A mathematical model of salt‐sensitive hypertension: the...

J Physiol 593.14 (2015) pp 3065–3076 3065

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A mathematical model of salt-sensitive hypertension:the neurogenic hypothesis

Viktoria A. Averina1, Hans G. Othmer1, Gregory D. Fink2 and John W. Osborn3

1Department of Mathematics, University of Minnesota, Minneapolis, MN, USA2Department of Pharmacology and Toxicology, Michigan State University, East Lansing, MI, USA3Integrative Biology and Physiology, University of Minnesota, Minneapolis, MN, USA

Abstract Salt sensitivity of arterial pressure (salt-sensitive hypertension) is a serious globalhealth issue. The causes of salt-sensitive hypertension are extremely complex and mathematicalmodels can elucidate potential mechanisms that are experimentally inaccessible. Until recently,the only mathematical model for long-term control of arterial pressure was the model of Guytonand Coleman; referred to as the G-C model. The core of this model is the assumption thatsodium excretion is driven by renal perfusion pressure, the so-called ‘renal function curve’. Thus,the G-C model dictates that all forms of hypertension are due to a primary shift of the renalfunction curve to a higher operating pressure. However, several recent experimental studies in amodel of hypertension produced by the combination of a high salt intake and administration ofangiotensin II, the AngII–salt model, are inconsistent with the G-C model. We developed a newmathematical model that does not limit the cause of salt-sensitive hypertension solely to primaryrenal dysfunction. The model is the first known mathematical counterexample to the assumptionthat all salt-sensitive forms of hypertension require a primary shift of renal function: we showthat in at least one salt-sensitive form of hypertension the requirement is not necessary. We willrefer to this computational model as the ‘neurogenic model’. In this Symposium Review wediscuss how, despite fundamental differences between the G-C model and the neurogenic modelregarding mechanisms regulating sodium excretion and vascular resistance, they generate similarhaemodynamic profiles of AngII–salt hypertension. In addition, the steady-state relationshipsbetween arterial pressure and sodium excretion, a correlation that is often erroneously presentedas the ‘renal function curve’, are also similar in both models. Our findings suggest that salt-sensitivehypertension is not due solely to renal dysfunction, as predicted by the G-C model, but may alsoresult from neurogenic dysfunction.

Viktoria Averina received an MS in mathematics from the University of Alaska, and is currently a PhDcandidate in Applied Mathematics at the University of Minnesota. Her thesis research is focused onapplying principles of mathematical modelling and sensitivity analysis to understanding the interactionsbetween physiological systems in long-term blood pressure control. She is also a Principal BiomedicalResearch Scientist at Boston Scientific developing sensor algorithms for the detection of worsening heartfailure. John Osborn received his PhD in physiology from the Medical College of Wisconsin in 1986 wherehe studied hormonal modulation of central sympathetic pathways with Dr Allen Cowley, Jr. He pursuedpostdoctoral studies with Dr Lawrence Schramm in biomedical engineering at Johns Hopkins School ofMedicine where he studied spinal level control of the sympathetic nervous system. He joined the facultyat the University of Minnesota in 1988 where he is currently Professor and the Marvin and HadassahBacaner Endowed Chair in Cardiovascular Physiology and Director of Graduate Studies. His career has focused primarily on neural mechanisms forlong-term control of arterial pressure.

This review was presented at the symposium Insights gleaned from pharmaco-genetic dissection and modeling of cardio-respiratory neural networks,which took place at Experimental Biology 2014, San Diego, CA, USA on 29 April 2014.

C© 2014 The Authors. The Journal of Physiology C© 2014 The Physiological Society DOI: 10.1113/jphysiol.2014.278317

3066 V. A. Averina and others J Physiol 593.14

(Received 28 May 2014; accepted after revision 5 September 2014; first published online 12 September 2014)Corresponding author: J. W. Osborn, Department of Integrative Biology and Physiology, 2231 6th Street SE, 3–138Cancer Cardiovascular Research Building, Minneapolis, MN 55455, USA. Email: [email protected]

Abbreviations AngII, angiotensin II; AP, arterial pressure; BV, blood volume; BW, body weight; CO, cardiac output;ECFV, extracellular fluid volume; G-C, Guyton–Coleman (model); MCFP, mean circulatory filling pressure; NaI, sodiumintake; NTS, nucleus tractussolitarius; Ras, arterial splanchnic resistance; Rar, arterial extra-splanchnic resistance; RVLM,rostral ventrolateral medulla; SNA, sympathetic nerve activity; TPR, total peripheral resistance.

Overview: why do we need a newmathematical model of salt-sensitivehypertension?

Salt sensitivity of arterial pressure is a global healthproblem. It is estimated that 25% of the normotensivepopulation is salt-sensitive and 50–75% of hyper-tensive patients exhibit an exaggerated arterial pressureresponse to increased salt intake (Weinberger, 1996).This is clinically significant since it is hypothesized thatsalt-sensitivity of arterial pressure is a stronger predictorof death and disability due to cardiovascular diseasethan arterial pressure itself (Weinberger, 1996). There areseveral definitions of salt sensitivity (Sanada et al. 2011)and here we define it as a steady-state increase in meanarterial pressure of more than 10 mmHg with a sustained5-fold increase in sodium intake.

Why do we need mathematical models of hypertension?Computational models are useful in at least two importantways. First, since the causes of salt-sensitive hyper-tension are extremely complex, mathematical models canelucidate potential mechanisms that are experimentallyinaccessible. Second, they generate novel hypothesesthat are not immediately apparent from experimentalstudies. Moreover, when two models predict experimentalobservations equally well but under different hypotheses,it may provide guidance to the experimental community indesigning experiments to distinguish between alternativeparadigms.

Until recently, the only mathematical model forlong-term control of arterial pressure was the model firstintroduced by Guyton and Coleman in 1967 (Guyton& Coleman, 1967). The core of this model is therelationship between renal perfusion pressure and sodiumexcretion, the so-called ‘renal function curve’, which actsas the primary long-term controller of arterial pressure(Guyton et al. 1972a). This model has been accepted bymany investigators, and is presented in most physiologytextbooks as the only explanation for the pathogenesis ofhypertension. In this review we will we refer to it as theG-C model.

If the G-C model is generally accepted, then whydo we need a new mathematical model? At the timethe G-C model was developed, very little was under-stood about neural control of the circulation beyondthe arterial baroreceptor reflex. However, a large number

of studies over the last five decades suggest thatthe sympathetic nervous system plays a much moreimportant role in salt-sensitive hypertension than pre-viously recognized (Grassi et al. 2008; Esler, 2010;Malpas, 2010). In particular, several recent reports suggestthat a well-established animal model of salt-sensitivehypertension, the AngII–salt model, is sympatheticallydriven independently of neurally mediated changes inkidney function. As such, these experimental findings areincompatible with the G-C model. We sought to determinewhether we could construct a predictive mathematicalmodel that did not limit the cause of salt-sensitive hyper-tension solely to primary renal dysfunction (Averina et al.2012). We refer to this computational model as the neuro-genic model.

In this Symposium Review we discuss how, despitefundamental differences between the G-C model andthe neurogenic model regarding mechanisms regulatingsodium excretion and vascular resistance, they generatesimilar haemodynamic profiles of AngII–salt hyper-tension.

In addition, the steady-state relationships betweenarterial pressure and sodium excretion, a correlation thatis often erroneously presented as the ‘renal function curve’,are also similar in both models. Our findings suggest thatsalt-sensitive hypertension may not be due solely to renaldysfunction, as predicted by the G-C model, but may alsoresult from neurogenic dysfunction. We will conclude bydiscussing new hypotheses generated by the neurogenicmodel and our plans for model expansion in the future.

The AngII–salt experimental modelof salt-sensitive hypertension

One of the most commonly studied animal models ofsalt-sensitive hypertension is the AngII-induced model.The mechanism(s) whereby chronic administration ofAngII causes hypertension has been debated for decadessince this hormone has vascular, renal and neural actionsthat can theoretically cause hypertension. However, onething that is generally agreed upon is that the magnitudeof AngII-induced hypertension is directly related to theprevailing level of dietary salt intake. A typical example ofthis is illustrated in Fig. 1A. In this study, the mean arterialpressure (MAP) response to chronic administration of

C© 2014 The Authors. The Journal of Physiology C© 2014 The Physiological Society

J Physiol 593.14 A mathematical model of neurogenic salt-sensitive hypertension 3067

AngII to rats consuming a low salt (0.1% NaCl) dietwas minimal, whereas the same dose of AngII causedprogressively greater increases in rats consuming normal(0.4% NaCl) and high (2.0% NaCl) diets.

The conventional explanation for this finding is thatAngII stimulates sodium and water reabsorption by thekidney leading to increased blood volume; and arterial

pressure rises as a direct consequence of the increasedvolume. Based on this explanation, the greater increasein arterial pressure in animals consuming a high salt dietis due to a larger degree of sodium retention leading togreater blood volume expansion. This is classically referredto as the ‘volume loading’ hypothesis of hypertension aspredicted by the G-C model.

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Figure 1.A, the response of mean arterial pressure (MAP) to angiotensin II (AngII) administration (150 ng kg–1 min–1) inSprague–Dawley rats consuming low (0.1%), normal (0.4%) or high (2.0%) salt diets. Values are 24 h averagesmeasured by radiotelemetry. Figure from Osborn et al. (2011). B, responses of arterial pressure (AP; mmHg),cardiac output (CO; ml min–1 kg–1), body weight (BW; g), total peripheral resistance (TPR; mmHg kg–1 min–1)to increased salt intake (NaI; mequiv) in conscious dogs with ‘clamped plasma AngII’. Figure from Averina et al.(2012). C, simplified representation of the G-C model explanation of the relationship between arterial pressure,sodium excretion and sodium intake in AngII–salt hypertension. The two determinants of the long-term level ofarterial pressure are: (1) the renal function curve and (2) sodium intake. The combination of a rightward shift ofthe renal function curve by AngII and increased sodium intake summates to increase extracellular fluid volume(ECFV), blood volume (BV), mean circulatory filling pressure (MCFP) and therefore cardiac output (CO). Cardiacoutput directly influences arterial pressure but also gradually increases total peripheral resistance as a result ofautoregulation.



The haemodynamic profile of AngII–salthypertension

The role of blood volume expansion and its impacton haemodynamic function in AngII–salt hypertensionhas been studied in chronically instrumented consciousdogs (Krieger et al. 1989, 1990). In this elegantstudy, haemodynamic variables (arterial pressure andcardiac output) and total body weight were measuredcontinuously in dogs in which plasma AngII was ‘clamped’at physiological levels by intravenous infusion. Total bodyweight was used as a surrogate for total body water totrack dynamic changes in body fluid volume over time.Following a control period, daily sodium intake wasincreased and haemodynamic and body weight changeswere measured.

As shown in Fig. 1B, the salt-induced increase in arterialpressure was correlated with an early increase in total bodyweight (i.e. total body water) and cardiac output. This wasfollowed by a delayed rise in total peripheral resistance(TPR) and a subsequent return of cardiac output towardscontrol levels. The steady-state profile of this classic‘volume loading’ haemodynamic profile is similar to whathas been reported in humans with established essentialhypertension; that is, increased arterial pressure and totalperipheral resistance with normal or near normal cardiacoutput.

Mechanisms of AngII–salt hypertension: theG-C model

The core concept of the G-C model is shown in Fig. 1C.As stated in the excellent monograph by Guyton, thismodel dictates that there are ‘two determinants’ of thelong-term level of arterial pressure; (1) the chronic renalfunction curve and (2) net sodium (and water) intake(Guyton, 1980). In this model, the renal function curveis the primary controller of renal sodium excretion, andtherefore plays a major role in the maintenance of sodiumbalance. The pressure natriuresis relationship is believedto be an intrinsic function of the kidney although it ismodulated by external hormonal and neural inputs. Moreimportantly, “ . . . the long-term level of arterial pressurecannot be changed in any way other than by changingone or both of these two determinants”(Guyton, 1980).In other words, the G-C model dictates that at any givenlevel of salt (and water) intake all forms of hypertensionare the result of a primary shift of the renal function curveto a higher operating pressure.

Figure 1C illustrates the G-C model explanation ofthe haemodynamic profile of AngII–salt hypertension.AngII causes a primary shift of the renal functioncurve to the right (i.e. higher operating pressure) as aresult of the actions of AngII on renal function. This islabelled in Fig. 1C as ‘1’ according to the G-C model.

The immediate consequence of this is a reduction ofurinary sodium excretion since arterial pressure at thispoint is still at a normal level (i.e. below the new setpoint of the renal function curve). Salt intake is alsoincreased in the AngII–salt protocol, which is labelledas ‘2’. The combination of a shift of the renal functioncurve and increased salt intake increases extracellularfluid volume (ECFV) and therefore blood volume. Bloodvolume expansion results in subsequent increases inmean circulatory filling pressure (MCFP) and cardiacoutput (CO), which is initially responsible for increasedarterial pressure. Finally, another key feature of the G-Cmodel is that the increase in total peripheral resistanceis mediated by ‘whole body autoregulation’, secondary tooverperfusion of tissues from the elevated cardiac output.As with the renal function curve, this is an intrinsicproperty of the vasculature and, as such, is not dependenton neural or hormonal controllers.

In summary, the G-C model predicts that thehaemodynamic profile of AngII–salt hypertension is dueto a primary shift of the renal function curve, initiatinga sequence of events driven by increased blood volume,which lead to the temporal patterns of cardiac output andtotal peripheral resistance shown in Fig. 1B. It is importantto keep in mind that the G-C model dictates that this is theonly cause for hypertension and that the haemodynamicprofile is independent of neural control of cardiovascularfunction.

Recent studies of AngII–salt hypertensionare inconsistent with the G-C model

In several recent studies we have reported that, when AngIIis administered to rats on a high salt diet, the resultinghypertension is caused, in part, by delayed activation of thesympathetic nervous system (King & Fink, 2006; Osbornet al. 2007, 2011; Osborn & Fink, 2010; Toney et al. 2010).Theoretically these findings could be consistent with theG-C model since neurogenic hypertension may occur asa result of increased sympathetic nerve activity (SNA) tothe kidney which would shift the renal function curve toa higher operating pressure as described above (Guyton,1980).

However, long-term continuous direct recording ofrenal SNA in conscious rats revealed that it is trans-iently decreased in AngII–salt rats, rather than increased(Yoshimoto et al. 2010). Furthermore, renal denervationdid not affect the development of AngII–salt hyper-tension (King et al. 2007), and hypertension was notassociated with chronically increased blood volume (King& Fink, 2006). Furthermore, splanchnic SNA seemedcritical to AngII–salt hypertension since denervation ofthe splanchnic vascular bed attenuated the developmentof hypertension (King & Fink, 2006; King et al. 2007),



probably by reducing sympathetically mediated changesin both splanchnic vascular resistance and capacitance(Kuroki et al. 2012).

We have also found that interventions that target thebrain specifically attenuate or abolish the neurogenicphase of AngII–salt hypertension. Lesion of forebrain sitesresponsive to AngII and osmolality, the subfornical organand the organum vasculosum of the lamina terminalis,attenuate hypertension in AngII–salt rats (Osborn et al.2012; Collister et al. 2013). More recently, we reportedthat chronic intracerebroventricular administration of thesodium channel blocker benzamil completely reversedthe neurogenic phase of AngII–salt hypertension (Osbornet al. 2014).

Taken together, these studies suggest that AngII–salthypertension in the rat is neurogenically driven byactivation of sodium-dependent sympathoexcitatorypathways in the brain that do not, as predicted by theG-C model, target the kidneys but rather the splanchnicvascular bed. Therefore, this form of hypertension cannotbe due to a primary shift of the renal function curveand subsequent blood volume expansion. This led us todevelop a mathematical model that would help explainthese new findings.

A new mathematical model of salt-sensitivehypertension: the neurogenic hypothesis

The goal of our mathematical modelling was to show thatone can reproduce the same physiological observationsunder quite different modelling assumptions. In such acase one could conclude that either set of assumptionsmay hold true in the actual circulation. Thus, wecreated a model that can simulate the haemodynamicprofile of AngII–salt hypertension based either on theassumptions of the G-C model or on assumptions derivedfrom more recent experimental findings that support theemerging neurogenic hypothesis. In particular, we focusedon regulation of two key variables that affect arterialpressure: sodium excretion and total peripheral resistance.

Key question 1: is pressure natriuresis the primarydeterminant of the renal response to increased saltintake?

It is a well-established empirical fact that urinary sodiumexcretion is tightly regulated to match sodium intakeunder steady-state conditions. But critical gaps remainin our understanding of the mechanisms responsible forthis relationship(Bie, 2009). Although renal perfusionpressure is one important factor influencing renal sodiumexcretion, a necessary link between mean arterial pressureand sodium excretion has been questioned (Seeliger et al.2004; Bie, 2009). In particular, at steady state, healthy

kidneys are capable of excreting a wide range of sodiumintakes with no measureable change in mean arterialpressure. Indeed, a recent study of circadian rhythmsof cardiovascular and renal function in conscious dogsshowed that urinary sodium excretion was increasedduring time intervals when arterial pressure was thelowest (Mochel et al. 2014).These findings raise thequestion: could the haemodynamic changes that occurin salt-sensitive hypertension be predicted by a model ofcirculatory regulation that did not include the pressurenatriuresis mechanism?

In the mathematical model we describe here, sodiumexcretion is made to exactly match changes in sodiumintake in one of two distinct ways: either in response tochanges in arterial pressure (i.e. pressure natriuresis), orby undefined mechanisms independent of arterial pressure(i.e. pressure-independent natriuresis). Note that the latterapproach for current purposes merely represents a lumpedfunction of all sodium excretory mechanisms other thanarterial pressure.The choice of the former represents thepressure natriuresis of the G-C model and the choice ofthe latter represents the neurogenic model. The overallconcept is that, in the G-C model, the renal functioncurve is operating in series with other pressure regulatorsso the latter work by affecting the pressure natriuresismechanism. In contrast, in the neurogenic model, anumber of potential regulators operate in parallel toregulate sodium excretion.

Key question 2: what mediates increased totalperipheral resistance in AngII–salt hypertension?

Acceptance of the G-C model as a valid mathematicaldescription of the circulation is based, in part, on thefact that it accurately predicts haemodynamic responses tonumerous physiological perturbations, including changesin salt intake and/or AngII administration (Guyton, 1980).These haemodynamic responses in the G-C model aredriven mainly by autoregulatory adjustments to vasculartone (i.e. total peripheral resistance) with relatively littlecontribution by neural controllers.

Our studies of AngII–salt hypertension in the ratdemonstrated that although renal SNA was trans-iently decreased, lumbar (mainly muscle) SNA wasmaintained (Yoshimoto et al. 2010). Furthermore,splanchnic SNA seemed critical to AngII–salt hyper-tension since denervation of the splanchnic vascularbed attenuated hypertension development (King & Fink,2006; King et al. 2007). This finding is consistent withour observations that splanchnic vascular resistance isincreased and total vascular capacitance is decreased inAngII–salt rats, and that both of these responses arereversed by acute ganglionic blockade (King & Fink, 2006;Kuroki et al. 2012). Therefore, splanchnic denervation



probably affects hypertension development by reducingsympathetically mediated changes in both splanchnicvascular resistance and capacitance (Osborn et al. 2011).Finally, we have reported that in rats both AngII andhigh salt intake are required to induce elevated SNA,while either factor alone does not trigger a sympatheticresponse (King et al. 2008). Since we are attempting tomodel AngII–salt hypertension, here we assume that thelong-term level of SNA is driven by a combination ofincreased sodium intake and circulating AngII.

In our mathematical model we describe arterialresistance control as driven by either the autoregulatoryresponse to overperfusion (i.e. autoregulation) or thesympathetic nervous system. The choice of the formerrepresents the whole-body autoregulation hypothesis ofthe G-C model and the choice of the latter represents theneural control of the neurogenic model.

Basic features of the model

The details of the mathematical model have been recentlydescribed elsewhere (Averina et al. 2012). Figure 2summarizes our approach. In simple terms, the aim ofour modelling exercise was to demonstrate that one canreproduce both the hypertensive haemodynamic profile

and pressure natriuresis relationship under very differentassumptions about the primary mechanism regulatingsodium excretion.

The circulatory subsystem used in both the G-Cmodel (Fig. 2A) and the neurogenic model (Fig. 2B)is the same. It is based on the lumped-parameterWindkessel approach widely used in cardiovascularmodelling. Lumped parameter models are used on bothshort time scales, such as the response to haemorrhage,baroreceptor stimulation and postural change (Ursinoet al. 1994; Ursino, 1998; Olufsen et al. 2005), andlong-term scales such as the G-C model (Guyton et al.1972b). In our model of the circulatory system, total bloodvolume is distributed among four capacitive vascularcompartments: the arteries, the veins of the splanchnicorgans, the veins of extra-splanchnic organs, and thelarge veins. The two compartments representing thesystemic vascular beds are connected in parallel. Oneof these two compartments is assumed to have a highercompliance than the other. Since splanchnic organs havelarger vascular compliance than other regions (Rothe,1983), we call the former compartment ‘splanchnic’ andthe latter ‘extra-splanchnic’. The pulmonary circulationis omitted and the heart is represented by a continuousnon-pulsatile pump which moves blood from the venous

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to the arterial side of systemic circulation. The flowgenerated by the pump is impeded by arterial and venousresistances located around each of the two parallel vascularbed compartments.

In the G-C model, the assumption is that sodiumexcretion is ultimately determined by arterial pressure (i.e.pressure natriuresis) and vascular resistance is a functionof ‘whole body autoregulation’. In the neurogenic modelthe assumption is that sodium output is independent ofarterial pressure (i.e. pressure independent natriuresis)and that vascular resistance is determined by sympatheticnerve activity (SNA). In the G-C model, hypertensioncaused by AngII in combination with high salt intake is dueto a primary shift in the pressure natriuresis mechanism(i.e. renal function curve) to a higher operating pressure.

In contrast, AngII–salt hypertension in the neurogenicmodel is due to primary activation of central sympatheticdrive.

Model simulations of the haemodynamicprofile of AngII–salt hypertension

Our first key finding was that both the G-C model andthe neurogenic model generate similar haemodynamicprofiles in response to the same input (i.e. increasedAngII and sodium intake). Figure 3A shows the key modelsimulations for the G-C (grey line) and neurogenic (blackline) models as compared to the haemodynamic profileof AngII–salt hypertension in dogs (Fig. 3B). Shown atthe bottom of Fig. 3A are the two forcing functions of

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Figure 3.A, simulations for the G-C model (grey lines) and the neurogenic model (black lines) produced by our mathematicalmodel (Fig. 2). Responses shown are; arterial pressure (AP), cardiac output (CO), blood volume (BV), total peripheralresistance (TPR), arterial splanchnic resistance (Ras), arterial extra-splanchnic resistance (Rar), sodium intake (NaI)and normalized plasma angiotensin II (AngII). Sodium excretion responses are also shown. B, haemodynamic profileof AngII–salt hypertension in dogs (same as Fig. 1B) to be compared to the simulation results in A.



the model; a 5-fold increase in sodium intake (NaI) and a3-fold increase in plasma AngII.

It is important to note that our simulation of theG-C model effectively reproduced the haemodynamicprofile of the original Guyton–Coleman model (Guyton& Coleman, 1967; Guyton, 1984). Specifically, the initialincrease in arterial pressure (AP) was due to a transientincrease in blood volume (BV) and cardiac output (CO).This was followed by a gradual increase in total peri-pheral resistance (TPR) and a near normalization of COto the steady state. More importantly, although the trans-ient responses were not identical, the neurogenic modelgenerated a haemodynamic profile similar to the G-Cmodel. The initial increase in CO and BV were followedby increased TPR and, at steady state, haemodynamics inboth models were identical.

Model simulations of the pressurenatriuresis relationships of AngII–salthypertension: the chronic pressurenatriuresis mechanism vs. pressurenatriuresis correlation

Our second key finding, as seen in the right panelof Fig. 3A, was that both the G-C model and theneurogenic model generated similar chronic pressurenatriuresis relationships. As seen in the right panelof Fig. 3A, the pressure natriuresis relationship andsodium excretion responses of our G-C model was similarto the Guyton–Coleman model. More importantly, apositive relationship between arterial pressure and sodiumexcretion was observed in the neurogenic model despitethe lack of a pressure natriuresis mechanism in the model.

The steady-state relationship between arterial pressureand sodium excretion is often presented as a ‘chronic renalfunction curve’ despite the fact that this relationship is notnecessarily causal in nature. This is illustrated in Fig. 4.The steady-state relationship between sodium intake andarterial pressure is easy to establish and graph as shown inFig. 4A. By definition, salt resistant subjects show little tono increase in arterial pressure over a wide range of sodiumintake whereas salt-sensitive subjects will exhibit directrelationships of varying strengths between salt intake andarterial pressure.

The argument has been made that, since the relationshipshown in Fig. 4A is measured at steady state, then thegraph can be rotated as shown in Fig. 4B (DeClueet al. 1978). Also, since at steady state sodium excretionmust equal sodium intake, this variable can be shownon the y-axis. Although these assumptions are correct,the graph shown in Fig. 4B, which is the ‘chronicpressure natriuresis relationship’, is often misunderstoodto represent a cause–effect relationship between arterialpressure and sodium excretion, which is not correct. Inother words, the graphical relationship shown in Fig. 4B

is presented as a ‘chronic renal function curve’ whichis not necessarily the case. This misleading presentationreinforces the concept that hypertension is ‘caused’ by ashift in the renal function curve, i.e. that a shift in therenal function curve is necessary to attain sodium balanceat elevated levels of arterial pressure (Guyton, 1990).

The results of the neurogenic model simulation in whichthe chronic pressure natriuresis relationship is shifted tohigher pressures, despite the lack of a pressure natriuresismechanism, underscores a very important point. That thismust happen in hypertension is obviously true just asthe arterial baroreceptor reflex is shifted in hypertension(Barrett & Malpas, 2005). Therefore, it seems likely thatresetting of both of these relationships is an adaptationto hypertension, rather than its cause. In fact, there is nodispute that all pressure controlling system must be resetin hypertension. The key question is whether this shiftis primary (i.e. causes hypertension) or secondary (i.e. iscaused by hypertension).

Addressing the issue of primary vs. secondary resettingof long-term pressure control systems is the single mostimportant question to answer if we are to unravel thecauses of long-term elevations of arterial pressure. Manyinvestigators have accepted the G-C model as the mostlogical explanation for the pathogenesis of hypertension,based on the concept of primary resetting of the renalfunction curve. Since the model was developed priorto the avalanche of studies on autonomic control ofcardiovascular function over the last few decades, thiswas a logical explanation at that time. This SymposiumReview, however, demonstrates that it is no longer theonly logical explanation. The neurogenic model is the firstmathematical model to simulate the same haemodynamic

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profile and pressure natriuresis correlations as the G-Cmodel under a new set of assumptions. Although thismodel is still in the early stages and is not meant asa replacement for the G-C model, it is consistent withexperimental studies and suggests the possibility thatsalt-sensitive hypertension can be of neurogenic originin the absence of primary alterations in renal function.

Future directions: modelling brainstemnetworks that generate the ‘AngII–saltsympathetic signature’

We have previously described the ‘AngII–salt sympatheticsignature’ as it relates to the pathogenesis of hypertensionin this model (Fig. 5). Based on several studies from ourgroup, this experimental model is characterized by anincrease in splanchnic SNA, transiently decreased renalSNA and no change in SNA to the skeletal muscle vascularbed (Osborn & Fink, 2010; Yoshimoto et al. 2010). Wehypothesize that this pattern of regional SNA in AngII–salthypertension results in a shift of blood volume from thehighly compliant splanchnic vascular bed to the arterialcompartment. We propose that this sympathetic patternis driven by the actions of AngII on osmotically sensitivepathways in the brain that regulate sympathetic premotorneurons in the rostral ventrolateral medulla (RVLM). The

inset in Fig. 5 illustrates our current hypothesis regardingdescending excitatory inputs to sympathetic premotorneurons for the splanchnic, renal and lumbar sympatheticnerves, as well as inhibitory baroreceptor inputs fromthe nucleus tractussolitarius (NTS). We hypothesize thatdifferential control of splanchnic, renal and lumbar SNA isthe result of differences in these excitatory and inhibitoryinputs. A computational model of this network is currentlyunderway.

Physiological and clinical relevance of theneurogenic model

The neurogenic model is based on the studies inwhich salt intake is increased in animals receivingexogenously administered AngII. One could argue that,since increased salt intake suppresses AngII under normalphysiological conditions, the model is not physiologicallyrelevant for human hypertension. While there is nosingle experimental animal model that fully mimicshuman essential hypertension, is there a human physio-logical condition under which AngII, plasma sodium andsympathetic nerve activity are increased chronically? Theanswer is yes; this occurs during chronic water deprivation.

Water deprivation is an environmental stress inwhich physiological control systems are critical to the

Resistance

NaCI

AngllCentral

Feedback InhibitoryInput (NTS)

Central pattern generation ofsympathetic outflow

LumbarRanal

NTS

RVLM

SFO

MnPO

PVN

OVLT

Splanchnic

ExcitatoryInput(PVN)

Angll

Days

Angll

SSNA

RSNA

LSNA

Days

Angll

Days

SS

NA

RS

NA

Angll

Days

MA

P

LSN

A

Capacitance

MAP

Figure 5.Hypothetical mechanisms responsible for generation of the ‘AngII–salt sympathetic signature’. Inset box illustratescurrent efforts to model brainstem networks that generate this differential pattern of sympathetic activity. Figureadapted from Osborn et al. (2011).



maintenance of body fluid homeostasis and perfusionof one of the most important organs for survival – thebrain. We hypothesize that water deprivation increasesplasma AngII, which acts on forebrain osmosensitive sites,to amplify the effects of increased plasma osmoticallyon central sympathetic pathways in the brain. Morespecifically these AngII-modulated osmotic pathways areresponsible for increased SNA to the splanchnic vascularbed specifically. This results in neurogenic splanchnicvenous and arteriolar constriction, which acts to mobilizeblood from this highly compliant vascular bed to thearterial compartment to maintain arterial pressure andcerebral perfusion.

What is the clinical relevance of this response in relationto salt-sensitive hypertension? We hypothesize that thesame interactions of plasma AngII with osmosensitivesympathetic pathways in the brain, which operate underconditions of water deprivation, are dysfunctional insalt-sensitive individuals such that they are not able tosuppress SNA in response to increased salt intake.

This neurogenic hypothesis is supported by thework of Krieger and colleagues in their salt-loadinghaemodynamic studies in dogs. As presented earlier,the haemodynamic profile of the AngII–salt dog model(Krieger et al. 1989, 1990) is consistent with the G-Cmodel. However, another study from this group, inwhich the identical salt-loading protocol was conductedin normal dogs in which plasma AngII was not clamped,is not consistent with the G-C model (Krieger et al.1990). The G-C model would predict that salt-inducedchanges in arterial pressure in normal dogs are negligiblebecause of the powerful ability of the kidneys to excrete thesodium load and maintain blood volume at normal levels.However, blood volume and cardiac output increases inresponse to salt loading in normal dogs (Krieger et al. 1990)were identical to those observed in dogs in which plasmaAngII–salt was clamped by exogenous administration ofthe peptide (Krieger et al. 1989, 1990). However, normaldogs were ‘salt-resistant’ as a result of decreased total peri-pheral resistance.

These findings are important for two reasons. First,they demonstrate that normotensive dogs (i.e. normalkidney function) exhibit increased blood volume andcardiac output in response to increased salt intake.Second, although salt loading increased cardiac outputin normotensive dogs, ‘whole body autoregulation’ wasnot observed and vascular resistance did not increase.Taken together, these studies (Krieger et al. 1989, 1990)demonstrate that the haemodynamic basis of AngII–salthypertension in the dog is not due to primary renaldysfunction, which results in blood volume expansion,increased cardiac output and whole body autoregulation.Rather, these studies show that salt-induced hypertensionin dogs with ‘clamped’ plasma AngII is the result ofimpaired vasodilatory response to salt intake and increased

blood volume. We hypothesize that this impaired vaso-dilatory response is due to the inability to suppress plasmaAngII, resulting in modulation of osmosensitive pathwaysin the brain that control sympathetic nervous systemactivity.

This hypothesis is consistent with other studies inrodents, e.g. chronic salt loading results in identicalincreases in blood volume and cardiac output inDahl salt-resistant and Dahl salt-sensitive rats (Greeneet al. 1990). However, Dahl salt-resistant rats remainnormotensive as a result of reduced vascular resistancewhereas Dahl salt-sensitive rats have an impaired vaso-dilatory response to increased salt intake. Finally, somestudies in humans are consistent with these animalstudies in dogs and rats. Whereas chronic increases insalt intake result in increased blood volume, reducedvascular resistance and no change in arterial pressurein normotensive salt-resistant humans, salt-sensitive sub-jects fail to vasodilate in response to salt inducedincrease in blood volume and cardiac output (Sullivan& Ratts, 1983). This similarity of these haemodynamicresponses to increased salt intake in rodent and caninemodels andin humans with salt-sensitive hypertensionsuggests that, although dogs were used for developmentof the G-C model, and rats were used for developmentof neurogenic model, the fundamental physiologicalresponses to increased salt intake are similar acrossspecies.

How are the above studies consistent with theneurogenic model? We hypothesize that increasedsalt intake normally suppresses plasma AngII and,therefore, reduces the AngII input to osmotically drivensympathoexcitatory pathways in the brain. This resultsin reduced sympathetic activity and vasodilatation (bothvenous and arterial) to accommodate blood volumeexpansion thereby maintaining normal arterial pressureunder chronic salt loading conditions. We hypothesizethat this response is impaired in salt-sensitive individualsresulting in hypertension. This could result from eitheran inability to suppress plasma AngII in response toincreased salt intake, or impaired responsiveness ofosmosensitive sympathoexcitatory pathways to AngIIsignalling mechanisms. This would result in aninappropriately high level of sympathetic activity duringperiods of blood volume expansion induced by a highsalt intake. Moreover, this would occur in the presenceof normal plasma AngII (impaired AngII response) oreven suppressed plasma AngII concentration (impairedneural response to AngII). These hypotheses remainto be tested by further experimental studies. Finally,although the neurogenic model is in its early stages, itprovides a platform the development of additional neuro-genic models, which can incorporate data from past andfuture experimental studies of neurogenic cardiovasculardiseases such as hypertension.



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Additional information

Competing interests

None declared

Funding

The work was supported in part by the National Institutes ofHealth grants HL076312 and GM29123.

Acknowledgements

The authors would like to thank Jason Foss for his constructivecomments during the preparation of the manuscript.


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