A feedback oscillator model for circulatory autoregulation
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This CellML version of the model has been checked in COR and OpenCell and the model runs to recreate the published results. We are grateful to the model author for their assistance in getting this CellML version of their model running. A PCEnv session is also available for this model and reproduces part of Figure 5 from the publication.
ValidateCellML confirms this model as valid CellML with full unit consistency.
Model Structure
Circulatory autoregulation can be defined as the ability of an isolated organ to maintain a constant, or almost constant, blood flow rate over a range of perfusion pressures. In the study described here Annraoi De Paor and Patrick Timmons have developed a mathematical model which is based on physiological data. Simulation results demonstrate that autoregulation can be achieved by pressure-induced oscillations in the arteriolar radius.
model diagram
Schematic diagram of the De Paor et al model.
The complete original paper reference is cited below:
A feedback oscillator model for circulatory autoregulation, Annraoi M. De Paor and Patrick Timmons, 1986,
International Journal of Control
, 43, 679-688.
$f=apr^{4.0}$
$\frac{d r}{d \mathrm{time}}=\mathrm{beta}(pr-\mathrm{alpha}(r-\mathrm{r0})^{2.0}\mathrm{ur0}+m)$
$y=(r-\mathrm{r1})\mathrm{ur1}$
$z=\frac{y-\mathrm{x1}}{\mathrm{t1}}$
$\frac{d \mathrm{x1}}{d \mathrm{time}}=\frac{y-\mathrm{x1}}{\mathrm{t1}}$
$q=k(1.0-e^{-(dz)})\mathrm{uz}$
$\frac{d \mathrm{x2}}{d \mathrm{time}}=\frac{q-\mathrm{x2}}{\mathrm{t2}}$
$\frac{d \mathrm{x3}}{d \mathrm{time}}=\frac{\mathrm{x2}-\mathrm{x3}}{\mathrm{t2}}$
$m=\mathrm{x3}\mathrm{phi}$
$\mathrm{phi}=\begin{cases}0.0 & \text{if $r< 0.25$}\\ 0.0 & \text{if $r> 2.0$}\\ 1.0-1.3061225(r-1.125)(r-1.125) & \text{otherwise}\end{cases}$
$\mathrm{ur0}=\begin{cases}1.0 & \text{if $r> \mathrm{r0}$}\\ 0.0 & \text{otherwise}\end{cases}$
$\mathrm{ur1}=\begin{cases}1.0 & \text{if $r> \mathrm{r1}$}\\ 0.0 & \text{otherwise}\end{cases}$
$\mathrm{uz}=\begin{cases}1.0 & \text{if $z> 0.0$}\\ 0.0 & \text{otherwise}\end{cases}$
$\frac{d h}{d \mathrm{time}}=\frac{f-h}{\mathrm{t4}}$
oscillator
circulation
Catherine Lloyd
keyword
James
Lawson
Richard
2007-10-25T10:09:25+13:00
c.lloyd@auckland.ac.nz
1986-00-00 00:00
The model author contacted us and provided the original source code. We were able to use this code to get the CellML version of the model oscillating and recreating the published results.
20
10000
0.1
Catherine
Lloyd
May
This model runs in PCEnv (0.2) and COR to recreate the published results.
The University of Auckland
The Bioengineering Institute
Annraoi
De Paor
M
Catherine
Lloyd
May
wall force
F
Patrick
Timmons
This is the CellML description of De Paor and Timmons's 1986 feedback oscillator model for circulatory autoregulation.
Journal of Pineal Research
Several variables have been annotated with cmeta:id's to allow creation of a PCEnv session. Also added some simulation metadata - duration = 20 time units (dimensionless).
A feedback oscillator model for circulatory autoregulation
43
679
688
The University of Auckland, Bioengineering Institute
2007-09-25T00:00:00+00:00
De Paor and Timmons's 1986 feedback oscillator model for circulatory autoregulation.
laminar flow
f
2007-10-25T09:00:16+13:00
Catherine Lloyd
radius
r