A novel mathematical method successfully determines unknown scale parameters in multiscale hemodynamic models, providing insights into the cellular mechanics of progressive hypertension.
Scale parameters are used to combine two or more models in different scales into one integrative model. One of the crucial issues in the research field of biosimulation in hemodynamics is how to determine the scale parameters in comprehensive hemodynamic models comprising a cardiac cellular contraction model and a circulation model. In this report, we propose a method for determining the scale parameters using mathematical equations derived from the shape of the left ventricle (LV), which is assumed to be a hemisphere. In this method, we derived five equations with seven unknown scale parameters. By using measured values of hemodynamic parameters such as the end-systolic and end-diastolic pressures and LV volume, we successfully determined seven scale parameters to reproduce pathological data of progressive hypertension in Dahl salt-sensitive rats. From the results, we found that accompanying the progression of hypertension, the active contraction force at end-diastole first increase by 54%, followed by 93% increase of the passive elastic force. We also successfully reproduced normal human physiological hemodynamics.
Utaki et al. (2016) studied this question.