Estimation of Young's modulus and Poisson's ratio of soft tissue using indentation

Abstract

Indentation is one of the widely used mechanical testing methods for biological soft tissue. Different from confined or unconfined compression test, in-vivo indentation test on soft tissues can be carried out in clinical application. However, to obtain Young's modulus of the tissue using indentation, its Poisson's ratio is traditionally assumed or obtained separately by another test which may cause experimental error and complexity. In this study, several calculation strategies were proposed to estimate Young's modulus and Poisson's ratio of soft tissue by single indentation simultaneously. By finite element analysis, the effects of finite deformation on the double indentation method were studied. The results showed that the estimated Poisson's ratio and Young's modulus were larger than the actual values by up to 11.73% and 22.75%, respectively. Moreover, the feasibility of estimating Young's modulus and Poisson's ratio in single indentation with different deformations and deformation-dependent indentation stiffness was also verified separately. More accurate results could be obtained if the aspect ratio between indentor and tissue thickness was large enough. So, estimating Young's modulus and Poisson's ratio of soft tissue by single indentation might be more suitable to apply on thin soft tissue. Beside finite element study, experiments on silicone phantoms were also carried out in this study. Mechanical indentations using material testing system and handheld tissue ultrasound palpation system were performed on two different kinds of silicone phantoms with the proposed calculation strategies. The comparison of the results between mechanical properties obtained by unconfined compression and proposed calculation algorithms revealed differently ranging from -3.1 % ~ 16.6 % in a harder silicone phantom. The lager the aspect ratio was between the specimen thickness and indentor radius, the smaller the error was obtained. After testing the feasibility of applying the proposed calculation strategies by the experiment on silicone phantoms, another experiment was performed on bovine patellar articular cartilage for estimating the Young's modulus and Poisson's ratio of Articular Cartilage. Four bovine patellae were tested before and after trypsin enzyme digestion using these two calculation strategies. The Poisson's ratio and Young's modulus of cartilage estimated by single indentation using deformation-dependent indentation stiffness ranged from 0.45 - 0.47 and 1.33 MPa - 2.21 MPa, respectively. While the Poisson's ratio and Young's modulus of cartilage estimated by single indentation with the information of different deformations ranged from 0.46 - 0.49 and 1.39 MPa - 2.40 MPa. The percentage changes of the results obtained using the two different proposed algorithms were less than 6 % for Poisson's ratio and 9 % for Young's modulus. The Young's modulus of cartilage after trypsin enzyme digestion was found to be greatly reduced by around 45 %. The results revealed that the proposed algorithms could improve the accuracy of estimation of Young's modulus and also be useful for calculating shear modulus. Further studies should be conducted to develop new finite element models, using indentors with different radii and applying non-destructive techniques for thickness measurement. The effects of changes in tissue thickness in indentation on the estimation results should be further studied and a novel hand-held indentation technique may be developed in the future.