Editorial comment: Montani versus Osborn exchange of views

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1 Exp Physiol 94.4 pp Experimental Physiology Introduction to Exchange of Views Editorial comment: Montani versus Osborn exchange of views The long-term control of blood pressure has been recognized as a complex mixture of neural, hormonal and intrinsic factors involving the brain, heart, vasculature and especially the kidney. While computational modelling approaches to organ function have offered much promise recently (Hunter & Borg, 2003; Hunter et al. 2003), allowing researchers to test hypotheses or simulate stimuli difficult to assess experimentally, their application to blood pressure control has been somewhat limited. In 1972, Guyton and Coleman published a model which attempted to provide the basis for long-term blood pressure control (Guyton et al. 1972). This model, composed of hundreds of equations, has both baffled and intrigued legions of physiologists. The model has been somewhat updated to reflect recent advances (Guyton, 1990), although the role of the central nervous system is predominantly lacking. The central feature of the model is the linkage between blood pressure and sodium balance, where any imbalance between salt intake and excretion leads to a progressive alteration in the filling of the vascular system and thus changes in blood pressure. This in turn alters sodium excretion, a feature defined as the pressure natriuresis relationship. A key aspect in this concept is that it puts the kidney at the very centre of long-term blood pressure control. This means that any chronic change in blood pressure must have been accompanied by an alteration in the pressure natriuresis relationship. One effect of this model and concept has been to focus much research in hypertension on the kidney. More recently, this fundamental role of the kidney has become a source of renewed debate (Osborn, 2005; Osborn et al. 2005; Korner, 2007). The question has arisen as to whether the Guyton Coleman model is still valid and can therefore form the basis of an updated model or whether it should be moved aside and a new structure built from the ground up. There is little doubt that the area has held itself back to some extent through the use of propriority modelling platforms and a failure to make the underlying code accessible. However, newer modelling tools, such as CMISS ( or Simulink in Matlab ( offer the prospect of providing an open-source platform for future modelling endeavours. This could allow multiple research groups to test and refine sections of the model in a collaborative nature. In this issue of Experimental Physiology, two opposing views are presented. Montani and Van Vliet (2009a,b) argue that the structure of the Guyton Coleman model is fundamentally sound. Osborn and co-workers (2009a,b) argue that in light of the evidence for a major role of the sympathetic nervous system in long-term control of arterial pressure and the pathogenesis of hypertension, new mathematical models for long-term control of arterial pressure may be necessary. They argue that renal control of total blood volume is not the only factor that affects the long-term level of arterial pressure, that the Guyton Coleman model overestimates the importance of renal control of body fluids and total blood volume in blood pressure regulation and that an alternative model can be developed in which sympathetic nervous system activity plays an important role in long-term control of arterial pressure independent of its effects on total blood volume. The aim in publishing these Exchange of Views articles is to stimulate debate and encourage further research in this area. At the first cardiovascular control conference, held 4 years ago in Jaipur, India, it was proposed (Evans et al. 2005) that computational modelling held much promise for the area of long-term blood pressure control but it was also one with few research groups active. At the second meeting, held in December 2008 in Mamallapuram, India, the need C 2009 The Author. Journal compilation C 2009 The Physiological Society DOI: /expphysiol

2 382 J.-P. Montani and B. N. Van Vliet Exp Physiol 94.4 pp for computational approaches was again emphasized and it was suggested that the area would lend itself well to a consortium of engineers and physiologists. Simon Malpas Department of Physiology and Bioengineering Institute, University of Auckland, Auckland, New Zealand s.malpas@auckland.ac.nz References Evans RG, Malpas SC, Osborn JW & Fink GD (2005). Neural, hormonal and renal interactions in long-term blood pressure control. Clin Exp Pharmacol Physiol 32, Guyton AC (1990). Long-term arterial pressure control: an analysis from animal experiments and computer and graphic models. Am J Physiol Regul Integr Comp Physiol 28, R865 R877. Guyton AC, Coleman TG & Granger HJ (1972). Circulation: overall regulation. Ann Rev Physiol 34, Hunter PJ & Borg TK (2003). Integration from proteins to organs: the Physiome Project. NatRevMolCellBiol4, Hunter PJ, Pullan AJ & Smaill BH (2003). Modeling total heart function. Annu Rev Biomed Eng 5, Korner PI (2007). Essential Hypertension and its Causes. Oxford University Press, New York. Montani J-P & Vliet BNV (2009a). Understanding the contribution of Guyton s large circulatory model to long-term control of arterial pressure. Exp Physiol 94, Montani J-P & Vliet BNV (2009b). Commentary on Current computational models do not reveal the importance of the nervous system in long-term control of arterial pressure. Exp Physiol 94, Osborn JW (2005). Hypothesis: set-points and long-term control of arterial pressure. A theoretical argument for a long-term arterial pressure control system in the brain rather than the kidney. Clin Exp Pharmacol Physiol 32, Osborn JW, Jacob F & Guzman P (2005). A neural set point for the long-term control of arterial pressure: beyond the arterial baroreceptor reflex. Am J Physiol Regul Integr Comp Physiol 288, R846 R855. Osborn JW, Averina VA & Fink GD (2009a). Current computational models do not reveal the importance of the nervous system in long-term control of arterial pressure. Exp Physiol 94, Osborn JW, Averina VA & Fink GD (2009b). Commentary on Understanding the contribution of Guyton s large circulatory model to long-term control of arterial pressure. Exp Physiol 94, Experimental Physiology Exchange of Views Understanding the contribution of Guyton s large circulatory model to long-term control of arterial pressure Jean-Pierre Montani 1 and Bruce N. Van Vliet 2 1 Department of Medicine, Division of Physiology, University of Fribourg, Chemin du Musée 5, CH-1700 Fribourg, Switzerland 2 Division of BioMedical Sciences, Faculty of Medicine, Memorial University of Newfoundland, St John s, Newfoundland, Canada A1B 3V6 With the publication in 1972 of a large computer model of circulatory control, Guyton and colleagues challenged the then prevailing views on how blood pressure and cardiac output were controlled. At that time, it was widely accepted that the heart controlled cardiac output and that peripheral resistance controlled arterial blood pressure. By incorporating the empirically demonstrated concepts of blood flow autoregulation and the pressure natriuresis relationship into their mathematical model, Guyton and colleagues were able to develop a number of revolutionary concepts. Guyton s circulatory model was particularly instrumental in exploring the linkage between blood pressure and sodium balance and in demonstrating an overriding importance of renal salt and water balance in setting the long-term blood pressure level. In both the model and experimental data, any long-lasting imbalance between salt intake and salt

3 Exp Physiol 94.4 pp Contribution of Guyton s model 383 excretion leads to a progressive alteration of the degree of filling of the vascular system and thustoparallelchangesinbloodpressure.inturn,changesinbloodpressurealtersodium excretion, opposing the initial salt imbalance. Although Guyton s model does not include the most recent cardiovascular discoveries, the concepts underlying the basic functioning of the cardiovascular system can serve as a well-built basis for the development of new, large and integrative cardiovascular models. (Received 11 September 2008; accepted after revision 22 January 2009; first published online 26 February 2009) Corresponding author J.-P. Montani: Department of Medicine, Division of Physiology, University of Fribourg, Rue du Musée 5, CH-1700 Fribourg, Switzerland. jean-pierre.montani@unifr.ch A short history of the development of Guyton s model In 1972, Guyton, Coleman and Granger published a detailed description of a large computer model of circulatory control (Guyton et al. 1972). The model consisted of several hundred mathematical equations aiming primarily at understanding the long-term regulation of blood pressure (BP) and cardiac output (CO). In the late 1950s, when Guyton started to be quite prolific in the field of physiology, considerable controversy existed concerning the regulation of these major cardiovascular variables. The two prevailing views in cardiovascular control were: (a) that the heart controls CO (cardiocentric view); and (b) that vascular resistance controls BP (vasculocentric view). The early contributions of Guyton (Guyton et al. 1959) challenged the cardiocentric view. Guyton used a circuit analysis based on simple physical laws of pressure flow and pressure volume relationships to dissect the major factors affecting the return of blood to the heart. Later, after investigating the manner in which the heart function is coupled to venous circulation, Guyton established the now classical graphical analysis of CO and venous return (Guyton et al. 1973), the principles of which were incorporated into his 1972 model and remain today a powerful didactic tool to explain CO regulation in a steadystate situation. While more advanced models of cardiac function have subsequently been developed (e.g. pressure volume analysis), the coupling of the heart with the venous circulation remains a core feature of modern circulatory models. Guyton and colleagues investigation of the linkage between the regulation of extracellular fluid volume (ECFV) and that of BP also strongly challenged the vasculocentric viewpoint. Extending traditional models consisting of circulatory pressures, flows and resistances, they added circulatory volumes and compliances and linked them to sources of fluid entry (absorption of salt and water by the digestive tract) and loss (chiefly salt and water excretion by the kidney). Analysis of the model s behaviour revealed an overriding importance of the relative filling of the vascular system in the feedback regulation of the long-term BP level. Any sustained imbalance between salt intake and salt excretion caused a change in the degree of filling of the vascular system and, in turn, parallel alterations in BP. This effect was opposed by the demonstrated ability of changes in BP to cause corresponding alterations in renal sodium excretion, the so-called acute pressure natriuresis relationship (PNR). Consequently, the long-term mean BP was found to represent the one BP level at which these effects were balanced, i.e. the one pressure level at which salt balance (intake = output) could be achieved. Thus, Guyton and colleagues came to realize that BP regulation was intimately linked with fluid volume regulation, and that the long-term BP was controlled at a level predicted by the PNR and not by the vascular resistance per se. With the 1972 publication of the large circulatory model, Guyton and colleagues paved the way to new thinking in the regulation of cardiovascular dynamics. The model was written in FORTRAN and ran initially on a large minicomputer (first on a PDP 9, from Digital Equipment Corporation, then in the mid- 1970s on a PDP 11/70). It was later transferred into the personal computer environment (Montani et al. 1989a,b), where it could be made freely available to the scientific community. Following 1972, Guyton continued to revise the model, mainly by developing the kidney components and incorporating more recent cardiovascular discoveries. However, the main features of the 1972 version (e.g. pressure natriuresis relationship, blood flow autoregulation) remained as core concepts of themodel.guytonmadeveryfewadditionstohismodel after his retirement in 1989 at the age of 70. He died in 2003, leaving behind the most recent version of his model dating from Why does the kidney play a dominant role in long-term blood pressure control? In Guyton s model, control of BP and sodium balance are tightly linked via the acute pressure natriuresis relationship, a concept so central to the regulation of sodium excretion that the many other factors and mechanisms that influence sodium excretion were considered by Guyton to act chiefly by modifying this

4 384 J.-P. Montani and B. N. Van Vliet Exp Physiol 94.4 pp relationship (Guyton, 1980). Based on this concept, one can understand the general renal body fluid feedback mechanism (Guyton et al. 1972; Guyton, 1980, 1990; Hall et al. 1986a) as illustrated in the block-diagram of Fig. 1. Any imbalance between intake and output of salt will lead to a cascade of events that oppose the initial disturbance, a classical negative feedback loop. For example, if salt intake is greater than salt excretion (Fig. 1A), there is a positive rate of change of the ECFV ( ECFV) which, integrated over time (Fig. 1B), results in an increase in ECFV and, in turn, to an increase in blood volume (Fig. 1C). The greater blood volume increases mean circulatory filling pressure (MCFP, which represents the degree of filling of the whole circulation, relating blood volume to vascular capacity), as shown by the relationship depicted in Fig. 1D. This results in a right and upward shift of the equilibrium point (Fig.1E) in Guyton s classic graphical analysis of the cardiac function curve and the venous return curve (Guyton et al. 1973), yielding both an increase in right atrial pressure and an increase in venous return. The resulting increase in cardiac output raises BP (Fig. 1F). In turn, by way of the acute pressure natriuresis mechanism, the higher BP increases salt output (Fig. 1G), which opposes the effects of the initial increase in salt intake. Being dependent on fluid volume changes, this system is inherently slow (hours or days). However, because the underlying changes in fluid volume accumulate over time until BP reaches a point at which salt balance is achieved, this feedback system is extremely effective. Theoretically, if given a sufficient period of time, such a system could completely correct any error in salt balance or blood pressure. It should be noted that the acute pressure natriuresis curve (PNC) depicted in Fig. 1G and Fig. 2A is not immovable, but can be modulated by a number of factors and conditions including changes in salt intake. For example, it becomes steeper and is shifted to the left during high salt intake (Fig. 2B). Conversely, during low salt intake, the PNC becomes flatter and is shifted to the right. Joining the equilibrium points at the various salt intakes now reveals a very steep steady-state relationship with little change in BP (the chronic pressure natriuresis relationship or renal function curve ). That is, BP has become relatively salt insensitive. Various neurohormonal mechanisms contribute to the adjustment of the acute PNC with varying salt intakes, such as sympathetic activity, natriuretic and antinatriuretic hormones. Above all, modulation of the renin angiotensin system (RAS) plays a crucial role in the adaptation to changes in salt intake, with suppression of the RAS at high salt intake facilitating sodium excretion and stimulation of the RAS at low salt intake contributing to sodium conservation G Extrarenal loss B _ A Excretion ECFV ECFV _ + 14 litres C Excretion of NaCl + H 2 O Intake Blood volume 5 litres 1 x Normal 100 BP 14 litres ECFV TPR 20 Autoregulation BP 100 mmhg F CO CO EP2 E MCFP MCFP 5 litres 7 mmhg Blood volume D 5 l min -1 EP1 RAtP MCFP 7 mmhg 5 litres Blood volume Figure 1. The renal body fluid feedback mechanism for control of blood volume and extracellular fluid volume in the face of large changes in salt intake See text for a detailed explanation of each block (A G) of the block-diagram. Abbreviations: ECFV, extracellular fluid volume; MCFP, mean circulatory filling pressure; RAtP, right atrial pressure; CO, cardiac output; EP, equilibrium point; TPR, total peripheral resistance; and BP, blood pressure.

5 Exp Physiol 94.4 pp Contribution of Guyton s model 385 (Montani & Van Vliet, 2004). In summary, the great sensitivity of the acute PNC to neurohumoral modulation can explain how sodium balance can be defended with little or no change in BP. Several lines of evidence are consistent with the central role of the kidney in long-term BP control, as follows. First, inability to modulate the pressure natriuresis curve leads to salt sensitivity. Indeed, dramatic saltinduced changes in BP occur when the RAS is blocked with an angiotensin-converting enzyme inhibitor or when circulating angiotensin II levels are fixed with an intravenous infusion of angiotensin II (Hall et al. 1980). Second, most renal transplantation studies support the notion that the kidney is a major determinant of long-term BP (Rettig, 1993). This concept is reinforced by a recent study in an experimental model of kidney cross-transplantation in the mouse, which shows that angiotensin II causes hypertension through its receptors in the kidney (Crowley et al. 2006). Third, in various experimental models of hormoneinduced hypertension [e.g. due to infusion of aldosterone (Hall et al. 1984b), angiotensin II (Hall et al. 1984a), vasopressin (Hall et al. 1986b) or noradrenaline (Hall et al. 1988)], shielding the kidney from the hormone-induced increase in BP (i.e. holding renal perfusion pressure near control levels) leads to marked fluid retention that persists throughout the infusion period despite larges increases in ECFV and severe systemic hypertension. Fourth, experiments in dogs instrumented for separate monitoring of left and right kidney functions have shown that the acute pressure natriuresis relationship does not reset during long-term changes in arterial pressure (Mizelle et al. 1993). Finally, support for the role of BP in the control of sodium balance comes from genetic studies. Many genes have been identified to be associated with essential hypertension or responsible for rare monogenic diseases that are characterized by low or high blood pressures (Lifton et al. 2001; Mullinset al. 2006). Intriguingly, most of these genes encode proteins that are directly involved with renal sodium handling. Mutations that favour renal sodium reabsorption increase BP, whereas mutations that diminish tubular sodium reabsorption tend to decrease BP. ChangesinBPseemthustobeahomeostaticmechanism to achieve sodium balance in the face of excessive or deficient salt reabsorption. Some common misconceptions in understanding Guyton s model Guyton limited the size of his model to several hundred equations in order to focus on the mechanisms that were most important in long-term control of BP and fluid volumes. Nevertheless, understanding his model requires that a number of components and concepts must be kept in mind simultaneously. This inherent complexity has occasionally led to misconceptions and apparent paradoxes that are worth clarifying. Misconception 1: a primary renal dysfunction is at the origin of all forms of hypertension. According to Guyton s analysis of BP regulation, any long-lasting Figure 2. The concept of the acute pressure natriuresis relationship and how adjustments of this relationship facilitate sodium balance during sustained changes in salt intake Equilibrium is reached at the intersection between the acute pressure natriuresis curve (PNC) and the corresponding level of salt excretion that matches salt intake. A, with a fixed PNC, equilibrium for the three depicted levels of salt intake (1 normal, 4 normal and 0.2 normal) would be reached at points A, B and C, respectively, yielding considerable salt sensitivity. B, after adjustments of the PNC with varying salt intakes (left-shift with steepening at high-salt intake, right-shift with flattening at low-salt intake), joining the intersection points (B,AandC ) reveals an almost vertical chronic pressure natriuresis relationship (see dotted line), i.e. the chronic renal function curve. The modulation of the acute PNC during alterations in salt intakes thus allows the body to achieve sodium balance with minimal changes in arterial pressure.

6 386 J.-P. Montani and B. N. Van Vliet Exp Physiol 94.4 pp alteration in BP requires a shift of the PNR (assuming salt intake is constant). However, a shift of the PNR does not need to be the primary event in the cascade of changes leading to hypertension; it can also be secondary to non-renal influences. Indeed, Guyton s model allows one to simulate many forms of hypertension of extrarenal origin, including a mineralocorticoid-producing tumour, coarctation of the aorta or even sympathetic overactivity. However, the model predicts that, whatever the cause of hypertension, it must in the end somehow modify the kidney s ability to excrete salt and water for a given level of BP; otherwise, the hypertension would lead to an increased excretion of salt and water through the PNR, ultimately returning BP to regular levels. Even the escape to the sodium-retaining effects of servo-controlled low renal perfusion pressure (Reinhardt et al. 1994), an experiment often suggested to challenge Guyton s body fluid feedback mechanism, can be explained by a leftward shift of the PNC as a consequence of volume expansion, systemic hypertension, suppression of antinatriuretic factors and stimulation of natriuretic factors (Montani & Van Vliet, 2007). Furthermore, in many instances, overt changes in BP are not required to achieve sodium balance. Indeed, a number of autocrine and paracrine factors generated within the kidney itself can influence renal sodium excretion. However, conceptually, these shortloop feedbacks are equivalent to a shift of the PNC. Misconception 2: Guyton s model dismisses the role of the central nervous system in long-term bloodpressure regulation. Although Guyton s model contains only a rudimentary representation of central nervous system (CNS) function (limited to basic cardiovascular reflexes, such as baroreceptors, chemoreceptors and central ischaemic reflex), Guyton left open a possible role of the CNS in long-term BP control. In his original 1972 description of his system s analysis and model, he noted suggestions by earlier authors that neurogenic hypertension could be mediated through a nervous influence on renal function. Subsequently, he provided analyses and model simulations illustrating how sustained hypertension could be induced by activation of sympathetic nerves throughout the body, or to the kidney alone, but that such effects did not occur if the sympathetic outflow to the kidney was excluded (figures 35-1 through 35-3 of Guyton, 1980). In Guyton s model, the direct effects of sympathetic stimulation are limited to renal effects, constriction of the vasculature and to increasing heart performance. The model does not exclude the possibility that sympathetic stimulation of non-renal tissues could also alter kidney function by other mechanisms, including an influence on circulating mediators (e.g. endothelin, digitalis glycosides and immune system components). It is also very possible that the CNS could alter renal function and BP by mechanisms other than sympathetic activation. Indeed, the CNS is known to release a number of substances that influence renal function (vasopressin, adrenocorticotrophic hormone, γ-melanocyte-stimulating hormone and digitalis glycosides) and others may remain to be identified. However, whatever the role of the CNS, Guyton s analyses suggest that any influence on the long-term BP level would imply a final pathway acting on the kidney. Misconception 3: changes in mean arterial pressure must be linked to changes in total blood volume. Although the analysis of Fig. 1 shows that ECFV and blood volume are essential components of long-term regulation of BP, a more careful examination reveals that the BP is not a function of total blood volume per se but of the volume in excess in the vascular tree (i.e. the distending volume in excess of the resting size of the vasculature), particularly in the arterial tree. This concept is analogous to the concept of effective arterial blood volume used by others (Schrier, 1990). With this in mind, one can easily see why the renal body fluid feedback mechanism also applies to hypertension models characterized by a low blood volume, such as noradrenaline-induced hypertension (Hall et al. 1988) or administration of angiotensin II at higher doses (Carroll et al. 1984). On the one hand, one would expect noradrenaline or angiotensin to promote sodium retention by acting directly on the kidney and thereby increasing total blood volume. On the other hand, both agents are also strong vasoconstrictors that increase BP rapidly, leading to initial natriuresis and thus to a decrease in blood volume. In parallel, these vasoconstrictor agents decrease vascular capacitance, permitting the maintenance of a high BP value with a low blood volume. Simulation of these hypertensive states with Guyton s model reveals a state of overfilling of the circulation, with increased MCFP and arterial volume in excess despite a decreased total blood volume. Misconception 4: whole body blood flow autoregulation is the cause of volume-loading hypertension. Auto regulation is the ability of an organ or tissue to adjust its blood flow by local mechanisms, in accordance with local needs, and is often evident in the relative consistency of tissue blood flow despite changes in perfusion pressure. In the intact circulation, volume-loading elevates CO and thus BP. The resulting overperfusion of the tissues leads then to secondary autoregulatory changes in vascular resistance (Coleman & Guyton, 1969). Unfortunately, this whole body form of autoregulation is often misinterpreted as the cause of systemic hypertension during volume-loading. However, autoregulation lies outside of the main feedback loop of the renal body fluid

7 Exp Physiol 94.4 pp Contribution of Guyton s model 387 feedback mechanism, as shown in Fig. 1. Consequently, the renal body fluid feedback mechanism is expected to act to regulate the long-term BP level in order to achieve sodium balance irrespective of the level of total peripheral resistance. By opposing pressure-induced distension of arterioles, autoregulation greatly reduces the change in ECFV, blood volume and CO that would otherwise be required to increase BP in order to achieve sodium balance (Guyton et al. 1988). Thus, autoregulation converts an initial high-co hypertension into a high-resistance hypertension, thus allowing the renal body fluid feedback mechanism to regulate the long-term BP level in a highly effective manner without the need for the large changes in fluid volumes. The relevance of Guyton s model to modern cardiovascular physiology Guyton was a pioneer of quantitative systems analysis, and his body of work clearly illustrated the power of such an approach when combined with physiological experimentation. It is important to stress that, while model building does involve insight and intuition, trial and error, the underlying components and parameters of Guyton s model were based on empirical data. Indeed, Guyton did not discover or invent the PNR or tissue blood flow autoregulation or the Frank Starling relationship; his contribution was in bringing these well-described phenomenatogetherinamannerthatrevealedremarkable insights about their role in cardiovascular regulation. Such insights led to countless cycles of experimentation, model refinement, further experimentation and so on. As Dr Guyton pointed out, the most helpful contribution of the model was when it failed to correctly predict an empirical outcome, since that clearly indicated a limitation in our understanding of the system. Guyton s model was initially developed in the sixties when computing power was poor and computer memory was scarce and expensive. Simplifications were mandatory to accommodate a large number of cardiovascular relationships. Shortcuts in solving equations were also required in order to run months of simulated experiments in a reasonable computing time. Over the years, the model evolved, the kidney acquired more details and atrial natriuretic peptide was included, but the core of the model and the basic concepts remained untouched. Although Guyton s model focuses on steady-state analysis and does not include the most recent cardiovascular discoveries, many of the principles contained in the original model have been incorporated by others into advanced models that elaborate on individual components or provide a more comprehensive representation of the entire circulation and its control by various influences, including the CNS (Karaaslan et al. 2005; Abram et al. 2007). Thus, Guyton s contributions continue to serve as a firm foundation on which contemporary cardiovascular modellers can build. References Abram SR, Hodnett BL, Summers RL, Coleman TG & Hester RL (2007). Quantitative Circulatory Physiology: an integrative mathematical model of human physiology for medical education. Adv Physiol Educ 31, Carroll RG, Lohmeier TE & Brown AJ (1984). Chronic angiotensin II infusion decreases renal norepinephrine overflow in conscious dogs. Hypertension 6, Coleman TG & Guyton AC (1969). Hypertension caused by salt loading in the dog. 3. Onset transients of cardiac output and other circulatory variables. Circ Res 25, CrowleySD,GurleySB,HerreraMJ,RuizP,GriffithsR,Kumar AP, Kim HS, Smithies O, Le TH & Coffman TM (2006). Angiotensin II causes hypertension and cardiac hypertrophy through its receptors in the kidney. Proc Natl Acad Sci USA 103, Guyton AC (1980). Circulatory Physiology III. Arterial Pressure and Hypertension. W. B. Saunders Company, Philadelphia, London, Toronto. Guyton AC (1990). Long-term arterial pressure control: an analysis from animal experiments and computer and graphic models. Am J Physiol Regul Integr Comp Physiol 259, R865 R877. Guyton AC, Abernathy B, Langston JB, Kaufmann BN & Fairchild HM (1959). Relative importance of venous and arterial resistances in controlling venous return and cardiac output. Am J Physiol 196, Guyton AC, Coleman TG & Granger HJ (1972). Circulation: overall regulation. Annu Rev Physiol 34, Guyton AC, Jones CE & Coleman TG (ed.) (1973). Circulatory Physiology: Cardiac Output and its Regulation, 2nd edn. W. B. Saunders Company, Philadelphia, London, Toronto. Guyton AC, Montani JP, Hall JE & Manning RD Jr (1988). Computer models for designing hypertension experiments and studying concepts. Am J Med Sci 295, Hall JE, Granger JP, Hester RL, Coleman TG, Smith MJ Jr & Cross RB (1984a). Mechanisms of escape from sodium retention during angiotensin II hypertension. Am J Physiol Renal Physiol 246, F627 F634. Hall JE, Granger JP, Hester RL & Montani JP (1986a). Mechanisms of sodium balance in hypertension: role of pressure natriuresis. J Hypertens Suppl 4, S57 S65. Hall JE, Granger JP, Smith MJ Jr & Premen AJ (1984b). Role of renal hemodynamics and arterial pressure in aldosterone escape. Hypertension 6, I183 I192. Hall JE, Guyton AC, Smith MJ Jr & Coleman TG (1980). Blood pressure and renal function during chronic changes in sodium intake: role of angiotensin. Am J Physiol Renal Physiol 239, F271 F280. Hall JE, Mizelle HL, Woods LL & Montani JP (1988). Pressure natriuresis and control of arterial pressure during chronic norepinephrine infusion. JHypertens6, Hall JE, Montani JP, Woods LL & Mizelle HL (1986b). Renal escape from vasopressin: role of pressure diuresis. Am J Physiol Renal Physiol 250, F907 F916.

8 388 J. W. Osborn and others Exp Physiol 94.4 pp Karaaslan F, Denizhan Y, Kayserilioglu A & Gulcur HO(2005). Long-term mathematical model involving renal sympathetic nerve activity, arterial pressure, and sodium excretion. Ann Biomed Eng 33, Lifton RP, Gharavi AG & Geller DS (2001). Molecular mechanisms of human hypertension. Cell 104, Mizelle HL, Montani JP, Hester RL, Didlake RH & Hall JE(1993). Role of pressure natriuresis in long-term control of renal electrolyte excretion. Hypertension 22, Montani JP, Adair TH, Summers RL, Coleman TG & Guyton AC (1989a). A simulation support system for solving large physiological models on microcomputers. Int J Biomed Comput 24, Montani JP, Adair TH, Summers RL, Coleman TG & Guyton AC (1989b). Physiological modeling and simulation methodology: from the mainframe to the microcomputer. JMissAcadSci34, Montani JP & Van Vliet BN (2004). General physiology and pathophysiology of the renin-angiotensin system. In Handbook of Experimental Pharmacology, vol. 163/1, Angiotensin, ed. Unger T & Scholkens BA, pp Springer Verlag, Berlin. Montani JP & Van Vliet BN (2007). Integrative renal regulation of sodium excretion. In Sodium in Health and Disease, ed. Burnier M, pp Informa Healthcare, New York. Mullins LJ, Bailey MA & Mullins JJ (2006). Hypertension, kidney, and transgenics: a fresh perspective. Physiol Rev 86, Reinhardt HW, Corea M, Boemke W, Pettker R, Rothermund L, Scholz A, Schwietzer G & Persson PB (1994). Resetting of 24-hsodiumandwaterbalanceduring4daysofservocontrolled reduction of renal perfusion pressure. Am J Physiol Heart Circ Physiol 266, H650 H657. Rettig R (1993). Does the kidney play a role in the aetiology of primary hypertension? Evidence from renal transplantation studies in rats and humans. JHumHypertens7, Schrier RW (1990). Body fluid volume regulation in health and disease: a unifying hypothesis. AnnInternMed113, Experimental Physiology Exchange of Views Commentary on Understanding the contribution of Guyton s large circulatory model to long-term control of arterial pressure John W. Osborn 1,ViktoriaA.Averina 2 and Gregory D. Fink 3 Departments of 1 Integrative Biology and Physiology and 2 Mathematics, University of Minnesota, MN, USA 3 Department of Pharmacology and Toxicology, Michigan State University, MI, USA The goal of this Exchange of Views was to highlight areas of agreement and disagreement concerning the validity of current mathematical models for long-term control of arterial pressure. This Exchange of Views focused on the Guyton Coleman (G C) model, since it is arguably the most well-known and accepted model in the field (Guyton et al. 1974). The views of Montani & Van Vliet (2009) provide an excellent synopsis of the history of the G C model and its key features. We agree with many of the ideas expressed by Montani & Van Vliet (2009). First, the kidney plays a critical role in the long-term control of arterial pressure. Second, the G C model was a major accomplishment and has had a long-lasting impact on the field. Third, although many details have been added since the model was introduced, the renal function curve and whole body autoregulation (WBA) remain as the core features of the model. Fourth, the implications of the model are often misunderstood, including the idea that whole body autoregulation causes hypertension. Finally, we agree that vascular capacitance, in combination with total blood volume, is important in the regulation of systemic haemodynamics. However, we respectfully disagree with several views expressed by Montani & Van Vliet (2009). First and foremost, we disagree that the G C model accurately represents all forms of hypertension. That is one of the major points of our paper. Second, although the G C model does indeed acknowledge that the sympathetic nervous system (SNS) can impact long-term control of arterial pressure, it dictates that this can only occur by controlling renal function. This is clearly not true, since renal denervation does not attenuate or abolish all forms of neurogenic hypertension (King et al. 2007). We propose that the SNS does indeed regulate the long-term level

9 Exp Physiol 94.4 pp Computational models of arterial pressure control 389 of arterial pressure independent of its actions on the kidney, and this needs to be incorporated into new models. Third, although we agree that WBA is not the cause of hypertension, we do not think that it is required to explain the haemodynamic profile of all forms of hypertension, since several studies are inconsistent with this concept (Sullivan & Ratts, 1983; Krieger et al. 1989, 1990; Greene et al. 1990; Fine et al. 2003). Finally, as previously reviewed (Osborn, 2005) and contrary to the opinion expressed by Montani & Van Vliet (2009), in our opinion there is relatively very little direct experimental support for the concept that the pressure natriuresis mechanism operates as an infinite gain pressure control system. We appreciate the opportunity to debate this important issue openly with our colleagues. Although we acknowledge the importance of the G C model in advancing our understanding of long-term control of arterial pressure and the pathogenesis of hypertension, we feel that it is not entirely consistent with recent advances in cardiovascular and neuroscience research, and new models are needed. Hopefully this exchange of views will spark new efforts in this important endeavour. References Fine D, Ariza P & Osborn JW (2003). Does whole body autoregulation mediate the hemodynamic responses to increased dietary salt in rats with clamped angiotensin II? Am J Physiol Heart Circ Physiol 285, H2760 H2678. Greene AS, Yu ZY, Roman RJ & Cowley AW Jr (1990). Role of blood volume expansion in Dahl rat model of hypertension. Am J Physiol Heart Circ Physiol 258, H508 H514. Guyton AC, Coleman TG, Cowley AW Jr, Manning RD Jr, Norman RA Jr & Ferguson JD (1974). A systems analysis approach to understanding long-range arterial blood pressure control and hypertension. Circ Res 35, King AJ, Osborn JW & Fink GD (2007). Splanchnic circulation is a critical neural target in angiotensin II salt hypertension in rats. Hypertension 50, Krieger JE, Liard J-F & Cowley AW Jr (1990). Hemodynamics, fluid volume, and hormonal responses to chronic high-salt intake in dogs. Am J Physiol Heart Circ Physiol 259, H1629 H1636. Krieger JE, Roman RJ & Cowley AW Jr (1989). Hemodynamics and blood volume in angiotensin II salt-dependent hypertension in dogs. Am J Physiol Heart Circ Physiol 257, H1402 H1412. Montani J-P & Van Vliet BN (2009). Understanding the contribution of Guyton s large circulatory model to long-term control of arterial pressure. Exp Physiol 94, Osborn J (2005). Hypothesis: set points and long-term control of arterial pressure. A theoretical argument for a long-term arterial pressure control system in the brain rather than the kidney. Clin Exp Pharmacol Physiol 32, Sullivan JM & Ratts TE (1983). Hemodynamic mechanisms of adaptation to chronic high sodium intake in humans. Hypertension 5, Experimental Physiology Exchange of Views Current computational models do not reveal the importance of the nervous system in long-term control of arterial pressure John W. Osborn 1,ViktoriaA.Averina 2 and Gregory D. Fink 3 Departments of 1 Integrative Biology and Physiology and 2 Mathematics, University of Minnesota, MN, USA 3 Department of Pharmacology and Toxicology, Michigan State University, MI, USA Arterial pressure is regulated over long periods of time by neural, hormonal and local control mechanisms, which ultimately determine the total blood volume and how it is distributed between the various vascular compartments of the circulation. A full understanding of the complex interplay of these mechanisms can be greatly facilitated by the use of mathematical models. In 1967, Guyton and Coleman published a model for long-term control of arterial pressure that focused on renal control of body sodium and water and thus total blood volume. The central point of their model is that the long-term level of arterial pressure is determined exclusively by the renal function curve, which relates arterial pressure to urinary excretion of salt

10 390 J. W. Osborn and others Exp Physiol 94.4 pp and water. The contribution of the sympathetic nervous system to setting the long-term level of arterial pressure in the model is limited. In light of the overwhelming evidence for a major role of the sympathetic nervous system in long-term control of arterial pressure and the pathogenesis of hypertension, new mathematical models for long-term control of arterial pressure may be necessary. Despite the prominence and general acceptance of the Guyton Coleman model in the field of hypertension research, we argue here that it overestimates the importance of renal control of body fluids and total blood volume in blood pressure regulation. Furthermore, we suggest that it is possible to construct an alternative model in which sympathetic nervous system activity plays an important role in long-term control of arterial pressure independent of its effects on total blood volume. (Received 10 September 2008; accepted after revision 22 January 2009; first published online 26 February 2009) Corresponding author J. W. Osborn: University of Minnesota, Department of Integrative Biology and Physiology, Room Jackson Hall, 321 Church Street, Minneapolis, MN 55455, USA. osbor003@umn.edu The central argument Mean systemic arterial pressure is the product of the rate at which blood is ejected from the left ventricle (cardiac output) into the arterial compartment and arteriolar resistance, which determines the rate at which blood moves from the arterial to the venous compartment. Regulation of arterial pressure involves a complex interaction of renal control mechanisms, which determine total blood volume, and mechanisms regulating the heart and vasculature to distribute that volume between the arterial and venous compartments (since the heart and lungs have relatively little blood storage capacity). On the surface, it seems logical to link the regulation of blood pressure to regulation of blood volume. However, since arterial pressure is also expressed as the quotient of stressed arterial blood volume and arterial compliance, it is more accurate to link the regulation of arterial pressure to arterial blood volume. In that context, it is clear that total blood volume is not the major determinant of arterial pressure but rather of how that volume is distributed between the arterial and venous compartments. The central argument of this article is that renal control of total blood volume is not the only factor that affects the long-term level of arterial pressure and that a previous mathematical model built on this foundation is therefore incomplete (Guyton & Coleman, 1967). As an alternative theoretical construct, we propose that the autonomic nervous system dynamically monitors the complex status of the cardiovascular system and exerts exquisite control over the distribution of blood volume in a variety of physiological conditions. We hypothesize that, in combination with powerful hormonal controllers of sodium and water balance (Bie, 2009), the autonomic nervous system is uniquely positioned as an important long-term controller of arterial pressure and that new mathematical models incorporating these mechanisms need to be developed. The Guyton Coleman model centres on renal control of blood volume and minimizes the role of the nervous system in long-term control of arterial pressure Although many mathematical models for short-term regulation of arterial pressure exist (Kappel & Peer, 1993; Ursino et al. 1994; Ursino & Magosso, 2003; Arts et al. 2005; Broskey & Sharp, 2007), there are relatively few for longterm control. The most well-known and accepted longterm model was first published by Guyton & Coleman (1967). The core concept around which the G C model is structured is shown in Fig. 1. Boxes with bold lines highlight key components of the model that will be discussed. The foundation of the G C model is the renal function curve or pressure natriuresis curve, which ultimately ties mean arterial pressure to total blood volume, mandating only one possible steady-state combination of the two variables. Simply stated, the steady-state relationship between the perfusion pressure of the kidney, which is essentially mean arterial pressure (MAP), and the excretion of sodium and water, establish the equilibrium point around which MAP is regulated. The balance between input of sodium and water and renal excretion of sodium and water determines extracellular fluid volume and therefore blood volume. Non-renal fluid losses are considered to be minor and fairly constant. The fundamental idea is that whenever arterial pressure increases above the equilibrium point, the kidneys will excretemoresodiumandwater,whichwillthendecrease blood volume and cardiac output and restore arterial pressure to its normal level. The opposite occurs when arterial pressure falls. The renal function curve is said to have infinite gain in that, even for minute changes in arterial pressure, the kidneys will always regulate pressure back to normal. Indeed, the G C model predicts that this mechanism dominates all other pressure-controlling systems over time; The infinite gain principle dictates that

11 Exp Physiol 94.4 pp Computational models of arterial pressure control 391 the long-term level to which arterial pressure is regulated can never change except by altering one of the above two factors, changing either the level of net fluid intake or changing the renal function curve (Guyton et al. 1988). A limitation of the G C model is that control of arterial pressure is almost entirely dependent on regulating one variable, namely blood volume. As we have previously discussed, from a teleological perspective, it seems unlikely that regulation of arterial pressure, which is vital to perfusion of the brain and heart, would be dependent on control of a single variable such as blood volume (Osborn, 2005). Moreover, the experimental support for a direct relationship between blood volume and the longterm level of arterial pressure in humans is extremely poor (Conway, 1984). It is important to note in Fig. 1 that the G C model did indicate that the relationship between blood volume and venous return to the heart is also dependent on vascular capacity which, to a large extent, is a function of venous capacitance, since veins are many times more compliant that arteries (Guyton et al. 1973; Levy, 1979; Rothe, 1983). This means that, technically, the model did not assume that blood volume alone was the driving force for venous return and cardiac output. However, since the primary controller of vascular capacity is thought to be the sympathetic nervous system and the G C model minimized the role of the sympathetic nervous system as an important longterm controller of arterial pressure regulation of vascular capacitance was not extensively considered (Guyton et al. 1988). As a result, the G C model focused on regulation of blood volume as the sole long-term determinant of arterial pressure. Although the G C model acknowledges that the nervous system controls arteriolar resistance and venous capacitance, it also dictates that the only way the nervous system can increase arterial pressure in the long term is by an increase in sympathetic nerve activity to the renal vascular bed and a rightward shift of the renal function curve. In other words, sympathetic activity to non-renal vascular beds (e.g. splanchnic and skeletal muscle) is insignificant in long-term control of arterial pressure, since it does not affect the renal function curve and thus total blood volume. Another reason why the role of the sympathetic nervous system is underappreciated in the G C model is that the primary controller of sympathetic activity is represented as a simple arterial baroreceptor reflex arc. The issue of whether or not the arterial baroreceptor reflex is important in long-term control of arterial pressure is still debated 40 years after the G C model was first published (Barrett & Malpas, 2005; Brooks & Sved, 2005; Lohmeier et al. 2005; Osborn et al. 2005; Thrasher, 2005). Guyton presented two empirical arguments for dismissing the arterial baroreceptor reflex as a longterm controller of arterial pressure (Guyton, 1980). First, arterial baroreceptors adapt and therefore cannot provide an accurate long-term negative feedback signal to the brain regarding arterial pressure. Second, surgical removal of the afferent projections of arterial baroreceptors (sinoaortic denervation; SAD), which removes tonic inhibitory input to the sympathetic premotor neurons in the brainstem, results in a transient increase in arterial pressure but does not lead to chronic hypertension (Cowley et al. 1973). This latter point was used to support the argument that the pressure natriuresis relationship dominated over sympathetic control of arterial pressure over long periods of time in SAD animals (Cowley et al. 1980; Guyton, 1988). However, it is now clear that the Figure 1. Schematic diagram of the core concept of the Guyton Coleman model for long-term control of arterial pressure Adapted from figure 6 4 of Guyton (1980). See text for details.

12 392 J. W. Osborn and others Exp Physiol 94.4 pp return of arterial pressure to normal levels after SAD is not due to the pressure natriuresis relationship but rather to a normalization of sympathetic nerve activity (Osborn & England, 1990; Osborn et al. 2005; Malpas et al. 2006). The mechanisms responsible for regulating sympathetic activity in SAD animals are unknown. One possibility is that that cardiopulmonary receptors compensate for the loss of arterial baroreceptor input, but the observation that arterial pressure is normal in rats with lesions of the nucleus tractus solitarius (Schreihofer & Sved, 1992), the site of synaptic input for both arterial and cardiopulmonary afferents, argues against this idea. Overall, these studies are consistent with the idea that the nervous system is important in long-term control of arterial pressure but that non-arterial baroreflex mechanisms dominate over the arterial baroreceptor reflex in long-term control of sympathetic activity and arterial pressure (Osborn et al. 2005). However, these concepts have not been incorporated into any current mathematical model for long-term control of arterial pressure. This subject is discussed in more detail below. The G C model predicts that a single haemodynamic profile in all forms of hypertension is triggered and maintained by blood volume expansion alone The G C model predicts that all forms of experimental and human essential hypertension are due to primary renal dysfunction, represented by a primary shift of the renal function curve to a higher operating pressure. This results Figure 2. Schematic representation of the combined effects of shifting the renal function curve and whole body autoregulation as proposed by Guyton (1989) Numbers 1-5 indicate the temporal sequence of events whereby a shift of the renal function curve (1) results in expansion of BV and increased CO (2). This is followed by whole body autoregulation (3) resulting in vasoconstriction (4) which results in increased TRR and normalization of CO (5). Abbreviations: MAP; mean arterial pressure; BV, blood volume; CO, cardiac output; TPR, total peripheral resistance; and UO, urine output. in blood volume expansion, which sets into motion the whole body autoregulation haemodynamic profile, which is characterized by an initial increase in cardiac output and a subsequent increase in total peripheral resistance and a return of cardiac output to near normal levels (Guyton, 1991). As shown in Figs 1 and 2, increased blood volume and cardiac output result in hyperperfusion of tissues, which triggers an autoregulatory vasoconstrictor response of systemic arterioles. The model predicts that this whole body autoregulation response is what mediates the increase in peripheral resistance in the later phases of hypertension. It is important to note that the sustained increase in resistance is dependent on sustained blood volume expansion, albeit at levels within 5% of control (Guyton, 1992). In other words, increased blood volume alone is the driving factor for initiation and maintenance of hypertension according to this theory. The model dictates that a shift of the renal curve alone determines the steadystate value of the arterial pressure, whereas whole body autoregulation establishes the balance between cardiac output and peripheral resistance (Guyton, 1991). The G C model is restrained by its dependence on the renal function curve control of blood volume and a single haemodynamic profile to explain all forms of hypertension. A recent study conducted in conscious, freely moving dogs has shown that pressure natriuresis only occurs when arterial pressure falls by 20% or increases by 10% from control levels (Seeliger et al. 2005). These investigators concluded that pressure natriuresis can be an important regulator of sodium and water balance, but only under pathophysiological conditions. More to the point, studies in normal rats (Greene et al. 1990; Krieger et al. 1990), dogs (Krieger et al. 1990) and humans (Sullivan & Ratts, 1983) have reported chronic salt-induced increases in blood volume and cardiac output but no change in arterial pressure, since peripheral vascular resistance was decreased. These studies are inconsistent with the concepts of a chronic renal function curve or blood volume as the exclusive long-term determinant of arterial pressure. Finally, although blood volume expansion and whole body autoregulation may explain some forms of hypertension, there are numerous examples where hypertension occurs independent of volume expansion and, in most cases, is associated with decreased blood volume (Conway, 1984). A mathematical model capable of simulating the several haemodynamic profiles that are known to occur in hypertension (Conway, 1984), which are not necessarily triggered and/or maintained by changes in total blood volume, is clearly needed. The autonomic nervous system is uniquely positioned as an important long-term controller of arterial pressure In the 40 years since the G C model was introduced, there has been an avalanche of new knowledge related