A Reactive Inelasticity Theoretical Framework for Modeling Viscoelasticity, Plastic Deformation, and Damage in Fibrous Soft Tissue

Assessment of the viscoelastic mechanical properties of the porcine optic nerve head using micromechanical testing and finite element modeling

Optic nerve head (ONH) biomechanics is centrally involved in the pathogenesis of glaucoma, a blinding ocular condition often characterized by elevation and fluctuation of the intraocular pressure and resulting loads on the ONH. Further, tissue viscoelasticity is expected to strongly influence the mechanical response of the ONH to mechanical loading, yet the viscoelastic mechanical properties of the ONH remain unknown. To determine these properties, we conducted micromechanical testing on porcine ONH tissue samples, coupled with finite element modeling based on a mixture model consisting of a biphasic material with a viscoelastic solid matrix. Our results provide a detailed description of the viscoelastic properties of the porcine ONH at each of its four anatomical quadrants (i.e., nasal, superior, temporal, and inferior). We showed that the ONH's viscoelastic mechanical response can be explained by a dual mechanism of fluid flow and solid matrix viscoelasticity, as is common in other soft tissues. We obtained porcine ONH properties as follows: matrix Young's modulus E=1.895[1.056,2.391] kPa (median [min., max.]), Poisson's ratio ν=0.142[0.060,0.312], kinetic time-constant τ=214[89,921] sec, and hydraulic permeability k=3.854×10^-1[3.457×10^-2,9.994×10^-1] mm⁴/(N.sec). These values can be used to design and fabricate physiologically appropriate ex vivo test environments (e.g., 3D cell culture) to further understand glaucoma pathophysiology. STATEMENT OF SIGNIFICANCE: Optic nerve head (ONH) biomechanics is an important aspect of the pathogenesis of glaucoma, the leading cause of irreversible blindness. The ONH experiences time-varying loads, yet the viscoelastic behavior of this tissue has not been characterized. Here, we measure the time-dependent response of the ONH in porcine eyes and use mechanical modeling to provide time-dependent mechanical properties of the ONH. This information allows us to identify time-varying stimuli in vivo which have timescales matching the characteristic response times of the ONH, and can also be used to design and fabricate ex vivo 3D cultures to study glaucoma pathophysiology in a physiologically relevant environment, enabling the discovery of new generations of glaucoma medications focusing on neuroprotection.

On the use of constrained reactive mixtures of solids to model finite deformation isothermal elastoplasticity and elastoplastic damage mechanics

This study presents a framework for plasticity and elastoplastic damage mechanics by treating materials as reactive solids whose internal composition evolves in response to applied loading. Using the framework of constrained reactive mixtures, plastic deformation is accounted for by allowing loaded bonds within the material to break and reform in a stressed state. Bonds which break and reform represent a new generation with a new reference configuration, which is time-invariant and provided by constitutive assumption. The constitutive relation for the reference configuration of each generation may depend on the selection of a suitable yield measure. The choice of this measure and the resulting plastic flow conditions are constrained by the Clausius-Duhem inequality. We show that this framework remains consistent with classical plasticity approaches and principles. Verification of this reactive plasticity framework, which is implemented in the open source FEBio finite element software (febio.org), is performed against standard 2D and 3D benchmark problems. Damage is incorporated into this reactive framework by allowing loaded bonds to break permanently according to a suitable damage measure, where broken bonds can no longer store free energy. Validation is also demonstrated against experimental data for problems involving plasticity and plastic damage. This study demonstrates that it is possible to formulate simple elastoplasticity and elastoplastic damage models within a consistent framework which uses measures of material mass composition as theoretically observable state variables. This theoretical frame can be expanded in scope to account for more complex behaviors.

Identifiability of tissue material parameters from uniaxial tests using multi-start optimization

Determining tissue biomechanical material properties from mechanical test data is frequently required in a variety of applications. However, the validity of the resulting constitutive model parameters is the subject of debate in the field. Parameter optimization in tissue mechanics often comes down to the "identifiability" or "uniqueness" of constitutive model parameters; however, despite advances in formulating complex constitutive relations and many classic and creative curve-fitting approaches, there is currently no accessible framework to study the identifiability of tissue material parameters. Our objective was to assess the identifiability of material parameters for established constitutive models of fiber-reinforced soft tissues, biomaterials, and tissue-engineered constructs and establish a generalizable procedure for other applications. To do so, we generated synthetic experimental data by simulating uniaxial tension and compression tests, commonly used in biomechanics. We then fit this data using a multi-start optimization technique based on the nonlinear least-squares method with multiple initial parameter guesses. We considered tendon and sclera as example tissues, using constitutive models that describe these fiber-reinforced tissues. We demonstrated that not all the model parameters of these constitutive models were identifiable from uniaxial mechanical tests, despite achieving virtually identical fits to the stress-stretch response. We further show that when the lateral strain was considered as an additional fitting criterion, more parameters are identifiable, but some remain unidentified. This work provides a practical approach for addressing parameter identifiability in tissue mechanics.

Evaluation of transverse poroelastic mechanics of tendon using osmotic loading and biphasic mixture finite element modeling

Tendon's viscoelastic behaviors are important to the tissue mechanical function and cellular mechanobiology. When loaded in longitudinal tension, tendons often have a large Poisson's ratio (ν>2) that exceeds the limit of incompressibility for isotropic material (ν=0.5), indicating that tendon experiences volume loss, inducing poroelastic fluid exudation in the transverse direction. Therefore, transverse poroelasticity is an important contributor to tendon material behavior. Tendon hydraulic permeability which is required to evaluate the fluid flow contribution to viscoelasticity, is mostly unavailable, and where available, varies by several orders of magnitude. In this manuscript, we quantified the transverse poroelastic material parameters of rat tail tendon fascicles by conducting transverse osmotic loading experiments, in both tension and compression. We used a multi-start optimization method to evaluate the parameters using biphasic finite element modeling. Our tendon samples had a transverse hydraulic permeability of 10^-4 to 10^-5 mm⁴. (Ns)^-1 and showed a significant tension-compression nonlinearity in the transverse direction. Further, using these results, we predict hydraulic permeability during longitudinal (fiber-aligned) tensile loading, and the spatial distribution of fluid flow during osmotic loading. These results reveal novel aspects of tendon mechanics and can be used to study the physiomechanical response of tendon in response to mechanical loading.

Multi-Scale Loading and Damage Mechanisms of Plantaris and Rat Tail Tendons

Tendinopathy, degeneration of the tendon that leads to pain and dysfunction, is common in both sports and occupational settings, but multi-scale mechanisms for tendinopathy are still unknown. We recently showed that micro-scale sliding (shear) is responsible for both load transfer and damage mechanisms in the rat tail tendon; however, the rat tail tendon is a specialized non-load-bearing tendon, and thus the load transfer and damage mechanisms are still unknown for load-bearing tendons. The objective of this study was to investigate the load transfer and damage mechanisms of load-bearing tendons using the rat plantaris tendon. We demonstrated that micro-scale sliding is a key component for both mechanisms in the plantaris tendon, similar to the tail tendon. Namely, the micro-scale sliding was correlated with applied strain, demonstrating that load was transferred via micro-scale sliding in the plantaris and tail tendons. In addition, while the micro-scale strain fully recovered, the micro-scale sliding was non-recoverable and strain-dependent, and correlated with tissue-scale mechanical parameters. When the applied strain was normalized, the % magnitudes of non-recoverable sliding was similar between the plantaris and tail tendons. Statement of clinical significance: Understanding the mechanisms responsible for the pathogenesis and progression of tendinopathy can improve prevention and rehabilitation strategies and guide therapies and the design of engineered constructs. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 37:1827-1837, 2019.

Evaluating Plastic Deformation and Damage as Potential Mechanisms for Tendon Inelasticity using a Reactive Modeling Framework

Inelastic behaviors, such as softening, a progressive decrease in modulus before failure, occur in tendon and are important aspect in degeneration and tendinopathy. These inelastic behaviors are generally attributed to two potential mechanisms: plastic deformation and damage. However, it is not clear which is primarily responsible. In this study, we evaluated these potential mechanisms of tendon inelasticity by using a recently developed reactive inelasticity model (RIE), which is a structurally-inspired continuum mechanics framework that models tissue inelasticity based on the molecular bond kinetics. Using RIE, we formulated two material models, one specific to plastic deformation and the other to damage. The models were independently fit to published experimental tensile tests of rat tail tendons. We quantified the inelastic effects and compared the performance of the two models in fitting the mechanical response during loading, relaxation, unloading, and reloading phases. Additionally, we validated the models by using the resulting fit parameters to predict an independent set of experimental stress-strain curves from ramp-to-failure tests. Overall, the models were both successful in fitting the experiments and predicting the validation data. However, the results did not strongly favor one mechanism over the other. As a result, to distinguish between plastic deformation and damage, different experimental protocols will be needed. Nevertheless, these findings suggest the potential of RIE as a comprehensive framework for studying tendon inelastic behaviors.