Closed-loop real-time simulation model of hemodynamics and oxygen transport in the cardiovascular system

Abstract

Background: Computer technology enables realistic simulation of cardiovascular physiology. The increasing number of clinical surgical and medical treatment options imposes a need for better understanding of patient-specific pathology and outcome prediction.

Methods: A distributed lumped parameter real-time closed-loop model with 26 vascular segments, cardiac modelling with time-varying elastance functions and gradually opening and closing valves, the pericardium, intrathoracic pressure, the atrial and ventricular septum, various pathological states and including oxygen transport has been developed.

Results: Model output is pressure, volume, flow and oxygen saturation from every cardiac and vascular compartment. The model produces relevant clinical output and validation of quantitative data in normal physiology and qualitative directions in simulation of pathological states show good agreement with published data.

Conclusion: The results show that it is possible to build a clinically relevant real-time computer simulation model of the normal adult cardiovascular system. It is suggested that understanding qualitative interaction between physiological parameters in health and disease may be improved by using the model, although further model development and validation is needed for quantitative patient-specific outcome prediction.

Figure 1

Sketch showing the cardiac and vascular components of the simulation model. The dark yellow area is the pericardium containing the cardiac chambers and coronary vessels. The light yellow area is the intra-thoracic space containing the pericardium, the pulmonary circulation and the thoracic aorta. The extra-thoracic space contains the carotid/subclavian circulation in the upper part and the rest of the systemic circulation in the lower left part.

Figure 2

Left ventricular pressure-volume loops during a preload reduction maneuver in a case with slightly reduced left ventricular function (E_max 1.4 and E_min 0.08). The diastolic and end-systolic pressure-volume relations are shown in thin black lines. The end-systolic line is curved due to the “heart law of Starling” reducing contractile strength during volume overload according to Additional file 2: Equation S2. The curved end-diastolic relation illustrates the increase in passive stiffness when the ventricle is dilated according to Additional file 2: Equation S3.

Figure 3

Effects of changing vascular damping factor λ on cardiac and vascular pressures (peripheral artery (light red), ascending aorta (dark red), left ventricle (red), pulmonary artery (orange), right ventricle (yellow), left atrium (brown), right atrium (blue)) related to the viscous properties of the vascular walls. Very low values results in numerical instability in the model. A value of 0.5 is chosen in all presented simulations.

Figure 4

Left ventricular (red), aortic root (pink) and left atrial pressure (brown) during two heart cycles. An early diastolic as well as a late positive ventriculo-atrial pressure gradient results in the mitral E and A-waves respectively. A post-ejection aortic pressure incisura is seen corresponding to aortic valve closure followed by a “reflected” wave.

Figure 5

Aortic valve flow (red), mitral valve flow (brown) and pulmonary vein flow (purple). Small regurgitant flows are seen when the valves are closing. A minimal reversal of pulmonary vein flow is seen corresponding to the left atrial contraction (mitral A-wave).

Figure 6

Intracardiac pressure-volume loops from the left ventricle (left panel) and left atrium (right panel) in simulation of pure systolic left heart failure (E_max 2.8 → 1.0). Stroke volume and blood pressure decrease. Left ventricular and atrial volumes as well as filling pressures increase.

Figure 7

Intracardiac pressure-volume loops from the left ventricle (left panel) and left atrium (right panel) in simulation of diastolic heart failure (E_min 0.05 → 0.12). Stroke volume and blood pressure decrease. Left ventricular volume decreases, while left atrial volume and filling pressures increase.

Figure 8

Intracardiac pressure-volume loops from the left ventricle in simulation of aortic stenosis (open area 5.0 → 0.7 cm², left panel) and aortic regurgitation (closed area 0.0 → 0.2 cm², right panel. Stroke volume decreases in aortic stenosis despite high intraventricular pressure. Apparent stroke volume increases and systemic blood pressure decreases in aortic regurgitation. Left ventricular end-diastolic pressure and volume increase in both scenarios.

Figure 9

Simulation of Valsalva maneuver (increase in intrathoracic pressure from zero to +10 mmHg between arrows) without (left panel) and with (right panel) baroreceptor reflex activated. ECG (blue), arterial pressure (red), pulmonary arterial pressure (orange) and central venous pressure (blue), pressure increase when increasing intrathoracic pressure (yellow arrow), decrease when releasing pressure (red arrow). The baroreceptor reflex increase heart rate, left ventricular contractility and systemic arterial resistance. Blood pressure is better maintained and a pressure overshoot is seen after release of the pressure.

Figure 10

a-e. Pressure volume loops in left (black) and right (gray) ventricle during stepwise simulation of moderate exercise. (a). Normal resting state. HR 72/min. CO 5.11 l/mint.SAP112/61(79). PAP 24/8(12). (b). Increase in heart rate +100%.HR 144/min. CO 7.08 l/mint.SAP132/86(102). PAP 26/9(14). (c). Increase in right and left ventricular systolic function +50%. HR 144/min. CO 8.41 l/mint SAP153/95(117). PAP 29/9(15). (d). Decrease in systemic arterial resistance. Increase in systemic arterioli diameter +50%. HR 144/min. CO 9.23 l/mint.SAP 86/48(60). PAP 30/9(15). (e). Decrease in pulmonary arterial resistance.Increase in pulmonic arterioli diameter +50%. HR 144/min. CO 10.18 l/mint.SAP 94/50(65). PAP 27/5(13).

Figure 11

Blood pressure in ascending aorta with changing vascular stiffness. When increasing (lighter) Young’s elastic modulus Y systolic pressure increases and diastolic pressure decreases. The increased stiffness also results in a shorter systolic ejection due to a premature arterial recoil/reflection. The increase in afterload also results in decreasing left ventricular stroke volume despite increasing stroke work.