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Communication Dans Un Congrès Année : 2023

Opto-mechanical characterisation of intervertebral disc phantoms

Résumé

1. Introduction Degeneration of the intervertebral discs (IVD) is a natural process that appears as early as twenty years of age and does not present any particular clinical symptoms. It is only after a period of several years to several decades, when pain appears, that a diagnosis can be made using usually magnetic resonance imaging. The severity of the disease is commonly assessed by grading schemes relying on contrast imaging analysis and one of the clinical goals in recent years is to better objectify the diagnosis through quantitative imaging. In this context, photoacoustics (PA) is a promising approach as it allows a non invasive spectroscopic probing of soft tissues to retrieve physiological markers of degeneration such as porosity or collagen concentration. A previous work by Metwally, et al, 2019 on lumbar porcine discs showed the potential of PA for such a goal. Hence, in this preliminary study we aim to create and characterise hydrogels which mimic the optical, mechanical and acoustic properties of an IVD to assess the possibility to use photoacoustics for disc degeneration estimation. Briefly, photoacoustics can be seen as a two-step process. First, a medium is hit by a laser pulse and then an acoustic wave is created as a result of the optical energy absorbed. From the measured acoustic signal which probed the medium, the goal is first to retrieve the initial acoustic pressure and subsequently the optical parameters through inverse problems resolutions. Finally, the chromophores concentrations of the medium that we target, water and collagen, can be deduced from the optical properties. The optical part is governed by the radiative transfer equation (Eq.1) which models the light propagation in the medium. This equation on the specific intensity (L in W.m-2.sr-1) is parametrised by the light speed c, a phase function p describing the optical scattering anisotropy of the medium and two coefficients µa and µs defining respectively the optical absorption and scattering of the medium. For soft tissues, this rather computationally expensive equation is often reduced to a diffusion equation (Eq.2) under the ‘light diffusion approximation’, which holds for IVD. This equation on the fluence (ϕ in W.m-2) is parametrised by µa and µs’ ≈ 0.1µs. A thorough derivation of these equations and their assumptions can be found in Arridge, 1999. Hence, knowing the values of these two parameters is required to optically characterise a medium. 2. Methods 2.1 Phantoms preparation With the end goal of mimicking an IVD, we used agarose hydrogels with TiO2 powder. We hypothesised that the mechanical response of our samples would be driven by the agarose concentration while the optical response would be mostly tuned by the TiO2 concentration. The agarose concentration ranges from 0.25 to 2 % w/w and the TiO2 ranges from 0.1 to 0.5mg/mL. Briefly, a mix of agarose and TiO2 was mixed in ddH20 and heated under magnetic stirring. Finally, the solution was poured in cylindrical moulds and stored at 4°C for gelation. As for now, only one sample was made for each combination of agarose and TiO2 concentration, resulting in 12 hydrogels to characterise. 2.2 Optical characterisation Under the light diffusion approximation, the optical coefficients µa and µs’ can be experimentally estimated using the integral reflectance and an empirical model as defined by Gobin, et al, 1999. Thus, with this approach we could find the relationships between the optical properties of our samples and the components’ concentrations and, on the other hand, by varying the wavelength of the light source from 590 to 815nm by step of 25nm, characterize the absorption spectrum of our samples. 2.3 Mechanical characterisation The hydrogels were punched to create 32mm-large and 20mm-tall cylindrical samples on which we performed an unconfined stress relaxation compression at the room temperature using a custom-built test bench. Then, we modelled the hydrogels by a Mooney-Rivlin law with two parameters (C10 and C01) and two viscoelastic branches following a Maxwell-generalised model. The inverse problem was solved using Levenberg-Marquardt algorithm and the built-in optimisation module of COMSOL Multiphysics 5.5. To ease the optimisation, the problem was solved in two steps: we first found the best values of the Mooney-Rivlin parameters and one viscoelastic branch and then we ran a second optimisation using these values to find the best parameters for the second viscoelastic branch. 3. Results and discussion Our first results suggest that optical scattering is mostly driven by the TiO2 concentration (CTiO2): µs’ increases linearly with CTiO2 and decreases with the wavelength (λ) between 590 and 815nm (Fig.1.A). Moreover, for CTiO2 above 0.5mg/mL, TiO2 appears to marginally impact the absorption spectrum (Fig.1.B); hence, the optical absorption can be tuned with the agarose concentration while the scattering is driven by the TiO2. Assuming the IVD as a biphasic medium made up of water and collagen and knowing the porosity, one can compute typical values of µa and µs’ for IVD at different levels of degeneration. Using the reference values of Sekar, et al, 2017, our hydrogels show optical scattering similar to IVD but the optical absorption appears too strong (Fig.1.A, B, D). This could be due to experimental limitations: the approach relying on the integral reflectance could be inaccurate for weakly absorbing samples; a validation experiment using integrating-spheres is planned. As for the mechanical problem, our models fit well the experimental relaxation curves (average RMSE<0.65N). Adding a second viscoelastic branch considerably improves the short-term fit (Fig.1.C). Notably, it decreases the maximal error by up to 50%. The average values of the Mooney-Rivlin and first viscoelastic branch parameters are reported in Table 1. Our results are in good agreement with the literature; similar trend are reported for hydrogels whose agarose concentration ranges from 3 to 5% (Wang, et al, 2021). In their hydrogels, Wang and colleagues reported values of 28.4kPa for C10 and -20.8kPa for C01 with a trend to increase with agarose concentration. However, these values fall short when compared to the one taken by Schmidt, et al (2007) in their numerical model of an IVD in which they use C10 = 180kPa and C01 = 45kPa for the annulus fibrosus. 4. Conclusions Our first results are promising as we now have baseline values for both mechanical and optical parameters. Acquisition and numerical simulations of photoacoustic signals are ongoing. Meanwhile, future work will consist in adapting the components to better model an IVD. To improve the optical absorption we plan to add collagen while we project to use chondroitin sulfate or crosslinking to better tune the mechanical response of our hydrogels. Acknowledgements This work is supported by the Emplois Jeunes Doctorants 2021 grant of the Région Provence Alpes Côte d’Azur. References Arridge, S, 1999. Optical tomography in medical imaging. Inverse problems, 15(2), R41. Gobin, L., et al. 1999. Integrating the digitized backscattered image to measure absorption and reduced-scattering coefficients in vivo. Applied optics, 38(19), 4217-4227. Metwally, K, et al. 2019. Probing intervertebral discs with photoacoustics. European Conference on Biomedical Optics. Optica Publishing Group. Schmidt, H., et al. 2007. Intradiscal pressure, shear strain, and fiber strain in the intervertebral disc under combined loading. Spine, 32(7), 748-755. Sekar, S., et al. 2017. Diffuse optical characterization of collagen absorption from 500 to 1700 nm. Journal of biomedical optics, 22(1). Wang, X., et al. 2021. A 3-D constitutive model for finite element analyses of agarose with a range of gel concentrations. Journal of the mechanical behavior of biomedical materials, 114, 104150. Keywords: Intervertebral disc; Photoacoustics; Soft tissue; Hydrogel; Characterisation *Corresponding author. Email: roman.allais@centrale-marseille.fr
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hal-04295598 , version 1 (22-11-2023)

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Roman Allais, Antoine Capart, Anabela da Silva, Olivier Boiron. Opto-mechanical characterisation of intervertebral disc phantoms. 48th Congress of the Society of Biomechanics, Oct 2023, Grenoble, France. ⟨hal-04295598⟩
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