An integrative model of the cardiovascular system coupling heart cellular mechanics with arterial network hemodynamics

Abstract

The current study proposes a model of the cardiovascular system that couples heart cell mechanics with arterial hemodynamics to examine the physiological role of arterial blood pressure (BP) in left ventricular hypertrophy (LVH). We developed a comprehensive multiphysics and multiscale cardiovascular model of the cardiovascular system that simulates physiological events, from membrane excitation and the contraction of a cardiac cell to heart mechanics and arterial blood hemodynamics. Using this model, we delineated the relationship between arterial BP or pulse wave velocity and LVH. Computed results were compared with existing clinical and experimental observations. To investigate the relationship between arterial hemodynamics and LVH, we performed a parametric study based on arterial wall stiffness, which was obtained in the model. Peak cellular stress of the left ventricle and systolic blood pressure (SBP) in the brachial and central arteries also increased; however, further increases were limited for higher arterial stiffness values. Interestingly, when we doubled the value of arterial stiffness from the baseline value, the percentage increase of SBP in the central artery was about 6.7% whereas that of the brachial artery was about 3.4%. It is suggested that SBP in the central artery is more critical for predicting LVH as compared with other blood pressure measurements.

Keywords: Blood Pressure; Computer Simulation; Hypertrophy, Left Ventricular; Integrative Cell-System-Arterial Network Model.

Fig. 1

Schematic of the integrative cell-system simulation model designed for effective multiscale numerical analysis from cellular to tissue mechanics. BLH, biological Laplace heart.

Fig. 2

Schematic of the integrative vascular system model. up, upper body; sup, superior vena cava; pa, pulmonary artery; pv, pulmonary vein; ro, right ventricular outflow; la, left atrium; lv, left ventricle; inf, inferior vena cava; ab, abdominal vena cava; kid, kidney; sp, splanchnic; ll, lower limbs; th, thoracic; rv, right ventricle.

Fig. 3

Numerical simulation results of sequential events of the integrative cell-system-arterial network model. Dotted lines, atrial events; solid lines, ventricular events. (A) Action potential. (B) Ca²⁺ concentration. (C) Cellular forces (solid line: active force generated by cross-bridges, thick dotted line: passive elastic force at the ventricular myocyte). (D) Cardiac volume. (E) Blood pressure in the left atrium and left ventricle, respectively (thick dotted line: aorta pressure). (F) Pressure pulse waves at three arterial positions (ascending aorta, common iliac artery, and anterior tibial artery).

Fig. 4

Simulated results of propagation delay of arterial pressure waves between the ascending aorta and the abdominal aorta with respect to differences in arterial stiffness. (A) E_n, (B) 2E_n, (C) 4E_n. Here, E_n represents the normal stiffness of the large arteries.

Fig. 5

Simulated results of the inotropic state of the left ventricular BLH in the cell-system model. (A) Cross-bridge elongation length (CBEL). (B) Concentration of cross-bridge-attached troponin ([TCa^*]+[T^*]). (C) Half sarcomere length. (D) Cross-bridge-generated contraction force (CBCF). (E) LV pressure according to arterial stiffness. Here, E_n represents the normal stiffness value of the large arteries.

Fig. 6

Simulation results of the (A) peak cellular stress of the ventricle, (B) pulse wave velocity (PWV) change, (C) brachial and central systolic blood pressures (SBP) with respect to arterial stiffness, and (D) peak cellular stress with respect to PWV.