COMPUTER MODELLING OF THE CARDIAC TISSUE LAYER FORMATION
N. N. Kudryashova1,2, V.A. Tsvelaya1, A.V. Panfilov2, and K.I. Agladze1
1Moscow Institute of Physics and Technology, 141701, Institustskiy per. 9, Dolgoprudny, Russia
2Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, Gent 9000, Belgium
Cardiac arrhythmias, or even sudden cardiac death, may occur at any age, but the risks are increasing among older generation. It is known, that heart loses some of the active cells, which are replaced with the passive fibroblasts, the size of the heart slightly increases, the collagen is deposited between the bundles of cardiac myocytes, and, finally, the cardiomyocytes themselves change, as far as the expression of the ionic channels differs. However, it is poorly understood, which of these factors results in an elevated risk of arrhythmia. In fact, all of the studies of the ageing or diseased human heart are limited to the observation of the final histological pattern, whereas the dynamics of the preceding structural changes stay hidden from the clinical researchers. This white space may be filled with aid of computer modelling.
Figure 1. Cell spreading on an isotropic substrate. Single big cell shows an experimentally obtained image, where blue indicates nucleus and green — F-actin. Multiple coloured cells around it show the results of computer simulation with the same parameters of the large Potts model, but different random seeds.
The goal of our studies is to reveal the underlying mechanisms of cardiac tissue formation and to develop a mathematical model of this process. As a first step, we aimed to reproduce the growth of engineered cardiac monolayer on various substrates. First, we studied the spreading of the single cell of each type on the glass and on the nanofibrous net (see Fig. 1). Next, we observed cell-cell interaction and collective behaviour of the cells in monolayers: segregation of the cell types and formation of the conducting pathways. As a result, our model of tissue development takes into account two types of cells (cardiomyocytes and fibroblasts), their adhesion, elasticity, surface tension, and the parameters are adjusted to fit the experimental data for the monolayers of neonatal rat cardiac cell.
To simulate the development processes in cardiac monolayer, we utilised large cellular Potts models[1,2]. The morphogenesis of cells and tissues in this paradigm was already described for plant growth, angiogenesis, stem cell differentiation, Dictyostelium discoideum, epidermal formation , vascular system development, etc. However, cardiac tissue was never studied with Potts models before. We explicitly introduced attachment sites and protrusion at the cell periphery, that was never done before. This approach allowed us to obtain a polygonal forms of the cells, which is characteristic for fibroblasts. Changing the ratio of elasticity and “spreading” forces, i.e. making the cell more rigid, turns cells into more cardiomyocyte-like shape and switches on polarization. Therefore, with this investigation we introduce a well-known tool from the field of developmental biology to serve as a basis for electrophisiological studies for a wide range of tissue growth conditions.
The ability to mimic tissue structure with engineered scaffolds coupled with in silico research provide us with a flexible tool for research in tissue development and analysis of the excitation propagation on the subcellular level. Our 2D mathematical model for the monolayer could be also extended to describe 3D tissue development, ageing and remodelling — the processes, that are impossible to observe in experiment.
The reported study was partially supported by RFBR, research project No. 16-34-00848.
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