Employing Topological Equivalence in Biomechanics

By its very nature, biomedical engineering is interdisciplinary, often combining tools and techniques originally developed for engineered systems and applying them to biological problems. Often techniques developed to solve one problem may be used to solve a very different problem. One useful concept from the field of mathematics is topological equivalence. Two dynamical systems are “topologically equivalent” if the phase portraits are qualitatively similar. That is, one portrait can be obtained from the other by a continuous transformation (Figure 1).