Feedback analysis of calcium homeostasis and parturient paresis

Abstract

In the technological and engineering sciences feedback control methods have been studied and applied extensively to man-made systems. Recently, there has been an increasing interest as to the applicability of feedback and control theory to the life sciences. In a previous paper (H. El-Samad et al., "Calcium homeostasis: a feedback control point of view," Proceedings of the 2000 American Control Conference, Chicago, Il, June 2000), the applicability of control theory to the analysis of calcium homeostasis was investigated. A mathematical model for this homeostatic mechanism was derived. Here, the authors provide an overview of this model, and then use it to study a pathological condition of the calcium regulatory mechanism in dairy cows. The clinical condition studied is referred to as parturient paresis (milk fever) and is the result of severe hypocalcemia at the time of parturition. The authors show that their mathematical feedback model for calcium homeostasis exhibits dynamic behavior that can correspond to milk fever. They then present a rigorous mathematical result that guarantees the presence of milk fever-like dynamics for a range of model parameters.