We have developed an integrative model of the ovine cardiovascular system that simulates the effects of posture and ventricular function to help design the circulatory and pulmonary assist devices often tested in conscious sheep that stand and recline during chronic experiments. Our present focus is the simulation itself and not the evaluation of specific assist devices. Adjusted parameters of the model provide good fits to in vivo experimental data and can describe the hemodynamic changes that follow balloon occlusion of the inferior vena cava and standing. Since circulatory assist devices are often tested in animal preparations of left heart failure, we extended the model to study the effects that standing and inferior vena cava occlusion would have in sheep with primarily systolic left heart dysfunction. We also developed an elastance-based formulation for ventricular muscular work and a sensitivity analysis of the autonomic reflexes affecting blood pressure. The model can analyze the biophysical mechanisms underlying the responses to orthostatic stress and left ventricular dysfunction and should help improve the development and testing of assist devices.
NOMENCLATUREa min constant (dimensionless) A i parameter of activation function of the heart (dimensionless) B i parameter of activation function of the heart (s) C i parameter of activation function of the heart (s) CBO caval balloon occlusion CO cardiac output D 0 volume parameter (mL) e(t) time-varying activation function (mmHgmL −1 ) E(t) time-varying elastance function (mmHgmL −1 ) E ES end-systolic elastance (mmHgmL −1 ) EDPVR end-diastolic pressure-volume relationship ESPVR end-systolic pressure-volume relationship ε E energy stored by elastance element (erg) ε M muscular energy provided to ventricle by metabolic energy (erg) F CON normalized sympathetic efferent discharge frequency controlling contractility (dimensionless) F HRS normalized sympathetic controlling heart rate frequency (dimensionless) F HRV normalized vagal controlling heart rate frequency (dimensionless) 53 1567-8822/05/0600-0053/0 C 2005 Springer Science+Business Media, Inc. 54 Ha, Qian, Ware, Zwischenberger, Bidani, and Clark F VASO normalized sympathetic efferent discharge frequency controlling vasomotor tone (dimensionless) FLV failing left ventricle h 1 -h 6 constants (bpm) HR heart rate (beats per minute, bpm) IVC inferior vena cava K a scaling parameter (mmHg) K p1 constant scaling parameter (mmHg) K p2 constant scaling parameter (mmHg) K r constant scaling parameter (mmHg) LA left atrium LV left ventricle LVMW left ventricular muscular work λ diastolic elastance coefficient (dimensionless) MAP mean arterial pressure NLV normal left ventricle P a ar systemic arterial pressure in the active state (fully constricted) (mmHg) P p ar systemic arterial pressure in the passive state (relaxed) (mmHg) P ED (V ) end-diastolic pressure (mmHg) P ES (V ) end-systolic pressure (mmHg) P LA left atrial pressure (mmHg) P LV left ventricular pressure (mmHg) P 0 diastolic pressure parameter (mmHg)...