An inverse method for predicting tissue-level mechanics from cellular mechanical input

Wangdo Kim, Derek C. Tretheway, Sean Kohles

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Extracellular matrix (ECM) provides a dynamic three-dimensional structure which translates mechanical stimuli to cells. This local mechanical stimulation may direct biological function including tissue development. Theories describing the role of mechanical regulators hypothesize the cellular response to variations in the external mechanical forces on the ECM. The exact ECM mechanical stimulation required to generate a specific pattern of localized cellular displacement is still unknown. The cell to tissue inverse problem offers an alternative approach to clarify this relationship. Developed for structural dynamics, the inverse dynamics problem translates measurements of local state variables (at the cell level) into an unknown or desired forcing function (at the tissue or ECM level). This paper describes the use of eigenvalues (resonant frequencies), eigenvectors (mode shapes), and dynamic programming to reduce the mathematical order of a simplified cell-tissue system and estimate the ECM mechanical stimulation required for a specified cellular mechanical environment. Finite element and inverse numerical analyses were performed on a simple two-dimensional model to ascertain the effects of weighting parameters and a reduction of analytical modes leading toward a solution. Simulation results indicate that the reduced number of mechanical modes (from 30 to 14 to 7) can adequately reproduce an unknown force time history on an ECM boundary. A representative comparison between cell to tissue (inverse) and tissue to cell (boundary value) modeling illustrates the multiscale applicability of the inverse model.

Original languageEnglish (US)
Pages (from-to)395-399
Number of pages5
JournalJournal of Biomechanics
Volume42
Issue number3
DOIs
StatePublished - Feb 9 2009

Fingerprint

Mechanics
Extracellular Matrix
Tissue
Structural dynamics
Inverse problems
Dynamic programming
Eigenvalues and eigenfunctions
Natural frequencies

Keywords

  • Cell biomechanics
  • Dynamic programming
  • Eigenvalue reduction
  • Extracellular matrix
  • Finite element analysis
  • Inverse problem
  • Mechanotransduction

ASJC Scopus subject areas

  • Orthopedics and Sports Medicine
  • Rehabilitation
  • Biophysics
  • Biomedical Engineering

Cite this

An inverse method for predicting tissue-level mechanics from cellular mechanical input. / Kim, Wangdo; Tretheway, Derek C.; Kohles, Sean.

In: Journal of Biomechanics, Vol. 42, No. 3, 09.02.2009, p. 395-399.

Research output: Contribution to journalArticle

Kim, Wangdo ; Tretheway, Derek C. ; Kohles, Sean. / An inverse method for predicting tissue-level mechanics from cellular mechanical input. In: Journal of Biomechanics. 2009 ; Vol. 42, No. 3. pp. 395-399.
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