Thoroughly Calibrated Modular Agent-Based Model of the Human Cardiovascular and Renal Systems for Blood Pressure Regulation in Health and Disease

Figures

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  FIGURE 1. An example of the modular representation of a two-equation model. Module 1 includes one ODE for y (output interface variable), as well as two parameters b and Ty. Module 2 comprises one ODE for x, one input interface variable a, and one parameter Tx.

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  FIGURE 2. A simulation example for the model defined in Figure 1 with Tx≫Ty and time Δ = 1000 between agent interactions.

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  FIGURE 3. Comparison between two schemes of the two-agent model simulation. The second scheme, instead of the long and unnecessary numerical calculations of the “fast” Agent 2, searches for the equilibrium at each point of the time span.

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  FIGURE 4. Modular modeling of the cardiovascular and renal systems. The original model decomposed into two modules in accordance with human physiology. The “Cardiovascular system” module is responsible for calculation of such variables as mean arterial pressure (MAP) and cardiac output (CO). The “Renal system” module in turn regulates total body blood volume (V) and concentration of angiotensin II bound to the AT1 receptors (AT1-ANG II). The value of hematocrit (Hct) is constant. It is determined in “Cardiovascular system” and passed to “Renal system” for use.

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  FIGURE 5. Modular agent-based physiological model of the cardiovascular and renal systems. (A) An example of the “Pulmonary arteries” module representation. (B) The model implemented in the BioUML platform is divided into nine modules responsible for the kidney function (green) and 11 modules that simulate dynamics of the cardiovascular system (purple). Blue arrows indicate directed connections between the renal and cardiovascular sub-diagrams (Figure 4). For visual simplicity of the diagram, we added transitional nodes (busses) which are used for connections between modules. The busses corresponding to one variable can be located far apart in the diagram. A complete list of equations for each module is given in the Supplementary Appendix Table A2.

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  FIGURE 6. Comparison of left ventricular pressure-volume loops simulated for different equilibrium states of the model. (A) Uncomplicated hypertension vs. normal state. (B) Non-hypertensive vs. hypertensive diastolic heart failure (DHF). (C) Pulmonary hypertension and left heart disease (PH/LHD) vs. systemic hypertension and left ventricular hypertrophy (SH/LVH).

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  FIGURE 7. Simulation results of the sodium load experiment for all states of the model. The simulation experiment was designed in accordance with experimental study by He et al. (2001) and involves a 5-day high sodium diet followed by a 5-day low sodium diet. Variable values are normalized to the initial equilibrium values declared in the states.