Definition and Comparison of Constitutive Models for the Characterization of Bovine Pericardium Heart Patches

The mechanical characterisation of bovine pericardium by means of macroscale and nanoscale experimental tests, combined with the use of constitutive models based on Strain Energy Function, aims firstly at the identification of a standard within the protocols used in the literature, but above all to the extrapolation of mechanical properties such as Young's modulus, Ultimate Tensile Strength (UTS) or elongation at break, useful to understand the integrity of the biological material downstream of decellularising treatments or downstream of preservation methods. At the same time, providing the constitutive models describing the strain-stress relationship with experimental data is of paramount importance in order to obtain a robust model that faithfully mimics the true nature of the tests, with the aim of translating the mechanical characterisation from the laboratory to the computer, saving money and time. In this work, two testing protocols were therefore developed, one relating to uniaxial tensile tests and one to nanoindentation tests. Following the washing of the specimens from the storage solution and the digital thickness measurement, the bovine pericardium sheets were first tested on the nanoscale in PBS solution at 37 °C, with single indentation tests on the central gage length of the specimens, resulting in two partially overlapping nanoindentation arrays spaced 250 μm apart, using the commercial nanoindenter (Feather, Optics 11, Netherlands). Subsequently, they were tested with uniaxial tensile tests under real hydration conditions after 5 cycles of preconditioning, on the Planar Biaxial TestBench Instrument (TA Instruments, USA). Using a load cell with a full scale of 225 N and optical methods, the mechanical properties were extrapolated. The stress-strain curves for the uniaxial tensile tests were fitted with two different constitutive models, which related the microscopic nature of the bovine pericardium to the mechanical properties at the macroscopic level. The model proposed by Dong et al., and the model developed by Yeoh et al., both based on hyperelasticity theory, the use of the strain energy function and both exploiting strain gradient tensors, were useful in extrapolating the characteristic parameters of the material, which, depending on the direction of shear of the patch, showed different curves at fracture, thus reflecting the different impact that the collagen fibres immersed in the extracellular matrix have on the mechanical properties of the pericardium. Dong's model therefore better described the curves for samples with the fibres arranged perpendicular to the direction of the test, while Yeoh's model achieved a good fit on samples where the fibres are more aligned with the direction of the test and are progressively recruited. In this context, there is certainly still a need to standardise the experimental testing of soft biological and composite tissues, and to find a single model that can capture the different mechanical behaviour of the pericardium as a function of the arrangement of the collagen fibres in relation to the axis in which the test is carried out.