Abstract
This work was aimed at providing a local mechanical characterisation of tissues from the healthy human atria. Thirty-two tissue specimens were harvested from nine adult subjects whose death was not directly related to cardiovascular diseases. Tissues were kept in Tyrode’s solution and tested using a planar biaxial device. Results showed that tissues from healthy human atria undergo large deformations under in-plane distributed tensions roughly corresponding to an in vivo pressure of 15 mmHg. The material was modelled as hyperelastic and a Fung-type elastic strain energy potential was chosen. This class of potentials is based on a function of a quadratic form in the components of the Green–Lagrange strain tensor, and it has been previously proved that the fourth-order tensor of this quadratic form is proportional to the linear elasticity tensor of the linearised theory. This has three important consequences: (i) the coefficients in Fung-type potentials have a precise physical meaning; (ii) whenever a microstructural description for the linear elasticity tensor is available, this is automatically inherited by the Fung-type potential; (iii) because of the presence of the linear elasticity tensor in the definition of a Fung-type potential, each of the three normal stresses is coupled with all three normal strains.We propose to include information on the microstructure of the atrium by writing the linear elasticity tensor as the volumetric-fraction-weighed sum of the linear elasticity tensors of the three constituents of the tissue: the ground matrix, the main fibre family and the secondary fibre family. To the best of our knowledge, this is the first time that a Fung-type potential is given a precise structural meaning, based on the directions and the material properties of the fibres. Because of the coupling between normal strains and normal stresses, this structurally-based Fung-type potential allows for discriminating among all testing protocols in planar biaxial stretch.
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Acknowledgments
The authors would like to thank Dr. D. Schwartzman (University of Pittsburgh Medical Center) for providing the tissue specimens, Dr. M. Sacks (Engineered Tissue Mechanics Laboratory in the McGowan Institute for Regenerative Medicine at the University of Pittsburgh) for the use of the biaxial machine and Ms. V. Brescianini for her precious contribution with the graphics. This work was supported in part by Alberta Innovates - Technology Futures (formerly Alberta Ingenuity Fund, Canada), through the AITF New Faculty Programme [SF], the Natural Sciences and Engineering Research Council of Canada, through the NSERC Discovery Programme [SF, EDM] and the NSERC CREATE Training Programme for Biomedical Engineers for the 21st century [CB], and the Werner Graupe International Fellowship in Engineering [CB].
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Associate Editor Seungik Baek oversaw the review of this article.
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Bellini, C., Di Martino, E.S. & Federico, S. Mechanical Behaviour of the Human Atria. Ann Biomed Eng 41, 1478–1490 (2013). https://doi.org/10.1007/s10439-012-0699-9
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DOI: https://doi.org/10.1007/s10439-012-0699-9