Model number


Short term response of parathyroid gland to changes in plasma Ca(2+) levels. Based on Shrestha et al. 2010 paper.


This JSim Model derived from CellML Implementation by Catherine LLoyd.
A complex bio-mechanism, 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 short-term 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 two-pool, 
linear, time-varying model to describe the dynamics of this calcium homeostasis 
subsystem, the Ca-PTH 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 two-pool, 
linear, time-varying model with an asymmetric reverse sigmoid relation 
characterizes the short-term dynamics of the Ca-PTH axis.

fig 1


The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

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Key terms
calcium homeostasis
parathyroid hormone
analytical model

Please cite in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.