Volume 33, Issue 5

The mechanistic modelling of blood clotting and fibrin-polymer mesh formation is of significant value for medical and biophysics applications. This paper presents a combination of two pointwise kinetic models represented by system of ODEs. One of them represents the reaction dynamics of clotting factors including the role of the platelet membranes. The second one describes the fibrin-polymer formation as a multistage polymerization process with a sol-gel transition at the final stage. Complex-value second order Rosenbrock method (CROS) is employed for the computational experiments. A sensitivity analysis method built into the computational scheme helps clarify non-evident dependencies in the exhaustive system of ODEs. The unified model was primarily verified using conditions of factor VII deficiency. The model, however requires a significant effort to be tested against experimental data available.

Transcranial ultrasound examination is hampered by the skull which acts as an irregular aberrator of the ultrasound signal. Numerical recovery of the ultrasound field can help in elimination of aberrations induced by the skull. In this paper, we address the simulation of medical phantom scanning through silicon aberrators with wave notching. The numerical model is based on the 2D acoustic equations which are solved by the wavefront construction raytracing method. Numerical B-scan images are compared with experimental B-scan images.

A stochastic age-structured population model with immigration of individuals is considered. We assume that the lifespan of each individual is a random variable with a distribution function which may differ fromthe exponential one. The immigration rate of individuals depends on the time and total population size. Upper estimates for the mean and variance of the population size are established based on the theory of branching processes with constant immigration rate. A Monte Carlo simulation algorithm of population dynamics is developed. The results of numerical experiments with the model are presented.

Electrocardiogram is a widespread method of diagnosis of heart diseases. Nevertheless, there are still issues related to connection of some physiological features of themyocardium with patterns observed on the electrocardiogram. In ourworkwe studied the effect of ventricular remodelling, i.e., thickening ofwalls of ventricles typical for hypertrophic cardiomyopathy (HCM), on the pseudo-electrocardiogram on the surface of a volume conductor during myocardial activation from different sources. A model of two ventricles of the heart was developed for this purpose allowing us to vary ventricular geometry. The volume conductor surrounding the heart was a cubic homogeneous volume conductor. Simulation of a pseudo-electrocardiogram was performed by using a realistic ionic model of cardiomyocytes of the ventricles of the human heart and the bidomain model of the myocardium [15]. The zone of initial activation in the model was given on a part of the subendocardial surface or at one or two points corresponding to positions of electrodes of most common implantable devices. In the course of the study we revealed an inversion of the T-wave when changing the thickness of the left ventricle wall regardless of changes of properties of cardiomyocytes or myocardium conductivity. A linear dependence between the wall thickness of the left ventricle and peak amplitudes and integrals under QRS complex and T wave of the electrocardiogram was shown. We have qualitatively shown that with a change in the wall thickness of the left ventricle the pseudo-electrocardiogram changes stronger in the case of activation from one point than in activation from two points or activation of the entire subendocardium.

A fast procedure for generation of regular tetrahedral finite element mesh for objects with complex shape cavities is proposed. The procedure like LBIE-Mesher can generate tetrahedral meshes for the volume interior to a polygonal surface, or for an interval volume between two surfaces having a complex shape and defined in STL-format. This procedure consists of several stages: generation of a regular tetrahedral mesh that fills the volume of the required object; generation of clipping for the uniform grid parts by a boundary surface; shifting vertices of the boundary layer to align onto the surface.We present a sequential and parallel implementation of the algorithm and compare their performance with existing generators of tetrahedral grids such as TetGen, NETGEN, and CGAL. The current version of the algorithm using the mobile GPU is about 5 times faster than NETGEN. The source code of the developed software is available on GitHub.