Volume 39, Issue 5

The paper is devoted to a three-dimensional mesoscale hemodynamic model for simulations of microvascular blood flows at cellular resolution. The focus is on creating a more accurate biomechanical model of red blood cells for further use in models of hemostasis and thrombosis. The presented model effectively and accurately reproduces peculiarities of blood flow under realistic hydrodynamic conditions in arterioles, venules, and capillaries, including the Fahraeus–Lindquist effect and subsequent platelet margination. In addition, shear-dependent platelet aggregation can also be captured using the proposed approach.

In this paper, we propose a novel temporally and spatially segregated numerical scheme to discretize the coupled electromechanical model of myocardium. We perform several numerical experiments with activation of a myocardial slab with structural inhomogeneity and evaluate the dependence of numerical errors on the size of spatial and temporal discretization steps. In our study, we show that the spatial step for the mechanical equations h m ⩽2.5 mm yields reasonable results with noticeable errors only in the region of myocardial inhomogeneity. We also show that time step τ m ⩽1 ms can be used for temporal discretization of mechanical equations, and the propagation velocity of the activation and contraction fronts differs from the reference one by no more than 1.3%for such time step. Finally, we show that the increase of time discretization steps of the mechanical equations τ m and the monodomain equation τ e leads to phase errors with opposite signs, and we can compensate these errors by tuning the relationship between the time steps.

This paper presents a novel methodology utilizing physics-informed neural network (PINN) as a junction condition for a 1D network model of blood flow in total cavopulmonary connection generated by the Fontan procedure. The technique integrates a 3D mesh generation process based on the parameterization of the junction geometry, along with a sophisticated physically regularized neural network architecture. Synthetic datasets are produced using 3D steady Stokes simulations within fixed boundaries. We use a physically informed feedforward neural network that utilizes a physically regularized loss function, which incorporates the principle of mass conservation. Our PINN achieves a tolerance of 6% on the test set. We develop a 1D-PINN multiscale model based on a previously developed method for multiscale 1D–3D simulations. Comparison with 1D–3D Stokes based model and 3D Navier–Stokes based model verifies the 1D-PINN model. In the first and second comparison, the maximum deviations of the averaged pressures and flows do not exceed 1.48% and 12.26%, respectively.

We formulate a compartmental model of the murine lymphatic system with the transfer rate parameters derived from the data on the geometric characteristics of the lymphatic system (LS) graph structure and the Hagen–Poiseuille-based values of the lymph flows through the system components, i.e., vertices and edges. It is supplemented by the physics-based model of lymph node draining-related function which considers a paradigmatic view of its geometry with one- and three-afferent lymphatic vessels and one efferent vessel, and the lymph flow described by the Darcy–Starling equations. We discuss further modelling work needed to gain a predictive understanding of the LS function in response to various perturbations including infections and therapeutic treatments.

Optimal disturbances of the periodic solution of the hepatitis B dynamics model corresponding to the chronic recurrent form of the disease are found. The dependence of the optimal disturbance on the phase of periodic solution is analyzed. Four phases of the solution are considered, they correspond to clinically different periods of development of the immune response and severity of the disease, namely, activation of antiviral immune reactions, attenuation of reactions, peak and minimum viral load. The possibility of using optimal disturbances to exit the domain of attraction of the considered periodic solution using minimal impact is studied. The components of disturbances that may underlie the phenomenon of spontaneous recovery from chronic hepatitis B observed in clinical practice are identified.

The study is devoted to the hemodynamics during cerebral vascular bypass surgery for the treatment of cerebral aneurysms in two patients. The location, morphological characteristics and treatment approaches of the patients were similar, but different outcomes were observed as a result of the performed microsurgical procedures . Computational approach was used to analyze the hemodynamic differences of aneurysms, treated via extra-intra cranial (EC-IC) cerebral bypass shunt. The paper presents a new criterion based on the energy parameters of healthy compartment of cerebral circulation. The applied approach demonstrates a new effective method of preoperative risk modelling for medical decision-making.

Nowadays, low-rank approximations are a critical component of many numerical procedures. Traditionally the problem of low-rank approximation of matrices is solved in unitary invariant norms such as Frobenius or spectral norm due to the existence of efficient methods for constructing approximations. However, recent results discover the potential of low-rank approximations in the Chebyshev norm, which naturally arises in many applications. In this paper, we investigate the problem of uniform approximation of vectors, which is the main component in the low-rank approximations of matrices in the Chebyshev norm. The principal novelty of this paper is the accelerated algorithm for solving uniform approximation problems. We also analyze the iterative procedure of the proposed algorithm and demonstrate that it has a geometric convergence rate. Finally, we provide an extensive numerical evaluation, which demonstrates the effectiveness of the proposed procedures.