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Po‐Poster ‐ 30: A method to estimate an exponential elastic model
Author(s) -
Zhong H,
Peters T
Publication year - 2005
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.2031009
Subject(s) - ogden , expression (computer science) , exponential function , stress (linguistics) , finite element method , mathematics , deformation (meteorology) , computer science , calculus (dental) , algorithm , mathematical analysis , physics , structural engineering , orthodontics , engineering , programming language , medicine , linguistics , philosophy , meteorology , thermodynamics
The response of soft tissue to interventional actions is an important subject in surgery simulation and planning. With properly calibrated elastic properties, it is possible to build a computational model to predict the deformation and stress of different organs. This paper studies the biomechanical properties of a pig liver and proposes a parameter evaluation method specifically for an exponential constitutive modelW ( I 1) = C ( eb ( I 1− 3 )− 1 ) which is extensively used in the literature. Under the assumption of the incompressibility, the uniaxial deformation mode allows us to generate a simplified stress expression:σ = 2 ( 1 − λ u − 3) ( λ u∂ W∂ I 1)Different from a general trial and error procedure employed when constructing a finite element computational model, here we fit the above simplified stress expression with the experimental curve of stress and strain using a least square method. The fitted result shows that for a sample of a pig liver, b =8.6, C =0.000169 (N/mm 2 ), and A =ln( bC )=−6.53. From the value A we also can deduce Young's module which satisfies E =6 bC under a small strain. Consequently we determine that E =6 e A =0.0088. We then compare the theoretic model with some published data, and find that the exponential model calibrated with this method matches well with both the Ogden model and an experimental result. Therefore the calibrated parameters could serve as a valuable reference in building a computational physics‐based deformable model for surgical simulation and radiation treatment planning.