modeling methodology forum Hemodynamic fluctuations and baroreflex sensitivity in humans: a beat-to-beat model R. W. DEBOER, J. M. KAREMAKER, AND J. STRACKEE Department of Physiology and Laboratory of Medical Physics, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands DEBoER, R. W., J. M. KAREMAKER, AND J. STRACKEE. Hemodynamic fluctuations and baroreflex sensitivity in humans: a beal-ta-beat morlp!. Am .• J. Physiol. 2fi:i (HeHrt rire. Physiol. 22): 680-689, 1987.-A beat-ta-beat model of the cardiovascular system is developed to study the spontaneous short-term vari- ability in arterial blood pressure (BP) and heart rate (HR) data from humans at rest. The model consists of a set of difference equations representing the following mechanisms: 1) control of HR and peripberal resistance by the baroreflex, 2) Windkessel properties ofthe systemic arterial tree, 3) contractile properties of the myocardium (Starling's law and restitution), and 4) mechanical effects of respiration on BP. The model is tested by comparing power spectra and cross spectra of simulated data from the model with spectra of actual data from resting sub- jects. To make spectra from simulated data and from actual data tally, it must be assumed that respiratory sinus arrhythmia at rest is caused by the conversion of respiratory BP variability into HR variability by the fast, vagally mediated baroreflex. The so-called 10-s rhythm in HR and BP appears as a reso- nance phenomenon due to the delay in the sympathetic control loop of the baroreflex. The simulated response of the model to an imposed increase of BP is shown to correspond with the BP and HR response in patients after administration of a BP- increasing drug, such as phenylephrine. It is concluded that the model correctly describes a number of important features of the cardiovascular system. Mathematical properties of the dif- ference-equation model are discussed. blood pressure fluctuations; heart rate variability; cardiovas- cular system; mathematical modeling; spectral analysis; power spectra; cross spectra; respiratory sinus arrhythmia; 10-s vari- ability; Mayer waves THE HEART IS NOT a continuous pump hut acts in a discrete fashion with the successive heartbeats leading to a series of fluctuating values of R-R intervals and systolic and diastolic pressures. Still, almost all models of the cardiovascular system (CVS) consist of sets of differential equations, representing relationships be- tween continuous signals such as mean arterial blood pressure (BP) and heart rate (HR) (for a recent review see Ref. 5). If one is only interested in the long-term regulation of the CVS, this neglect of the pulsatile char- acter of the heartbeat seems justified. However, as we wish to study the relationship between short-term fluc- tuations in BP and HR, we have developed a beat-to- beat model of the human CVS based on physiological considerations. The model can be used to obtain simu- 1ated BP data and R-R interval data, both for subjects at rest and after the administration of a vasoconstricting, hence BP-increasing, drug (e.g., phenylephrine). The performance of the model is assessed by comparison of simulated data and actual human data. In resting humans, beat-to-beat fluctuations in BP and HR are mainly due to respiratory influences and to the slower Mayer waves (for a review see Ref. 23). The fastest and often the most conspicuous Mayer waves constitute the so-called 10-s rhythm, having a period of -10 s (13). One of the purposes of our study is to obtain information about the functioning of the CVS under normal physiological conditions from the relationship between these spontaneous BP and HR fluctuations, thus dispensing with the need for pharmacological or other interventions. We use spectral-analysis techniques to differentiate between fluctuations due to the lO-s rhythm (at -0.1 Hz) and due to respiratory influences (usually 10-20 breaths/min or 0.15-0.35 Hz). Examples of power spectra and cross spectra of HR variability and BP variability from healthy human subjects at rest were presented in a previous paper (9). At that time we gave only a partial interpretation of these spectra, using a very simple beat- to-beat model of the CVS (10). This old model was not able to explain the shape of the phase spectrum of systolic pressure variability against interval variability that was ohtained from actual data. It was then found that the phase spectrum derived from the model and the phase spectrum computed from actual data agreed only for respiratory frequencies (0.2-0.35 Hz), hut at the frequency of the lO-s rhythm the old model predicted a phase difference of 0" (pressure and interval in phase), whereas the experimental data show a phase difference of --70" (pressure leads interval). It will be shown that the present model greatly improves on these results (see Simulation of Resting Data). The results of our simulations suggest that respiratory H680 0363-6135/87 $1.50 Copyright © 1987 the American Physiulogical Society