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

Abstract

Salt sensitivity of arterial pressure (salt-sensitive hypertension) is a serious global health issue. The causes of salt-sensitive hypertension are extremely complex and mathematical models 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 Guyton and Coleman; referred to as the G-C model. The core of this model is the assumption that sodium 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 renal function curve to a higher operating pressure. However, several recent experimental studies in a model of hypertension produced by the combination of a high salt intake and administration of angiotensin II, the AngII-salt model, are inconsistent with the G-C model. We developed a new mathematical model that does not limit the cause of salt-sensitive hypertension solely to primary renal dysfunction. The model is the first known mathematical counterexample to the assumption that all salt-sensitive forms of hypertension require a primary shift of renal function: we show that in at least one salt-sensitive form of hypertension the requirement is not necessary. We will refer to this computational model as the 'neurogenic model'. In this Symposium Review we discuss how, despite fundamental differences between the G-C model and the neurogenic model regarding mechanisms regulating sodium excretion and vascular resistance, they generate similar haemodynamic profiles of AngII-salt hypertension. In addition, the steady-state relationships between arterial pressure and sodium excretion, a correlation that is often erroneously presented as the 'renal function curve', are also similar in both models. Our findings suggest that salt-sensitive hypertension is not due solely to renal dysfunction, as predicted by the G-C model, but may also result from neurogenic dysfunction.

Figure 1

A, the response of mean arterial pressure (MAP) to angiotensin II (AngII) administration (150 ng kg^–1 min^–1) in Sprague–Dawley rats consuming low (0.1%), normal (0.4%) or high (2.0%) salt diets. Values are 24 h averages measured 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 of arterial pressure are: (1) the renal function curve and (2) sodium intake. The combination of a rightward shift of the 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). Cardiac output directly influences arterial pressure but also gradually increases total peripheral resistance as a result of autoregulation.

Figure 2

Schematic representation of the similarities and differences between the G-C (A) and ‘neurogenic’ (B) models. See text for details.

Figure 3

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

Figure 4

Schematic representation of the steady-state relationship between (A) sodium (Na) intake and arterial pressure and (B) arterial pressure and sodium excretion. See text for details.

Figure 5

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