A 1-D model to explore the effects of tissue loading and tissue concentration gradients in the revised Starling principle

Xiaobing Zhang, Roger H. Adamson, Fitz Roy E Curry, Sheldon Weinbaum

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

The recent experiments in Hu et al. (Am J Physiol Heart Circ Physiol 279: H1724-H1736, 2000) and Adamson et al. (J Physiol 557: 889-907, 2004) in frog and rat mesentery microvessels have provided strong evidence supporting the Michel-Weinbaum hypothesis for a revised asymmetric Starling principle in which the Starling force balance is applied locally across the endothelial glycocalyx layer rather than between lumen and tissue. These experiments were interpreted by a three-dimensional (3-D) mathematical model (Hu et al.; Microvasc Res 58: 281-304, 1999) to describe the coupled water and albumin fluxes in the glycocalyx layer, the cleft with its tight junction strand, and the surrounding tissue. This numerical 3-D model converges if the tissue is at uniform concentration or has significant tissue gradients due to tissue loading. However, for most physiological conditions, tissue gradients are two to three orders of magnitude smaller than the albumin gradients in the cleft, and the numerical model does not converge. A simpler multilayer one-dimensional (1-D) analytical model has been developed to describe these conditions. This model is used to extend Michel and Phillips's original 1-D analysis of the matrix layer (J Physiol 388: 421-435, 1987) to include a cleft with a tight junction strand, to explain the observation of Levick (Exp Physiol 76: 825-857, 1991) that most tissues have an equilibrium tissue concentration that is close to 0.4 lumen concentration, and to explore the role of vesicular transport in achieving this equilibrium. The model predicts the surprising finding that one can have steady-state reabsorption at low pressures, in contrast to the experiments in Michel and Phillips, if a backward-standing gradient is established in the cleft that prevents the concentration from rising behind the glycocalyx.

Original languageEnglish (US)
JournalAmerican Journal of Physiology - Heart and Circulatory Physiology
Volume291
Issue number6
DOIs
StatePublished - 2006

Fingerprint

Starlings
Glycocalyx
Tight Junctions
Albumins
Mesentery
Microvessels
Anura
Theoretical Models
Observation
Pressure
Water

Keywords

  • Capillary permeability
  • Endothelial glycocalyx
  • Tight junction
  • Vesicular transport

ASJC Scopus subject areas

  • Physiology

Cite this

A 1-D model to explore the effects of tissue loading and tissue concentration gradients in the revised Starling principle. / Zhang, Xiaobing; Adamson, Roger H.; Curry, Fitz Roy E; Weinbaum, Sheldon.

In: American Journal of Physiology - Heart and Circulatory Physiology, Vol. 291, No. 6, 2006.

Research output: Contribution to journalArticle

@article{76ff5ffd14564238ae34e637b4c1cea4,
title = "A 1-D model to explore the effects of tissue loading and tissue concentration gradients in the revised Starling principle",
abstract = "The recent experiments in Hu et al. (Am J Physiol Heart Circ Physiol 279: H1724-H1736, 2000) and Adamson et al. (J Physiol 557: 889-907, 2004) in frog and rat mesentery microvessels have provided strong evidence supporting the Michel-Weinbaum hypothesis for a revised asymmetric Starling principle in which the Starling force balance is applied locally across the endothelial glycocalyx layer rather than between lumen and tissue. These experiments were interpreted by a three-dimensional (3-D) mathematical model (Hu et al.; Microvasc Res 58: 281-304, 1999) to describe the coupled water and albumin fluxes in the glycocalyx layer, the cleft with its tight junction strand, and the surrounding tissue. This numerical 3-D model converges if the tissue is at uniform concentration or has significant tissue gradients due to tissue loading. However, for most physiological conditions, tissue gradients are two to three orders of magnitude smaller than the albumin gradients in the cleft, and the numerical model does not converge. A simpler multilayer one-dimensional (1-D) analytical model has been developed to describe these conditions. This model is used to extend Michel and Phillips's original 1-D analysis of the matrix layer (J Physiol 388: 421-435, 1987) to include a cleft with a tight junction strand, to explain the observation of Levick (Exp Physiol 76: 825-857, 1991) that most tissues have an equilibrium tissue concentration that is close to 0.4 lumen concentration, and to explore the role of vesicular transport in achieving this equilibrium. The model predicts the surprising finding that one can have steady-state reabsorption at low pressures, in contrast to the experiments in Michel and Phillips, if a backward-standing gradient is established in the cleft that prevents the concentration from rising behind the glycocalyx.",
keywords = "Capillary permeability, Endothelial glycocalyx, Tight junction, Vesicular transport",
author = "Xiaobing Zhang and Adamson, {Roger H.} and Curry, {Fitz Roy E} and Sheldon Weinbaum",
year = "2006",
doi = "10.1152/ajpheart.01160.2005",
language = "English (US)",
volume = "291",
journal = "American Journal of Physiology - Renal Fluid and Electrolyte Physiology",
issn = "1931-857X",
publisher = "American Physiological Society",
number = "6",

}

TY - JOUR

T1 - A 1-D model to explore the effects of tissue loading and tissue concentration gradients in the revised Starling principle

AU - Zhang, Xiaobing

AU - Adamson, Roger H.

AU - Curry, Fitz Roy E

AU - Weinbaum, Sheldon

PY - 2006

Y1 - 2006

N2 - The recent experiments in Hu et al. (Am J Physiol Heart Circ Physiol 279: H1724-H1736, 2000) and Adamson et al. (J Physiol 557: 889-907, 2004) in frog and rat mesentery microvessels have provided strong evidence supporting the Michel-Weinbaum hypothesis for a revised asymmetric Starling principle in which the Starling force balance is applied locally across the endothelial glycocalyx layer rather than between lumen and tissue. These experiments were interpreted by a three-dimensional (3-D) mathematical model (Hu et al.; Microvasc Res 58: 281-304, 1999) to describe the coupled water and albumin fluxes in the glycocalyx layer, the cleft with its tight junction strand, and the surrounding tissue. This numerical 3-D model converges if the tissue is at uniform concentration or has significant tissue gradients due to tissue loading. However, for most physiological conditions, tissue gradients are two to three orders of magnitude smaller than the albumin gradients in the cleft, and the numerical model does not converge. A simpler multilayer one-dimensional (1-D) analytical model has been developed to describe these conditions. This model is used to extend Michel and Phillips's original 1-D analysis of the matrix layer (J Physiol 388: 421-435, 1987) to include a cleft with a tight junction strand, to explain the observation of Levick (Exp Physiol 76: 825-857, 1991) that most tissues have an equilibrium tissue concentration that is close to 0.4 lumen concentration, and to explore the role of vesicular transport in achieving this equilibrium. The model predicts the surprising finding that one can have steady-state reabsorption at low pressures, in contrast to the experiments in Michel and Phillips, if a backward-standing gradient is established in the cleft that prevents the concentration from rising behind the glycocalyx.

AB - The recent experiments in Hu et al. (Am J Physiol Heart Circ Physiol 279: H1724-H1736, 2000) and Adamson et al. (J Physiol 557: 889-907, 2004) in frog and rat mesentery microvessels have provided strong evidence supporting the Michel-Weinbaum hypothesis for a revised asymmetric Starling principle in which the Starling force balance is applied locally across the endothelial glycocalyx layer rather than between lumen and tissue. These experiments were interpreted by a three-dimensional (3-D) mathematical model (Hu et al.; Microvasc Res 58: 281-304, 1999) to describe the coupled water and albumin fluxes in the glycocalyx layer, the cleft with its tight junction strand, and the surrounding tissue. This numerical 3-D model converges if the tissue is at uniform concentration or has significant tissue gradients due to tissue loading. However, for most physiological conditions, tissue gradients are two to three orders of magnitude smaller than the albumin gradients in the cleft, and the numerical model does not converge. A simpler multilayer one-dimensional (1-D) analytical model has been developed to describe these conditions. This model is used to extend Michel and Phillips's original 1-D analysis of the matrix layer (J Physiol 388: 421-435, 1987) to include a cleft with a tight junction strand, to explain the observation of Levick (Exp Physiol 76: 825-857, 1991) that most tissues have an equilibrium tissue concentration that is close to 0.4 lumen concentration, and to explore the role of vesicular transport in achieving this equilibrium. The model predicts the surprising finding that one can have steady-state reabsorption at low pressures, in contrast to the experiments in Michel and Phillips, if a backward-standing gradient is established in the cleft that prevents the concentration from rising behind the glycocalyx.

KW - Capillary permeability

KW - Endothelial glycocalyx

KW - Tight junction

KW - Vesicular transport

UR - http://www.scopus.com/inward/record.url?scp=33845395242&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845395242&partnerID=8YFLogxK

U2 - 10.1152/ajpheart.01160.2005

DO - 10.1152/ajpheart.01160.2005

M3 - Article

C2 - 16905594

AN - SCOPUS:33845395242

VL - 291

JO - American Journal of Physiology - Renal Fluid and Electrolyte Physiology

JF - American Journal of Physiology - Renal Fluid and Electrolyte Physiology

SN - 1931-857X

IS - 6

ER -