Shrestha2010_HyperCalcemia_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):46-57.
20406649,

Abstract:

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.

The model corresponds to hypercalcemic 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, t0, Ca0, Ca1 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
1.2200
1.2513
1.2480

Ca1
0.2624
0.2267
0.2132

t0
575
575
575

alpha
0.0569
0.0563
0.0421

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