Model Status
This CellML model cannot be opened in COR and it cannot be run in PCEnv due to the use of vectors - something which may be included in the CellML 1.2 specification. The way this model is written it is not ideally suited for expression in CellML. However, we have attempted to describe the model in CellML with the hope that in the future it may be further validated and curated.
Model Structure
ABSTRACT: In this paper, concepts from network automata are adapted and extended to model complex biological systems. Specifically, systems of nephrons, the operational units of the kidney, are modelled and the dynamics of such systems are explored. Nephron behaviour can fluctuate widely and, under certain conditions, become chaotic. However, the behaviour of the whole kidney remains remarkably stable and blood solute levels are maintained under a wide range of conditions even when many nephrons are damaged or lost. A network model is used to investigate the stability of systems of nephrons and interactions between nephrons. More sophisticated dynamics are explored including the observed oscillations in single nephron filtration rates and the development of stable ionic and osmotic gradients in the inner medulla which contribute to the countercurrent exchange mechanism. We have used the model to explore the effects of changes in input parameters including hydrostatic and osmotic pressures and concentrations of ions, such as sodium and chloride. The intrinsic nephron control, tubuloglomerular feedback, is included and the effects of coupling between nephrons are explored in two-, eight- and 72-nephron models.
The original paper reference is cited below:
A computational model for emergent dynamics in the kidney, Moss R, Kazmierczak E, Kirley M, and Harris P, 2009, Philosophical Transactions of the Royal Society A, 367, 2125-40. PubMed ID: 19414449
Schematic diagram representing the model for the single-nephron tubule as a network automata, showing the edges that capture fluid flow, solute transport and tubulo-glomerular feedback.
$t$
$t=\mathrm{time}$
$\mathrm{delta\_t}=1.0$
R_A
Resistance of the afferent arteriole
$\mathrm{R\_A}_{t+\mathrm{delta\_t}}=\mathrm{epsilon}_{t}e^{\mathrm{gamma}\mathrm{H\_A}}$
P_G
hydrostatic pressure in the glomerulus
$\mathrm{P\_G}_{t+\mathrm{delta\_t}}=\frac{\mathrm{P\_V}+\mathrm{P\_A}\frac{\mathrm{R\_E}_{t}}{\mathrm{R\_A}_{t}}\frac{\mathrm{C\_A}_{t}}{\mathrm{C\_E}_{t}}}{(1.0+\frac{\mathrm{R\_E}_{t}}{\mathrm{R\_A}_{t}})\frac{\mathrm{C\_A}_{t}}{\mathrm{C\_E}_{t}}}$
phi
tubuloglomerular feedback signal
$\mathrm{phi}_{t+\mathrm{delta\_t}}=\mathrm{epsilon\_max}-\frac{\mathrm{psi}}{1.0+e^{\mathrm{kappa}\mathrm{Na\_M}_{t-\mathrm{D\_TGF}}-\mathrm{Na\_half}}}$
epsilon
response of the afferent arteriole to the tubuloglomerular feedback signal
$\mathrm{epsilon}_{t+\mathrm{delta\_t}}=\frac{\mathrm{phi}_{t}+\mathrm{epsilon}_{t}(\frac{2.0\mathrm{zeta}}{\mathrm{omega}\mathrm{delta}}+\frac{2.0}{(\mathrm{omega}\mathrm{delta})^{2.0}})-\frac{\mathrm{epsilon}_{t-\mathrm{delta}}}{(\mathrm{omega}\mathrm{delta})^{2.0}}}{1.0+\frac{2.0\mathrm{zeta}}{\mathrm{omega}\mathrm{delta}}+\frac{1.0}{(\mathrm{omega}\mathrm{delta})^{2.0}}}$
pi_G
oncotic pressure in the glomerulus
$\mathrm{pi\_G}=\mathrm{pi}\frac{\mathrm{C\_A}+\mathrm{C\_E}}{2.0}$
pi
oncotic pressure
$\mathrm{pi}_{C}=aC+bC^{2.0}$
SNGFR
filtration rate at the glomerulus
$\mathrm{SNGFR}=\mathrm{Kf}(\mathrm{P\_G}-\mathrm{P\_BC}+\mathrm{pi\_G})$
Na_I
sodium filtrate
$\mathrm{Na\_I}_{t}=\frac{\mathrm{Na\_R}_{t}}{0.67}$
H2O_I
water filtrate
$\mathrm{H2O\_I}_{t}=\frac{\mathrm{H2O\_R}_{t}}{0.67}$
H2O_D_M
water conservation
$\mathrm{H2O\_D\_M}_{t}=\mathrm{H2O\_D\_M}_{t+\mathrm{delta\_t}}$
Na_D_M
sodium conservation
$\mathrm{Na\_D\_M}_{t}=\mathrm{Na\_D\_M}_{t+\mathrm{delta\_t}}$
Na_D
sodium concentration in the descending limb
$\mathrm{Na\_D}_{t}=\frac{\mathrm{Na\_M}_{t}}{\mathrm{H2O\_M}_{t+\mathrm{delta\_t}}}\mathrm{H2O\_D}_{t+\mathrm{delta\_t}}$
Na_M
sodium concentration in the interstitial fluid
$\mathrm{Na\_M}_{t+\mathrm{delta\_t}}=\mathrm{H2O\_M}_{t}(\frac{\mathrm{Na\_A}_{t+\mathrm{delta\_t}}}{\mathrm{H2O\_A}_{t}}+\mathrm{Na\_G})$
H2O_D
water in the descending limb
$\mathrm{H2O\_D}_{t+\mathrm{delta\_t}}=\frac{\mathrm{Na\_D}_{t}}{\mathrm{Na\_D\_M}_{t}}\mathrm{H2O\_D\_M}_{t}$
H2O_M
water in the interstitial fluid
$\mathrm{H2O\_M}_{t+\mathrm{delta\_t}}=\frac{\mathrm{Na\_M}_{t}}{\mathrm{Na\_D\_M}_{t}}\mathrm{H2O\_D\_M}_{t}$
Na_A
sodium concentration in the ascending limb
$\mathrm{Na\_A}_{t+\mathrm{delta\_t}}=\frac{\mathrm{H2O\_A}_{t}}{\mathrm{H2O\_M\_A}_{t+\mathrm{delta\_t}}}(\mathrm{Na\_M\_A}_{t}-\mathrm{Na\_G}_{t}\mathrm{H2O\_M}_{t})$
Na_G
sodium concentration gradient between the interstitial fluid and the ascending limb
$\mathrm{Na\_G}=\mathrm{Na\_M}-\mathrm{Na\_A}$
H2O_A
water in the ascending limb
H2O_I_IF
water in ?
Na_I_IF
sodium in ?
Na_M_A
sodium concentration in the interstitial fluid and the ascending limb
$\mathrm{Na\_M\_A}=\mathrm{Na\_M}+\mathrm{Na\_A}$
H2O_M_A
water concentration in the interstitial fluid and the ascending limb
$\mathrm{H2O\_M\_A}=\mathrm{H2O\_M}+\mathrm{H2O\_A}$
R_ADH
antidiuretic hormone reabsorption
$\mathrm{R\_ADH}=\frac{\lg (\mathrm{ADH\_I}\times 1e12)}{2.0}$
R_ALD
aldosterone reabsorption
$\mathrm{R\_ALD}=\frac{\lg (\mathrm{ALD\_I}\times 1e11)}{3.0}$
H2O_R
water reabsorption
$\mathrm{H2O\_R}=\mathrm{R\_ADH}(\mathrm{H2O\_I}-\mathrm{Na\_I}\frac{\mathrm{H2O\_I\_IF}}{\mathrm{Na\_I\_IF}})$
Na_R
sodium reabsorption
$\mathrm{Na\_R}=\mathrm{R\_ALD}\mathrm{Na\_max}\mathrm{Na\_I}$
Robert
Moss
Catherine Lloyd
keyword
nephron
ion_transport
kidney
2009-05-05T10:11:51+12:00
NOTE: This is not a modification to the CellML file (as this is version 1), but I want to document how the CellML model varies from the published model, and make the curation notes for this model visible...
This CellML model cannot be opened in COR and it cannot be run in PCEnv due to the use of vectors - something which may be included in the CellML 1.2 specification. The way this model is written it is not ideally suited for expression in CellML. However, we have attempted to describe the model in CellML with the hope that in the future it may be further validated and curated.
Also, regardless of the use of vectors - there will be other errors in the model as we haven't been able to use the tools to properly validate the code.
Finally, there are some issues that we are aware of. In certain places the units don't balance. Also the CellML model is underconstrained. There are several parameters which need a constant value or a defining equation. These include:
C_E, C_A, a, b, C, Na_half, D_TGF, delta, Pi, H2O_I_IF, Na_I_IF, H2O_A, ADH_I, ALD_I and Na_max.
For the moment these have been assigned a temporary value (a complete guess in most cases!).
We will continue to work with the original model author to try to get some of these values.
c.lloyd@auckland.ac.nz
2009-05-00 00:00
Philosophical Transactions of the Royal Society A
Catherine
Lloyd
May
This CellML model cannot be opened in COR and it cannot be run in PCEnv due to the use of vectors - something which may be included in the CellML 1.2 specification. The way this model is written it is not ideally suited for expression in CellML. However, we have attempted to describe the model in CellML with the hope that in the future it may be further validated and curated.
Also, regardless of the use of vectors - there will be other errors in the model as we haven't been able to use the tools to properly validate the code.
Finally, there are some issues that we are aware of. In certain places the units don't balance. Also the CellML model is underconstrained. There are several parameters which need a constant value or a defining equation. These include:
C_E, C_A, a, b, C, Na_half, D_TGF, delta, Pi, H2O_I_IF, Na_I_IF, H2O_A, ADH_I, ALD_I and Na_max.
For the moment these have been assigned a temporary value (a complete guess in most cases!).
We will continue to work with the original model author to try to get some of these values.
2009-05-05T00:00:00+00:00
Peter
Harris
Michael
Kirley
The University of Auckland
Auckland Bioengineering Institute
Ed
Kazmierczak
A computational model for emergent dynamics in the kidney
13
2125
2140
2009-06
19414449
Catherine
Lloyd
May