Theoretical models of changes in haemodynamic parameters and gas exchange in univentricular circulation

Aim. To develop theoretical models of changes in haemodynamic parameters of patients with univentricular haemodynamics. Methods. We analysed the effects of redistributing blood flow between the two circulatory systems (pulmonary and systemic) on systemic oxygen delivery and examined changes in the arterial and venous blood gas compositions. Mathematical analyses on the basis of oxygen flow into the pulmonary circulatory system and its consumption during circulation were performed according to Fick principle for cardiac output. Calculations were performed using equations describing changes in the delivery and consumption of oxygen during univentricular circulation. Furthermore, computer simulations were employed to investigate changes in haemodynamic parameters and gas exchange associated with pathological processes such as pulmonary venous hypoxemia, reduction in systemic flow rate and mixed venous blood desaturation. Calculations were performed under conditions with oxygen concentration of >0% or <100%. Results. A number of theoretical models were developed, which described (i) the distribution of systemic and pulmonary blood flow and changes in arterial oxygenation depending on Qp/Qs; (ii) the ratio of systemic blood flow to Qp/Qs; (iii) changes in arterial oxygenation depending on Qp/Qs at different levels of central venous saturation; (iv) changes in pulmonary venous saturation depending on arterial saturation and Qp/Qs under conditions of normal and reduced blood flow; (v) level of central venous saturation depending on changes in Qp/Qs and SpvO 2 at systemic SaO 2 of 75% and (vi) PaO2 dynamics depending on changes in PpvO 2 and Qp/Qs. Conclusion. Changes in the oxygen status of patients with univentricular haemodynamics with sufficient combined cardiac output are indicative of the distribution of blood flow. Assessments of the developed models demonstrated that a number of additional factors affect changes in the oxygen composition of blood including (i) the initial level of arterial oxygenation; (ii) the level of oxygenation in the pulmonary veins and (iii) the ratio of pulmonary to systemic blood flow. In addition, the results indicated that PCO 2 recorded in the pulmonary veins, arteries and mixed venous blood largely depends on Qp/Qs. The theoretical models presented here can be used to compare the results of haemodynamic status assessments of patients with univentricular physiology. Received 22 May 2019. Revised 4 November 2019. Accepted 10 November 2019. Funding: The study did not have sponsorship. Conflict of interest: Authors declare no conflict of interest.