Modeling the response of exogenously crosslinked tissue to cyclic loading: The effects of permanent set

Abstract

Bioprosthetic heart valves (BHVs), fabricated from exogenously crosslinked collagenous tissues, remain the most popular heart valve replacement design. However, the life span of BHVs remains limited to 10–15 years, in part because the mechanisms that underlie BHV failure remain poorly understood. Experimental evidence indicates that BHVs undergo significant changes in geometry with in vivo operation, which leads to stress concentrations that can have significant impact on structural damage. These changes do not appear to be due to plastic deformation, as the leaflets only deform in the elastic regime. Moreover, structural damage was not detected by the 65 million cycle time point. Instead, we found that this nonrecoverable deformation is similar to the permanent set effect observed in elastomers, which allows the reference configuration of the material to evolve over time. We hypothesize that the scission-healing reaction of glutaraldehyde is the underlying mechanism responsible for permanent set in exogenously crosslinked soft tissues. The continuous scission-healing process of glutaraldehyde allows a portion of the exogenously crosslinked matrix, which is considered to be the non-fibrous part of the extracellular matrix, to be re-crosslinked in the loaded state. Thus, this mechanism for permanent set can be used to explain the time evolving mechanical response and geometry of BHVs in the early stage. To model the permanent set effect, we assume that the exogenously crosslinked matrix undergoes changes in reference configurations over time. The changes in the collagen fiber architecture due to dimensional changes allow us to predict subsequent changes in mechanical response. Results show that permanent set alone can explain and, more importantly, predict how the mechanical response of the biomaterial change with time. Furthermore, we found is no difference in permanent set rate constants between the strain controlled and the stress controlled cyclic loading studies. An important finding we have is the collagen fiber architecture has a limiting effect on the maximum changes in geometry that the permanent set effect can induce. This is due to the recruitment of collagen fibers as the changes in geometry due to permanent set increases. This means we can potentially optimize the BHV geometry based on the predicted the final BHV geometry after permanent set has largely ceased. Thus, we have developed the first structural constitutive model for the permanent set effect in exogenously crosslinked soft tissue, which can help to simulate BHV designs and reduce changes in BHV geometry during cyclic loading and thus potentially increasing BHV durability.

A Reactive Inelasticity Theoretical Framework for modeling Viscoelasticity, Plastic Deformation, and damage in Soft Tissue

“…Plastic deformation has been experimentally observed in tissue at the macro- (Maher et al, 2012), micro- (Szczesny & Elliott, 2014;Lee et al, 2017), and nano-scale (Shen et al, 2008). Several phenomenological ISV modeling approaches have been taken to address these phenomena that often are focused to address specific inelastic behaviors and usually omit the relationships between different inelastic behaviors and their mechanisms (Zhang & Sacks, 2017;Fereidoonnezhad et al, 2016;Peña, 2014;Maher et al, 2012). In the current framework, we particularly focused on providing a consistent formulation between different inelastic behaviors and their structural relevance.…”

“…For instance, decomposition of strain (Reese & Govindjee, 1998) and stress (Holzapfel & Simo, 1996) tensors into elastic and inelastic components is a common practice to model viscoelasticity, where the inelastic components are hidden internal variables that correspond to the non-equilibrium part of the mechanical response. For plastic deformation (permanent set) in tissue (Zhang & Sacks, 2017) used a structural approach to model this inelastic behavior in cyclic loading by proposing a shift in reference configuration of exogenously crosslinked matrix of tissue. In another study, to model softening based on permanent set and damage two weight factors were used based on alterations to the fibrous structure of tissue due to mechanical loading (Peña, 2011(Peña, , 2014.…”

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

“…Plastic deformation has been experimentally observed in tissue at the macro- [4], micro- [57,70], and nano-scale [71]. Several phenomenological ISV modeling approaches have been taken to address these phenomena that often are focused to address specific inelastic behaviors and usually omit the relationships between different inelastic behaviors and their mechanisms [4,14,16,17,72]. In the current framework, we particularly focused on providing a consistent formulation between different inelastic behaviors and their structural relevance.…”

“…For instance, decomposition of strain [12] and stress [13] tensors into elastic and inelastic components is a common practice to model viscoelasticity, where the inelastic components are hidden internal variables that correspond to the nonequilibrium part of the mechanical response. For plastic deformation (permanent set) in tissue, Zhang and Sacks [14] used a structural approach to model this inelastic behavior in cyclic loading by proposing a shift in reference configuration of exogenously crosslinked matrix. In another study, to model softening based on permanent set and damage, two weight factors were used based on alterations to the fibrous structure of tissue due to mechanical loading [15,16].…”

Computational methods for the aortic heart valve and its replacements

“…Recently, Sacks and Zhang [95, 96] developed a novel constitutive model for exogenously crosslinked soft tissue to evaluate BHV leaflet behavior. This novel structural model accounts for three contributors to the mechanical response of soft tissue: collagen fibers, exogenously crosslinked (EXL) matrix, and the interactions between the fiber-fiber components.…”