Frequency-domain optical tomographic image reconstruction algorithm with the simplified spherical harmonics (SP3) light propagation model

Abstract

We introduce here the finite volume formulation of the frequency-domain simplified spherical harmonics model with n-th order absorption coefficients (FD-SPN) that approximates the frequency-domain equation of radiative transfer (FD-ERT). We then present the FD-SPN based reconstruction algorithm that recovers absorption and scattering coefficients in biological tissue. The FD-SPN model with 3rd order absorption coefficient (i.e., FD-SP3) is used as a forward model to solve the inverse problem. The FD-SP3 is discretized with a node-centered finite volume scheme and solved with a restarted generalized minimum residual (GMRES) algorithm. The absorption and scattering coefficients are retrieved using a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. Finally, the forward and inverse algorithms are evaluated using numerical phantoms with optical properties and size that mimic small-volume tissue such as finger joints and small animals. The forward results show that the FD-SP3 model approximates the FD-ERT (S12) solution within relatively high accuracy; the average error in the phase (<3.7%) and the amplitude (<7.1%) of the partial current at the boundary are reported. From the inverse results we find that the absorption and scattering coefficient maps are more accurately reconstructed with the SP3 model than those with the SP1 model. Therefore, this work shows that the FD-SP3 is an efficient model for optical tomographic imaging of small-volume media with non-diffuse properties both in terms of computational time and accuracy as it requires significantly lower CPU time than the FD-ERT (S12) and also it is more accurate than the FD-SP1.

Diagnostic Evaluation of Rheumatoid Arthritis (RA) in Finger Joints Based on the Third-Order Simplified Spherical Harmonics (SP3) Light Propagation Model

“…In contrast, the reconstruction time with the ERT model exceeded 100 min on the same computing platform [33]. Additionally, reconstructions with the ERT always required over 6 GB of RAM, while the DE and SP 3 models always required less than 200 MB of RAM [37,38].…”

“…It has been shown that the SP 3 model is reliable for use in much of both transport and diffusion regimes, with higher-than-DE accuracy and similar-to-DE speed [38]. In 2017, we reported that the FD-SP 3 model was able to accurately capture the differences in optical properties due to the onset of RA using the forward and inverse simulations of RA-affected and healthy subjects [37].…”

“…In other words, the high diagnostic accuracy of FD-ERT based DOT imaging can only be achieved at the expense of reconstruction speed, while the DE model is much faster than the ERT but not reliable for achieving clinically relevant sensitivity and specificity. To overcome the shortcomings of these two most common models (DE and ERT), we employed here the frequency-domain third-order simplified spherical harmonics model (FD-SP 3 ) [37] as an alternative to the FD-ERT for the diagnosis of RA, for its clinically relevant accuracy and computational efficiency. It has been shown that the SP 3 model is reliable for use in much of both transport and diffusion regimes, with higher-than-DE accuracy and similar-to-DE speed [38].…”

“…Motivated by this unmet need, we have placed the focus of this work on the evaluation of the FD-SP 3 -based DOT imaging on its ability to diagnose RA. To this end, the FD-SP 3 model [37] is used in this work to recover the absorption and scattering coefficients from the existing clinical data of 219 proximal interphalangeal (PIP) finger joints available from our previous clinical study. For feature extraction and classification of FD-SP 3 -based DOT images, we used the k-fold cross validation method that consists of data mining and a support vector machine (SVM) algorithm.…”

High Resolution, Deep Imaging Using Confocal Time-of-flight Diffuse Optical Tomography

“…However, this expression can only be applied to simple scene geometries, such as a single homogeneous slab, and assumes that the scene is highly scattering [8]. As a consequence the approximation is not appropriate in many situations such as (a) near surface, where we are not yet in the diffuse regime, (b) inhomogeneous tissue or (c) layered tissue that contain low-scattering regions (such as skull, cerebrospinal fluid and brain) [29]. Monte Carlo simulations of the forward model.…”