This thesis presents a mathematical model of long-term blood pressure control that explains how latent activation of the sympathetic nervous system in the AngII-salt model of hypertension can lead to chronic blood pressure elevation without modifying renal ability to excrete sodium. Previous mathematical models of hypertension were built on the assumption that such modification is necessary. The model integrates four major systems of body fluid and solute control: the cardiovascular system, kidneys, microvascular exchange between extracellular and intracellular compartments, and the sympathetic nervous system. The model excludes two major hypotheses used in previous mathematical models: the chronic pressure-natriuresis mechanism and the whole-body autoregulation mechanism; the model adds a hypothesis of slow long-term activation of the sympathetic nervous system, which acts to increase pressure via increased non-renal arterial resistances and venous tone. Despite the difference in assumptions, the model's predictions agree well with all major classical observations associated with AngII-salt hypertension, including the pressure-natriuresis phenomenon. Analysis of the model demonstrates that the pressure-natriuresis curves are projections of a three-dimensional dynamics driven by both renal and neural control and reflect an additive impact of both controls on blood pressure. Thus, the current interpretation of pressure-natriuresis curves as the result only of a direct mechanistic impact of arterial pressure on renal function may not be warranted in some cases of hypertension. The presented model conclusively demonstrates that AngII-salt hypertension can be maintained without the sole renal dominance.
University of Minnesota Ph.D. dissertation. January 2015. Major: Mathematics. Advisors: Hans G. Othmer, John W. Osborn. 1 computer file (PDF); vii, 165 pages, appendices A-C.
A mathematical model of neurally-mediated Angiotensin II-salt hypertension.
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