results of computational experiments with the model are presented illustrating the dynamics of the development of a population of cells formed from multiplying antigen-specific naive T-lymphocytes (memory and effector cells).