Three-dimensional diffuse optical tomography of

Three-dimensional diffuse optical tomography of osteoarthritis: A study of 38 finger joints Qizhi Zhang1, Zhen Yuan1, Eric S. Sobel2, Huabei Jiang1 1 2

Department of Biomedical Engineering, University of Florida, Gainesville, Florida 32611-6131

Division of Rheumatology, College of Medicine, University of Florida, Gainesville, Florida 32611 ABSTRACT

Our previous work has shown that near-infrared diffuse optical tomography has the potential to be a clinical tool in diagnosis of osteoarthritis. Here we report a study of 38 joints from 38 females, including 20 OA and 18 healthy joints. The quantitative results obtained show that there exists clear difference between OA and healthy joints in terms of the ratio of optical properties of the joint soft tissues to that of the associated bone. Statistic analysis of these clinical data is also presented. Key words: Osteoarthritis, finger joint, diffuse optical tomography.

1. INTRODUCTION Osteoarthritis (OA), which is characterized by the damaged cartilage of a joint, is a most common joint disease worldwide in older people. The cartilage of a joint is a tough, gristle-like material that is found on the ends of the bones. When OA progress the breakdown of cartilage causes the bones to rub against each other, causing stiffness, pain and loss of movement in the joint. Several imaging technologies are developed to detect this disease, including plain x-ray,1 magnetic resonance imaging (MRI)2-3 and computed tomography (CT)4. Thus far, the traditional plain x-ray is still the gold standard in diagnosis of OA since it is inexpensive and quick. Diffuse optical tomography (DOT) is recognized by its high sensitivity, noninvasiveness and cost effectiveness. Recently it has found its potential in diagnosis of OA5 and rheumatoid arthritis (RA).6 In our pilot study of 5 finger joints difference of optical absorption coefficients between the OA and healthy joints has been revealed.5 Here we report an expanded-38 joints study focusing on differentiating OA from normal joints with statistical significance. Since OA mostly affects the distal interphalangeal (DIP) joints in the hand, our DOT examinations are concentrated on this joint. Moreover, the imaging system used in the previous study has been upgraded from a pure DOT system to a hybrid x-ray/DOT system, allowing optical imaging to be co-registered with x-ray imaging of the same joint.

2. IMAGING SYSTEM A hybrid x-ray/DOT imaging system was built to perform all the measurements in this study. The system integrates a modified mini C-arm x-ray system with a homemade 64x64-channel photodiodes-based DOT system. Its schematic is shown in Fig. 1. The DOT system has been described in detail previously.5 Briefly, it consists of laser modules, a hybrid light delivery subsystem, a fiber optics/tissue interface, light detection modules and a data acquisition module. A total of eight laser modules working at wavelengths from 633nm to 974nm are available. A hybrid subsystem that comprises a 1x8 optical switch and a motorized rotator is used to deliver laser light to the excitation points. 64 low noise photodiodes are used for parallel signal acquisitions. A full set of data (64x64 channels) at one wavelength can be collected in about 5 minutes. The cylindrical fiber optics/tissue interface is composed of 64 source and 64 detector fiber bundles that are positioned in 4 layers along the surface of a plexiglass container and cover a volume of 15mm x 30mm. In each layer 16 source and 16 Optics in Bone Biology and Diagnostics, edited by Andreas Mandelis, Proc. of SPIE Vol. 7166, 71660K · © 2009 SPIE CCC code: 1605-7422/09/$18 · doi: 10.1117/12.809495 Proc. of SPIE Vol. 7166 71660K-1

detector fiber bundles are alternatively arranged. Light intensities were collected at 64 detector positions for each illumination location. The space between the finger and the wall of the plexiglass container is filled with tissue-like phantom materials as coupling media consisting of distilled water, agar powder, Indian Ink and Intralipid.7

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Fig.1 (a) Schematic of the imaging system. (b) Close-up view of the optical/finger interface (indicated by the yellow circle in (a)).

In the hybrid imaging of joints, the x-ray imaging is performed immediately after the DOT data acquisition. The optical interface is slid back along finger tip holder for x-ray exposure while the finger stays at the same position, see Fig.1(b). Four small metal spheres with diameters of 1mm are embedded along the surface of the plastic ring as markers for accurate co-registration of the x-ray and optical imaging.

3. RECONSTRUCTION METHOD A brief outline of our 3D reconstruction algorithm is described in the following. The reconstruction algorithm is based on the diffusion equation and type III boundary conditions:8

∇ ⋅ D(r )∇Φ(r ) − μ a (r )Φ(r ) = − S (r )

− D∇Φ ⋅ n = αΦ

(1) (2)

where Φ ( r ) is the photon density, D(r ) = 1 /(3( μa (r ) + μs′ (r ))) is the diffusion coefficient, μ a (r ) and μ s′ (r ) are the absorption coefficient and the reduced scattering coefficient, respectively, α is a coefficient related to the internal reflection at the boundary, and S(r) is the source term. Point sources were used in this study. The discretized form of equations (1) and (2) can be written as

[ A]{Φ} = {b}

(3)

where the elements of the matrix [A] are α = (− D∇φ ⋅ ∇φ − μ φ φ )dV + (−αφ φ )dΓ and the integrations are performed ij j i a j i j i ∫V ∫Γ

over the problem domain (V) and boundary domain (Γ). {b} is the source vector. The inverse solution is obtained through the following equations:

[ A]{∂Φ / ∂χ} = {∂b / ∂χ} − [∂A / ∂χ ]{Φ}

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(4)

( ℑT ℑ + λI )Δχ = ℑT (Φ o − Φ c ) where χ expresses D and

μ a , and ℑ

is a scalar and I is the identity matrix.

(5)

is the Jacobian matrix formed by ∂Φ/∂χ at the boundary measurement sites. λ

Δχ is the updating vector for the optical properties. Φ io and Φ ic are observed

and computed photon density at boundary locations.

The reconstruction process involves the iterative solution of the above Eqs. (3)-(5) with updating the optical property distribution at each iteration.

4. Human Subjects All the human subjects in this study were recruited under the protocol approved by the Institutional Review Board (IRB) of University of Florida. Based on the clinical facts that the occurrence of OA is usually noted between the ages of 45-90 and OA affects females more than males, most of the recruited subjects with OA are females older than 45. To minimize the affect of age and gender on the comparison between OA and healthy joints, healthy subjects are also females with similar ages. Each healthy subject was asked to visit us only once while some of the OA subjects had multiple visits at different time points (from 2 weeks to 10 months) for system stability test and OA monitoring study.

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Fig. 2 Images from a typical OA case. (a)-(f) Coronal slices from the reconstructed 3D images at selected cut-plane. (a)-(c) and (d)-(f) are the absorption and scattering images, respectively. (g) A coronal x-ray image of the same joint.

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Fig. 3 One of the absorption slice shown in Fig. 2 with five lines used for quantitative analysis.

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5. RESULTS While data were collected at all eight available wavelengths for each subject, the absorption and scattering images shown in this paper were reconstructed at 805nm. A full set of data (64 sources x 64 detectors) and a mesh with 3,000 nodes and 14,200 tetrahedral elements were used for 3D reconstructions for all the cases. Recovered optical images from a typical OA case are shown in Fig. 2. They are coronal slices from three cut-planes with an interval of 2mm crossing the imaged joint. A coronal x-ray image of the same joint is displayed in Fig.2 (g) for comparison. From both the absorption and scattering images the two bones associated with the joint can be clearly observed. The joint space between the two bones, where the cartilage and fluid should be, can also be visualized. However, the contrast between the bone and the cartilage and fluid is not high. This finding is consistent with the x-ray (Fig. 2g) where we see that the subject had a late-stage OA and that part of the cartilage had been damaged. In fact, new bone formation, termed osteophytes, had already been found at the joint margins. Since the subchondral bone became exposed and resulted in sclerosis, osteophytes grow in response to these stresses. To analyze the optical properties quantitatively the full width at 30% maximum method described in our previous work was applied to the reconstructed images.5 First, several slices at the cut-planes crossing the finger joint were obtained at intervals of 2mm. The number of the slices depended on the size of finger. Secondly, five lines were plotted in each selected slice along the direction of the two bones, as shown in Fig. 3. Since these lines need to be limited in the finger domain the pitch of the lines is also related to the finger size. The full width at 30% maximum curve for each line was divided into three parts: bone, cartilage, and fluid. The interface points among bone, cartilage, and fluid were taken as 30% of the nearest highest values on the curves. Finally, the mean values of the optical properties in the three parts were calculated. Fig. 4 gives the scatter plot of cartilage absorption vs. fluid absorption. We note that most of the blue circles in the plot representing the healthy cases are located in the bottom-left area while most of the red stars indicating the OA cases are positioned in the central to top-right areas. Thus the OA and healthy joints are disguisable. Although there are a bunch of health cases in the central area also, the OA group shows its difference from the healthy group. To confirm that a significant different does exist between the two groups a standard t-test has been applied to cartilage and fluid absorption coefficients. The p values from the t-test were found to be 0.22% and 0.07% for the absorption coefficients of the cartilage and fluid, respectively.

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Fig. 4 Scatter plot of fluid absorption vs. cartilage absorption. Blue circles and red starts are for health cases and OA cases, respectively.

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Fig. 5 The ratio of fluid absorption to that of bones vs. the ratio of cartilage absorption to that of bones. Blue circles and red starts are for health cases and OA cases, respectively.

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Remarkable difference between OA and normal joints is seen from Fig. 5 where the ratio of fluid absorption to that of bones vs. the ratio of cartilage absorption to that of bones is plotted. Based on the results shown in Fig. 5, we found the sensitivity is 95% and the specificity is 83.3%. The overall accuracy for OA detection is 89.5%. In summary, 20 OA joints and 18 healthy joints have been examined using a hybrid x-ray/DOT imaging system. Significant difference is observed between OA group and healthy group in term of absorption coefficients of the cartilage and fluid. The OA and healthy joints can be successfully distinguished using the ratio of the absorption of cartilage and fluid to that of bones.

ACKNOWLEDGMENT This research was supported in part by the National Institutes of Health (R01 AR048122).

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Creamer, P., “Osteoarthritis pain and its treatment,” Curr Opin Rheumatol 12(5), 450-5 (2000). Recht, M.P., Goodwin, D.W., Winalski C.S., “MRI of articular cartilage: revisiting current status and future directions,” AJR Am J Roentgenol 185(4), 899-914 (2005). Moskowitz, R.W., Altman, R.D., Hochberg, M.C., Buckwalter, J.A. and Goldberg, V.M., [Osteoarthritis: Diagnosis and Medical/Surgical Management], Lippincott Williams & Wilkins, Philadelphia, (2007). Palmer, A.W., Guldberg, R.E. and Levenston, M.E., “Analysis of cartilage matrix fixed charge density and three-dimensional morphology via contrastenhanced microcomputed tomography,” Proc Natl Acad Sci USA 103, 19255-60 (2006). Yuan, Z., Zhang, Q., Sobel, E. and Jiang, H., “Three-dimensional diffuse optical tomography of osteoarthritis: initial results in the finger joints,” Journal of Biomedical Optics 12(3), 034001 (2007). Scheel, A.K., Backhaus, M., Klose, A.D., Moa-Anderson, B., Netz, U.J., Hermann, K-G.A., Beuthan, J., Mu¨ller, G.A., Burmester, G.R. and Hielscher, A.H., “First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints,” Ann Rheum Dis 64, 239–245 (2005). Zhang, Q. and Jiang, H., “Three-dimensional diffuse optical imaging of hand joints: System description and phantom studies,” Optics and lasers in Engineering 43(11), 1237-1251 (2005). Jiang, H., Paulsen, K.D., Osterberg, U., Pogue, B. and Patterson, M., “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996)

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