Large deformation shear properties of liver tissue

Characterization of the mechanical properties of soft biological tissues is important for establishing the mechanical tolerances of the tissues, and for input to computational models. In this work, the viscoelastic properties of bovine liver tissue in shear loading have been measured using relaxation and constant shear rate loading. The tissue is nonlinearly viscoelastic for strains greater than 0.2%, has a yield strain of approximately 10, and shows moderate strain-rate sensitivity. The response can be modelled using a nonlinear viscoelastic differential model previously developed for brain tissue.     

A phase-field model for fracture in biological tissues

This work presents a recently developed phase-field model of fracture equipped with anisotropic crack driving force to model failure phenomena in soft biological tissues at finite deformations. The phase-field models present a promising and innovative approach to thermodynamically consistent modeling of fracture, applicable to both rate-dependent or rate-independent brittle and ductile failure modes. One key advantage of diffusive crack modeling lies in predicting the complex crack topologies where methods with sharp crack discontinuities are known to suffer. The starting point is the derivation of a regularized crack surface functional that \({\varGamma }\)-converges to a sharp crack topology for vanishing length-scale parameter. A constitutive balance equation of this functional governs the crack phase-field evolution in a modular format in terms of a crack driving state function. This allows flexibility to introduce alternative stress-based failure criteria, e.g., isotropic or anisotropic, whose maximum value from the deformation history drives the irreversible crack phase field. The resulting multi-field problem is solved by a robust operator split scheme that successively updates a history field, the crack phase field and finally the displacement field in a typical time step. For the representative numerical simulations, a hyperelastic anisotropic free energy, typical to incompressible soft biological tissues, is used which degrades with evolving phase field as a result of coupled constitutive setup. A quantitative comparison with experimental data is provided for verification of the proposed methodology.     

A finite nonlinear hyper-viscoelastic model for soft biological tissues

Soft tissues exhibit highly nonlinear rate and time-dependent stress-strain behaviour. Strain and strain rate dependencies are often modelled using a hyperelastic model and a discrete (standard linear solid) or continuous spectrum (quasi-linear) viscoelastic model, respectively. However, these models are unable to properly capture the materials characteristics because hyperelastic models are unsuited for time-dependent events, whereas the common viscoelastic models are insufficient for the nonlinear and finite strain viscoelastic tissue responses. The convolution integral based models can demonstrate a finite viscoelastic response; however, their derivations are not consistent with the laws of thermodynamics. The aim of this work was to develop a three-dimensional finite hyper-viscoelastic model for soft tissues using a thermodynamically consistent approach. In addition, a nonlinear function, dependent on strain and strain rate, was adopted to capture the nonlinear variation of viscosity during a loading process. To demonstrate the efficacy and versatility of this approach, the model was used to recreate the experimental results performed on different types of soft tissues. In all the cases, the simulation results were well matched ($R^2⩾0.99$) with the experimental data.     

Fracture-toughening mechanisms responsible for differences in work to fracture of hydrated and dehydrated dentine

This study investigates the nature of deformation and differences in the mechanisms of fracture and properties of dentine where there has been a loss of moisture, as may occur with removal of the pulp in the endodontic treatment of teeth. Controlled fracture toughness testing was conducted on bovine teeth to determine the influence of hydration on the work of fracture of dentine. Significant differences (p<0.01) were observed between the fracture toughness of hydrated (554+/-27.7J/m2) and dehydrated (113+/-17.8J/m2) dentine. Observations of the crack tip region during crack extension revealed extensive ligament formation occurred behind the crack tip. These ligaments provide considerable stability to the crack by significantly increasing the work of fracture, thereby acting as a fracture-toughening mechanism. Micro-cracking, reported as a fracture-toughening mechanism in bone, is also clearly seen. A zone of in-elastic deformation may occur as hydrated specimens revealed upon crack extension, a region about the tip that appeared to suck water into the structure and to exude water behind the crack tip. In dehydrated dentine, no in-elastic zone was observed. Micro-cracking is present though the cracks are smaller, straighter and with less opening than hydrated dentine. Only limited ligament formation just behind the crack tip was observed. These differences resulted in a significantly lower work of fracture with unstable brittle fracture characteristics. Based on these results, several fracture-toughening mechanisms were identified in dentine, with micro-cracking not considered the most important. These findings may be relevant for bone, a similar mineralised hydrated tissue.     

Imaging of Scleral Collagen Deformation Using Combined Confocal Raman Microspectroscopy and Polarized Light Microscopy Techniques

This work presents an optospectroscopic characterization technique for soft tissue microstructure using site-matched confocal Raman microspectroscopy and polarized light microscopy. Using the technique, the microstructure of soft tissue samples is directly observed by polarized light microscopy during loading while spatially correlated spectroscopic information is extracted from the same plane, verifying the orientation and arrangement of the collagen fibers. Results show the response and orientation of the collagen fiber arrangement in its native state as well as during tensile and compressive loadings in a porcine sclera model. An example is also given showing how the data can be used with a finite element program to estimate the strain in individual collagen fibers. The measurements demonstrate features that indicate microstructural reorganization and damage of the sclera’s collagen fiber arrangement under loading. The site-matched confocal Raman microspectroscopic characterization of the tissue provides a qualitative measure to relate the change in fibrillar arrangement with possible chemical damage to the collagen microstructure. Tests and analyses presented here can potentially be used to determine the stress-strain behavior, and fiber reorganization of the collagen microstructure in soft tissue during viscoelastic response.     

Experimental study and constitutive modeling of the viscoelastic mechanical properties of the human prolapsed vaginal tissue

In this paper, the viscoelastic mechanical properties of vaginal tissue are investigated. Using previous results of the authors on the mechanical properties of biological soft tissues and newly experimental data from uniaxial tension tests, a new model for the viscoelastic mechanical properties of the human vaginal tissue is proposed. The structural model seems to be sufficiently accurate to guarantee its application to prediction of reliable stress distributions, and is suitable for finite element computations. The obtained results may be helpful in the design of surgical procedures with autologous tissue or prostheses.     

Quasi-Static and Dynamic Nanoindentation of Some Selected Biomaterials

This study details an investigation of the viscoelastic behavior of some biomaterials （nacre, cattle horn and beetle cuticle） at lamellar length scales using quasi-static and dynamic nanoindentation techniques in the materials＇ Transverse Direction （TD） and Longitudinal Direction （LD）. Our results show that nacre exhibits high fracture toughness moving towards a larger cam- paniForm as the stress frequency varies from 10 Hz to 200 Hz. Elytra cuticle exhibits the least fracture toughness presenting little energy dissipation in TD. It was initially speculated that the fracture toughness of the subject materials would be directly related to energy-dissipating mechanisms （mechanical hysteresis）, but not the maximum value of the loss tangent tan＆ However, it was found that the materials＇ elastic modulus and hardness are similar in both the TD and LD when assessed using the quasi-static nanoindentation method, but not dynamic nanoindentation. It is believed that the reported results can be useful in the design of new crack arrest and damping materials based on biological counterparts.     

The effect of microcracking in the peritubular dentin on the fracture of dentin

Dentin is a biocomposite possessing elegant hierarchical structure, which allows it to resist fracture effectively. Despite the considerable efforts to unravel the peculiar fracture behavior of dentin, the effect of microstructural features on the fracture process is largely unknown. In this study, we explore the interaction between the primary crack with crack tip located in intertubular dentin (ITD) and microcracking of peritubular dentin (PTD) ahead of the primary crack. A micromechanical model accounting for the unique composite structure of dentin is developed, and computational simulations are performed. It is found that the microcracking of PTD located in the crack plane in front of the primary crack tip can promote the propagation of the primary crack, increasing the propensity of coalescence of primary crack and microcracks nucleating in PTD. We show that the two-layer microstructure of dentin enables reduction in driving force of primary crack, potentially enhancing fracture toughness. The high stiffness of PTD plays a critical role in reducing the driving force of primary crack and activating microcracking of PTD. It is further identified that the microcracking of PTD arranged parallel to the crack plane with an offset could contribute to the shielding of primary crack.     

Callus Formation and Mineralization after Fracture with Different Fixation Techniques: Minimally Invasive Plate Osteosynthesis versus Open Reduction Internal Fixation

Minimally invasive plate osteosynthesis(MIPO) has been considered as an alternative for fracture treatment. Previous study has demonstrated that MIPO technique has the advantage of less soft tissue injury compared with open reduction internal fixation (ORIF). However, the comparison of callus formation and mineralization between two plate osteosynthesis methods remains unknown. In this experiment, ulna fracture model was established in 42 beagle dogs. The fractures underwent reduction and internal fixation with MIPO or ORIF. Sequential fluorescent labeling and radiographs were applied to determine new callus formation and mineralization in two groups after operation. At 4, 8 and 12 weeks postoperatively, the animals were selected to be sacrificed and the ulna specimens were analyzed by Micro-CT. The sections were also treated with Masson staining for histological evaluation. More callus formation was observed in MIPO group in early stage of fracture healing. The fracture union rate has no significant difference between two groups. The results indicate that excessive soft tissue stripping may impact early callus formation. As MIPO technique can effectively reduce soft tissue injury with little incision, it is considered to be a promising alternative for fracture fixation.     

Measurement of the microstructural fracture toughness of cortical bone using indentation fracture

The purpose of this work is to investigate the use of indentation fracture as a method of measuring toughness at the microscale in cortical bone. Indentation fracture employs sharp indenters to initiate cracks, whose length can be used to calculate the toughness of the material. Only a cube corner indenter tip is found to initiate cracks at a suitable size scale for microstructural measurement. Cracks from 7 to 56 microm in length are produced using loads from 0.05 to 3N. Preliminary data predicts rising toughness with increasing crack length (rising R-curve behaviour) at the microscale. This technique provides a new insight into fracture in cortical bone since it allows the investigator to observe mechanisms and measure toughness at a size scale at which in vivo damage is known to exist.     

A strain-hardening bi-power law for the nonlinear behaviour of biological soft tissues

Biological soft tissues exhibit a strongly nonlinear viscoelastic behaviour. Among parenchymous tissues, kidney and liver remain less studied than brain, and a first goal of this study is to report additional material properties of kidney and liver tissues in oscillatory shear and constant shear rate tests. Results show that the liver tissue is more compliant but more strain hardening than kidney. A wealth of multi-parameter mathematical models has been proposed for describing the mechanical behaviour of soft tissues. A second purpose of this work is to develop a new constitutive law capable of predicting our experimental data in the both linear and nonlinear viscoelastic regime with as few parameters as possible. We propose a nonlinear strain-hardening fractional derivative model in which six parameters allow fitting the viscoelastic behaviour of kidney and liver tissues for strains ranging from 0.01 to 1 and strain rates from 0.0151 s^?1 to 0.7 s^?1.     

Tissue Aspiration and Inverse Finite Element Characterisation of Soft Tissues

In this work we examined the determination of soft tissue parameters via tissue aspiration experiments and inverse finite element characterisation. An aspiration tube was put against the target tissue. The deformation of the tissue inside the tube caused by weak suction was tracked with a video based system. A strain energy function was employed to model the elastic behaviour of soft tissue and viscoelasticity was accounted for by means of a quasi-linear viscoelastic formulation. Friction between the aspiration tube and the aspirated tissue was included in the model. Based on the assumed material model, an optimal set of material parameters was found, in order to best fit the experimental data obtained from ex-vivo experiments on pig kidney cortex. The inverse method resulted in robust determination of the unknown material parameters.     

Cohesive finite element modeling of age-related toughness loss in human cortical bone

Although the age-related loss of bone quality has been implicated in bone fragility, a mechanistic understanding of the relationship is necessary for developing diagnostic and treatment modalities in the elderly population at risk of fracture. In this study, a finite element based cohesive zone model is developed and applied to human cortical bone in order to capture the experimentally shown rising crack growth behavior and age-related loss of bone toughness. The cohesive model developed here is based on a traction–crack opening displacement relationship representing the fracture processes in the vicinity of a propagating crack. The traction–displacement curve, defining the cohesive model, is composed of ascending and descending branches that incorporate material softening and nonlinearity. The results obtained indicate that, in contrast to initiation toughness, the finite element simulations of crack growth in compact tension (CT) specimens successfully capture the rising R-curve (propagation toughness) behavior and the age-related loss of bone toughness. In close correspondence with the experimentally observed decrease of 14–15% per decade, the finite element simulation results show a decrease of 13% in the R-curve slope per decade. The success of the simulations is a result of the ability of cohesive models to capture and predict the parameters related to bone fracture by representing the physical processes occurring in the vicinity of a propagating crack. These results illustrate that fracture mechanisms in the process zone control bone toughness and any modification to these would cause age-related toughness loss.     

Cavitation induced fracture of intact brain tissue

Nonpenetrating traumatic brain injuries (TBIs) are linked to cavitation. The structural organization of the brain makes it particularly susceptible to tears and fractures from these cavitation events, but limitations in existing characterization methods make it difficult to understand the relationship between fracture and cavitation in this tissue. More broadly, fracture energy is an important, yet often overlooked, mechanical property of all soft tissues. We combined needle-induced cavitation with hydraulic fracture models to induce and quantify fracture in intact brains at precise locations. We report here the first measurements of the fracture energy of intact brain tissue that range from 1.5 to 8.9 J/m², depending on the location in the brain and the model applied. We observed that fracture consistently occurs along interfaces between regions of brain tissue. These fractures along interfaces allow cavitation-related damage to propagate several millimeters away from the initial injury site. Quantifying the forces necessary to fracture brain and other soft tissues is critical for understanding how impact and blast waves damage tissue in vivo and has implications for the design of protective gear and tissue engineering.     

Anisotropy of age-related toughness loss in human cortical bone: a finite element study

A mechanistic understanding of the role of bone quality on fracture processes is essential for determining the underlying causes of age-related changes in the mechanical response of the human bone. In this study, a previously developed cohesive finite element model was used to investigate the effects of age-related changes and the orientation of crack growth on the toughening behavior of human cortical bone. The change in the anisotropy of toughening mechanisms with age was also studied. Finite element method (FEM) simulations showed that the initiation toughness decreased by 3% and 8%/decade for transverse and longitudinal crack growth, respectively. In contrast, fracture resistance curve slope for transverse and longitudinal crack growth decreased by 2% and 3%/decade, respectively. Initiation fracture toughness values were higher for the transverse than for the longitudinal for a given age. On the other hand, propagation fracture toughness values were higher for longitudinal than for transverse crack growth for a given age. With respect to age, the toughness ratio for crack initiation decreased by 6%/decade, but that for propagation showed almost no change (less than 1%). In light of these findings, an analytical model evaluating the crack arresting feature of cement lines, is proposed to explain the factors that determine crack penetration into osteons or its deflection by cement lines.     

A visco-hyperelastic constitutive approach for modeling polyvinyl alcohol sponge

This study proposes the quasi-linear viscoelastic (QLV) model to characterize the time dependent mechanical behavior of poly(vinyl alcohol) (PVA) sponges. The PVA sponges have implications in many viscoelastic soft tissues, including cartilage, liver, and kidney as an implant. However, a critical barrier to the use of the PVA sponge as tissue replacement material is a lack of sufficient study on its viscoelastic mechanical properties. In this study, the nonlinear mechanical behavior of a fabricated PVA sponge is investigated experimentally and computationally using relaxation and stress failure tests as well as finite element (FE) modeling. Hyperelastic strain energy density functions, such as Yeoh and Neo-Hookean, are used to capture the mechanical behavior of PVA sponge at ramp part, and viscoelastic model is used to describe the viscose behavior at hold part. Hyperelastic material constants are obtained and their general prediction ability is verified using FE simulations of PVA tensile experiments. The results of relaxation and stress failure tests revealed that Yeoh material model can define the mechanical behavior of PVA sponge properly compared with Neo-Hookean one. FE modeling results are also affirmed the appropriateness of Yeoh model to characterize the mechanical behavior of PVA sponge. Thus, the Yeoh model can be used in future biomechanical simulations of the spongy biomaterials. These results can be utilized to understand the viscoelastic behavior of PVA sponges and has implications for tissue engineering as scaffold.     

Modelling of global boundary effects on harmonic motion imaging of soft tissues

Biomechanical imaging techniques have been developed for soft tissue characterisation and detection of breast tumours. Harmonic motion imaging (HMI) uses a focused ultrasound technology to generate a harmonic radiation force in a localised region inside a soft tissue. The resulting dynamic response is used to map the local distribution of the mechanical properties of the tissue. In this study, a finite element (FE) model is developed to investigate the effect of global boundary conditions on the dynamic response of a soft tissue during HMI. The direct-solution steady-state dynamic analysis procedure is used to compute the harmonic displacement amplitude in FE simulations. The model is parameterised in terms of boundary conditions and viscoelastic properties, and the corresponding raster-scan displacement amplitudes are captured to examine its response. The effect of the model's global dimensions on the harmonic response is also investigated. It is observed that the dynamic response of soft tissue with high viscosity is independent of the global boundary conditions for regions remote to the boundary; thus, it can be subjected to local analysis to estimate the underlying mechanical properties. However, the dynamic response is sensitive to global boundary conditions for tissue with low viscosity or regions located near to the boundary.     

The relative contributions of non-enzymatic glycation and cortical porosity on the fracture toughness of aging bone

The risk of fracture increases with age due to the decline of bone mass and bone quality. One of the age-related changes in bone quality occurs through the formation and accumulation of advanced glycation end-products (AGEs) due to non-enzymatic glycation (NEG). However as a number of other changes including increased porosity occur with age and affect bone fragility, the relative contribution of AGEs on the fracture resistance of aging bone is unknown. Using a high-resolution nonlinear finite element model that incorporate cohesive elements and micro-computed tomography-based 3d meshes, we investigated the contribution of AGEs and cortical porosity on the fracture toughness of human bone. The results show that NEG caused a 52% reduction in propagation fracture toughness (R-curve slope). The combined effects of porosity and AGEs resulted in an 88% reduction in propagation toughness. These findings are consistent with previous experimental results. The model captured the age-related changes in the R-curve toughening by incorporating bone quantity and bone quality changes, and these simulations demonstrate the ability of the cohesive models to account for the irreversible dynamic crack growth processes affected by the changes in post-yield material behavior. By decoupling the matrix-level effects due to NEG and intracortical porosity, we are able to directly determine the effects of NEG on fracture toughness. The outcome of this study suggests that it may be important to include the age-related changes in the material level properties by using finite element analysis towards the prediction of fracture risk.