Shrestha2010_HypoCalcemia_PTHresponse
This a model from the article:
A mathematical model of parathyroid hormone response to acute changes in plasma ionized calcium concentration in humans.
Shrestha RP, Hollot CV, Chipkin SR, Schmitt CP, Chait Y.
Math Biosci.2010 Jul;226(1):4657.
20406649,
Abstract:
A complex biomechanism, commonly referred to as calcium homeostasis, regulates plasma ionized calcium (Ca(2+)) concentration in the human body within a narrow range which is crucial for maintaining normal physiology and metabolism. Taking a step towards creating a complete mathematical model of calcium homeostasis, we focus on the shortterm dynamics of calcium homeostasis and consider the response of the parathyroid glands to acute changes in plasma Ca(2+) concentration. We review available models, discuss their limitations, then present a twopool, linear, timevarying model to describe the dynamics of this calcium homeostasis subsystem, the CaPTH axis. We propose that plasma PTH concentration and plasma Ca(2+) concentration bear an asymmetric reverse sigmoid relation. The parameters of our model are successfully estimated based on clinical data corresponding to three healthy subjects that have undergone induced hypocalcemic clamp tests. In the first validation of this kind, with parameters estimated separately for each subject we test the model's ability to predict the same subject's induced hypercalcemic clamp test responses. Our results demonstrate that a twopool, linear, timevarying model with an asymmetric reverse sigmoid relation characterizes the shortterm dynamics of the CaPTH axis.
The model corresponds to hypocalcemic clamp test explained in the paper and parameter values used in the model are that of "subject 1". In order to obtain the plots corresponding to "subject 2" and "subject 3" the following parameters to be changed: lambda_1, lambda_2, m1, m2, R, beta, x1_n, x2_n, x2_min, x2_max, Ca0, Ca1, t0 and alpha.
parameter  Subject 1  Subject 2  Subject 3 

lambda_1  0.0125  0.0122  0.0269 
lambda_2  0.5595  0.4642  0.4935 
m1  112.5200  150.0000  90.8570 
m2  15.0000  15.0000  15.0000 
R  1.2162  1.1627  1.1889 
beta  10e+06  10e+06  10e+06 
x1_n  490.7800  452.8200  298.8200 
x2_n  6.6290  9.5894  5.4600 
x2_min  0.6697  1.4813  0.8287 
x2_max  14.0430  17.8710  15.1990 
Ca0  1.2550  1.2369  1.2475 
Ca1  0.1817  0.2211  0.1985 
t0  575  577  575 
alpha  0.0442  0.0488  0.0472 
This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 20052010 The BioModels.net Team.
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To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le NovÃ¨re N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.
 A mathematical model of parathyroid hormone response to acute changes in plasma ionized calcium concentration in humans.
 Shrestha RP, Hollot CV, Chipkin SR, Schmitt CP, Chait Y
 Mathematical biosciences , 7/ 2010 , Volume 226 , pages: 4657
 Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003, USA.
 A complex biomechanism, commonly referred to as calcium homeostasis, regulates plasma ionized calcium (Ca(2+)) concentration in the human body within a narrow range which is crucial for maintaining normal physiology and metabolism. Taking a step towards creating a complete mathematical model of calcium homeostasis, we focus on the shortterm dynamics of calcium homeostasis and consider the response of the parathyroid glands to acute changes in plasma Ca(2+) concentration. We review available models, discuss their limitations, then present a twopool, linear, timevarying model to describe the dynamics of this calcium homeostasis subsystem, the CaPTH axis. We propose that plasma PTH concentration and plasma Ca(2+) concentration bear an asymmetric reverse sigmoid relation. The parameters of our model are successfully estimated based on clinical data corresponding to three healthy subjects that have undergone induced hypocalcemic clamp tests. In the first validation of this kind, with parameters estimated separately for each subject we test the model's ability to predict the same subject's induced hypercalcemic clamp test responses. Our results demonstrate that a twopool, linear, timevarying model with an asymmetric reverse sigmoid relation characterizes the shortterm dynamics of the CaPTH axis.
Metadata information
 Model originally submitted by : Vijayalakshmi Chelliah
 Submitted: Nov 17, 2010 2:15:24 PM
 Last Modified: Oct 9, 2014 5:15:39 PM
Revisions

Version: 2
 Submitted on: Oct 9, 2014 5:15:39 PM
 Submitted by: Vijayalakshmi Chelliah
 With comment: Current version of Shrestha2010_HypoCalcemia_PTHresponse

Version: 1
 Submitted on: Nov 17, 2010 2:15:24 PM
 Submitted by: Vijayalakshmi Chelliah
 With comment: Original import of Shrestha2010_HypoCalcemia_PTHresponse
(added: 09 Dec 2010, 16:49:39, updated: 09 Dec 2010, 16:49:39)