Quantitative Photoacoustic Reconstruction of the Optical Properties of Intervertebral Discs Using a Gradient Descent Scheme

Antoine Capart,Julien Wojak,Moncef Ghiss,Roman Allais,Olivier Boiron,Anabela Da Silva

doi:10.3390/photonics9020116

Abstract

The intervertebral discs (IVD) are among the essential organs of the human body, ensuring the mobility of the spine. These organs possess a high proportion of water. However, as the discs age, this content decreases, which can potentially lead to various diseases called degenerative disc diseases. This water content is therefore an important indicator of the well-being of the disc. In this paper, we propose photoacoustic imaging as a means of probing a disc and quantitatively recovering its molecular composition, which should allow concluding on its state. An adjoint-assisted gradient descent scheme is implemented to recover the optical absorption coefficient in the disc, from which, if spectroscopic measurements are performed, the molecular composition can be deduced. The algorithm was tested on synthetic measurements. A realistic numerical phantom was built from magnetic resonance imaging of an actual IVD of a pig. A simplified experiment, with a single laser source, was performed. Results show the feasibility of using photoacoustics imaging to probe IVDs. The influences of exact and approximate formulations of the gradient are studied. The impact of noise on the reconstructions is also evaluated.

Highlights

The intervertebral discs (IVD) are fibrocartilaginous organs present between the vertebrae of the spine
Reconstructions of the absorption coefficient when the scattering coefficient was known were performed in three different situations: (i) by considering a perfect measurement; (ii) in the same situation but without considering the radiance term in the gradient definition in Equation (6); (iii) when Gaussian noise was added to the measurement to test the robustness of the algorithm. 107 photons were simulated for all reconstructions for both the forward and adjoint radiance calculations
The gradient descent was initiated by setting a homogeneous absorption coefficient of 0.01 cm−1 in the disc, which corresponds to an underestimated value

Summary

Introduction

The intervertebral discs (IVD) are fibrocartilaginous organs present between the vertebrae of the spine. Together, they ensure the mobility of the back and act as shock absorbers. They ensure the mobility of the back and act as shock absorbers These organs contain a high percentage of water [1]. As time goes by, they progressively lose their water content. This perfectly natural process can lead to degenerative disc diseases [2] and pain. Low back pain is one of the most common consequences of the degeneration of the discs, and has important social and economical consequences in today’s society [3]

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Conclusion