Volume 36, Issue 5

Pathophysiology of ischemic heart disease is a complex phenomenon determined by the interaction of multiple processes including the inflammatory, immunological, infectious, mechanical, biochemical and epigenetic ones. A predictive clinically relevant modelling of the entire trajectory of the human organism, from the initial alterations in lipid metabolism through to atherosclerotic plaque formation and finally to the pathologic state of the ischemic heart disease, is an open insufficiently explored problem. In the present review, we consider the existing mathematical frameworks which are used to describe, analyze and predict the dynamics of various processes related to cardiovascular diseases at the molecular, cellular, tissue, and holistic human organism level. The mechanistic, statistical and machine learning models are discussed in detail with special focus on the underlying assumptions and their clinical relevance. All together, they provide a solid computational platform for further expansion and tailoring for practical applications.

Palliation of congenital single ventricle heart defects suggests multi-stage surgical interventions that divert blood flow from the inferior and superior vena cava directly to the right and left pulmonary arteries, skipping the right ventricle. Such system with cavopulmonary anastomoses and single left ventricle is called Fontan circulation, and the region of reconnection is called the total cavopulmonary connection (TCPC). Computational blood flow models allow clinicians to predict the results of the Fontan operation, to choose an optimal configuration of TCPC and thus to reduce negative postoperative consequences. We propose a two-scale (1D3D) haemodynamic model of systemic circulation for a patient who has underwent Fontan surgical operation. We use CT and 4D flow MRI data to personalize the model. The model is tuned to patient’s data and is able to represent measured time-averaged flow rates at the inlets and outlets of TCPC, as well as pressure in TCPC for the patient in horizontal position.We demonstrate that changing to quiescent standing position leads to other patterns of blood flow in regional (TCPC) and global haemodynamics. This confirms clinical data on exercise intolerance of Fontan patients.

In the present paper, we consider a compartmental epidemic model which simulates the co-circulation of three influenza strains, A(H1N1)pdm09, A(H3N2), and B, in a population with the history of exposure to these virus strains. A strain-specific incidence data for the model input was generated using long-term weekly ARI incidence and virologic testing data. The algorithm for model calibration was developed as a combination of simulated annealing and BFGS optimization methods. Two simulations were carried out, assuming the absence and the presence of protected individuals in the population, with 2017– 2018 and 2018–2019 epidemic seasons in Moscow as a case study. It was shown that strain-specific immune levels defined by virologic studies might be used in the model to obtain plausible incidence curves. However, different output parameter values, such as fractions of individuals exposed to particular virus strain in the previous epidemic season, can correspond to similar incidence trajectories, which complicates the assessment of herd immunity levels based on the model calibration. The results of the study will be used in the research of the interplay between the immunity formation dynamics and the circulation of influenza strains in Russian cities.

The paper is focused on stochastic modelling of the process of transition of infected cells and virions of HIV-1 infection between two lymph nodes. The model is based on the following assumptions: (1) the duration of transition of infected cells and virions between two lymph nodes is set using a time-dependent function, (2) infected cells produce virions in the process of transition between two lymph nodes, (3) infected cells and virions may die when moving between two lymph nodes. The methods of the theory of branching random processes are used to study analytically the model variables. An algorithm for statistical modelling of the number of infected cells and virions in the second lymph node is presented. The results of computational experiments studying the distribution law of the number of virions produced by one infected cell depending on the duration of movement between two lymph nodes are presented.

In the present paper we construct the model of coronary flow which utilizes the patient’s CT data on both large CA and perfusion. We reconstruct large coronary vessels based on the CT data and extrude possibly invisible vessels from the branches of the left coronary artery so that every terminal point supply every of standardized zone of myocardium. We apply a previously developed and validated 1D model of haemodynamics. Utilizing the patient-specific CTP data for modifying outflow terminal resistance at rest and under stress conditions is the major novelty of the present work. From our results it follows that acceptable values of fractional flow reserve (FFR) after the stenotic treatment may produce false negative output. Therefore healthy FFR values may be observed after ineffective revascularization. We also conclude that microvascular perfusion impairment plays significant role in correct computational estimation of haemodynamic indices before stenotic treatment. The advantage of the presented approach is the availability of transmural perfusion ratio assessment in everyday practice.