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An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential

Ankush Aggarwal1

  • 1Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, Swansea, UK. a.aggarwal@swansea.ac.uk.

Biomechanics and Modeling in Mechanobiology
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This study reveals that exponential functions in soft tissue models create parameter ambiguities. Simple algebraic changes improve parameter estimation and enable more reliable comparisons of tissue mechanics.

Keywords:
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Area of Science:

  • Biomechanics
  • Materials Science
  • Computational Biology

Background:

  • Soft tissue constitutive laws often use exponential functions due to stress-stiffness proportionality.
  • This approach can lead to challenges in accurately estimating and comparing elastic parameters.

Purpose of the Study:

  • To analyze the impact of exponential functions on soft tissue parameter estimation.
  • To propose modifications for improved accuracy and robustness in mechanical parameter analysis.

Main Methods:

  • Analysis of exponential function properties in constitutive models.
  • Application of elementary algebra to modify parameter norms and spaces.
  • Testing robustness against noise and heterogeneity.

Main Results:

  • Identified lines of high covariance in elastic parameter space due to exponential functions.
  • Demonstrated that modified norms and parameter spaces improve convergence and robustness.
  • Showed enhanced problem conditioning and reduced local minima entrapment for heterogeneous materials.

Conclusions:

  • Exponential functions in soft tissue models can obscure true mechanical properties.
  • Proposed algebraic modifications offer a more robust and reliable method for parameter estimation.
  • A transformed parameter space facilitates rational comparisons, preventing misleading conclusions in soft tissue mechanics research.