A nonlinear model for myogenic regulation of blood flow to bone: Equilibrium states and stability characteristics

Research output: Contribution to journalArticle

Abstract

A simple compartmental model for myogenic regulation of interstitial pressure in bone is developed, and the interaction between changes in interstitial pressure and changes in arterial and venous resistances is studied. The arterial resistance is modeled by a myogenic model that depends on transmural pressure, and the venous resistance is modeled by using a vascular waterfall. Two series capacitances model blood storage in the vascular system and interstitial fluid storage in the extravascular space. The static results mimic the observed effect that vasodilators work less well in bone than do vasoconstrictors. The static results also show that the model gives constant flow rates over a limited range of arterial pressure. The dynamic model shows unstable behavior at small values of bony capacitance and at high enough myogenic gain. At low myogenic gain, only a single equilibrium state is present, but at high enough myogenic gain, two new equilibrium states appear. At additional increases in gain, one of the two new states merges with and then separates from the original state, and the original state becomes a saddle point. The appearance of the new states and the transition of the original state to a saddle point do not depend on the bony capacitance, and these results are relevant to general fluid compartments. Numerical integration of the rate equations confirms the stability calculations and shows limit cycling behavior in several situations. The relevance of this model to circulation in bone and to other compartments is discussed.

Original languageEnglish (US)
Pages (from-to)211-221
Number of pages11
JournalAnnals of biomedical engineering
Volume24
Issue number2
DOIs
StatePublished - Jan 1 1996
Externally publishedYes

Fingerprint

Bone
Blood
Capacitance
Fluids
Dynamic models
Flow rate

Keywords

  • Compartmental model
  • Fluid capacitance
  • Limit cycling

ASJC Scopus subject areas

  • Biomedical Engineering

Cite this

@article{d77fb35bbbb64a2e8a5d083af57e553c,
title = "A nonlinear model for myogenic regulation of blood flow to bone: Equilibrium states and stability characteristics",
abstract = "A simple compartmental model for myogenic regulation of interstitial pressure in bone is developed, and the interaction between changes in interstitial pressure and changes in arterial and venous resistances is studied. The arterial resistance is modeled by a myogenic model that depends on transmural pressure, and the venous resistance is modeled by using a vascular waterfall. Two series capacitances model blood storage in the vascular system and interstitial fluid storage in the extravascular space. The static results mimic the observed effect that vasodilators work less well in bone than do vasoconstrictors. The static results also show that the model gives constant flow rates over a limited range of arterial pressure. The dynamic model shows unstable behavior at small values of bony capacitance and at high enough myogenic gain. At low myogenic gain, only a single equilibrium state is present, but at high enough myogenic gain, two new equilibrium states appear. At additional increases in gain, one of the two new states merges with and then separates from the original state, and the original state becomes a saddle point. The appearance of the new states and the transition of the original state to a saddle point do not depend on the bony capacitance, and these results are relevant to general fluid compartments. Numerical integration of the rate equations confirms the stability calculations and shows limit cycling behavior in several situations. The relevance of this model to circulation in bone and to other compartments is discussed.",
keywords = "Compartmental model, Fluid capacitance, Limit cycling",
author = "Timothy Harrigan",
year = "1996",
month = "1",
day = "1",
doi = "10.1007/BF02667350",
language = "English (US)",
volume = "24",
pages = "211--221",
journal = "Annals of Biomedical Engineering",
issn = "0090-6964",
publisher = "Springer Netherlands",
number = "2",

}

TY - JOUR

T1 - A nonlinear model for myogenic regulation of blood flow to bone

T2 - Equilibrium states and stability characteristics

AU - Harrigan, Timothy

PY - 1996/1/1

Y1 - 1996/1/1

N2 - A simple compartmental model for myogenic regulation of interstitial pressure in bone is developed, and the interaction between changes in interstitial pressure and changes in arterial and venous resistances is studied. The arterial resistance is modeled by a myogenic model that depends on transmural pressure, and the venous resistance is modeled by using a vascular waterfall. Two series capacitances model blood storage in the vascular system and interstitial fluid storage in the extravascular space. The static results mimic the observed effect that vasodilators work less well in bone than do vasoconstrictors. The static results also show that the model gives constant flow rates over a limited range of arterial pressure. The dynamic model shows unstable behavior at small values of bony capacitance and at high enough myogenic gain. At low myogenic gain, only a single equilibrium state is present, but at high enough myogenic gain, two new equilibrium states appear. At additional increases in gain, one of the two new states merges with and then separates from the original state, and the original state becomes a saddle point. The appearance of the new states and the transition of the original state to a saddle point do not depend on the bony capacitance, and these results are relevant to general fluid compartments. Numerical integration of the rate equations confirms the stability calculations and shows limit cycling behavior in several situations. The relevance of this model to circulation in bone and to other compartments is discussed.

AB - A simple compartmental model for myogenic regulation of interstitial pressure in bone is developed, and the interaction between changes in interstitial pressure and changes in arterial and venous resistances is studied. The arterial resistance is modeled by a myogenic model that depends on transmural pressure, and the venous resistance is modeled by using a vascular waterfall. Two series capacitances model blood storage in the vascular system and interstitial fluid storage in the extravascular space. The static results mimic the observed effect that vasodilators work less well in bone than do vasoconstrictors. The static results also show that the model gives constant flow rates over a limited range of arterial pressure. The dynamic model shows unstable behavior at small values of bony capacitance and at high enough myogenic gain. At low myogenic gain, only a single equilibrium state is present, but at high enough myogenic gain, two new equilibrium states appear. At additional increases in gain, one of the two new states merges with and then separates from the original state, and the original state becomes a saddle point. The appearance of the new states and the transition of the original state to a saddle point do not depend on the bony capacitance, and these results are relevant to general fluid compartments. Numerical integration of the rate equations confirms the stability calculations and shows limit cycling behavior in several situations. The relevance of this model to circulation in bone and to other compartments is discussed.

KW - Compartmental model

KW - Fluid capacitance

KW - Limit cycling

UR - http://www.scopus.com/inward/record.url?scp=0030111107&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030111107&partnerID=8YFLogxK

U2 - 10.1007/BF02667350

DO - 10.1007/BF02667350

M3 - Article

C2 - 8678353

AN - SCOPUS:0030111107

VL - 24

SP - 211

EP - 221

JO - Annals of Biomedical Engineering

JF - Annals of Biomedical Engineering

SN - 0090-6964

IS - 2

ER -