Reply from authors: Toward physiologically meaningful biomechanical parameters from ex vivo biaxial testing.

Reply to the Editor:

The authors reported no conflicts of interest.

The Journal policy requires editors and reviewers to disclose conflicts of interest and to decline handling or reviewing manuscripts for which they may have a conflict of interest. The editors and reviewers of this article have no conflicts of interest.

Stemming from the Commentary by Tang and colleagues on our article, we were excited to be invited to elaborate more on the biaxial ex vivo biomechanical parameters for assessing ascending aortic aneurysms. Particularly, Tang and colleagues raise an excellent point regarding the limitations of ex vivo testing.

Some researchers have tried to estimate an in vivo baseline strain to calculate the modulus of elasticity, this is the case for some of previous work by Chung and colleagues, who used a physiological strain estimate of 10%. To our knowledge, there is yet no definitive method for calculating a physiological baseline stress/strain. The Law of Laplace, used to calculate stress, likely overestimates the pressure by not considering the transmural pressure within the aorta and there is currently no accurate way to assess residual strains. As such, we have chosen to move away from defining a modulus/stiffness at a specific value (not to mention that these values would need to be patient- and even region-specific) and toward defined features of the aortic material itself such as the low strain tangential modulus (LTM) and stress at the transition zone (TZo). LTM and TZo were chosen as physiologically meaningful given that healthy aortic tissue is not likely to reach the high strain modulus at the displacement control protocol used in this article, which is set to cause 60% biaxial strain in grip-to-grip distances. For our aneurysm samples, only 25 out of 41 samples presented full TZos.

Therefore, comparing LTM and TZo seems more meaningful than comparing tangent moduli at a fixed strain because they are likely to not be equivalent measures for aneurysms with different stages of pathology progression. Additionally, these properties are believed to correlate with the microstructure of the tissue and may provide more information beyond a general assessment of stiffening. Tracking changes in LTM over time may shed light on the level of degradation of the elastic lamellae, whereas a lower TZo may illustrate structural changes to collagen.

The energy loss in our article was calculated from the machine grip-to-grip measurements versus local central dot deformation used to calculate LTM and TZo. As such, our measurement of energy loss was determined with the limitations of nonlocalized deformation and using a standard strain of 60% across all samples. Our research group is cautiously optimistic about energy loss as presented by Chung and colleagues. We are very excited to see the rigorous analysis conducted by Tang and colleagues, on sensitivity of energy loss as well as the meaningful discussion on the physics behind this parameter. Studies like the one by Tang and colleagues raise our confidence in using this parameter in the future.

Finally, it might be too ambitious to expect a single biomechanical parameter to capture disease progression as complex as the ascending aortic aneurysm. As mentioned, we view LTM, TZo, and energy loss as complementary measures each potentially reflecting different structural alterations and, when combined, providing a more comprehensive picture of disease progression.