Bifurcation study of blood flow control in the kidney

Versypt, Ashlee N. Ford; Makrides, Elizabeth; Arciero, Julia; Ellwein, Laura

doi:10.1016/j.mbs.2015.02.015

Cited by 11 publications

(7 citation statements)

References 40 publications

(53 reference statements)

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“…3(e)). These results are consistent with previous modeling studies (Ford Versypt et al, 2015; Layton et al, 1991, 2006; Ryu and Layton, 2012; Layton et al, 2012). …”

Section: Resultssupporting

confidence: 93%

“…The mathematical model we use to investigate the interactions between TGF and CTGF is based on a recently published model of TGF (Arciero et al, 2015; Ford Versypt et al, 2015). Briefly, the model describes flow dynamics along a superficial nephron 2 in a rat kidney by coupling partial differential equations (PDEs) describing [Cl − ] transport along the nephron with a system of ordinary differential equations (ODEs) describing the vessel wall mechanics of the afferent arteriole.…”

Section: Model Equationsmentioning

confidence: 99%

“…To represent both TGF and CTGF, the target activation A total is given by

A_{t o t a l} \frac{1}{1 + \exp true[- S_{t o n e} true(C (L_{TGF}, t - τ_{TGF}), C (L_{CTGF}, t - τ_{CTGF}), D (t) true) true]}

where S tone is given by

\begin{matrix} right S_{t o n e} & left = c_{m y o} \frac{P_{a v g} D (t)}{2} + \frac{c_{2}}{1 + exp [- c_{TGF} (L_{TGF}, t - τ_{TGF}) - C_{TGF, op}]} \\ right & left - \frac{c_{3}}{1 + exp [- c_{CTGF} (L_{CTGF}, t - τ_{CTGF}) - C_{CTGF, op}]} - c_{t o n e} \end{matrix}

Parameter values are summarized in Table 1. Justification for key parameters for TGF and myogenic response can be found in our previous studies (Arciero et al, 2015; Ford Versypt et al, 2015). The new CTGF parameters are not well characterized.…”

Section: Model Equationsmentioning

confidence: 99%

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Modeling the effects of positive and negative feedback in kidney blood flow control

Liu

2016

Mathematical Biosciences

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Blood flow in the mammalian kidney is tightly autoregulated. One of the important autoregulation mechanisms is the myogenic response, which is activated by perturbations in blood pressure along the afferent arteriole. Another is the tubuloglomerular feedback, which is a negative feedback that responds to variations in tubular fluid [Cl−] at the macula densa1. When initiated, both the myogenic response and the tubuloglomerular feedback adjust the afferent arteriole muscle tone. A third mechanism is the connecting tubule glomerular feedback, which is a positive feedback mechanism located at the connecting tubule, downstream of the macula densa. The connecting tubule glomerular feedback is much less well studied. The goal of this study is to investigate the interactions among these feedback mechanisms and to better understand the effects of their interactions. To that end, we have developed a mathematical model of solute transport and blood flow control in the rat kidney. The model represents the myogenic response, tubuloglomerular feedback, and connecting tubule glomerular feedback. By conducting a bifurcation analysis, we studied the stability of the system under a range of physiologically-relevant parameters. The bifurcation results were confirmed by means of a comparison with numerical simulations. Additionally, we conducted numerical simulations to test the hypothesis that the interactions between the tubuloglomerular feedback and the connecting tubule glomerular feedback may give rise to a yet-to-be-explained low-frequency oscillation that has been observed in experimental records.

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“…3(e)). These results are consistent with previous modeling studies (Ford Versypt et al, 2015; Layton et al, 1991, 2006; Ryu and Layton, 2012; Layton et al, 2012). …”

Section: Resultssupporting

confidence: 93%

Section: Model Equationsmentioning

confidence: 99%

“…To represent both TGF and CTGF, the target activation A total is given by

A_{t o t a l} \frac{1}{1 + \exp true[- S_{t o n e} true(C (L_{TGF}, t - τ_{TGF}), C (L_{CTGF}, t - τ_{CTGF}), D (t) true) true]}

where S tone is given by

\begin{matrix} right S_{t o n e} & left = c_{m y o} \frac{P_{a v g} D (t)}{2} + \frac{c_{2}}{1 + exp [- c_{TGF} (L_{TGF}, t - τ_{TGF}) - C_{TGF, op}]} \\ right & left - \frac{c_{3}}{1 + exp [- c_{CTGF} (L_{CTGF}, t - τ_{CTGF}) - C_{CTGF, op}]} - c_{t o n e} \end{matrix}

Section: Model Equationsmentioning

confidence: 99%

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Modeling the effects of positive and negative feedback in kidney blood flow control

Liu

2016

Mathematical Biosciences

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“…Independently of the myogenic response which is triggered by local blood pressure perturbations, tubuloglomerular feedback is triggered by salt reabsorption in the downstream nephron that, in turn, depends on filtration rate. As the triggering signals of the two mechanisms are largely independent but interrelated through blood flow which influences both local pressure and filtration rate, highly non-trivial interactions among the two mechanisms are developed [4,7,26,77]. A potential extension of the present afferent arteriole model would be to include a model of nephron transport (e.g., [78][79][80][81][82]) and tubuloglomerular feedback (e.g., [7,[83][84][85]).…”

Section: Discussionmentioning

confidence: 99%

A Multicellular Vascular Model of the Renal Myogenic Response

2018

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Abstract:The myogenic response is a key autoregulatory mechanism in the mammalian kidney. Triggered by blood pressure perturbations, it is well established that the myogenic response is initiated in the renal afferent arteriole and mediated by alterations in muscle tone and vascular diameter that counterbalance hemodynamic perturbations. The entire process involves several subcellular, cellular, and vascular mechanisms whose interactions remain poorly understood. Here, we model and investigate the myogenic response of a multicellular segment of an afferent arteriole. Extending existing work, we focus on providing an accurate-but still computationally tractable-representation of the coupling among the involved levels. For individual muscle cells, we include detailed Ca 2+ signaling, transmembrane transport of ions, kinetics of myosin light chain phosphorylation, and contraction mechanics. Intercellular interactions are mediated by gap junctions between muscle or endothelial cells. Additional interactions are mediated by hemodynamics. Simulations of time-independent pressure changes reveal regular vasoresponses throughout the model segment and stabilization of a physiological range of blood pressures (80-180 mmHg) in agreement with other modeling and experimental studies that assess steady autoregulation. Simulations of time-dependent perturbations reveal irregular vasoresponses and complex dynamics that may contribute to the complexity of dynamic autoregulation observed in vivo. The ability of the developed model to represent the myogenic response in a multiscale and realistic fashion, under feasible computational load, suggests that it can be incorporated as a key component into larger models of integrated renal hemodynamic regulation.

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“…Podocytes express certain RAS enzymes and hormones differently than the systemic RAS with much higher ANG II concentration [8][9][10]. While several computational models have been proposed for various aspects of renal physiology [18][19][20][21][22][23][24][25][26][27][28][29], models for the mechanism of hyperglycemia-induced podocyte injury in DKD are only recently appearing in the literature. In a previous publication, we created a podocyte-specific local RAS model that had parameters dependent on the glucose concentration [30].…”

mentioning

confidence: 99%

A Glucose-Dependent Pharmacokinetic/ Pharmacodynamic Model of ACE Inhibition in Kidney Cells

2019

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Diabetic kidney disease (DKD) is a major cause of renal failure. Podocytes are terminally differentiated renal epithelial cells that are key targets of damage due to DKD. Podocytes express a glucose-stimulated local renin-angiotensin system (RAS) that produces angiotensin II (ANG II). Local RAS differs from systemic RAS, which has been studied widely. Hyperglycemia increases the production of ANG II by podocyte cells, leading to podocyte injury. Angiotensin-converting enzyme (ACE) is involved in the production of ANG II, and ACE inhibitors are drugs used to suppress elevated ANG II concentration. As systemic RAS differs from the local RAS in podocytes, ACE inhibitor drugs should act differently in local versus systemic contexts. Experimental and computational studies have considered the pharmacokinetics (PK) and pharmacodynamics (PD) of ACE inhibition of the systemic RAS. Here, a PK/PD model for ACE inhibition is developed for the local RAS in podocytes. The model takes constant or dynamic subject-specific glucose concentration input to predict the ANG II concentration and the corresponding effects of drug doses locally and systemically. The model is developed for normal and impaired renal function in combination with different glucose conditions, thus enabling the study of various pathophysiological conditions. Parameter uncertainty is also analyzed. Such a model can improve the study of the effects of drugs at the cellular level and can aid in development of therapeutic approaches to slow the progression of DKD.

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Bifurcation study of blood flow control in the kidney

Cited by 11 publications

References 40 publications

Modeling the effects of positive and negative feedback in kidney blood flow control

Modeling the effects of positive and negative feedback in kidney blood flow control

A Multicellular Vascular Model of the Renal Myogenic Response

A Glucose-Dependent Pharmacokinetic/ Pharmacodynamic Model of ACE Inhibition in Kidney Cells

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