Modeling TGF‐mediated flow dynamics in a system of three coupled nephrons

Bayram, Saziye

doi:10.1002/cnm.2471

Cited by 3 publications

(2 citation statements)

References 21 publications

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“…Similar signals from other afferent arterioles reach the vascular node, and the interaction among them enables synchronization of oscillations from the participating nephrons (9,15,18,34,46). These synchronization events increase the stability of the oscillations (1,2,27,28,41) and augment the force of smooth muscle contraction in response to a signal from the macula densa (24). Mean arterial blood pressure in conscious animals fluctuates over time scales of minutes to hours in a 1/f pattern (16,30).…”

Section: Discussionmentioning

confidence: 99%

Architecture of the rat nephron-arterial network: analysis with micro-computed tomography

Marsh

Postnov

Rowland

et al. 2017

American Journal of Physiology-Renal Physiology

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Among solid organs, the kidney's vascular network stands out, because each nephron has two distinct capillary structures in series and because tubuloglomerular feedback, one of the mechanisms responsible for blood flow autoregulation, is specific to renal tubules. Tubuloglomerular feedback and the myogenic mechanism, acting jointly, autoregulate single-nephron blood flow. Each generates a self-sustained periodic oscillation and an oscillating electrical signal that propagates upstream along arterioles. Similar electrical signals from other nephrons interact, allowing nephron synchronization. Experimental measurements show synchronization over fields of a few nephrons; simulations based on a simplified network structure that could obscure complex interactions predict more widespread synchronization. To permit more realistic simulations, we made a cast of blood vessels in a rat kidney, performed micro-computed tomography at 2.5-μm resolution, and recorded three-dimensional coordinates of arteries, afferent arterioles, and glomeruli. Nonterminal branches of arcuate arteries form treelike structures requiring two to six bifurcations to reach terminal branches at the tree tops. Terminal arterial structures were either paired branches at the tops of the arterial trees, from which 52.6% of all afferent arterioles originated, or unpaired arteries not at the tree tops, yielding the other 22.9%; the other 24.5% originated directly from nonterminal arteries. Afferent arterioles near the corticomedullary boundary were longer than those farther away, suggesting that juxtamedullary nephrons have longer afferent arterioles. The distance separating origins of pairs of afferent arterioles varied randomly. The results suggest an irregular-network tree structure with vascular nodes, where arteriolar activity and local blood pressure interact.

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Section: Discussionmentioning

confidence: 99%

Architecture of the rat nephron-arterial network: analysis with micro-computed tomography

Marsh

Postnov

Rowland

et al. 2017

American Journal of Physiology-Renal Physiology

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“…Saziye Bayram presents a mathematical model of the flow dynamics mediated by the tubuloglomerular feedback (TGF) mechanism in rat kidney. TGF is a negative feedback loop in which filtration rate is adjusted on the basis of tubular fluid chloride concentration.…”

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confidence: 99%

Interface methods for biological and biomedical problems

Wei¹

2012

Numer Methods Biomed Eng

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This special issue contains eight papers on interface methods for biological and biomedical problems. Interface problems arise frequently in science and engineering because of the spatial separation of different material properties between regions or because of a force exerted on the materials of differential physical, chemical, and/or biological properties. Theoretical modeling of interface problems often involves partial differential equations (PDEs) with discontinuous coefficients and singular sources. Mathematical techniques, such as the immersed boundary method, the immersed interface method, and the match interface and boundary method, have emerged in the last few decades as suitable candidates for interface modeling and computations. Some of the recent technical development emphasizes high-order schemes, geometric complexity, stability analysis, geometric singularities, and level set approaches for interface tracking. Indeed, interface techniques have been instrumental to a wide range of advances in real-world biological and biomedical problems. The focus of this special issue is on recent advances in computational methods and theoretical models for interface problems and their applications. A broad range of topics are addressed, including the theoretical, analytical, and computational aspects of interface problems and related biomolecular surfaces.The work of Zheng, Yang, and Wei [1] offers a new framework for the biomolecular surface generation based on the PDE transform. Biomolecular surfaces serve as interfaces in elliptic interface problems, such as those in the Poisson-Boltzmann model for electrostatic analysis and the Poisson-Nernst-Planck model for charge permeation. The PDE transform has been shown to be efficient, stable, and robust for the surface modeling of large proteins and virus molecules.The article by Griffith [2] presents the application of an adaptive, staggered-grid version of the immersed boundary method to the three-dimensional simulation of the fluid dynamics of the aortic heart valve.The paper by Zhao [3] provides an improvement to the differential-geometry-based multiscale solvation model for biomolecular surface representation and solvation analysis originally introduced by Wei. A time-dependent Poisson-Boltzmann equation is proposed to make it easier to deal with the nonlinear term in the original Poisson-Boltzmann equation, which is coupled to the Laplace-Beltrami equation for the surface modeling. A filtering process is employed to stabilize the time integration. The new model is validated by biological properties of macromolecules.Sohn, Li, Li, and Lowengrub [4] present an energy variation approach to investigate the role of hydrodynamic forces on three-dimensional axisymmetric multicomponent vesicles. A set of governing equations for the system is derived by the energy variation. Numerical methods are developed to solve governing PDEs, including fourth-order nonlinear and nonlocal ones. Research described in this article may shed light on the role of vesicles in biological...

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Hormonal regulation of salt and water excretion: a mathematical model of whole kidney function and pressure natriuresis

Moss

Thomas

2014

American Journal of Physiology-Renal Physiology

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We present a lumped-nephron model that explicitly represents the main features of the underlying physiology, incorporating the major hormonal regulatory effects on both tubular and vascular function, and that accurately simulates hormonal regulation of renal salt and water excretion. This is the first model to explicitly couple glomerulovascular and medullary dynamics, and it is much more detailed in structure than existing whole organ models and renal portions of multiorgan models. In contrast to previous medullary models, which have only considered the antidiuretic state, our model is able to regulate water and sodium excretion over a variety of experimental conditions in good agreement with data from experimental studies of the rat. Since the properties of the vasculature and epithelia are explicitly represented, they can be altered to simulate pathophysiological conditions and pharmacological interventions. The model serves as an appropriate starting point for simulations of physiological, pathophysiological, and pharmacological renal conditions and for exploring the relationship between the extrarenal environment and renal excretory function in physiological and pathophysiological contexts.

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Modeling TGF‐mediated flow dynamics in a system of three coupled nephrons

Cited by 3 publications

References 21 publications

Architecture of the rat nephron-arterial network: analysis with micro-computed tomography

Architecture of the rat nephron-arterial network: analysis with micro-computed tomography

Interface methods for biological and biomedical problems

Hormonal regulation of salt and water excretion: a mathematical model of whole kidney function and pressure natriuresis

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