A structure preserving model order reduction method for calcium homeostatic system

Bibhukalyan Biswal; Siddhartha Sen; Srinivasu Maka

doi:10.1016/j.mbs.2019.03.002

A structure preserving model order reduction method for calcium homeostatic system

Math Biosci. 2019 Jun:312:8-22. doi: 10.1016/j.mbs.2019.03.002. Epub 2019 Mar 29.

Authors

Bibhukalyan Biswal¹, Siddhartha Sen², Srinivasu Maka²

Affiliations

¹ Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721302, India. Electronic address: bibhukalyan@iitkgp.ac.in.
² Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721302, India.

PMID: 30930136
DOI: 10.1016/j.mbs.2019.03.002

Abstract

Calcium Homeostasis is a complex physiological process. Its mathematical model results in high order differential equation. In this paper, a model order reduction technique, based on time scale separation is proposed for a 27th order Calcium Homeostasis and Bone Remodeling (CHBR) system. The original state-space model after linearization has been decoupled into three reduced order subsystems: "Very-Slow", "Slow" and "Fast", at the same time preserving the structure of the system. The time and frequency response of individual reduced order model has been compared with the response of the original system. Furthermore, the effect of administering a therapeutic daily moderate dose of PTH has been studied with the help of reduced order models.

Keywords: Calcium homeostasis; Eigenvalue clustering; Order reduction; Participation factor; Permutation matrix; Timescale separation.

MeSH terms

Bone Remodeling / physiology*
Calcium / metabolism
Calcium / physiology*
Homeostasis / physiology*
Humans
Models, Biological*

Substances

Calcium