Mathematical functions and their properties as relevant to the biomechanical modeling of cell and tissue damage

Research output: Contribution to journalArticlepeer-review

Abstract

The extrapolation of biological damage from a biomechanical model requires that a closed-form mathematical damage threshold function (DTF) be included in the model. A DTF typically includes a generic load variable, being the critical load (e.g., pressure, strain, temperature) causing irreversible tissue or cell damage, and a generic time variable, which represents the exposure to the load (e.g., duration, strain rate). Despite the central role that DTFs play in biomechanical studies, there is no coherent literature on how to formulate a DTF, excluding the field of heat-induced damage studies. This technical note describes six mathematical function types (Richards, Boltzmann, Morgan-Mercer-Flodin, Gompertz, Weibull, Bertalanffy) that are suitable for formulating a wide range of DTFs. These functions were adapted from the theory of restricted growth, and were fitted herein to describe biomechanical damage phenomena. Relevant properties of each adapted function type were extracted to allow efficient fitting of its parameters to empirical biomechanical data, and some practical examples are provided.

Original languageEnglish
Pages (from-to)93-103
Number of pages11
JournalJournal of Applied Biomechanics
Volume26
Issue number1
DOIs
StatePublished - Feb 2010

Keywords

  • Computational simulations
  • Damage extrapolation
  • Injury tolerance

Fingerprint

Dive into the research topics of 'Mathematical functions and their properties as relevant to the biomechanical modeling of cell and tissue damage'. Together they form a unique fingerprint.

Cite this