## 1 Introduction
Later, this same FD-ERT based DOT images were re-analyzed using advanced machine learning algorithms, which led to an improved sensitivity (96%) and specificity (94%) [35; 36]. While all these DOT results are promising for RA diagnosis, there is still room for improvement, particularly with respect to accuracy and reconstruction speed, in order to further the clinical utility of the technique. 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]. 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]. To our best knowledge, there is no work reported on the clinical utility of FD-SP\({}_{3}\)-based DOT imaging as applied to a large-scale clinical data. 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. This is based on our previous findings [35; 36] in which the SVM with a polynomial kernel was shown to yield the highest sensitivities and specificities in the diagnosis of RA. We compared the performance of SP\({}_{3}\)-based DOT images against the FD-ERT-based DOT images (slow but accurate) and the FD-DE-based DOT images (fast but inaccurate) with respect to diagnostic accuracy and computational efficiency. The diagnostic accuracy is presented in terms of the sensitivity (\(S_{e}\)) and specificity (\(S_{p}\)), and computational efficiency in terms of the memory requirement and image reconstruction time. Furthermore, we compared the performance of the DE, SP\({}_{3}\), and ERT models for their diagnostic accuracy. In Section 2, we provide a brief description of the FD-SP\({}_{3}\) model, the image reconstruction algorithm, and the clinical data, followed by the method of feature extraction and selection. Then, we present and discuss FD-SP\({}_{3}\)-based DOT images and their classification results in in Section 3. In Section 4, we conclude this work with a summary of the key findings presented in this work.