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


J. W. Osborn: Department of Integrative Biology and Physiology, 321 Church Street SE, Rm 6-125 Jackson Hall, Minneapolis, MN 55455, USA. Email: osbor003@umn.edu

Key points

  • • Causes of chronically-elevated arterial blood pressure (hypertension) are highly debated and difficult to study experimentally. Mathematical models can help elucidate potential causes of hypertension that are experimentally inaccessible.
  • • All current models are based on one key assumption that long-term regulation of blood pressure depends on sodium excretion by the kidney. This assumption leads to the conclusion that hypertension must be caused by kidney dysfunction.
  • • However, some experimental evidence suggests that kidney function can remain normal and that instead elevated neural activity to the vasculature causes hypertension.
  • • We developed a mathematical model where sodium excretion is independent of blood pressure and neural activation to the vasculature triggers hypertension. Our model reproduces the solutions of earlier models, yet still shows the empirically well-established correlation between changes in sodium excretion and blood pressure.
  • • Thus the model provides a novel platform for studying non-kidney based theories of hypertension aetiology.

Abstract  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.