This is the second part of a two-part paper on the application of computer-aided diagnosis to diffuse optical tomography (DOT) for diagnosing rheumatoid arthritis (RA). A comprehensive analysis of techniques for the classification of DOT images of proximal interphalangeal joints of subjects with and without RA is presented. A method for extracting heuristic features from DOT images was presented in Part 1. The ability of five classification algorithms to accurately label each DOT image as belonging to a subject with or without RA is analyzed here. The algorithms of interest are the k -nearest-neighbors, linear and quadratic discriminant analysis, self-organizing maps, and support vector machines (SVM). With a polynomial SVM classifier, we achieve 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). These results underscore the high potential for DOT to become a clinically useful diagnostic tool and warrant larger prospective clinical trials to conclusively demonstrate the ultimate clinical utility of this approach.
This is the first part of a two-part paper on the application of computer-aided diagnosis to diffuse optical tomography (DOT). An approach for extracting heuristic features from DOT images and a method for using these features to diagnose rheumatoid arthritis (RA) are presented. Feature extraction is the focus of Part 1, while the utility of five classification algorithms is evaluated in Part 2. The framework is validated on a set of 219 DOT images of proximal interphalangeal (PIP) joints. Overall, 594 features are extracted from the absorption and scattering images of each joint. Three major findings are deduced. First, DOT images of subjects with RA are statistically different (p<0.05 ) from images of subjects without RA for over 90% of the features investigated. Second, DOT images of subjects with RA that do not have detectable effusion, erosion, or synovitis (as determined by MRI and ultrasound) are statistically indistinguishable from DOT images of subjects with RA that do exhibit effusion, erosion, or synovitis. Thus, this subset of subjects may be diagnosed with RA from DOT images while they would go undetected by reviews of MRI or ultrasound images. Third, scattering coefficient images yield better one-dimensional classifiers. A total of three features yield a Youden index greater than 0.8. These findings suggest that DOT may be capable of distinguishing between PIP joints that are healthy and those affected by RA with or without effusion, erosion, or synovitis.
Based on light propagation theory, the measurements of a contact-free imaging system with generalized optical components can be obtained from a linear transformation of the light intensity distribution on the surface of the imaging object. In this work, we derived the linear measurement operator needed to perform this transformation. Numerical experiments were designed and conducted for validation.
We apply the Fourier Transform to absorption and scattering coefficient images of proximal interphalangeal (PIP) joints and evaluate the performance of these coefficients as classifiers using receiver operator characteristic (ROC) curve analysis. We find 25 features that yield a Youden index over 0.7, 3 features that yield a Youden index over 0.8, and 1 feature that yields a Youden index over 0.9 (90.0% sensitivity and 100% specificity). In general, scattering coefficient images yield better one-dimensional classifiers compared to absorption coefficient images. Using features derived from scattering coefficient images we obtain an average Youden index of 0.58 ± 0.16, and an average Youden index of 0.45 ± 0.15 when using features from absorption coefficient images.
We introduce here a temporally constrained image reconstruction algorithm for fast dynamic imaging of the
spatial distribution of tissue parameters such as oxy-hemoglobin, HbO2, or deoxy-hemoglobin, Hb, and their
derived parameters, e.g., HbT or StO2. An unknown spatial-temporal distribution of the tissue parameter is
represented by a combination of basis functions where bases are predefined and their coefficients are
unknown. The performance of the new algorithm is evaluated using experimental studies with dynamic
imaging of vascular disease in foot. The results show that the temporally constrained algorithm leads to 26-
fold acceleration in the image reconstruction as compared to more traditional methods that have to
reconstruct all time frames data sequentially.
We present a study on the effectiveness of computer-aided diagnosis (CAD) of rheumatoid arthritis (RA) from frequency-domain diffuse optical tomographic (FDOT) images. FDOT is used to obtain the distribution of tissue optical properties. Subsequently, the non-parametric Kruskal-Wallis ANOVA test is employed to verify statistically significant differences between the optical parameters of patients affected by RA and healthy volunteers. Furthermore, quadratic discriminate analysis (QDA) of the absorption (μa) and scattering (μa or μ's) distributions is used to classify subjects as affected or not affected by RA.
We evaluate the classification efficiency by determining the sensitivity (Se), specificity (Sp), and the Youden index (Y). We find that combining features extracted from μa and μa or μ's images allows for more accurate classification than when μa or μa or μ's features are considered individually on their own. Combining μa and μa or μ's features yields values of up to Y = 0.75 (Se = 0.84 and Sp = 0.91). The best results when μa or μ's features are considered individually are Y = 0.65 (Se = 0.85 and Sp = 0.80) and Y = 0.70 (Se = 0.80 and Sp = 0.90), respectively.
In this work we introduce the finite volume (FV) approximation to the simplified spherical harmonics (SPN)
equations for modeling light propagation in tissue. The SPN equations, with partly reflective boundary conditions,
are discretized on unstructured grids. The resulting system of linear equations is solved with a Krylov
subspace iterative method called the generalized minimal residual (GMRES) algorithm. The accuracy of the
FV-SPN algorithm is validated through numerical simulations of light propagation in a numerical phantom with
embedded inhomogeneities. We use a FV implementation of the equation of radiative transfer (ERT) as the
benchmark algorithm. Solutions obtained using the FV-SPN (N > 1) algorithm are compared to solutions
obtained with the ERT and the diffusion equation (SP1). Compared to the SP1, the SP3 solutions obtained
using the FV-SPN algorithm can better approximate ERT solutions near boundary sources and in the vicinity
of void-like regions. Solutions using the SP3 algorithm are obtained 9.95 times faster than solutions with the
ERT-based algorithm.
We developed a method for solving the fluorescence equation of radiative transfer in the frequency domain on blockstructured
grids. In this way fluorescence light propagation in arbitrarily shaped tissue can be modeled with high
accuracy without compromising on the convergence speed of these codes. The block-structure grid generator is
developed as a multi-purpose tool that can be used with many numerical schemes. We present results from numerical
studies that show that it is possible to resolve curved boundaries with grids that maintain much of the intrinsic structure
of Cartesian grids. The natural ordering of this grid allows for simplified algorithms. In simulation studies we found that
we can reduce the error in boundary fluence by a factor of five by using a two-level block structured grid. The increase
in computational cost is only two-fold. We compare benchmark solutions to results with various levels of refinement,
boundary conditions, and different geometries.
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