1.1.

Dynamic Optical Tomography

Within the field of optical tomography, the area of dynamic optical imaging appears particularly promising. In dynamic imaging studies, one attempts to image changes in optical properties and/or physiological parameters as they occur during a system perturbation. The most prominent example may be imaging of hemodynamic effects during functional or drug-induced stimulation of the brain. ^{1, 2, 3, 4, 5, 6, 7} The advantage of dynamic imaging over static imaging is that images change against a baseline that is defined by the system itself. For example, the state of the brain during a stimulation (e.g., various motor tasks such as finger flexing, rat whisker stimulation, or visual stimulation) relative to its state prior to the stimulation. These measurements allow the calculation of changes in oxy- and deoxyhemoglobin without the need for data calibration using a separate reference measurement, for example, on an ${\mathrm{Intralipid}}^{\circledR }$ tissue phantom. The drawback of dynamic imaging is that absolute values for hemodynamic parameters, such as deoxyhemoglobin concentration [Hb], oxyhemoglobin concentration $\left[{\mathrm{HBO}}_2\right]$ , or total hemoglobin concentration [HBT], cannot be obtained without additional assumptions or measurements.⁸

With recent advances in algorithms^{9, 10, 11} and instrumentation^{12, 13, 14} geared specifically to dynamic imaging, this technique has increasingly been applied to other clinically and preclinically relevant areas, such as breast imaging,¹⁵ fluorescence tomography,¹⁶ and cancer research in small animals.¹⁷ In this paper, we explore the potential of optical dynamic imaging for the characterization of joint diseases, particularly rheumatoid arthritis (RA) in finger joints. We investigated a total of six healthy volunteers and eight patients with RA. Discussing three representative cases in detail, we illustrate the aptitude of dynamic optical measurements and tomography to image hemodynamic effects in these joints.

1.2.

RA

RA is a chronic, systemic, inflammatory disease that primarily attacks peripheral joints and surrounding tendons and ligaments.¹⁸ This progressive disease, associated with significant pain and disability, affects about 1% of the population worldwide, and approximately 2.1 million people in the United States.^{19, 20} Women are about three to four times as likely as men to develop RA.^{21, 22} Although RA can be mild, 10% of affected subjects suffer total disability.

The onset and progression of RA is marked by a sequence of progressive physiological changes that affect the joint. Initially, there is a primary inflammatory response of the synovial membrane that encapsulates the joint space and retains the synovial fluid. This inflammatory process is referred to as synovitis. Subsequently, there is accumulation of synovial fluid in the joint space that causes the joint to swell. This distention triggers a change in membrane permeability yielding a migration of inflammatory cells such as lymphocytes and neutrophils into the joint assembly. The inflamed synovial membrane thickens and creates a pannus, which aggressively invades the articular cartilage and adjacent osseous structures. The end result is frank erosion of the joints structural components causing deformity of the fingers and functional disability.

Aside from the aforementioned structural differences of the rheumatic joint, it is well known that there are alterations in the metabolic activities and vascular organization of the synovium. ^{23, 24, 25, 26, 27} As the disease progresses, oxygen demand and consumption in the affected joint rises markedly, as does the production of carbon dioxide $\left({\mathrm{CO}}_2\right)$ .^{28, 29, 30} Studies report a decline in the partial pressure of oxygen $\left({\mathrm{PO}}_2\right)$ as the disease intensifies creating a hypoxic environment inside the joint capsule. Furthermore, RA joints exhibit an elevated carbon dioxide partial pressure $\left({\mathrm{PCO}}_2\right)$ whose value rises with the severity of the disease. In an attempt to meet this increased demand, the vascular network undergoes reorganization, adaptation, and redistribution.³¹ Significant angiogenesis has been reported in RA joints,^{32, 33} and a rise in the rate of vascular cell turnover has been observed through morphometric and histologic studies.²⁷ Blood flow through a RA joint was shown to be elevated and exponential.^{34, 35} Such quantities were determined using Doppler imaging techniques and radioisotope clearance rates. These combined results along with the identification of high lactic acid content (which suggests anaerobic respiration) demonstrate an oxygen-starved environment. Therefore, although the vascular bed undergoes reorganization and proliferation, it does not adequately compensate for the sharp rise in metabolic demand.

1.3.

Optical Imaging of Joint Disease

Several studies have already explored the use of optical techniques for the characterization of joint disease. ^{36, 37, 38, 39, 40, 41, 42, 43} Most of the early work tried to exploit the changes in the optical properties of the synovial fluid, which fills the joint cavity. The fluid transforms from a liquid that is a clear yellowish color to a turbid grayish substance in the course of RA.³⁶ More specifically, it has been shown that at $\lambda =685\mathrm{nm}$ , the absorption and reduced-scattering coefficients, ${\mu }_a$ and ${\mu }_s^{\prime }$ , respectively, are two to three times greater in the synovial fluid of a rheumatoid joint $({\mu }_a=0.011{\mathrm{cm}}^{-1}$ , ${\mu }_s=0.12{\mathrm{cm}}^{-1}$ ) when compared against a healthy one ( ${\mu }_a=0.004{\mathrm{cm}}^{-1}$ , ${\mu }_s=0.06{\mathrm{cm}}^{-1}$ ).⁴⁴ Similar findings were reported by the same authors for the synovial membrane as well. Extensive experimental and numerical phantom studies suggested that these differences can be detected through transillumination measurements of the joint.

Going beyond transillumination measurements, our group recently explored the use of optical tomographic imaging techniques as a diagnostic tool for joint inflammation.⁴⁵ To perform the optical measurements, a sagittal scanner was employed to collect steady-state data along the span of the finger. In initial case studies, it was found that the joints affected by RA have higher scattering and absorption coefficients. Subsequently a clinical evaluation of the steady-state sagittal laser optical tomography technique was implemented to detect synovitis in arthritic finger joints.⁴⁶ To assess the diagnostic merit of this method, statistical analysis was applied to the data of 78 finger joints. By comparing results of the optical imaging method with identifications formed through clinical examination in conjunction with ultrasound imaging, the sensitivity and specificity were found to be in the 70% range. Attempting to possibly increase the sensitivity and specificity of optical tomographic imaging, along with the appeal of gaining additional insight into the effects of RA, motivates our pursuit of acquiring dynamic data in addition to static measurements performed so far.

We hypothesize that dynamic optical tomography is well suited for imaging the hemodynamic effects in RA joints as described in Sec. 1.1. Especially differences in the vascular network between healthy and affected joints should lead to different responses to carefully applied stimuli. This should provide additional complementary information to changes in the synovial fluid observed previously. In particular, we focus on effects of pressure cuffs on the forearm, which lead to a temporary blockage of the venous return. For this pilot study, we enrolled six healthy volunteers and eight patients diagnosed with RA. In the following, we will describe in detail the experimental methods used and observations made.

2.1.

Instrumentation and Experimental Setup

Measurements on the finger were performed with a dynamic near-infrared optical tomography (DYNOT) imager. This instrument operates in continuous-wave mode, and allows obtaining up to 10 full tomographic measurement sets per second depending on the number of sources used. A combined optical beam consisting of two laser diodes (760 and $832\mathrm{nm}$ ) acts as the illuminating source. This source is sequentially coupled into different 1-mm multimode fiber bundles that distribute light to multiple areas along the measurement probe. The current of each laser diode is modulated to a distinct amplitude and frequency. In this way, multiple wavelengths may be illuminated simultaneously, and their respective amplitude and phase contribution on the attenuated detected signal can be extracted using synchronous detection techniques. The total power incident on the target is about $30\mathrm{mW}$ . Once the light is disbursed throughout and attenuated by the finger structures surrounding the joint, it exits the probe and is collected in parallel by the numerous fiber bundles positioned around the target. The light is then guided to the detection circuitry that converts the optical signal into an electrical current and, ultimately, into a corresponding amplitude. Silicone photodiodes are used as the transducer. Fast source switching synchronized with adaptive on-the-fly gain control affords rapid detection over a large dynamic range. A more detailed description of the DYNOT instrument can be found in Schmitz ¹⁴

For these studies, our objective was to standardize a means of generating transverse measurements around the proximal interphalangeal (PIP) joint over a wide range of finger shapes and sizes. To this end, we constructed a cylindrical imaging head with an inner diameter measuring $3.0\mathrm{cm}$ and a wall thickness of $10\mathrm{mm}$ machined from a solid rod of opaque (white-colored) acetal resin engineering plastic material also known as ${\mathrm{Delrin}}^{\circledR }$ . Borrowing from the concept of a bolt, the inner wall of the lower third of the cylinder is threaded and accepts a custom bolt, also machined from the same ${\mathrm{Delrin}}^{\circledR }$ material. In this way, a multitude of varying finger sizes can be accommodated by adjusting the effective interior length of the probe. An indentation is bored into the end of the bolt wherein the finger rests. This serves to stabilize the distal tip of the finger during an experiment and reduce the tremors that are characteristic of extended, free hanging skeletal muscles. Similarly, because $3.0\mathrm{cm}$ is larger than the average finger size, many fingers will “float” within the walls of the cylinder possibly creating large motion artifacts. Therefore, in an effort to secure the base of the finger, caps with varying diameter holes drilled through the center, cover the top of the cylinder. A subject would then place a finger through the cap and into the cylinder until it is supported by the bolt at the bottom. A picture of the measurement probe is shown in Fig. 1 .

Fig. 1

Transverse measurement probe for optical tomographic finger scans.

Two rings that slide over the cylinder accommodate the source and detector fiber bundles. The rings are translated along the longitudinal axis of the imaging head until they are positioned parallel to the joint under investigation, at which point they are fastened to the probe. Each ring can hold up to 24 fibers. For the measurements presented in this paper, we employ 12 sources and 12 detectors per ring in an alternating clockwise arrangement for a total of $24\times 24=576$ source-detector combinations. Approximately 2.5 complete tomographic data sets were acquired per second. A single time frame consisted of illuminating each of the 24 sources in succession and detecting the transmitted light received through all 24 detectors simultaneously.

2.2.

Experimental Protocol for Dynamic Measurements

The experiments were designed to study vascular and possibly metabolic effects of the disease on the PIP joint. Prior to each experiment, the blood pressure of each patient is established. This serves to standardize the measurement protocol (see below) as well as provide possible insight when interpreting the dynamic behavior of the joint. Additional setup procedures include measuring the length of the patient’s finger and adjusting the effective height of the measuring head so that the distal tip of the finger rests securely in the internal holder and the complete finger is immersed inside the cylinder. Similarly, the distance between the top of the probe and the patient’s PIP joint is measured and the fiber optic rings are translated accordingly so that they lie on the transverse plane of the joint under examination. With the fibers correctly positioned and the height properly fixed, the patient inserts a finger into the measurement head. A matching fluid of 1% Intralipid was added to fill the voids between the finger and the wall of the probe. Once the patient rests the finger comfortably and securely, the instrument must run a self-calibration where it determines and stores the ideal gain setting for each channel at every source position. This is implemented to maximize the signal-to-noise ratio without saturating the electronics. The data acquisition is started after the calibration is complete.

To illicit a controlled hemodynamic response, we employ a sphygmomanometer cuff placed around the forearm. This cuff is inflated at a predetermined point in time after a baseline measurement is obtained for each individual subject. The timing and induced perturbation protocol used in these dynamic studies evolves as follows: First a baseline measurement of $10\mathrm{s}$ is made. This is followed by an inflation of the arm cuff to the pressure $P_{diastolic}+(P_{systolic}-P_{diastolic})∕2$ . By applying this pressure, the intention is to shut down venous return and ${\mathrm{CO}}_2$ removal of the blood supply from the finger while still maintaining blood and oxygen delivery. The pressure is maintained in the cuff for $30\mathrm{s}$ , at which point the pressure is rapidly yet steadily released. Data is acquired for another 40-s rest period before the cuff is inflated a second time. During the second perturbation, the pressure is held to $P_{systolic}+15\mathrm{mmHg}$ for another $30\mathrm{s}$ , which is intended to shut off both the venous return and arterial supply. The experiment concludes with a 40-s rest period during which data is still being collected. We repeat this experiment for the PIP joint of the index, middle, and ring fingers on both the right and left hands.

2.3.

Experimental Protocol for Static Measurements

In addition to the dynamic measurements, we also performed static measurements. As already mentioned, in previous studies we showed that affected joints typically show lower absorption and scattering coefficients in the joint cavity when compared to joints affected by RA.^{44, 45} However, the scanner used in the previous studies provided sagittal sections through the joint, and the scanner used in the current study provides coronal sections through the joint.

To obtain static measurement data with the DYNOT system, we do not induce a provocation, but rather, measure the difference signal between the finger joint immersed in an Intralipid suspension versus an undisturbed homogenous Intralipid suspension. In contrast to the dynamic measurements, here the system calibration is performed on a pure Intralipid phantom without the finger being immersed. The timing protocol begins by acquiring 50 frames of this liquid phantom after which the data acquisition is paused. Some of the liquid is extracted from the cylinder, and the subject inserts the right index finger inside cylinder. The data acquisition is resumed for another 50 frames after which it is paused again and prepared for the middle finger. This procedure is repeated until the index, middle, and ring finger of both hands have been scanned. To increase the signal-to-noise level, we average the 50 data points obtained for each measurement. Therefore, a tradeoff exists between the quality of the data, the acquisition period, and the comfort for the patient, who has to endure six dynamic scans with a single setup or scan time of about $5\min$ .

All experiments and procedures were performed in accordance with institutional guidelines and informed consent was obtained from all participants.

2.4.

Preprocessing

Once the data has been collected, it must be prepared for an image reconstruction. To this end we have developed an intuitive and user-friendly MATLAB script, which guides the user through the preprocessing routines. Data sets for both wavelengths are loaded into the program. The user can choose to view and analyze data from either a single measurement plane or channels from both fiber optic rings. At the outset, because the instrument generates data in the form of difference measurements, the time trace for each source-detector pair is normalized to the mean of its baseline scan. For the subsequent steps, the nature of the data processing depends upon the type of experiment that was performed.

When processing dynamic measurements, we developed a technique for eliminating common system noise that is present on all channels. For each source locality $i$ , the value of each detector $j$ , $P_{i,j}$ , is renormalized to the detector value that is closest to that source, $P_{i,i}$ . Due to its adjacent proximity to the light source and comparative distance from the finger, we can safely assume that this detected intensity is not actually probing tissue so it may function as a reference channel for that particular source position. Following this renormalization, the time trace is further smoothed by a moving average low-pass filter

When processing so-called static measurements, each perturbation from baseline is acquired over many time points. Therefore, the best way to increase the signal-to-noise ratio on such a data set is by averaging over the entire block of data, and we do not need to renormalize to the closest source-detector separation.

After the measurement set has been appropriately processed, the user can save all source-detector measurements for a selected time point to be used by the reconstruction algorithm. All operations are performed on both wavelengths in parallel.

2.5.

Image Reconstruction Algorithm

Data generated by the DYNOT instrument is in the form of difference measurements. The primary reasons for this is the varying effective response among detector channels operating in parallel and associated coupling differences at each fiber interface along the photon trajectory. As a result, it becomes difficult to relate one source-detector measurement with another. By performing these perturbation-based measurements though, several advantages can be realized. First, because a perturbation only affects the specific areas of change while the physical boundary conditions remain unchanged, the system becomes less sensitive to boundary affects. Second, it becomes less sensitive to the poor diffusion representation of low-scattering regions characteristic of synovial finger joints. A drawback to this approach, however, is that the absolute distribution of optical properties cannot be derived, unless additional assumptions or measurements are made. Only relative changes of absorption or scattering relative to a baseline can be determined.

To generate the three-dimensional reconstructions of the optical properties in the joint, we employ a model-based iterative image reconstruction (MOBIIR) scheme.^{47, 48, 49} This technique consists of three individual components: (1) a forward model that uses photon propagation theory to predict the detector readings at the boundary based on an assumed initial spatial distribution of the optical properties inside the medium; (2) an analysis step that compares the measured values with the theoretical model; (3) an updating scheme that adjusts the optical parameters of the model. These steps are repeated until the error between the predicted and measured quantities is sufficiently small. The final distribution of optical properties when the solution converges represents the spatial mapping of the target medium.

The forward model used in these studies is the time-independent diffusion equation given by

During the analysis phase of the MOBIIR scheme, an objective function is defined which quantifies how well the actual experimental data correlates with the theoretical prediction. To do this, we use a modified standard least-squares objective function as suggested by Pei, ⁵⁰ which is formulated for difference data. To update the initial and subsequent spatial distributions of the optical properties, the gradient of the objective function with respect to the absorption and diffusion coefficients ( ${\mu }_a$ and $D$ ) is calculated. Further details on the reconstruction methods can be found at Bluestone ⁵¹

By using the scheme outlined above, MOBIIR calculates the change in absorption profile $\mathrm{\Delta }{\mu }_a$ in response to some stimulus. All measurements are recorded at two wavelengths ( ${\lambda }_1=765\mathrm{nm}\text{and}{\lambda }_2=832\mathrm{nm}$ ) enabling us to reconstruct a profile for both ${\lambda }_1$ and ${\lambda }_2$ (therefore, the numbers 1 and 2 should be an index-subscript!). The absorption coefficient is related to the chromophore concentration and its extinction coefficient by ${\mu }_a=\epsilon \left[C\right]$ . Recognizing that the primary chromophores in tissue at these wavelengths $\left(\lambda \right)$ are oxy- $\left[{\mathrm{HBO}}_2\right]$ and deoxyhemoglobin [Hb], we can express the overall absorption as a linear combination of each weighted by their respective extinction coefficients⁵²

The diffusion equation 2 is solved over a finite element volume. To this end, we make use of the adaptive geometrical modeling software package distributed by GID (http://www.gidhome.com) to construct a finite element volumetric mesh equivalent to our imaging head dimensions and experimental setup (Fig. 2 ). Because data quality is critically dependent on optode placement, care must be taken to precisely match the source and detector coordinates with the physical setup and to maintain them when generating the mesh. Any deviation in their positions will produce adverse artifacts in the image. Our cylindrical geometry was $3.2\mathrm{cm}$ wide and $6\mathrm{cm}$ tall. Two rings of 24 equally spaced points seated at the boundary were separated by $1.3\mathrm{cm}$ , corresponding to the optode arrangement around the imaging head. The mesh is formed from $\sim 1000$ finite elements comprising approximately 2000 nodes, approximately 8000 volumetric tetrahedral elements, and approximately 2000 triangular surface elements. After the mesh was generated, the optical properties for 1% Intralipid at approximately $800\mathrm{nm}$ were assigned to each node. All node locations were initially assigned an absorption coefficient of ${\mu }_a=1.0{\mathrm{cm}}^{-1}$ and a diffusion coefficient of $D=c∕\left(3{\mu }_s^{\prime }\right)=0.9{\mathrm{cm}}^2∕\mathrm{ns}$ , values that are documented in literature.

Fig. 2

Finite element volumetric mesh for reconstructions.

The computation usually converges in about 15 to 25 iterations and is determined by the magnitude of the perturbation relative to the baseline at that time point. Using a Linux workstation with two 1.2-GHz processors, the required computation time ranges from 5 to $30\min$ depending on the number of experimental parameters (source-detector pairs) defined for the reconstruction.

3.1.

Dynamic Time Traces

Figures 3, 4, 5 show signal traces corresponding to fingers on the left and right hand for a healthy volunteer, RA case 1, and RA case 2, respectively. The traces depict the transmission profile over all detector channels for a single illumination position at one wavelength $(\lambda =765\mathrm{nm})$ . The response is plotted as change in intensity $\mathrm{\Delta }I$ versus time $t$ in seconds recorded at a data acquisition rate of $2.4\mathrm{Hz}$ . All traces are normalized to the mean of the initial rest period, which defines the baseline for the experiment.

Fig. 3

Temporal response of lateral detector intensities for healthy volunteer. (a) Left index PIP joint, source 1, detectors 1 to 24, $\lambda =765\mathrm{nm}$ . (b) Right index PIP joint, source 1, detectors 1 to 24, $\lambda =765\mathrm{nm}$ . (c) Enlarged section of effusion process for left index finger. (d) Enlarged section of effusion process for right index finger.

Fig. 4

Temporal response of lateral detector intensities for RA patient, case study 1. (a) Left index PIP joint, source 1, detectors 1 to 24, $\lambda =765\mathrm{nm}$ . (b) Right index PIP joint, source 1, detectors 1 to 24, $\lambda =765\mathrm{nm}$ . (c) Enlarged section of effusion process for left index finger. (d) Enlarged section of effusion process for right index finger.

Fig. 5

Temporal response of lateral detector intensities for RA patient, case study 2. (a) Left index PIP joint, source 1, detectors 1 to 24, $\lambda =765\mathrm{nm}$ . (b) Right index PIP joint, source 1, detectors 1 to 24, $\lambda =765\mathrm{nm}$ . (c) Enlarged section of effusion process for left index finger. (d) Enlarged section of effusion process for right index finger.

3.2.

Tomographic Reconstructions (Dynamic Data)

Besides analyzing features in the dynamic time traces, we also performed tomographic reconstructions that show the spatial distribution of optical properties and physiological parameters. We start our discussion by examining the reconstructed ${\mu }_a$ distribution. In this and the following cases, we show two-dimensional cross sections that were extracted from three-dimensional reconstruction results.

3.2.1.

Healthy control

Figure 6 shows a set of cross-sectional images taken on the plane parallel to the joints. They represent the spatial changes in the absorption coefficient ${\mu }_a$ at $\lambda =765\mathrm{nm}$ for the left and right index fingers of the healthy control. The reconstruction is computed at the time point of maximum deflection from the baseline, which occurs just prior to releasing the pressure cuff when the change in intensity $\mathrm{\Delta }I$ is the greatest [see Fig. 3a $t=40\mathrm{s}$ ]. The left index finger is displayed in the left column and the right index finger on the right. All images are oriented so that the top of the graphic coincides with the posterior surface of the finger.

Fig. 6

Cross-sectional images of $\mathrm{\Delta }{\mu }_a$ $(\lambda =765\mathrm{nm})$ through PIP joints of left and right index fingers of healthy subject, determined at maximum change in intensity [ $t\sim 40\mathrm{s}$ in Figs. 3a and 3b].

The joints in this healthy volunteer show approximately a 40% increase in absorption, predominantly in the posterior and anterior regions of the finger joint, in the vicinity of the main vascular branches that supply the finger.⁵⁵ Because varying finger sizes will have a direct affect on the signal change (larger fingers have larger vessels), more important than the actual percentage change in ${\mu }_a$ is the general profile of absorption around the joint. Specifically, high areas of absorption occur in a circular geometry around the joint cavity whereas there is almost no absorption change in the center. This pattern is confirmed on both healthy hands.

3.2.2.

RA case 1

A similar set of two-dimensional cross-sectional images for our first case study is depicted in Fig. 7 . Here, an image of the unaffected joint is displayed on the left and the imaging belonging to the RA-affected joint is shown on the right. Although not as distinct as the healthy subject, the absorption map of the unaffected joint also follows a circular pattern around the joint with a low absorption center. In contrast, the joint affected by RA reveals an elevated ${\mu }_a$ pocket distributed across the joint cavity. The skewed image location is the result of off-centered finger positioning inside the measurement probe.

Fig. 7

Cross-sectional images of $\mathrm{\Delta }{\mu }_a$ $(\lambda =765\mathrm{nm})$ through PIP joints of left and right index fingers of RA patient, determined at maximum change in intensity [ $t\sim 40\mathrm{s}$ in Figs. 4a and 4b].

3.2.3.

RA case 2

The absorption profile for the second case study is shown in Fig. 8 . The image on the right represents the right RA index finger, and the image on the left characterizes the stronger affected left RA index finger. Again, the reconstructions capture the time point of maximum $\mathrm{\Delta }I$ [see Fig. 5a at $t\sim 40\mathrm{s}$ ].

Fig. 8

Cross-sectional images of $\mathrm{\Delta }{\mu }_a$ $(\lambda =765\mathrm{nm})$ through PIP joints of left (swollen and irritated) and right index fingers of RA patient, determined at maximum change in intensity [ $t\sim 40\mathrm{s}$ in Figs. 5a and 5b].

The images similarly corroborate that in joints affected by RA, the increase in absorption penetrates the joint cavity as large pockets of $\mathrm{\Delta }{\mu }_{\alpha }$ form in the center of the graphics. This effect is particularly strong in the inflamed and irritated joint (Fig. 8). Looking at the outlines of Fig. 8 implies that the lateral joints are approximately the same geometrical size and that the irritated finger is not larger, which is in accordance with the visual inspection of the fingers.

These collective results suggest a significant redistribution and proliferation of vascular structures around the affected joint of rheumatic patients. Vessels supplying healthy joints are arranged surrounding the synovial cavity and do not penetrate into the articular joint space occupied by synovial fluid. An elevated and unorganized spatial distribution of the vascular supply, particularly extending into the articular cavity, characterizes the formation of the vascular network in a rheumatoid joint. Furthermore, as the disease progresses, a denser vascular network is implied by the pronounced percentage change in the optical transmission of the joint suffering from a more advanced stage of RA when compared to a lesser affected joint on the same person.

3.3.

Reconstructions of Hemodynamic Parameters

To extract differences in metabolic activity, we used our dual wavelength data set to monitor fluctuations in hemoglobin parameters. A comparison of the spatial variations of $\left[{\mathrm{HbO}}_2\right]$ , [Hb], and [HbT], which is directly proportional to blood volume, is illustrated in Fig. 9 . As anatomical reference, we have provided a magnetic resonance (MR) image of a healthy PIP joint [Fig. 9b], which shows the main features, such as tendons, arteries, and joint cavities. However, it should be noted that the joint has a curved, saddlelike geometry, and that the joint cavity filled with synovial fluid is only about $0.5\mathrm{mm}$ thick and the adjacent cartilage varies between 0.5 and $1\mathrm{mm}$ in thickness. Given a typical axial resolution of $2\mathrm{mm}$ , the shown MR image averages over some of these structures.

Fig. 9

(a) Comparison of spatial mappings of [ ${\mathrm{HbO}}_2$ ], [Hb], and [HbT] for a healthy subject and two RA patients. Left column: right index finger of healthy joint [see also Figs. 3b and 6]; middle column: right index of RA joint [see also Figs. 4b and 7]; right column: right index finger of another RA infected joint [see also Figs. 5b and 8]. (b) Axial T1-weighted MR image (slice thickness $2\mathrm{mm}$ ) of the proximal interphalangeal joint of the middle finger of a healthy volunteer. The features identified in this image include (a) palmar digital arteries, (b) tendon of muscle flexor digitorum, (c) cartilage of proximal interphalangeal joint, (d) synovial fluid in proximal interphalangeal joint, (e) tendon of muscle extensor digitorum, (f) collatoral ligament, (g) dorsal digital arteries.

3.4.

Static Images

Figure 10 shows the cross-sectional slices of the three-dimensional reconstructions for the three subjects. Analogous to the dynamic review, we present the lateral images. Both left and right images of the healthy index fingers exhibit similar profiles. They reveal an elevated absorption distributed in a circular pattern around the joint. At the center is a voidlike region where near-infrared absorption is minimal. Very similar features also exist in the joints of RA case 1, with the primary difference being a slightly thicker ring of absorption around the joint cavity. This affect is more pronounced in the images of RA case 2. In this occurrence, the right rheumatoid joint shows a thick ring of elevated absorption around a smaller low-absorption center. For the left joint which is stiffer and more inflamed, the ring structure is lost at the center and now an area of larger absorption is seen through the center of the image. These results are in agreement with our previous steady-state studies. However, in these previous studies a saggital section of the joint was presented, while in this paper we show images of a transverse section through the joints.

Fig. 10

Two-dimensional cross-section of static reconstructions $(\lambda =765\mathrm{nm})$ for three experimental cases. Results for the PIP joint of the left and right index fingers are displayed in the left and right columns, respectively. The upper row corresponds to a healthy patient, the middle and bottom rows to RA patients in case studies 1 and 2.

These combined results seem to propose a structural progression in ${\mu }_a$ . Being that the primary chromophore is the vascular supply, this has direct implications on vascular organization in RA. In a healthy joint, upon inflating a cuff, ${\mu }_a$ increases in a relatively small circular arrangement around the circumferance of the joint; possibly in and around the synovial membrane that contains blood vessels. However, the vessels do not penetrate into the articular cavity that is filled with the nonabsorbing synovial fluid. As the disease progresses, the high-absorption ring begins to thicken—most likely indicating a thickening of synovial membrane in which new vessels are formed (angiogenesis). Concurrently, the voidlike center region starts to shrink in diameter. In advanced RA stages, when joints become stiff and irritated, the vascular growth and distribution is so large that the ring structure is lost and the entire joint cavity shows an increase in ${\mu }_a$ .