TY - JOUR

T1 - Identification of mechanical properties of heterogeneous soft bodies using gravity loading

AU - Babarenda Gamage, Thiranja P.

AU - Rajagopal, Vijayaraghavan

AU - Ehrgott, Matthias

AU - Nash, Martyn P.

AU - Nielsen, Poul M. F.

PY - 2011/3/1

Y1 - 2011/3/1

N2 - This study investigates the use of multiple gravity-loaded configurations of a soft heterogeneous body for the identification of its mechanical properties. It is largely motivated by the need for in vivo, non-invasive determination of the mechanical properties of biological tissue, such as the breast, for the purposes of tracking and predicting tumor locations. In order to validate this approach, experiments were performed on a heterogeneous two-layered silicone gel cantilever beam, laser scanned in eight different orientations under gravity loading. A finite element model of the beam was constructed and analyzed using non-linear finite elasticity and a neo-Hookean stress–strain relationship. The constitutive parameters representing the stiffness of each layer were estimated, using non-linear optimization techniques, to best fit the laser-scanned data. Different subsets of the experiments were used for training (parameter fitting), with the remaining experiments being used for validation. In both experimental sets, a cross-validation study was performed in order to compare and assess the predictive power of the identified parameters. Several determinability criteria were used to assess the objective function in the neighborhood of the identified minimum. We found that individual experiments were not sufficient for reliable parameter identification of heterogeneous soft bodies under gravity loading, but that a small number of gravity-loaded configurations were sufficient to reliably estimate the parameters within the scale of experimental errors. We also discuss the practical and numerical issues related to both single and multi-experiment parameter estimation.

AB - This study investigates the use of multiple gravity-loaded configurations of a soft heterogeneous body for the identification of its mechanical properties. It is largely motivated by the need for in vivo, non-invasive determination of the mechanical properties of biological tissue, such as the breast, for the purposes of tracking and predicting tumor locations. In order to validate this approach, experiments were performed on a heterogeneous two-layered silicone gel cantilever beam, laser scanned in eight different orientations under gravity loading. A finite element model of the beam was constructed and analyzed using non-linear finite elasticity and a neo-Hookean stress–strain relationship. The constitutive parameters representing the stiffness of each layer were estimated, using non-linear optimization techniques, to best fit the laser-scanned data. Different subsets of the experiments were used for training (parameter fitting), with the remaining experiments being used for validation. In both experimental sets, a cross-validation study was performed in order to compare and assess the predictive power of the identified parameters. Several determinability criteria were used to assess the objective function in the neighborhood of the identified minimum. We found that individual experiments were not sufficient for reliable parameter identification of heterogeneous soft bodies under gravity loading, but that a small number of gravity-loaded configurations were sufficient to reliably estimate the parameters within the scale of experimental errors. We also discuss the practical and numerical issues related to both single and multi-experiment parameter estimation.

KW - finite elasticity

KW - finite element method

KW - inverse problem

KW - parameter estimation

KW - mechanical properties

KW - heterogeneous soft bodies

U2 - 10.1002/cnm.1429

DO - 10.1002/cnm.1429

M3 - Journal article

VL - 27

SP - 391

EP - 407

JO - International Journal for Numerical Methods in Biomedical Engineering

JF - International Journal for Numerical Methods in Biomedical Engineering

SN - 2040-7939

IS - 3

ER -