Mathematical modeling of renal autoregulation. (2009)
AuthorsKleinstreuer, Nicole Churchillshow all
Renal autoregulation is unique and critically important in maintaining homeostasis in the body via control of renal blood flow and filtration. The myogenic reflex responds directly to pressure variation and is present throughout the vasculature in varying degrees, while the tubuloglomerular feedback (TGF) mechanism adjusts microvascular resistance and glomerular filtration rate (GFR) to maintain distal tubular NaCl delivery. No simple models are available which allow the independent contributions of the myogenic and TGF responses to be compared and which include control over multiple metabolic and physiological parameters. Independently developed mathematical models of myogenic autoregulation and TGF control of GFR have been combined to produce a comprehensive model for the rat kidney which is responsive to multiple small step changes in mean arterial pressure. The system encompasses every level of the renal vasculature and the tubular system of the nephrons while simultaneously incorporating the modulatory effects of changes in viscosity and shear stress-induced nitric oxide (NO) production. The vasculature of the rat kidney has previously been divided via a Strahler ordering scheme using morphological data derived from micro-CT imaging. This data, combined with an extensive literature review of the relevant experimental data, led to the development of order-specific parameter sets for each of the eleven vascular levels. The model of the myogenic response depends primarily on circumferential wall tension, corresponding to a distally dominant resistance distribution with the highest contributions localized to the afferent arterioles and interlobular arteries. The constrictive response is tempered by the vasodilatory influence of flow-induced NO. Experimental comparison with data from groups that inhibited the TGF mechanism showed that the model was able to accurately reproduce the characteristics of renal myogenic autoregulation. This myogenic model was coupled with a system of equations that represented both spatial and temporal changes in concentration of the filtrate in the tubular system of the nephrons and the corresponding resistance changes of the afferent arteriole via the TGF mechanism. Computer simulation results of the system response to pressure perturbations were examined, as well as the interaction between mechanisms and the modulatory influences of metabolic and hemodynamic factors on the steady state and transient characteristics of whole-organ renal autoregulation. The responses of the model were consistent with experimental observations and showed that the frequency of the myogenic reflex was approximately 0.4 Hz while that of TGF was 0.06 Hz, corresponding to a 2-3 sec response time for myogenic contraction and 16.7 sec for TGF. Within the autoregulatory range step increases in pressure induced damped oscillations in tubular flow, macula densa NaCl concentration, arteriolar diameter, and renal blood flow. The model demonstrated that these oscillations were triggered by TGF and confined to vessels less than 100 micrometer in diameter. The pressure response in larger vessels remained important in characterizing total autoregulatory efficacy. Examination of the steady-state and transient characteristics of the model results demonstrates the necessity of considering the whole organ response in studies of renal autoregulation. A comprehensive model of autoregulation also allows for the examination of pathological states, such as the altered NO production in hypertension or the excess tubular reabsorption of water seen in diabetes. The model was able to reproduce experimental results when simulating diseased states, enabling the analysis of impaired autoregulation as well as the identification of key factors affecting the autoregulatory response.