A mathematical model of the myogenic response to systolic pressure in the afferent arteriole

Chen, Jing; Sgouralis, Ioannis; Moore, Leon C.; Layton, Harold E.

doi:10.1152/ajprenal.00382.2010

Cited by 47 publications

(57 citation statements)

References 40 publications

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“…4, B2 and B3. Instead of responding to the high-frequency pressure variations passively without attenuation, the model vessel exhibited a sustained vasoconstriction, owing to the cumulative effect of the faster contractile responses (5,24,25 …”

Section: Model Resultsmentioning

confidence: 99%

“…The model is an extension of our previous AA cell model (5) and represents a segment of an AA of length L (L ϳ300 m), consisting of a series of N cell ϭ 101 smooth muscle cell models (5), coupled via their gap junctions and via an endothelial cell layer. (An odd number of smooth muscle cell models were represented so that there is a middle cell that can be stimulated to study any asymmetry in the conduction of vasoconstrictive response.)…”

Section: Mathematical Modelmentioning

confidence: 99%

“…A detailed description of the equations for the AA smooth muscle cell model and the model parameters can be found in the APPENDIX and in Ref. 5. Below we describe a few key equations, including those that are modified from the previous model (5).…”

Section: Mathematical Modelmentioning

confidence: 99%

“…5. Below we describe a few key equations, including those that are modified from the previous model (5).…”

Section: Mathematical Modelmentioning

confidence: 99%

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Autoregulation and conduction of vasomotor responses in a mathematical model of the rat afferent arteriole

Sgouralis

Layton

2012

American Journal of Physiology-Renal Physiology

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Steinhausen et al. (37) analyzed the propagation of vasomotor responses, induced by local electrical stimulation, in split hydronephrotic rat kidneys. Their results indicate that the responses decay with increasing distance from the stimulation site and that the decay is significantly faster upstream than downstream. An explanation for the asymmetric decay rates, which was elusive, is a motivation for the present study.In a previous study (5), we developed a detailed mathematical model of the myogenic response of a small segment of the afferent arteriole (AA) wall, including the endothelium and the surrounding smooth muscle cells. That model was used to examine the response of the AA segment to changes in mean and pulsatile pressure. Simulation results of that model are consistent with the hypothesis that the AA myogenic response plays an important role in protecting the glomerular capillaries against elevated systolic pressures. The goal of this study is to develop a multicell model of the AA by connecting a series of AA smooth muscle cells and endothelial cells via gap junction coupling and to use the model to study the myogenic response of the AA and its response to local electrical stimulation. The AA model is intended to be used as an essential component in models of integrated renal hemodynamic regulation. MATHEMATICAL MODELMulticell AA model. The model is an extension of our previous AA cell model (5) and represents a segment of an AA of length L (L ϳ300 m), consisting of a series of N cell ϭ 101 smooth muscle cell models (5), coupled via their gap junctions and via an endothelial cell layer. (An odd number of smooth muscle cell models were represented so that there is a middle cell that can be stimulated to study any asymmetry in the conduction of vasoconstrictive response.) The model AA segment is connected in series to a fixed resistor, denoted R end. The inflow pressure [P 0(t) at x ϭ 0] and the pressure at the end of the fixed resistor P end (at x ϭ 2L) are assumed to be known a priori. A schematic diagram is shown in Fig. 1. When the inflow pressure P 0 is varied or when a vasoconstrictive or vasodilative response is induced, the pressure at the end of the AA segment, which is denoted P(L, t) and which we refer to as the "outflow pressure," may also vary. We set P end to 0 mmHg and R end to equal the time-averaged value of the total resistance of the unstimulated AA with P 0 ϭ 100 mmHg, so that when the inflow pressure P 0 ϭ 100 mmHg, the outflow pressure P(L) Ϸ 50 mmHg.Each AA smooth muscle cell model incorporates the ionic transports, cell membrane potential, muscle contraction of the AA smooth muscle cells, and the mechanics of a thick-walled cylinder. The model represents the interaction of Ca 2ϩ and K ϩ fluxes mediated by voltagegated and voltage-calcium-gated channels, respectively, which gives rise to the periodicity of those transports. This results in a timeperiodic cytoplasmic calcium concentration, myosin light chains phosphorylation, and crossbridge formation with the attending muscle s...

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Section: Model Resultsmentioning

confidence: 99%

Section: Mathematical Modelmentioning

confidence: 99%

Section: Mathematical Modelmentioning

confidence: 99%

“…5. Below we describe a few key equations, including those that are modified from the previous model (5).…”

Section: Mathematical Modelmentioning

confidence: 99%

See 2 more Smart Citations

Autoregulation and conduction of vasomotor responses in a mathematical model of the rat afferent arteriole

Sgouralis

Layton

2012

American Journal of Physiology-Renal Physiology

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“…Since second messengers in the cytosol are thought to modulate the activation and inactivation of channels that facilitate an increased cytosolic Ca 2ϩ and contraction, the governing stimulus could be sensed by structures other than the channels themselves. This separation between mechanisms at the channel level and the overall governing mechanical stimulus are implied in recent theoretical studies in which activation of stretch-activated channels is actually formulated to respond proportionally to vessel wall stress (5,24,25,53). In all previous theoretical studies, model validation to represent the myogenic response is made only qualitatively, and comparison of different controlling mechanical stimuli and possible transduction pathways is not discussed.…”

Section: Discussionmentioning

confidence: 99%

Mechanical control of cation channels in the myogenic response

Carlson

Beard

2011

American Journal of Physiology-Heart and Circulatory Physiology

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Microcirculatory vessel response to changes in pressure, known as the myogenic response, is a key component of a tissue's ability to regulate blood flow. Experimental studies have not clearly elucidated the mechanical signal in the vessel wall governing steady-state reduction in vessel diameter upon an increase in intraluminal pressure. In this study, a multiscale computational model is constructed from established models of vessel wall mechanics, vascular smooth muscle (VSM) force generation, and VSM Ca 2ϩ handling and electrophysiology to compare the plausibility of vessel wall stress or strain as an effective mechanical signal controlling steady-state vascular contraction in the myogenic response. It is shown that, at the scale of a resistance vessel, wall stress, and not stretch (strain), is the likely physiological signal controlling the steady-state myogenic response. (28), and large-conductance, Ca 2ϩ -activated K ϩ (BK Ca ) channel, which has a large influence on the level of membrane polarization (17). Many of these studies identifying channels with mechanotransductive qualities have investigated the channels in isolation by patch clamping and exposure to exogenous substances or mechanical conditions representative of those thought to be present in the intact cellular environment. Foundational work on mechanotransductive channels focused on how the strain or tension directly affects channel-gating probabilities (39 -41). It is clear that many of these channels respond to mechanical stimulation; however, it cannot be determined from these studies whether vessel wall stress or strain is the controlling mechanical stimulus and how these stimuli may control channel function in the myogenic response. Therefore, to understand how these channels are controlled and play a role in the acute regulatory response to pressure through the complex interactions in an intact single vessel, an integrated theoretical model taking into consideration VSM electrophysiology, VSM force generation, and vessel wall mechanics must be employed. Such a theoretical platform is a valuable hypothesis-testing method aimed at assessing which underlying channel function or set of functions is sufficient to describe the observed whole-vessel response and will be important in determining future experimental design.Several detailed models of VSM electrophysiology have been previously developed and used in integrated models of acute regulation of arteriolar vessels. Yang et al. (53,54) -induced Ca 2ϩ release and cytosolic buffering. Simulation protocols utilizing a depolarizing voltage pulse and applied strain were used to interrogate the model function with respect to qualitative and quantitative features from experimental studies of VSM cells. Koenigsberger et al. (24,25) investigated the myogenic response and oscillatory behavior of microvessels known as vasomotion with a similar model but focused on the influence of stretch-activated channels that were formulated to be activated by stress in the vessel. VSM force generation based on cy...

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