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

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 lead 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 extra-cellular 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 that 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 increase. 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.