An Information-Theoretic Framework for Optimal Design: Analysis of Protocols for Estimating Soft Tissue Parameters in Biaxial Experiments

A new framework for optimal design based on the information-theoretic measures of mutual information, conditional mutual information and their combination is proposed. The framework is tested on the analysis of protocols—a combination of angles along which strain measurements can be acquired—in a bi...

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Bibliographic Details
Published in:Axioms 2021-06, Vol.10 (2), p.79
Main Authors: Aggarwal, Ankush, Lombardi, Damiano, Pant, Sanjay
Format: Article
Language:English
Subjects:
Algorithms
biaxial experiment
Biomechanics
Computer Science
Constitutive models
Design optimization
Experiments
Information theory
inverse problems
Lagrange multiplier
Mathematical models
Measurement techniques
Modeling and Simulation
mutual information
optimal design
Parameter estimation
Protocol
soft tissue mechanics
Soft tissues
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Summary:A new framework for optimal design based on the information-theoretic measures of mutual information, conditional mutual information and their combination is proposed. The framework is tested on the analysis of protocols—a combination of angles along which strain measurements can be acquired—in a biaxial experiment of soft tissues for the estimation of hyperelastic constitutive model parameters. The proposed framework considers the information gain about the parameters from the experiment as the key criterion to be maximised, which can be directly used for optimal design. Information gain is computed through k-nearest neighbour algorithms applied to the joint samples of the parameters and measurements produced by the forward and observation models. For biaxial experiments, the results show that low angles have a relatively low information content compared to high angles. The results also show that a smaller number of angles with suitably chosen combinations can result in higher information gains when compared to a larger number of angles which are poorly combined. Finally, it is shown that the proposed framework is consistent with classical approaches, particularly D-optimal design.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms10020079