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

A Histomorphometric and Computational Investigation of the Stabilizing Role of Pectinate Ligaments in the Aqueous Outflow Pathway

Murine models are commonly used to study glaucoma, the leading cause of irreversible blindness. Glaucoma is associated with elevated intra-ocular pressure (IOP), which is regulated by the tissues of the aqueous outflow pathway. In particular, pectinate ligaments (PLs) connect the iris and trabecular meshwork (TM) at the anterior chamber angle, with an unknown role in maintenance of the biomechanical stability of the aqueous outflow pathway, thus motivating this study. We conducted histomorphometric analysis and optical coherence tomography-based finite element (FE) modeling on three cohorts of C57BL/6 mice: "young" (2-6 months), "middle-aged" (11-16 months), and "elderly" (25-32 months). We evaluated the age-specific morphology of the outflow pathway tissues. Further, because of the known pressure-dependent Schlemm's canal (SC) narrowing, we assessed the dependence of the SC lumen area on varying IOPs in age-specific FE models over a physiological range of TM/PL stiffness values. We found age-dependent changes in morphology of outflow tissues; notably, the PLs were more developed in older mice compared to younger ones. In addition, FE modeling demonstrated that murine SC patency is highly dependent on the presence of PLs and that increased IOP caused SC collapse only with sufficiently low TM/PL stiffness values. Moreover, the elderly model showed more susceptibility to SC collapse compared to the younger models. In conclusion, our study elucidated the previously unexplored role of PLs in the aqueous outflow pathway, indicating their function in supporting TM and SC under elevated IOP.

The Effects of Negative Periocular Pressure on Biomechanics of the Optic Nerve Head and Cornea: A Computational Modeling Study

Purpose

The purpose of this study was to evaluate the effects of negative periocular pressure (NPP), and concomitant intraocular pressure (IOP) lowering, on the biomechanics of the optic nerve head (ONH) and cornea.

Methods

We developed a validated finite element (FE) model of the eye to compute tissue biomechanical strains induced in response to NPP delivered using the Multi-Pressure Dial (MPD) system. The model was informed by clinical measurements of IOP lowering and was based on published tissue properties. We also conducted sensitivity analyses by changing pressure loads and tissue properties.

Results

Application of -7.9 mmHg NPP decreased strain magnitudes in the ONH by c. 50% whereas increasing corneal strain magnitudes by c. 25%. Comparatively, a similar increase in corneal strain was predicted to occur due to an increase in IOP of 4 mmHg. Sensitivity studies indicated that NPP lowers strain in the ONH by reducing IOP and that these effects persisted over a range of tissue stiffnesses and spatial distributions of NPP.

Conclusions

NPP is predicted to considerably decrease ONH strain magnitudes. It also increases corneal strain but to an extent expected to be clinically insignificant. Thus, using NPP to lower IOP and hence decrease ONH mechanical strain is likely biomechanically beneficial for patients with glaucoma.

Translational Relevance

This study provides the first description of how NPP affects ONH biomechanics and explains the underlying mechanism of ONH strain reduction. It complements current empirical knowledge about the MPD system and guides future studies of NPP as a treatment for glaucoma.

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.