Proposed cardio-pulmonary model to investigate the effects of COVID-19 on the cardiovascular system

Figures

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  Fig. 1. Human cardiovascular system [32].

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  Fig. 2. Analogous lumped parameter system of cardio-pulmonary system, The system is made of pulmonary artery (Pa), pulmonary veins (Pv), right and left ventricles (rv and lv) systemic artery (Sa) and systemic vein (Sv). The parameters Rmi, Rpv, Rtc and Rav stand for the resistances of the mitral valve, the pulmonary valve, the tricuspid valve and the aortic valve, respectively. The factors Lmi, Ltc, Lpv and Lav designate, respectively, the inertia of the mitral valve, the tricuspid valve, the pulmonary valve and the aortic valve. The quantities Qmi, Qpv, Qtc and Qav are, respectively, the flow through the mitral valve, the pulmonary valve, the tricuspid valve and the aortic valve. The grandeurs Rp and Rs define the resistances of the pulmonary circulation and the systemic circulation, respectively. The organs in the interrupted area are in contact with the respiratory system.

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  Fig. 3. Diagram of the elastic compartment of the cardiovascular system displaying the out flow Fo(t), the inflow Fi(t), the pressure P(t) and the volume V(t) of the elastic chamber.

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  Fig. 4. Model of an infected alveolus in the lung. Type I and type II pneumocytes make up the alveolar walls and resident alveolar macrophages and pulmonary surfactant exist in the airspace (A). In the acute phase of SARS-CoV infection (B), type I and type II pneumocytes are infected and secrete inflammatory cytokines, while surfactant levels decrease. During the late stage/tissue damage portion of viral infection, viral titers decrease, while airway debris, pulmonary oedema and hyaline membrane formation impede respiration (C) [31].

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  Fig. 5. Temporal evolution of the lung resistance with each breath (a) model of [33] (b) our proposed model defined by Eq. (22). These plots display the increase in pulmonary resistance with each breath. It appears that growth in Smith's model (case a) is not as fast as in our model (case b). In (b) case, the lung resistance is greater.

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  Fig. 6. Cardiopulmonary system model: simulations of the mechanical ventilation with constant pulmonary vascular resistance (Rp=0.1552Kpa.s.mL−1) exhibiting the temporal evolution of: (a) pressure in pulmonary artery; (b) pressure in systemic artery; (c) Flow rate in the pulmonary vein; (d) Flow in systemic artery; (e) Pleural pressure and (f) Volume of the right ventricle. We recover the results established by Ref. [33].

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  Fig. 7. Effect of the high frequency induced by covid-19 (β=2), augmentation of the frequency due to the lung disease: (a) flow in the pulmonary artery; (b) systemic artery flow; (c) right ventricle volume; (d) right ventricle pressure.

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  Fig. 8. Effect of the time varying pulmonary resistance Rp(t) on the vascular circulation with the value of Cr=7×103Kpa.s.m−3: (a) pulmonary resistance; (b) pressure in pulmonary atery; (c) pressure in the pulmonary vein; (d) pressure in systemic atery; (e) pressure of left ventricle; (f) volume of left ventricle.