# Viscous deformation of relaxing ventricle and pulsatile blood propelling (numerical model)

## TL;DR

This paper presents a numerical model of heart circulation that uses viscous deformation to explain ventricular filling and blood flow.

## Contribution

The model introduces viscous deformation as a mechanism for ventricular filling, enabling calculations based on stress and time.

## Key findings

- Ventricular filling can be modeled as a function of stress and time using viscous deformation.
- The model explains the asymmetry in the working ranges of brady-rhythms and tachy-rhythms.
- An equation was derived to balance the system with varying parameters like arterial resistance and flow rate.

## Abstract

The numerical model of one-loop circulation exploits viscous deformation as mechanism of ventricular filling. Mathematical advantage of viscous deforming is a possibility to present the ventricular filling as the function of two independent variables (stress and time); two-dimensional argument frames a table which permits to calculate end-diastolic ventricular volume due to information about measured venous pressure and duration of ventricular diastole. The equation was deduced which balances the system while varying of such parameters as arterial resistance, the value of normal rhythm and the volume flow rate. The model pays attention on the phenomenon of asymmetrical position of normal rhythm (the steady rhythm in conditions of rest) and explains why the operating range of brady-rhythms is much narrower than the operating range of tachy-rhythms.