Pilhwa Lee, Daniel A. Beard1Department of Physiology and Biotechnology and Bioengineering Center, Medical College of Wisconsin, Milwaukee, WI

Computer modeling of peristaltic contraction and solute concentration in 3D inner medulla of the rat

Abstract

Modeling and simulation

Results / Conclusions

Future Work

References

The primary physiological mechanism governing concentration of solutes in the renal inner medulla is thought to be the passive permeation of the solutes through tubules. Yet it is recognized that other factors, such as contraction of the renal papilla, contribute to the concentration mechanism. In order to investigate how tubular water transport is affected by pelvic contraction, we developed a computational model based on a realistic three-dimensional representation of the inner medulla. The advection of solutes in the intra-tubular domains is described in a Lagrangian formulation. The diffusion of solutes at the extra-tubular domain and the interstitial fluid flow is described in the Eulerian domain. The osmotic effect across the tubule is represented by the radial change of the tubule governed by Darcy’s law. Model simulations reveal the potential effects of contraction on concentration gradients in the papilla.

Electrokinetic transport in interstitial tissue

Interstitial flow in porous medium

Epithelial transport and osmotic effect

Luminal advection

Peristaltic contraction

Diffusion

Repulsion from tubule

Drift from electrical potential

Darcy’s law

Contractive force from pelvic wall

Incompressibility

[1] B. Schmidt-Nielsen and B. Graves, 1982, Changes in fluid compartments in hampster renal papilla to peristalsis in the pelvic wall, Kidney Int., 22, 613-625

[2] B. Schmidt-Nielsen and B. Schmidt-Nielsen, 2011, On the function of the mammalian renal papilla and the peristalsis of the surrounding pelvis, Acta Physiol., 202, 379-385

[3] P. Lee, 2007, The immersed boundary method with advection-electrodiffusion, Ph.D. Dissertation, New York University

At basolateral membrane

At apical membrane

Axisymmetric Navier-Stokes 1D flow

Tubular pressure transmitted from pelvic wall

Constant concentration at the inflow

Luminal fluid flow

Simulation

Longitudinal contraction

Generated elastic force in pelvic wall

Three dimensional 40 x 40 x 40 grids in interstitial tissue,One dimensional 128 nodes in tubule,An immersed boundary method [3], PETSc, CUDA

Electrical effects in the peristaltic concentration

Fig 3 (a) Peristalsis at the pelvic wall (b) Solute and water transport across epithelium wall; For solutes, sodium and chloride ions as well as urea are considered.

Fig 1 (a) Schematic drawing of a hamster papilla [1] (b,c) Peristalsis moves the green colored urine in waves through collecting ducts in the renal papilla [2]

Fig 2 A cross-section of papilla 300 above the tip, collecting ducts (a) closed with peristaltic contraction and (b) open with peristaltic relaxation [1]

(a) (b) (c)

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(a) (b)

Advection from interstitial flow

Electrical potentialCONCLUSION: Hydrostatic pressure redistribution from peristalsis and water transport at the tubular epithelium is not sufficient to change tubular concentration gradient without electrical effects.

Electrical force

Passive permeation between epithelium and lumen

Interstitial elasticity