A control engineering model of calcium regulation.

Abstract

A control engineering perspective provides a framework for representing important mechanistic details of the calcium (Ca) regulatory system efficiently. The resulting model facilitates the testing of hypotheses about mechanisms underlying the emergence of known Ca-related pathologies. The objective of this work is to develop a comprehensive computational model that will enable quantitative understanding of plasma Ca regulation under normal and pathological conditions. Ca regulation is represented as an engineering control system where physiological subprocesses are mapped onto corresponding block components (sensor, controller, actuator, and process), and underlying mechanisms are represented by differential equations. The resulting model is validated with clinical observations of induced hypo- or hypercalcemia in healthy subjects, and its applicability is demonstrated by comparing model predictions of Ca-related pathologies to corresponding clinical data. Our model accurately predicts clinical responses to induced hypo- and hypercalcemia in healthy subjects within a framework that facilitates the representation of Ca-related pathologies in terms of control system component defects. The model also enables a deeper understanding of the emergence of pathologies and the testing of hypotheses about related features of Ca regulation-for example, why primary hyperparathyroidism and hypoparathyroidism arise from "controller defects." The control engineering framework provides an efficient means of organizing the subprocesses constituting Ca regulation, thereby facilitating a fundamental understanding of this complex process. The resulting validated model's predictions are consistent with clinically observed short- and long-term dynamic characteristics of the Ca regulatory system in both healthy and diseased patients. The model also enables simulation of currently infeasible clinical tests and generates predictions of physiological variables that are currently not measurable.