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

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.

A new conceptual paradigm for the haemodynamics of salt-sensitive hypertension: a mathematical modelling approach.

A conceptually novel mathematical model of neurogenic angiotensin II-salt hypertension is developed and analysed. The model consists of a lumped parameter circulatory model with two parallel vascular beds; two distinct control mechanisms for both natriuresis and arterial resistances can be implemented, resulting in four versions of the model. In contrast with the classical Guyton-Coleman model (GC model) of hypertension, in the standard version of our new model natriuresis is assumed to be independent of arterial pressure and instead driven solely by sodium intake; arterial resistances are driven by increased sympathetic nervous system activity in response to the elevated plasma angiotensin II and increased salt intake (AngII-salt). We compare the standard version of our new model against a simplified Guyton-Coleman model in which natriuresis is a function of arterial pressure via the pressure-natriuresis mechanism, and arterial resistances are controlled via the whole-body autoregulation mechanism. We show that the simplified GC model and the new model correctly predict haemodynamic and renal excretory responses to induced changes in angiotensin II and sodium inputs. Importantly, the new model reproduces the pressure-natriuresis relationship--the correlation between arterial pressure and sodium excretion--despite the assumption of pressure-independent natriuresis. These results show that our model provides a conceptually new alternative to Guyton's theory without contradicting observed haemodynamic changes or pressure-natriuresis relationships. Furthermore, the new model supports the view that hypertension need not necessarily have a renal aetiology and that long-term arterial pressure could be determined by sympathetic nervous system activity without involving the renal sympathetic nerves.

Current computational models do not reveal the importance of the nervous system in long-term control of arterial pressure.

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 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.