Abstract 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.

Abstract 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.

Abstract 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.

Abstract 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).

Abstract 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.

Abstract The paper describes the numerical methods and the associated parallel computing code ‘Gerbera’ designed to analyse the aerodynamics and tonal noise of arbitrary aircraft propeller systems. The capabilities, robustness and accuracy of ‘Gerbera’ are demonstrated on a series of validation and verification studies, including single propellers, distributed propellers, and contra-rotating open rotor. The correct calculation of the propeller thrust characteristics and the main noise harmonics, including quite ‘subtle’ interaction effects, is shown. The presented scalability tests confirm good speed-up up to thousands of CPU cores.

Abstract In this work we propose an extension of the low-rank Monte Carlo algorithm for modelling aggregation process with multiple sources of particles. This implementation utilizes the low-rank structure of the coagulation kernel and reduces the number of operations for selection of pairs of coagulating particles. This approach does not require the kernel itself to be low-rank or to have such an approximation. Instead, it is sufficient to use an auxiliary low-rank kernel as a majorant function. We demonstrate the convergence of our method using the known theoretical solutions and show an agreement of the numerical particle size distributions with the results obtained by the deterministic numerical method. In addition, we analyze the performance of the Monte Carlo method for a simplified system with active monomers and collisional shattering events. We remind that numerical modelling based on relatively small number of finite samples can deviate from analytical solution of the kinetic equations.

Abstract The aim of this work is the substantiation of the applicability of the splitting scheme to the solution of reactive transport in porous media problems involving precipitation–dissolution reactions and variable media porosity. The reasons why this scheme was abandoned for modelling this type of problems in the previous works are analyzed. We consider a corrected scheme featuring mass conservation and convergence. It is tested on problems with analytical solutions and its performance is shown on a benchmark of the dissolution of concrete minerals.

Abstract The problems of numerical modelling of viscous incompressible fluid flows are widely considered in computational fluid dynamics. Stationary solutions of boundary value problems for the Navier–Stokes equations exist at large Reynolds numbers, but they are unstable and lead to transient or turbulent unsteady regimes. In addition, the solution of the boundary value problem at large values of Reynolds number may be non-unique. In this paper, we consider numerical algorithms for finding such stationary solutions. We use natural pressure-velocity variables under standard finite element approximation on triangular grids. Iterative methods with different linearizations of convective transport are used to test a two-dimensional problem of incompressible fluid flow in a square-section cavity with a movable top lid. The developed computational algorithm allowed us to obtain two solutions when the Reynolds number exceeds a critical value for flows in a cavity of semi-elliptical cross-section.