Title: Computational Methods For The Diagnosis of Rheumatoid Arthritis With Diffuse Optical Tomography
Description: Diffuse optical tomography (DOT) is an imaging technique where near infrared (NIR) photons are used to probe biological tissue. DOT allows for the recovery of three-dimensional maps of tissue optical properties, such as tissue absorption and scattering coefficients. The application of DOT as a tool to aid in the diagnosis of rheumatoid arthritis (RA) is explored in this work. Algorithms for improving the image reconstruction process and for enhancing the clinical value of DOT images are presented in detail. The clinical data considered in this work consists of 99 fingers from subjects with RA and 120 fingers from healthy subjects. DOT scans of the proximal interphalangeal (PIP) joint of each finger is performed with modulation frequencies of 0, 300, and 600 MHz. A computer-aided diagnosis (CAD) framework for extracting heuristic features from DOT images and a method for using these same features to classify each joint as affected or not affected by RA is presented. The framework is applied to the clinical data and results are discussed in detail.

Then, an algorithm for recovering the optical properties of biological media using the simplified spherical harmonics (SPN) light propagation model is presented. The computational performance of the algorithm is analyzed and reported. Finally, the SPN reconstruction algorithm is applied to clinical data of subjects with RA and the resulting images are analyzed with the CAD framework. As the first part of the CAD framework, heuristic image features are extracted from the absorption and the scattering coefficient images using multiple compression and dimensionality reduction techniques. Overall, 594 features are extracted from the images of each joint. Then, machine-learning techniques are used to evaluate the ability to discriminate between images of joints with RA and images of healthy joints. An evolution-strategy optimization algorithm is developed to evaluate the classification strength of each feature and to find the multidimensional feature combination that results in optimal classification accuracy.

Classification is performed with k-nearest neighbors (KNN), linear (LDA) and quadratic discriminate analysis (QDA), self-organizing maps (SOM), or support vector machines (SVM). Classification accuracy is evaluated based on diagnostic sensitivity and specificity values. Strong evidence is presented that suggest there are clear differences between the tissue optical parameters of joints with RA and joints without RA. It is first shown that data obtained at 600 MHz leads to better classification results than data obtained at 300 and 0 MHz. Analysis of each extracted feature shows that DOT images of subjects with RA are statistically different (p < 0.05) from images of subjects without RA for over 90% of the features. Evidence shows that subjects with RA that do not have detectable signs of erosion, effusion, or synovitis (i.e. asymptomatic subjects) in MRI and US images have optical profiles similar to subjects who do have signs of erosion, effusion, or synovitis; furthermore, both of these cohorts differ from healthy controls subjects.

This shows that it may be possible to accurately identify asymptomatic subjects with DOT scans. In contrast, these subjects remain difficult to identify from MRI and US images. The implications of these results are profound, as they suggest it may be possible to identify RA with DOT at an earlier stage compared to standard imaging techniques. Results from the feature-selection algorithm show that the SVM algorithm (with a third order polynomial kernel) achieves 100.0% sensitivity and 97.8% specificity. Lower bounds for these results (at 95.0% confidence level) are 96.4% and 93.8%, respectively. Image features most predictive of RA are from the spatial variation of optical properties and the absolute range in feature values. The optimal classifiers are low dimensional combinations (< 7 features). Robust cross- validation is performed to ensure the generalization of these classification results. The SPN -based reconstruction algorithm uses a reduced-Hessian sequential quadratic programming (rSQP) PDE-constrained optimization approach to maximize computational efficiency.

The complex-valued forward model, or frequency domain SPN equations (N = 1, 3), is discretized using the finite-volume method and solved on unstructured computational grids using the restarted GMRES algorithm. The image reconstruction algorithm is presented in detail and its performance benchmarked against the ERT algorithm. The algorithm is subsequently used to recover the absorption and scattering coefficient images of joints scanned in the RA clinical study. While the SPN model is inherently less accurate than the ERT model, it is nevertheless shown that the images obtained with the SP3-based reconstruction algorithm are sufficiently accurate and allow for the diagnosis of RA at clinically relevant sensitivity [87.9% (78.1%, 100.0%)] and specificity [92.9% (84.6%, 100.0%)] values (the 95.0% confidence interval is specified in brackets). In contrast to results obtained with the SP3 model, the images generated with the SP1 algorithm yield significantly lower sensitivity [66.7% (46.6%, 100.0%)] and specificity [81.0% (64.8%, 100.0%)] values.

While some numerical accuracy is sacrificed by selecting the SP3 model over the ERT model, the superior computational performance of the SP3 algorithm allows for computation of the absorption and the scattering coefficient images in under 15 minutes and requires less than 200 MB of RAM per finger (compared to the over 180 minutes and over 6 GB of RAM needed by the ERT-based algorithm). Overall, results indicate that the SP3-based reconstruction algorithm provides computational advantages over the ERT-based algorithm without sacrificing significant classification accuracy. In contrast, the SP1 model provides computational advantages compared to the ERT at the expense of classification accuracy. This indicates that the frequency-domain SP3 model is an ideal light propagation model for use in DOT scanning of finger joints with RA. Altogether, the results presented in this dissertation underscore the high potential for DOT to become a clinically useful diagnostic tool. The algorithms and framework developed as part of this dissertation can be directly used on future data to help further validate the hypotheses presented in this work and to further establish DOT imaging as a valuable diagnostic tool.