A Method for Determining Scale Parameters in a Hemodynamic model incorporating Cardiac Cellular Contraction model

Abstract

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 eld 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 ve 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 rst increase by 54%, followed by 93% increase of the passive elastic force. We also successfully reproduced normal human physiological hemodynamics.

Mathematical Analysis of Left Ventricular Elastance with respect to Afterload Change During Ejection Phase

“…In this research, a simplified hemodynamic model proposed by our group [49, 45] was used for mathematical analysis. The model was constructed from a circulation model, a LV geometry model, and a muscle contraction model.…”

“…Utaki et al [49, 45] used the following reported data to define the relation between R ιυ and L . Rodriguez et al [31] also measured the time course of canine LV sarcomere length.…”

“…In this study, we used the same equation shown in Eq. (3) that Utaki et al [49] used. Here, K L and L b are constants.…”

“…Thus, wall thickness is not always proportional to the LV volume [13, 44], and the quantitative mechanism of wall thickness remains unclear. Utaki et al [49] assumed that wall thickness is linearly related to the cellular contraction force. However, in this study, to simplify the mathematical analysis, we used constant wall thickness during ejection phase.…”

Influence of Activation Time on Hemodynamic Parameters: a Simulation Study

“…We thus introduced a scale factor, K s , which is multiplied only to F b to adjust cellular contraction stress. K s was determined using the method proposed by Utaki et al [27] which resulted in K s = 6.65. Finally, total muscle stress F [mN/mm 2 ] as used in Eq.…”