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A structure preserving model order reduction method for calcium homeostatic system.

Bibhukalyan Biswal1, Siddhartha Sen1, Srinivasu Maka1

  • 1Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721302, India.

Mathematical Biosciences
|April 2, 2019
PubMed
Summary

This study simplifies a complex 27th order mathematical model of Calcium Homeostasis and Bone Remodeling (CHBR) using time scale separation. The reduced models accurately represent the original system and aid in studying therapeutic interventions.

Keywords:
Calcium homeostasisEigenvalue clusteringOrder reductionParticipation factorPermutation matrixTimescale separation

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Area of Science:

  • Physiology
  • Biomathematics
  • Systems Biology

Background:

  • Calcium Homeostasis and Bone Remodeling (CHBR) involves complex physiological processes.
  • Mathematical modeling of CHBR results in high-order differential equations, posing computational challenges.

Purpose of the Study:

  • To propose a model order reduction technique for a 27th order CHBR system.
  • To simplify the complex CHBR model while preserving its essential structure and dynamics.

Main Methods:

  • Linearization of the original state-space model.
  • Application of time scale separation for model order reduction.
  • Decoupling the system into "Very-Slow", "Slow", and "Fast" subsystems.

Main Results:

  • Successfully reduced a 27th order CHBR model into three lower-order subsystems.
  • Validated the accuracy of reduced-order models by comparing time and frequency responses with the original system.
  • Demonstrated the utility of reduced models for analyzing therapeutic interventions, such as PTH administration.

Conclusions:

  • Time scale separation is an effective method for reducing the order of complex physiological models like CHBR.
  • Reduced-order CHBR models provide a computationally efficient tool for understanding system dynamics and evaluating treatment strategies.