Integrated Model of Cardiovascular Hemodynamics

The model of left ventricular wall mechanics is incorporated in lumped parameter models for the coronary and systemic circulation (Fig. 2). The aortic (AV) and mitral valve (MV) are modeled as an ideal diode. Vessels are modeled with constant resistances R, inertances L and capacitances C. The pressure drop Δp across each of these components is given by
with V the volume in the capacitance and q the flow through a resistance or an inertance. The pressure–volume relation of the capacitance represents a linearization around the physiologic working point, V₀ representing the volume at zero pressure. Values of parameters in the circulation model were based on literature (Table 2).Table 2.

Reference settings for parameters in the circulation model; coronary resistance values in parentheses represent maximum vasodilation.

Systemic circulation			Coronary circulation
Parameter	Value	Unit	Parameter	Value	Unit
Rart	5	106 Pa s m−3	Rart,c	700 (200)	106 Pa s m−3
Rper	120	106 Pa s m−3	Rmyo,1	900 (100)	106 Pa s m−3
Rven	5	106 Pa s m−3	Rmyo,2	900 (100)	106 Pa s m−3
Cart	20	10−9 m3 Pa−1	Rven,c	200	106 Pa s m−3
Cven	800	10−9 m3 Pa−1	Cart,c	0.03	10−9 m3 Pa−1
Vart,0	500	10−6 m3	Cmyo,c	1.4	10−9 m3 Pa−1
Vven,0	3000	10−6 m3	Cven,c	0.7	10−9 m3 Pa−1
Lart	60	103 Pa s m−3	Vart,c0	6	10−6 m3
Lven	60	103 Pa s m−3	Vmyo,c0	7	10−6 m3
Vblood	5000	10−6 m3	Vven,c0	10	10−6 m3

The connection between the model of LV mechanics and the coronary circulation model is made through the intramyocardial pressure, that acts on the myocardial capacitance C_myo,c. The values of the coronary capacitances were based on measurements by Spaan et al.:23 (link) 0.0022, 0.091 and 0.045 ml mm Hg⁻¹ 100 g⁻¹ LV in large coronary arteries, myocardial coronary bed, and coronary veins, respectively. Zero pressure volumes were chosen such that under normal physiological conditions, time-averaged coronary volume was about 15 ml 100 g⁻¹ of LV tissue, distributed over arterial, myocardial and venous vessels in a ratio of 1:2:2.23 (link)
In the coronary circulation, resistance values during normoxia and hyperemia were derived from Chilian et al.7 (link) In that study, total coronary resistance under normal and vasodilated conditions was measured to be 66 and 14 mm Hg min g ml⁻¹, respectively. Distribution of resistance over the arterial, myocardial and venous compartment was measured to be 25, 68 and 7% under normal conditions, and 42, 27 and 31% under maximal vasodilation.
Systemic parameters are chosen to yield representative function curves for a 70 kg adult, at a heart rate of 75 bpm. LV wall volume was set to 200 ml, and cavity volume at zero pressure was set to 30% of this volume. The arterial load was modeled by a three-element windkessel model, consisting of a characteristic aortic impedance R_art, an arterial compliance C_art, and a peripheral resistance R_per. The peripheral resistance was chosen to yield realistic time-averaged values of aortic pressure and aortic flow. Next, arterial capacitance was chosen to yield realistic values of minimum and maximum aortic pressure. Total blood volume was set to 5000 ml. The blood volume at which mean systemic pressure is zero was assumed to be equal 70% of total blood volume, about 85% of which is contained in the venous system. Venous capacitance was chosen such that the additional 30% of blood volume leads a mean systemic pressure of about 2 kPa.