Proceedings of the 7th IFAC Symposium on Modelling and Control in Biomedical Systems On the Track of Syncope induced by Orthostatic Stress - Feedback Mechanisms Regulating the Cardiovascular System Ottesen JT.* and Olufsen MS.** *Roskilde University, 4000 Roskilde, Denmark (Tel: (+45 4674 2298; e-mail: Johnny@ruc.dk). **North Carolina State University, Raleigh, NC-27695, USA (e-mail: msolufse@unity.ncsu.edu) Abstract: A physiological realistic model of the controlled cardiovascular system is constructed and validated against clinical data. Special attention is paid to the heart rate control. Both sit-to-stand and head-up-tilt experiments are encapsulated by the model. The model may be used in studies of syncope. Furthermore, the impact of the mechanical movement of diaphragm driving the respiration is considered. It turns out that this mechanical effect is significant. Keywords: Cardiovascular, control, sit-to-stand, head-up-tilt, syncope 1. INTRODUCTION During postural change in sit-to-stand (STS) and head-up-tilt (HUT) experiments blood is first drawn by gravity from the upper body regions toward the lower body regions causing an immediately decrease in central pressure. The drop in arterial pressure is rapidly counteracted by various feedback mechanisms regulating the blood pressure resulting in the reestablishment of the normal blood pressure. Figure 1 shows typical responses in arterial blood pressures during STS experiments. Note that heart rate may be extracted from the pulsatile pressure curves. In addition to these data cerebral blood flow velocities are frequently measured. The main short term feedback mechanism in this regulation is believed to be the barorecepter feedback mechanism controlling heart rate and vein compliances among other quantities. 1 140 40 50 55 65 70 75 85 90 time [sec] Fig. 1. Pressure [mmhg] versus time [sec] during sit-to-stand experiments for a healthy young subject (left) and a hypertensive elderly subject (right). Low et al (1997), Mosqueda-Garcia et al (2000), Robertson et al (2005), and Heusden et al (2006) have studied STS and HUT under various setting in humans for investigating, autonomic and cerebral autoregulation by use of modelling. The overall function of the baroreceptor feedback mechanism is known. However, the underlying bio-chemical mechanistic 1 1 140 50 55 65 70 75 85 90 time [sec] processes are not fully understood and they are not easily investigated in vivo for ethical reasons. We present a parsimonious, physiological realistic and well validated model capable of explaining several experiments and details. Modeling of STS experiments is used to investigate the short term baroreceptor feedback mechanism. A completed description can be found in Olufsen et al (2004), Olufsen et al (2005), Olufsen et al (2006), Olufsen et al (2008), Ottesen (1997a), Ottesen (1997b), Ottesen (2000), Ottesen et al (2003), and Ottesen et al (2004). 2. MODEL AND VALIDATION By an in silico investigation of the feedback mechanism the inaccessible parts become accessible. In our case the methodology illustrates how access to the otherwise inaccessible separate links of the barorecepter feedback chain regulating the heart rate can be obtained. Hereby insight into an individuals control system like a fingerprint may be obtained which may be of relevance for the treatment of several diseases such as hypertension, see Olufsen et al. (2004), Olufsen et al (2005). Figure 2 illustrates the elements of the feedback chain controlling heart rate. First an open loop model of the heart rate control is constructed and afterward the model is closed by coupling it with a compartmental cardiovascular model similar to that shown in figure 4. Beyond heart rate, cardiac contractility, peripheral vascular resistances and compliances, and volume of the systemic veins are controlled using similar constructions; see Olufsen et al. (2004), Olufsen et al. (2005). In addition also cerebral autoregulation is included. Typical results are similar to those of figure 5 where mechanical movement of the diaphragm is included. 978-3-902661-49-4/09/$20.00 2009 IFAC 187 10.3182/20090812-3-DK-2006.0042
Fig. 2. Elements of the baroreceptor feedback chain controlling heart rate. The model of the heart rate with arterial pressure as input is able to imitate various patient types such as healthy young subject, healthy elderly subject, and hypertensive elderly subject as shown in figure 3. Many parameters and mechanisms are inaccessible by clinical experiments for ethical reasons, but a mathematical modeling may made them accessible as demonstrated by the model of the heart rate. The coupling between respiration and blood flow is another example of a system with inaccessible parts. Thus the model is expanded further by including mechanical movements originating from the diaphragm. It is incorporated into the model by a varying external trunk pressure as shown in figure 4. Hereby the mechanical modulation from respiration can be studied. P 0 Vena cava Cerebral veins Atria Head Ventricle Cerebral arteries Aorta P 0+dP 0 Upper upper upper P 0-dP 0 lower Diaphragm (movable) Lower lower P 0 legs Legs legs Fig. 4. Diagram of the cardiaovascular compartmental model including the movement of the diaphragm and the external trunk pressure. Fig. 3. Heart rate model predictions (green trace) plotted against measured data (blue trace). Upper panel shows results from a healthy young subject, the middle panel shows results from a healthy elderly subject, and the lower panel shows results from a hypertensive elderly subject. The dotted line indicates where the blood pressure is starting to decrease. Arrows indicate contributions from sympathetic activation, parasympathetic withdrawal, and sympathetic activation. The respiratory movements of the diaphragm affect the overall flow distribution and favor some regions at the expense of others. These phenomena can be studied by allowing the external trunk pressure in our model and the effects turn out to be large for strong respiration. A typical respond in pressure and flow velocity during STS experiments are shown in figure 5. Respiration also affects the overall flow distribution and favors some bres at the expense of others and Starling s law of the heart follows as a result. Furthermore, including such mechanical coupling also affect results in obtained parameter values obtained from parameter estimation. Especially are those related to the ventricles and the control mechanisms very sensitive to whether respiration is included or not. 188
case caused by a sudden drop in blood pressure due to STS and HUT. A slight modification of the model is made to encompass intermediate control mechanisms essential for describing HUT experiments. These mechanisms include fluid shift, arterial compliance regulation and a minor diaphragm tension. The resulting model nicely describes both STS and HUT experiments as seen in figure 7. Fig. 5. Pressure [mmhg] (top pallet) and flow velocity [cm/sec] (bottom pallet) during sit-to-stand with respiratory mechanical effect included. Surprisingly the impact of mechanical movement giving rise to respiration is somehow strong as see in figure 6, the movement of the diaphragm during respiration is significant. Flow [ml] 130 110 90 70 Amplitude Depth Flow effects of amplitude and depth on CO -35-30 -25-20 -15-10 -5 0 Mean pressure in upper Fig. 6. The upper panel shows atria, ventricular, aortic, and respiratory pressure [mmhg] versus time [sec] when respiration is included. The lower panel shows how average flow through the heart (cardiac output) [ml/sec] is affected versus mean pressure in upper when changing respiration amplitude and depth (mean), respectively. Fig. 7. Heart rate [beats/sec] versus time [sec] during sittingto-standing (upper panel) and during head-up-tilt (lower panel). Red curves are model results and blue curves are data. The adjustments of the model open up the possibility of investigating syncope in silico. Injury as a result of syncope is a common problem, accounting for 3 percent of emergency room visits and 6 percent of hospital admissions. Syncope is a sudden incident believed by some to be the result of a crash in or breakdown of the control system. In contrast to the heart rate regulation a unifying description of pressure changes during STS and HUT shows that multiple simultaneous control mechanisms may be important in order to understand both STS and HUT experiments. This complex multi-input multi-output control system is subject for further investigation to appear elsewhere. Beyond respiration gravitational effects are essential during everyday activities. Thus the control mechanisms of the cardiovascular system should guarantee adaptation to orthostatic stress during such everyday activities. Syncope is the medical term for temporary loss of consciousness, described as fainting or passing out. It is usually related to temporary insufficient blood flow to the brain and in our 189
only between and lower body. In Head-up-tilt gravitational forces act between the head and as well as between the and lower body, due to the tilt-angle, leading to draining of flow from the cerebral circulation to the heart and from the heart to the lower body, which in turn has a hydrostatic impact on blood pressure and thus on baroreflex firing rate. 2. CONCLUSIONS A physiological realistic model of the controlled cardiovascular system is constructed and validated against clinical data. Special attention is paid to the heart rate control. Both sit-to-stand and head-up-tilt experiments are encapsulated by the model and preliminary results shows that the model may be used in studies of syncope. Furthermore, the impact of the mechanical movement of diaphragm driving the respiration is considered. It turns out that this mechanical effect is significant. REFERENCES Time [sec] Fig. 8. Upper panel shows measured arterial pulsatile pressure [mmhg] versus time [sec], the middle panel shows the corresponding heart rate [bpm] versus time [sec] for a head-up-tilt experiment, and the lower panel shows the pulsatile arterial pressure [mmhg] versus time [sec] for the model. Note that the control mechanisms re their saturation causing the syncope. The main differences between head-up-tilt and sit-to-stand are: Sit-to-stand occurs rapidly over 1-4 seconds. Head-up-tilt is a slow procedure, 5-10 seconds (thus regulatory response is initiated before the subject is fully tilted). Sit-to-stand requires active muscle contraction and engagement of central command for movement initiation, leading to an increase in heart rate as the subject contracts his/her muscles to initiate standing (possibly a combined effect of the muscle sympathetic stimulation, stimulation of the vestibular system, and central command). Head-up-tilt is a passive procedure and require limited muscle activity. Sit-to-stand does not display hydrostatic effects between the head and but Heusden K, Gisolf J, Stok WJ, Dijkstra S and Karemaker JM (2006), Mathematical modeling of gravitational effects on the circulation: importance of the time course of venous pooling and blood volume changes in the lungs. Am J Physiol Heart Circ Physiol 291:2152-2165 Low PA and Bannister RG (1997). Multiple System Atrophy and Pure Autonomic Failure. In: Low PA(eds). Clinical Autonomic Disorders. Lippincott-Raven Publishers, Philadelphia, PE, pp. 555--575. Mosqueda-Garcia R, Furlan R, Tank JMD and Fernandez-Violante R (2000), The Elusive Pathophysiology of Neurally Mediated Syncope. Circulation;102;2898-2906. Print ISSN: 0009-7322. Online ISSN: 1524-4539. Olufsen MS, Tran HT, and Ottesen JT (2004). Modeling cerebral blood flow during posture change from sitting to standing. J Cardiovasc Eng 4(1): p. 47-58. Olufsen MS, Ottesen JT, Tran HT, Ellwein L, Lipsitz LA, and Novak V (2005). Blood pressure and blood flow variation during postural change from sitting to standing: model development and validation. J Appl Physiol 99: 1523-1537. Olufsen MS, Tran HT, Ottesen JT, Lipsitz LA, Novak V (2006). Modeling baroreflex regulation of heart rate during orthostatic stress. Am J Physiol 291: R1355-R1368. Olufsen MS, Alston AV, Tran HT, Ottesen JT Novak V (2008). Modeling heart rate regulation, Part I: Sit-tostand versus head-up tilt. J Cardiovasc Eng 8: p. 73-87. Ottesen, JT (1997a). Nonlinearity of baroreceptor nerves. Surv Math Ind 7: 187-201. 190
Ottesen, JT (1997b). Modeling of the baroreflexfeedback mechanism with time-delay. J Math Biol 36: 41-63. Ottesen JT (2000). Modeling the dynamical baroreflexfeedback control. Math Comp Mod 31: 167-173. Ottesen JT and Danielsen M (2003). Modeling ventricular contraction with heart rate changes. J Theo Biol 22: p. 337-3346. Ottesen, J., M. Olufsen, and J. Larsen (2004). Applied mathematical models in human physiology. SIAM. Robertson D, Low PA, and Polinsky RJ (2005). Primer on the autonomic nervous system. Academic Press, Boston, MA, 2nd ed. dφ H 0 (1 + M SC )(1 M PC Heart beats when φ becomes1 and then it resets to 0 ) Appendix EQUATIONS IN THE HEART RATE MODEL d p p p(t) + τ ( ) ( / 2) 2 dn ( ) ( ) i dp n p M n p ni ki M τ na ( + nb ( + nc ( + N i T par ( n) M T s ( n) 1 M T sym (n) T d s (n) + u(t) 1 + βt par (n) where u(t) is impulse and β is the damping coefficient dc C τ + T sym dc C τ + T par 191