A Mathematical Analysis for the Cardiovascular Control Adaptations in Chronic Renal Failure

Abstract: A model of baroreflex control of blood pressure (BP) is proposed in terms of a delay differential equation and this is used to predict the adaptation of short-term cardiovascular control in chronic renal failure (CRF) patients. Cardiac pump dynamics are explored by means of plots of blood flow vs. mean BP. The parameters of the model were determined from available data and from a sensitivity analysis. The model predicts stable and unstable equilibria close to the steady BP. It is shown that the unstable equilibrium point generates a quasiperiodic solution with two main harmonics for healthy subjects. We also show that the parameters for CRF patients predict solutions whose spectra exhibit a small high frequency component. This is due to the coalescence of the equilibrium points. The heart rate variability (HRV) time series and power spectra from healthy volunteers and CRF patients were compared with the model predictions. As an adequate measure of the sympathovagal balance we use the LF/HF index obtained from the power spectrum. The model allows the interpretation of the variability of the LF/HF index in terms of a specific set of cardiovascular parameters which are known to change from healthy to CRF patients. Comparisons of the changes in the LF/HF index predicted by the model are in agreement with actual observations for both the healthy and the CRF patients. These results show that the cardiac pump has a more restricted response in CRF patients. The model quantifies the cardiovascular adaptations to the CRF condition in terms of increased peripheral resistance and baroreflex delay and decreased arterial compliance, cardiac period, and stroke volume.