A systems approach to tissue remodeling.

Remodeling of tissue in response to physical stress is a very complex process. The changes in the stimulus (cause) and response (effect) must be measured and the results must be organized into mathematical forms that are suitable for predictions and applications. An experiment where the stimulus (pressure, flow, shear stress, etc.) can be changed approximately as a step function (a step plus a perturbation) and the response (structure, material properties, function, etc.), which can be measured over time, can be simulated by indicial response functions (IRFs). The IRF is a mathematical expression of the ratio of the change in a particular feature of the system in response to a unit step change in stimulus. The IRF approach provides a quantitative description of the remodeling process, simplifies the interpretation of data, and greatly increases the potential of using the experimental data for prediction of the outcome for future experiments. The objective of this review is to provide an overview of the IRF approach including some exemplary systems. The goal is to illustrate how the indicial expressions make it possible to integrate biological complexity by convolution. The time courses of stimuli represent half of the convolution while the time course of changes in response represents the second half of the convolution. The IRF approach provides an understanding of the physiological problems with mathematical accuracy and may be conducive to new findings.