Experimental Bi-axial tensile tests of spinal meningeal tissues and constitutive models comparison

Abstract

Introduction This study aims at identifying mechanical characteristics under bi-axial loading conditions of extracted swine pia mater (PM) and dura and arachnoid complex (DAC). Methods 59 porcine spinal samples have been tested on a bi-axial experimental device with a pre-load of 0.01 N and a displacement rate of 0.05 mm·s^-1. Post-processing analysis included an elastic modulus, as well as constitutive model identification for Ogden model, reduced Gasser Ogden Holzapfel (GOH) model, anisotropic GOH model, transverse isotropic and anisotropic Gasser models as well as a Mooney-Rivlin model including fiber strengthening for PM. Additionally, micro-structure of the tissue was investigated using a bi-photon microscopy. Results Linear elastic moduli of 108 ± 40 MPa were found for DAC longitudinal direction, 53 ± 32 MPa for DAC circumferential direction, with a significant difference between directions (p < 0.001). PM presented significantly higher longitudinal than circumferential elastic moduli (26 ± 13 MPa vs 13 ± 9 MPa, p < 0.001). Transversely isotropic and anisotropic Gasser models were the most suited models for DAC (r² = 0.99 and RMSE:0.4 and 0.3 MPa) and PM (r² = 1 and RMSE:0.06 and 0.07 MPa) modelling. Conclusion This work provides reference values for further quasi-static bi-axial studies, and is the first for PM. Collagen structures observed by two photon microscopy confirmed the use of anisotropic Gasser model for PM and the existence of fenestration. The results from anisotropic Gasser model analysis depicted the best fit to experimental data as per this protocol. Further investigations are required to allow the use of meningeal tissue mechanical behaviour in finite element modelling with respect to physiological applications. STATEMENT OF SIGNIFICANCE: This study is the first to present biaxial tensile test of pia mater as well as constitutive model comparisons for dura and arachnoid complex tissue based on such tests. Collagen structures observed by semi-quantitative analysis of two photon microscopy confirmed the use of anisotropic Gasser model for pia mater and existence of fenestration. While clear identification of fibre population was not possible in DAC, results from anisotropic Gasser model depicted better fitting on experimental data as per this protocol. Bi-axial mechanical testing allows quasi-static characterization under conditions closer to the physiological context and the results presented could be used for further simulations of physiology. Indeed, the inclusion of meningeal tissue in finite element models will allow more accurate and reliable numerical simulations.

Keywords: Bi-axial testing; Meningeal tissue; Pia and dura mater.