Erratum: "A Numerical Scheme for Anisotropic Reactive Nonlinear Viscoelasticity" [ASME J. Biomech Eng., 2023, 145(1), p. 011004; DOI: 10.1115/1.4054983].

In this erratum, we correct a mistake in a subcomponent of the numerical algorithm proposed in our recent study for modeling anisotropic reactive nonlinear viscoelasticity (doi:10.1115/1.4054983), for the special case where multiple weak bond families may be recruited with loading. This correction overcomes a nonphysical response noted under uni-axial cyclical loading.

A Numerical Scheme for Anisotropic Reactive Nonlinear Viscoelasticity.

Reactive viscoelasticity is a theoretical framework based on the theory of reactive constrained mixtures that encompasses nonlinear viscoelastic responses. It models a viscoelastic solid as a mixture of strong and weak bonds that maintain the cohesiveness of the molecular constituents of the solid matter. Strong bonds impart the elastic response while weak bonds break and reform into a stress-free state in response to loading. The process of bonds breaking and reforming is modeled as a reaction where loaded bonds are the reactants and bonds reformed into a stress-free state are the products of a reaction. The reaction is triggered by the evolving state of loading. The state of stress in strong bonds is a function of the total strain in the material, whereas the state of stress in weak bonds is based on the state of strain relative to the time that these bonds were reformed. This study introduces two important practical contributions to the reactive nonlinear viscoelasticity framework: (1) normally, the evaluation of the stress tensor involves taking a summation over a continually increasing number of weak bond generations, which is poorly suited for a computational scheme. Therefore, this study presents an effective numerical scheme for evaluating the strain energy density, the Cauchy stress, and spatial elasticity tensors of reactive viscoelastic materials. (2) We provide the conditions for satisfying frame indifference for anisotropic nonlinear viscoelasticity, including for tension-bearing fiber models. Code verifications and model validations against experimental data provide evidence in support of this updated formulation.

Damage Mechanics of Biological Tissues in Relation to Viscoelasticity.

This study examines the theoretical foundations for the damage mechanics of biological tissues in relation to viscoelasticity. Its primary goal is to provide a mechanistic understanding of well-known experimental observations in biomechanics, which show that the ultimate tensile strength of viscoelastic biological tissues typically increases with increasing strain rate. The basic premise of this framework is that tissue damage occurs when strong bonds, such as covalent bonds in the solid matrix of a biological tissue, break in response to loading. This type of failure is described as elastic damage, under the idealizing assumption that strong bonds behave elastically. Viscoelasticity arises from three types of dissipative mechanisms: (1) Friction between molecules of the same species, which is represented by the tissue viscosity. (2) Friction between fluid and solid constituents of a porous medium, which is represented by the tissue hydraulic permeability. (3) Dissipative reactions arising from weak bonds breaking in response to loading, and reforming in a stress-free state, such as hydrogen bonds and other weak electrostatic bonds. When a viscoelastic tissue is subjected to loading, some of that load may be temporarily supported by those frictional and weak bond forces, reducing the amount of load supported by elastic strong bonds and thus, the extent of elastic damage sustained by those bonds. This protective effect depends on the characteristic time response of viscoelastic mechanisms in relation to the loading history. This study formalizes these concepts by presenting general equations that can model the damage mechanics of viscoelastic tissues.

Bendable osteochondral allografts for patellar resurfacing: A finite element analysis of congruence.

Osteochondral allograft (OCA) transplantation provides a safe and effective treatment option for large cartilage defects, but its use is limited partly due to the difficulty of matching articular surface curvature between donor and recipient. We hypothesize that bendable OCAs may provide better curvature matching for patella transplants in the patellofemoral joint (PFJ). This finite element study investigates PFJ congruence for unbent and bendable OCAs, at various flexion angles. Finite element models were created for 12 femur-patella OCA pairings. Two grooves were cut in each OCA bony substrate, allowing the articular layer to bend. PFJs with either unbent (OCA) or permanently bent (BOCA) allografts were articulated from 40 to 70 degrees flexion and contact area was calculated. OCAs and BOCAs were then shifted 6 mm distally toward the tibia (S-OCA, S-BOCA) to investigate the influence of proximal-distal alignment on congruence. On average, no significant difference in contact area was found between native PFJs and either OCAs or BOCAs (p > 0.25), indicating that both types of allografts restored native congruence. This result provides biomechanical support in favor of an emerging surgical procedure. S-BOCAs resulted in a significant increase in contact area relative to the remaining groups (p < 0.02). The fact that BOCAs produced equally good results implies that bendable allografts may prove useful in future surgical procedures, with the possibility of transplanting them with a small distal shift. Surgeons who are reluctant to use OCAs for resurfacing patellae based on curvature matching capabilities may be more amenable to adopting BOCAs.

A Friction Testing-Bioreactor Device for Study of Synovial Joint Biomechanics, Mechanobiology, and Physical Regulation.

In primary osteoarthritis (OA), normal 'wear and tear' associated with aging inhibits the ability of cartilage to sustain its load-bearing and lubrication functions, fostering a deleterious physical environment. The frictional interactions of articular cartilage and synovium may influence joint homeostasis through tissue level wear and cellular mechanotransduction. To study these mechanical and mechanobiological processes, a device capable of replicating the motion of the joint is described. The friction testing device controls the delivery of reciprocal translating motion and normal load to two contacting biological counterfaces. This study adopts a synovium-on-cartilage configuration, and friction coefficient measurements are presented for tests performed in a phosphate-buffered saline (PBS) or synovial fluid (SF) bath. The testing was performed for a range of contact stresses, highlighting the lubricating properties of SF under high loads. This friction testing device can be used as a biomimetic bioreactor for studying the physical regulation of living joint tissues in response to applied physiologic loading associated with diarthrodial joint articulation.