For subject1, alpha=0.0569; subject2, alpha=0.0563; subject3, alpha=0.0421
For subject1, Ca0=1.22; subject2, Ca0=1.2513; subject3, Ca0=1.2480
For subject1, lambda_2=0.5595; subject2, lambda_2=0.4642; subject3, lambda_2=0.4935
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 This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2010 The BioModels.net Team. For more information see the terms of use . 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 Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.
For subject1, lambda_1=0.0125; subject2, lambda_1=0.0122; subject3, lambda_1=0.0269
Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003, USA
For subject1, t0=575; subject2, t0=575; subject3, t0=575
For subject1, x2_max=14.043; subject2, x2_max=17.871; subject3, x2_max=15.199