1. Introduction
Rheumatoid arthritis (RA) is a chronic, progressive, systemic, inflammatory autoimmune disorder that causes chronic inflammation of the synovial membrane of small and large joints [
1,
2]. Thus, people with RA can suffer from severe pain, joint stiffness, swelling of multiple joints, and lack of joint mobility. When untreated, these symptoms can lead to self-limiting arthritis or rapidly progressing multi-system inflammation with significant morbidity and mortality (including cardiac, neurological, and hematological complications). Studies show that up to 14 million people around the world [
3] and approximately 1.5 million people in the US [
4] are affected by RA and up to 10% of individuals suffering from RA can experience total disability [
5]. In the US alone, RA leads to 9 million physician visits per year [
6]. Despite recent advances in therapeutic intervention including biological therapies [
7,
8], there is currently no cure for RA [
9]. The early treatment of RA, however, has been shown to significantly improve clinical outcomes and management of the disease. It is, therefore, important to diagnose a subject with RA as early as possible.
Early diagnosis of RA has been attempted using various imaging modalities such as X-ray, ultrasound (US), or MRI scans. X-ray imaging has the best-established role in the assessment of the severity of RA [
10]. Radiography can document bone damage (erosion) that results from RA and visualize the narrowing of cartilage spaces. However, radiography is insensitive to the early manifestations of RA, namely, effusion and hypertrophy of the synovial membrane. US is more sensitive than radiography at assessing erosion and synovitis, which allows clinicians to provide early diagnostic imaging at the point of care. However, a main disadvantage of US is a high level of operator dependence for obtaining quality images [
11]. MRI is most useful in assessing soft tissue problems, avascular necrosis, the degree of cartilage erosion, osteonecrosis, and carpal tunnel syndrome [
12]. The study showed that contrast-enhanced MRI could achieve a sensitivity and specificity of 70 and 64% [
13], respectively (82.5 and 84.5% in another study [
14]) for the detection of RA. However, long data-acquisition times during which the subject needs to be immobilized, large costs, and the need for contrast agents (e.g., gadolinium to detect increased blood volume caused by neovascularization in the hypertrophic synovial membrane that can be toxic for RA patients with critical renal failure) have prevented MRI from becoming a widely used imaging modality for detection of RA. Thus, there is no single ideal modality for imaging RA diagnosis, i.e., X-ray, US, and MRI are complementary with their own strengths and drawbacks.
Optical imaging techniques [
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36] for the diagnosis of RA have also been extensively studied using a continuous wave (CW) system in early works [
23,
26], and later a frequency domain (FD) system [
34,
36], combined X-ray and photoacoustic tomography [
29], and furthermore, molecular imaging approaches such as bioluminescence and fluorescence tomography [
16,
21,
22]. The basis for optical methods is that in the early stages of RA, optical properties such as absorption and scattering are expected to increase in the synovium and the synovial fluid as the inflammatory process starts in this region. These studies were mostly based on the diffusion equation (DE) as a model of light propagation in tissue. More recently, a deep learning technique has also emerged as a viable tool for the diagnosis of RA [
18]. Our research team has explored the potential of DOT imaging for detecting and characterizing RA by using the CW-ERT [
25,
26] and the FD-ERT [
32,
33,
34,
35,
36]. We reported that the CW-ERT-based DOT images yielded a sensitivity and specificity of 78 and 76%, respectively [
25], and the FD-ERT based DOT images achieved a sensitivity and specificity of 85% and higher [
34]. 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
-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 (
) and specificity (
), 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.
4. Discussion
We compared the performance of the DE, SP3, and ERT models with respect to three categories: feature extraction optimality, image classification performance, and computational efficiency.
The first category is feature extraction optimality, where we compared the number of “optimal” features selected during the training process. In general, we prefer optimal feature vectors with low-dimensionality as this helps reduce the probability of over-fitting the data [
36,
43]. Over-fitting can result in classification results that do not generalize well and therefore may be an unreliable predictor of future performance. In this work, the number of optimal features was eight for the DE model, three for the SP
3 model, and five for the ERT model. As we are generally interested in the fewest possible features to avoid over-fitting problems, it is clear that the SP
3 model is superior in this category to the ERT and DE models.
The second category to compare was the classification performance of the three models. Here, we were primarily concerned with the sensitivity and the specificity that are computed by processing the data set reserved for testing with the classifier that results from the training phase. In addition to seeking values of the sensitivity and the specificity as close to 100.0% as possible, we were also interested in comparing the 95% confidence interval for each parameter. The CI is important because it informs us of the range within which we expect the true values of the sensitivity and the specificity to exist [
35,
36,
44].
The reconstruction images computed with the SP3 model allow for higher sensitivity and specificity values than the images obtained with the DE model. The DE model yielded a sensitivity of 67% at CI (47, 100)% and a specificity of 81% at CI (65, 100)%. The SP3 model yielded a sensitivity of 88% at CI (78, 100)% and a specificity of 93% at CI (84.6, 100)%. Images computed with the ERT-based algorithm yielded a sensitivity of 91% at CI (83, 100)% and specificity of 98% at CI (85, 100)% specificity. Thus, the SP3 model clearly outperformed the DE model and compares favorably to the ERT.
We note that the upper bound of the CI for all models is 100%. The lower bound varies between the models and between the sensitivity and the specificity. As in the case of the sensitivity and the specificity values, the CI of the ERT was smaller than those obtained with the DE and SP3 models. However, the lower bounds of the SP3 model are significantly higher than the lower bounds of the DE model. The lower bound of the sensitivity with the DE model is in only 47%, which is significantly lower than the 78% lower bound that was computed with the SP3 model. Furthermore, the sensitivity computed with the DE images (67%) is even lower than the lower bound of the sensitivity computed with the SP3 model (78%). Similar results were observed when comparing the specificity values.
The third category in which we compared the models was computational efficiency, which consists of the total reconstruction time and the total system resources needed. The reconstruction times with the DE and SP
3 models were similar, typically requiring less than 1 min to complete one reconstruction process on an Intel Core i9 processor. 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]. In the computational efficiency category, thus, the DE and SP
3 models outperform the ERT model.
Overall, all these results discussed in this section indicate that the SP3-based reconstruction algorithm provides significant computational advantages over the ERT-based algorithm without compromising classification accuracy. In contrast, the DE model provides computational advantages when compared to the ERT but only at the expense of classification accuracy.
5. Conclusions
The SP3-model-based image reconstruction was performed on a set of 219 human PIP joints, with 99 joints belonging to subjects with RA and 120 joints belonging to healthy subjects. The k-fold cross validation was employed to evaluate the diagnostic performance of SP3-based DOT images of absorption and scattering coefficients in the fingers. A comparison of sensitivity and specificity values was made between SP3-based images, DE-based images, and ERT-based images. The sensitivity and specificity values were 88 and 93% with the SP3 based images, 91 and 98% with the ERT based images, and 67 and 81% with the DE based images, respectively. It was also shown that the SP3 model performs better in achieving the fewest optimal features than the DE and ERT models. In terms of computational efficiency, the SP3 model is approximately 100 times faster and takes 30-fold less memory than the ERT model. In conclusion, the results presented here demonstrate that the SP3 model provides sufficiently accurate DOT images with a sensitivity of 88% and specificity of 93% to achieve clinically significant diagnostic results that compare favorably to the ERT model, while leading to a significant reduction in computation time and system resources. Therefore, it is expected that the SP3-based DOT reconstruction can translate into direct clinical benefits, allowing researchers to image finger joints in near real-time and to evaluate DOT images for RA diagnosis at its early stage and treatment monitoring at a clinical setting.
Future work involves the application of the algorithms and classifiers presented in this work to therapeutic areas of monitoring drug responses in a longitudinal clinical study, refinement of fragmented algorithms into a clinically useful all-in-one package, and further enhancement of the SP3 reconstruction algorithm through the use of parallel computing neural network techniques.