On The Constitutive Modeling And Hyperelastic Response Of Soft Biological Tissues Reinforced By Collagen Fibers

With the rapid development of imaging,computer science,robotics and many other techniques,computer-assisted medical technology is becoming more mature.Theoretical biomechanical modelling and numerical simulation of biological soft tissues are the basis of computer medical technology,which can provide necessary theoretical support for the computer-assisted surgical planning and selection of repair materials.However,the mechanical behavior of soft tissue involves anisotropic hyperelastic and viscoelastic deformations,and is closely related to its complex microstructure.Hence,it is still a great challenge to develop accurate and reasonable biomechanical models of soft tissues.In this dissertation,the constitutive modeling and hyperelastic responses of two typical soft tissues,i.e.liver and sclera tissues,were studied by combining the theoretical analysis,numerical simulation,and experimental tests.Soft tissue is often assumed as nearly or completely incompressible materials in theoretical analysis and numerical simulation.However,the experimental and theoretical research on the compressibility of soft tissue is still not sufficient.Therefore,in Chapter 2,a volumetric experiment on the porcine liver was conducted,the volumetric response of liver tissue was characterized,and the difference of compressibility of samples with various initial volumes was analyzed.In addition,most of the biomechanical models of soft tissues are based on the right Cauchy Green deformation tensor,which is not compatible with physical conditions when describing the extremely large tension/compression problem.In Chapter 3 and 4,a new strain measure which can describe the extreme state was introduced.Combined with theoretical derivation,a transversely isotropic hyperelastic model considering fiber-reinforced soft tissue with one preferred orientation was developed,and the tissue response under extreme deformation was studied.Finally,imaging studies have shown that collagen fibers are interweaving in biological soft tissues on the microscale.However,it is still not fully understood that how the interweaving architecture influences the macroscale biomechanical properties.Therefore,in Chapter 5,the effect of fiber interweaving on the overall biomechanical properties of soft tissue was discussed using the inverse finite element method.In this dissertation,the following work has been conducted:1.Experimental study and theoretical modeling of the compressibility of porcine liver tissue.The confined compression experiments were conducted on the porcine liver tissues to explore the relationship between liver tissue compressibility and initial volume.The experimental results showed that the compressibility of liver tissues was closely related to the initial specimen volume: the samples with smaller initial volumes were more compressible compared to the ones with larger initial volumes.A novel volumetric strain energy model with two parameters,i.e.,the bulk modulus and the compressibility factor,was developed on the basis of the experimental data and the physical requirements of the volumetric strain energy function.The bulk modulus was positively related to the initial volume and controls the gradient of volumetric response at the initial phase.The compressibility factor was independent of the initial volume and controls the nonlinearity of the volumetric response.Based on the Taylor expansion approximation principle,the method of model parameter identification was proposed.The predictions with the developed model were consistent with the experimental data,which highlights that the proposed model can properly characterize the approximate compressible response of liver tissue.2.Transversely isotropic hyperelastic constitutive model of fiber-reinforced biological soft tissue with one preferred directionDarijani-Naghdabadi's current-initial strain measurement is compatible with the physical conditions of the initial state and extremely large deformations correctly.Based on this strain measure,a positive definite generalized deformation tensor was proposed,the conjugate stress tensor was deduced,and a transversely isotropic hyperelastic model of biological soft tissue was developed.The analytical solutions of fiber-reinforced soft tissue under uniaxial stretch and simple shear in parallel or transverse to the fiber direction were deduced theoretically.The proposed model was verified by comparison with experiments in the literature.The model could effectively predict the anisotropic hyperelastic response of collagen fiber-reinforced soft tissue under extremely large uniaxial tension/compression loadings.3.The effects of interweaving architecture of collagen fibers in scleral tissue on the overall biomechanical propertiesAlthough studies of sclera microstructure showed collagen fiber interweaving,the role of fiber interweaving on scleral biomechanics was not fully understood.We developed models with non-interweaving or interweaving fibers over a wide range of collagen volume fractions.For each model,we estimated fiber stiffness using inverse modeling matching biaxial experimental data of human sclera.We found that interweaving increased the estimated fiber stiffness.The differences in the estimated fiber stiffness due to interweaving were more pronounced at higher collagen volume fractions.Adding interweaving to the non-interwoven model,or removing the interweaving of the interwoven model results in changes in the overall biomechanics of the tissue.Thus,interweaving plays an important role in determining the structural stiffness of sclera.