Math @ Duke

Publications [#243674] of Anita T. Layton
Papers Published
 Chen, J; Sgouralis, I; Moore, LC; Layton, HE; Layton, AT, A mathematical model of the myogenic response to systolic pressure in the afferent arteriole.,
American journal of physiology. Renal physiology, vol. 300 no. 3
(2011),
pp. F669F681 [21190949], [doi]
(last updated on 2018/02/22)
Abstract: Elevations in systolic blood pressure are believed to be closely linked to the pathogenesis and progression of renal diseases. It has been hypothesized that the afferent arteriole (AA) protects the glomerulus from the damaging effects of hypertension by sensing increases in systolic blood pressure and responding with a compensatory vasoconstriction (Loutzenhiser R, Bidani A, Chilton L. Circ Res 90: 13161324, 2002). To investigate this hypothesis, we developed a mathematical model of the myogenic response of an AA wall, based on an arteriole model (GonzalezFernandez JM, Ermentrout B. Math Biosci 119: 127167, 1994). The model incorporates ionic transport, cell membrane potential, contraction of the AA smooth muscle cell, and the mechanics of a thickwalled cylinder. The model represents a myogenic response based on a pressureinduced shift in the voltage dependence of calcium channel openings: with increasing transmural pressure, model vessel diameter decreases; and with decreasing pressure, vessel diameter increases. Furthermore, the model myogenic mechanism includes a ratesensitive component that yields constriction and dilation kinetics similar to behaviors observed in vitro. A parameter set is identified based on physical dimensions of an AA in a rat kidney. Model results suggest that the interaction of Ca(2+) and K(+) fluxes mediated by voltagegated and voltagecalciumgated channels, respectively, gives rise to periodicity in the transport of the two ions. This results in a timeperiodic cytoplasmic calcium concentration, myosin light chain phosphorylation, and crossbridge formation with the attending muscle stress. Furthermore, the model predicts myogenic responses that agree with experimental observations, most notably those which demonstrate that the renal AA constricts in response to increases in both steady and systolic blood pressures. The myogenic model captures these essential functions of the renal AA, and it may prove useful as a fundamental component in a multiscale model of the renal microvasculature suitable for investigations of the pathogenesis of hypertensive renal diseases.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

