Renal countercurrent system: Role of collecting duct convergence and pelvic urea predicted from a mathematical model

Lory, Peter; Gilg, Albert; Horster, Michael

doi:10.1007/bf00276508

Cited by 36 publications

(21 citation statements)

References 54 publications

(93 reference statements)

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“…Cf. [4,7,18,19] (together with the references cited there) and the recent results of [56]. Again, most of these measurements are in rabbits.…”

Section: Simulationsand Resultsmentioning

confidence: 88%

“…Table 2 lists those thermodynamic parameters which are held fixed during the computations. They are discussed and jüstified in [4,19]. Table 3.…”

Section: Simulationsand Resultsmentioning

confidence: 99%

“…The length of the distal tubule is L DT = 2.625 mm. The cross-sectional area AC(S) of the central core and the circumference of the total medulla are chosen analogously to [4]. The other parameters are allowed to vary over certain intervals.…”

Section: Simulationsand Resultsmentioning

confidence: 99%

“…The diagram reflects the impermeability of the ALH to water and the impermeability of the CD to salt (cf. the discussion in [4]). In äddition, Figure 1 defines a numbering of the various segments.…”

Section: The Boundary-value Problem Modeling the Renal Concentrating mentioning

confidence: 92%

“…The Systems modeling technique used in this section has been employed previously by several authors to stud[y various aspects of the integrated renal fimction [1,4,7,8,[12][13][14][15][16][17][18][19][20]. Finite-difference methods [12-14, 16, 20-23], quasilinearization [1,[24][25][26][27], invariant imbedding [27][28][29][30][31], and multiple shooting [4,17,32] have been suggested for the numerical Solution of the resulting boundary-value problems. A semidiscrete method combining collocation and shooting has been given in [19,33].…”

Section: Cf5(s)mentioning

confidence: 99%

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The kidney model as an inverse problem

Breinbauer¹,

Lory

1991

Applied Mathematics and Computation

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The mammalian kidney is modeled by a multipoint boundary-value problem for a System of nonlinear ordinary differential equations. A corresponding inverse problem is presented, which allows the rigorous judgement of the potential of the given modeling technique. For its numerical Solution a discretization is proposed, which is tailor-made for kidney models. It leads to a nonlinear-programming problem with nonlinear equality and inequality constraints. The suggested methods are applied to current research problems in renal physiology.

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“…Cf. [4,7,18,19] (together with the references cited there) and the recent results of [56]. Again, most of these measurements are in rabbits.…”

Section: Simulationsand Resultsmentioning

confidence: 88%

“…Table 2 lists those thermodynamic parameters which are held fixed during the computations. They are discussed and jüstified in [4,19]. Table 3.…”

Section: Simulationsand Resultsmentioning

confidence: 99%

Section: Simulationsand Resultsmentioning

confidence: 99%

Section: The Boundary-value Problem Modeling the Renal Concentrating mentioning

confidence: 92%

Section: Cf5(s)mentioning

confidence: 99%

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The kidney model as an inverse problem

Breinbauer¹,

Lory

1991

Applied Mathematics and Computation

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Urinary Concentration and Dilution: Models

Stephenson

1992

Comprehensive Physiology

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The sections in this article are: Whole‐Body Water and Solute Balance Osmolal Clearance Effect on Plasma Osmolality of Urine Flow of a Given Osmolality Hypertonic Urine Implies a Hypotonic Tubular Reabsorbate and Vice Versa Free Water Clearance Antidiuretic Hormone Controls Water Excretion Functional Implications of Renal Architecture Production of Hyperosmotic Urine Is Related to the Loop of Henle Significance of the S‐Shaped Configuration of the Mammalian Nephron for the Concentration of Urine New Functional Features Introduced by the S‐Shaped Configuration A Short History of Models of the Renal Counterflow System Active Water Transport Concentration by Differential Permeabilities and Counterflow Concentration by Multiplication of a “Single Effect” along the Loop of Henle Active Salt Transport out of the AHL Is the Probable Single Effect Experimental Predictions of the Kuhn Models Problems with the Kuhn Models Vasa Recta Models Nephrovascular Models Equations for the Renal Medulla Differential Equations Integrated Mass Balance Equations Generalized Multiplication Rule Nephrovascular Coupling Transmural Fluxes Analytical Solution of the Differential Equations Solutions for Single Flow Tubes Analytical Solutions of Multitube Counterflow Problems Solutions for Central Core Model Externally Driven Central Core Multiplier Multiplication in Inner and Outer Medullae Non‐Zero Diffusion Coefficient Solution of Time‐Dependent Equations Numerical Solution of the Differential Equations Method of Lines Shooting Method Quasilinearization Finite Difference Methods Results of Computer Simulation Origin of Inner Medullary Concentration Gradient Role of Collecting Duct Role of Vasa Recta Transition from Diuresis to Antidiuresis Free‐Energy Balance in Renal Counterflow Systems Summary and Future Directions

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Intrarenal Control of Medullary Blood Flow and the Urinary Concentrating Mechanism

Moore¹

1984

Nephrology

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Renal countercurrent system: Role of collecting duct convergence and pelvic urea predicted from a mathematical model

Cited by 36 publications

References 54 publications

The kidney model as an inverse problem

The kidney model as an inverse problem

Urinary Concentration and Dilution: Models

Intrarenal Control of Medullary Blood Flow and the Urinary Concentrating Mechanism

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