Frequency-domain optical tomographic imaging of arthritic finger joints.
ABSTRACT We are presenting data from the largest clinical trial on optical tomographic imaging of finger joints to date. Overall we evaluated 99 fingers of patients affected by rheumatoid arthritis (RA) and 120 fingers from healthy volunteers. Using frequency-domain imaging techniques we show that sensitivities and specificities of 0.85 and higher can be achieved in detecting RA. This is accomplished by deriving multiple optical parameters from the optical tomographic images and combining them for the statistical analysis. Parameters derived from the scattering coefficient perform slightly better than absorption derived parameters. Furthermore we found that data obtained at 600 MHz leads to better classification results than data obtained at 0 or 300 MHz.
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ABSTRACT: WWe present what is believed to be the first absorption and scattering images of in vitro and in vivo bones and joints from continuous-wave tomographic measurements. Human finger and chicken bones embedded in cylindrical scattering media were imaged at multiple transverse planes with Clemson multi-channel diffuse optical imager. Both absorption and scattering images were obtained using our nonlinear, finite element based reconstruction algorithm. This study shows that diffuse optical tomography (DOT) has the potential to be used for detection and monitoring of bone and joint diseases such as osteoporosis and arthritis.Optics Express 04/2001; 8(7):447-51. · 3.55 Impact Factor
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ABSTRACT: To identify classifiers in images obtained with sagittal laser optical tomography (SLOT) that can be used to distinguish between joints affected and not affected by synovitis. 78 SLOT images of proximal interphalangeal joints II-IV from 13 patients with rheumatoid arthritis were compared with ultrasound (US) images and clinical examination (CE). SLOT images showing the spatial distribution of scattering and absorption coefficients within the joint cavity were generated. The means and standard errors for seven different classifiers (operator score and six quantitative measurements) were determined from SLOT images using CE and US as diagnostic references. For classifiers showing significant differences between affected and non-affected joints, sensitivities and specificities for various cut off parameters were obtained by receiver operating characteristic (ROC) analysis. For five classifiers used to characterise SLOT images the mean between affected and unaffected joints was statistically significant using US as diagnostic reference, but statistically significant for only one classifier with CE as reference. In general, high absorption and scattering coefficients in and around the joint cavity are indicative of synovitis. ROC analysis showed that the minimal absorption classifier yields the largest area under the curve (0.777; sensitivity and specificity 0.705 each) with US as diagnostic reference. Classifiers in SLOT images have been identified that show statistically significant differences between joints with and without synovitis. It is possible to classify a joint as inflamed with SLOT, without the need for a reference measurement. Furthermore, SLOT based diagnosis of synovitis agrees better with US diagnosis than CE.Annals of the Rheumatic Diseases 03/2005; 64(2):239-45. · 9.11 Impact Factor
Article: Diffuse radiation in the GalaxyThe Astrophysical Journal 12/1940; 93:70-83. · 6.73 Impact Factor
IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO. 10, OCTOBER 2011 1725
Frequency-Domain Optical Tomographic
Imaging of Arthritic Finger Joints
Andreas H. Hielscher*, Member, IEEE, Hyun Keol Kim, Ludguier D. Montejo, Member, IEEE, Sabine Blaschke,
Uwe J. Netz, Paul A. Zwaka, Gerd Illing, Gerhard A. Müller, and Jürgen Beuthan
Abstract—We are presenting data from the largest clinical trial
on optical tomographic imaging of finger joints to date. Overall we
evaluated 99 fingers of patients affected by rheumatoid arthritis
of 0.85 and higher can be achieved in detecting RA. This is accom-
plished by deriving multiple optical parameters from the optical
tomographic images and combining them for the statistical anal-
ysis. Parameters derived from the scattering coefficient perform
slightly better than absorption derived parameters. Furthermore
we found that data obtained at 600 MHz leads to better classifica-
tion results than data obtained at 0 or 300 MHz.
Index Terms—Computer aided diagnostics, light propagation in
tissue, optical tomography, rheumatoid arthritis (RA).
and other joint diseases. Jiang et al. have performed extensive
studies to show the potential of optical tomography to detect
osteoarthritis (OA). In 2001 they introduced a continuous-wave
(CW) system for reconstructing absorption and scattering co-
efficients of joints . Using experimental data from a human
finger and several chicken bones, this group subsequently
showed that 3-D volumetric reconstructions can provide details
of the joint structure and composition that would be impossible
from 2-D imaging methods . For this study they employed
VER the last decade several groups have pursued the
use of optical tomographic methods to image arthritis
Manuscript received February 06, 2011; accepted March 08, 2011. Date of
publication April 05, 2011; date of current version September 30, 2011. This
work was supported in part by a grant from the National Institute of Arthritis
of the National Institutes of Health. Asterisk indicates corresponding author.
*A. H. Hielscher is with the Departments of Biomedical Engineering, Radi-
H. K. Kim and L. D. Montejo are with the Department of Biomedical En-
gineering, Columbia University, New York 10027 USA (e-mail: hkk2107@
S. Blaschke and G. A. Müller are with the Department of Nephrology
and Rheumatology, Georg-August-University, University Medical Center
Göttingen, 37075 Göttingen, Germany.
U. J. Netz is with the Laser- und Medizin-Technologie GmbH Berlin, 14195
Berlin-Dahlem, Germany and with the Department of Medical Physics and
Laser Medicine, Charité-Universitätsmedizin Berlin, 10117 Berlin, Germany.
P. A. Zwaka is with the Department of Radiology, Georg-August-University,
University Medical Center Göttingen, 37075 Göttingen, Germany.
G. Illing is with Laser- und Medizin-Technologie GmbH Berlin, 14195
J. Beuthan is with the Department of Medical Physics and Laser Medicine,
Charité-Universitätsmedizin Berlin, 10117 Berlin, Germany.
Color versions of one or more of the figures in this paper are available online
Digital Object Identifier 10.1109/TMI.2011.2135374
a finite-element algorithm that was based on the diffusion
equation of light transport in tissue. Refining the imaging
hardware and software further, they presented first clinical
results involving data from two OA patients and three healthy
volunteers in 2007 –. They found that the reconstructed
images demonstrated differences in optical properties in the
joint region between the OA and healthy joints. Since then
this group has further improved their system by introducing a
combined X-ray optical-imaging system , developed a new
instrument based on photo-acoustic imaging , and moved be-
yond the diffusion model to include higher-order reconstruction
schemes that account for light-transport effects not previously
covered . The X-ray system was used to image the distal
inter-phalangeal (DIP) joints of 22 patients and 18 healthy
volunteers, while the photo-acoustic system was explored by
imaging DIP joints of 2 OA patients and four healthy subjects.
In 2007, Wang et al. showed the potential of photo-acoustic
tomography (PAT) for imaging of human peripheral joints by
studying the method’s resolution in cadaver human fingers and
small animals , . More recently, several researchers have
suggested molecular imaging approaches that involved bio-
luminescence and fluorescence markers –. However,
they did not apply tomographic imaging methods.
Our research team has focused in the past on application of
optical tomographic imaging for detecting and characterizing
inflammation in rheumatoid arthritis (RA). RA is an autoim-
mune disease characterized by chronic inflammation of the syn-
ovial membrane of joints , . The etiology of RA is un-
known, however, it affects an estimated 1.5 million Americans.
PatientswithRA cansuffer from cripplingpainandlack ofjoint
mobility. These handicaps can result in large financial costs due
to health care expenses and loss of productivity at work. De-
spite recent advances in therapeutic intervention including bi-
ological therapies, there is currently no cure of RA. However,
early treatment of RA has been shown to significantly improve
clinical outcome and management of the disease. It is therefore
important to diagnose a patient with RA as early as possible.
inside the joint cavity are elevated in patients with RA com-
parameter [for example, the smallest or the largest absorption
ties (Se) and specificities (Sp) of only 0.71 were achieved. Sub-
sequently, Klose et al. , showed that if optically derived pa-
rameters, such as
the classification process, sensitivities and specificities can be
increased to 0.76 and 0.78, respectively.
] for classification, sensitivi-
, are combined for
0278-0062/$26.00 © 2011 IEEE
1726IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO. 10, OCTOBER 2011
In these previous studies a continuous wave (CW) instru-
ment was used that measured the amplitude of transmitted light
intensities. However, it is known that CW systems have diffi-
culties separating absorption and scattering effects, which may
limit the achievable sensitivities and specificities. In this work
we present first clinical results obtained with a frequency-do-
main imaging system. In addition to amplitude information,
frequency-domain data contains phase information, which has
been shown to improve the separation of scattering and absorp-
tion effects . By imaging over 200 fingers at three different
modulation frequencies (0, 300, and 600 MHz) and comparing
the results to established clinical criteria, ultrasound (US) and
magnetic resonance imaging (MRI), we sought to demonstrate
that frequency-domain imaging leads to higher sensitivities
and specificities. Furthermore, by combining a multitude of
optically derived parameters, we explored the possibility of
using computer aided diagnostic tools that could assist in the
diagnosis of rheumatoid arthritis.
II. PATIENTS AND METHODS
In this study 36 patients, previously diagnosed with rheuma-
toid arthritis (RA), were enrolled at the Department of
Nephrology and Rheumatology, University Medicine of Göet-
tingen, Germany. Data from three patients was discarded
because the optical tomographic imaging system failed to
operate correctly during the exam. Of the remaining 33 RA
patients, 24 were female and 9 male, which reflects the fact that
RA is 2–3 times more common in women than in men. The
mean age of these patients was 51.5
years). All patients met the criteria for the diagnosis of RA
established by the American College of Rheumatology (ACR)
and the European League Against Rheumatism (EULAR) ,
. Most of the patients (21/33; 63.6%) received standard
disease-modifying anti-rheumatic drug therapy (methotrexate,
leflunomide, adalimumab) and low-dose prednisone ( 10
mg/d). Positivity for the rheumatoid factor was found in 8 out
of 33 cases (24%). All patients had active disease, defined as
at least three swollen and tender peripheral joints and morning
1 hour, with or without an elevated erythrocyte
mg/l . The mean clinical disease activity,
assessed according to the method previously defined by van der
Heijde et al. , was 4.6 (range 1.59–8.02).
All patients were subjected to clinical examination (CE), ul-
trasound (US) imaging and low-field MRI of the clinically pre-
dominant hand. Furthermore, proximal interphalangeal (PIP)
joints II-IV were subjected to frequency-domain optical tomog-
raphy (FDOT), resulting in 99 images of fingers from RA pa-
tients. As controls 20 healthy persons male:female
with a mean age of 38.814.1 years (range 22–60 years) were
included and subjected to FDOT analysis of PIP joints II–IV
of both hands (resulting in
of healthy finger joints). The study was approved by the Institu-
tional Review Board (IRB) and each patient and healthy control
gave informed consent prior to study entry.
13.9 years (range 21–77
mm/h or C-reactive protein
B. Gold Standard
To establish a gold standard for classification results CE,
MRI, and US were used to determine if a finger was affected
by RA or not. The CE of each PIP joint was performed by
bi-manual palpation to assess the degree of swelling, tender-
ness and warmth. The joints were classified according to a
clinical synovitis score (CSS) , . To assess the overall
state of the disease, laboratory tests included the erythrocyte
sedimentation rate (ESR) and C-reactive protein (CRP). Both
blood tests used to detect inflammation within the body. Higher
sedimentation rates indicate the presence of inflammation and
occur in inflammatory disease, such as RA. The CRP is a
protein built in liver tissue and also considered a parameter
of inflammation as part of activating the immune system.
Although not specific, both parameters show a good correlation
to RA disease activity. Finally, an overall disease activity score
(DAS) was assessed as part of the clinical exam. The DAS28
is a combined index that has been developed to measure the
disease activity in patients with RA , . It includes a
classification of 28 joints according to the degree of swelling
and tenderness, the ESR, and a patient self-assessment ac-
cording to the visual analogue scale (VAS). The DAS28 results
in a number between 0 and 10, indicating how active the RA
is at this moment. Using the DAS28, several thresholds have
been developed for high disease activity, low disease activity,
or disease inactivity. Disease activity is defined as inactive
, moderately active if
and highly active if
MRI was performed using a dedicated low-field (0.2 T) MRI
system (C-scan, ESAOTE, Genova, Italy) equipped with a
specifically designed hand coil. Imaging sequences included
native gradient-echo short-tau inversion-recovery (STIR) se-
quence in coronal slice orientation, T1-weighted spin-echo
high resolution sequence in transversal and coronal orienta-
tions, and T1-weighted 3-D gradient-echo sequence in coronal
slice orientation before and after bolus administration of the
paramagnetic contrast medium gadolinium diethylenetriamine-
pentaacetic acid (Gd-DTPA, Magnevist, Schering, Berlin,
Germany) at a dose of 0.2 mmol/kg body weight. The data set
acquired with the T1-weighted 3-D gradient echo sequence was
used for reconstruction of axial views. Examples are shown
in Fig. 1, which display how synovitis [Fig. 1(a) and (b)] and
joint erosions [Fig. 1(c) and (d)] appear in MR images before
and after administration of the contrast agent. Synovitis is
clearly apparent in the contrast-enhanced image, while erosion
is visible even before the administration of a Gd-DTPA bolus.
Scoring of synovitis and erosions was performed according to
the EULAR OMERACT criteria , using a semi-quantitative
scoring system as previously described by Schirmer et al. .
Ultrasound imaging (US) was performed with an Esaote
Technos MPX ultrasound system. We used a 14-8 MHz hockey
stick linear array transducer for examination of the PIP joints.
Fig. 2. A healthy joint is shown in Fig. 2(a), while Fig. 2(b)–(d)
show joints with inflammation. In US, two criteria of active
inflammation were evaluated following Szkudlarek et al. .
Joint effusion (E) was visible as an anechoic area between the
capsule and the bone in the proximal part from the palmar side
HIELSCHER et al.: FREQUENCY-DOMAIN OPTICAL TOMOGRAPHIC IMAGING OF ARTHRITIC FINGER JOINTS 1727
Fig. 1. (a), (b) The two figures show T1-weighted images (a) before and (b) after administration of a bolus of Gd-DTPA. The region marked with a white circle
shows synovitis in a PIP joint. (c), (d) The two figures show T1-weighted images (c) before and (d) after administration of a bolus of Gd-DTPA. The region marked
with a white circle shows erosions in all three joints inside the circle.
of the hand [Fig. 2(b)–(d)]. Second, thickening of the synovial
membrane (S, synovitis) could be visualized as hyper-echoic
structures within the region affected by effusion [Fig. 2(d)]. We
performed US from palmar because we found that synovitis
and effusion can best be evaluated from the palmar as opposed
to the dorsal side. This is probably due to the small amount of
tissue overlying the joint from the dorsal side.
MRI and US images of patients with RA were analyzed by
two independent investigators including a radiologist and a
rheumatologist. According to US and MRI findings, PIP joints
were classified into joints affected by RA (Group A) and joints
unaffected by RA (Group U). To be classified as affected by
RA, joints had to show either signs of effusion, synovitis or
erosions. Joints classified as unaffected by RA did not show
any of these signs. In almost all cases consensus was reached in
classification results. In the few case of discrepant evaluations
of the two initial reviewers a third reviewer was consulted and
his finding was used to determine group membership. This
classification was used as ground truth for the evaluation of the
frequency-domain optical tomography (FDOT) images.
C. Optical Tomographic Imaging
1) Optical Tomographic Instrument: As optical imaging
system we employed a recently developed frequency-domain
system that allows for source-modulation frequencies up to
1 GHz . A laser beam (wavelength
, beam diameter 1.0 mm) was directed onto the
back of a finger and scanned across the PIP joint in a sagittal
plane (Fig. 3). Transmitted light intensities were measured
with an intensified CCD (ICCD) camera. The ICCD camera
was operated in homodyne mode, i.e., the gain of the ICCD is
modulated by a slave signal generator at the same frequency as
is imaged to the CCD. The signal in every pixel depends on
the phase between source and detector modulation. Master and
adjustable. To detect the complete oscillation of the modulation
multiple images are taken at phase delays covering the range of
and are transferred to a computer. From the stack of images
More details concerning this setup can be found in .
In addition to the transmission measurements, accurate sur-
face coordinates of the finger were generated by a newly in-
troduced laser scanner unit. The finger was scanned simulta-
neously by two red laser lines (wavelength
, line width
the palm (Fig. 4). In this setup the diode lasers are mounted
on a gear-wheel each. Slight rotation of the gear-wheel by a
stepping motor yields a step of the laser line on the finger sur-
face. Both gear-wheels are driven by one stepping motor to ac-
complish simultaneous scanning of the two lines. The shapes of
the deformed laser lines on the finger surface are imaged with
a fast video camera (SPC 900 NC, Philips, The Netherlands),
which is controlled by the DAVID laser-scanner software (ver.
1.6b, TU-Braunschweig, Germany). Two thin walls besides the
finger arranged in certain angle serve as calibration background
to adjust the coordinate system of the camera. According to the
camera coordinate system the line shapes are transformed into
3-D surface coordinates in real-time. These coordinates were
employed to generate a surface mesh of the scanned part of
http://www.mmech.com/) [Fig. 4(b)], which is input into the re-
constructionproceduretogether withthetransmission data.Test
surface details with an accuracy of at least 0.4 mm. Both the to-
mographic unit and the laser-scanning unit are equipped with
mm) at the back and
1728IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO. 10, OCTOBER 2011
Fig. 2. Ultrasound images of a healthy joint (a), and joints affected by RA (b),
(c), (d). The larger the anechoic area and/or extent of synovial hypertrophy, the
extensive effusion/hypertrophy). Images were produced by placing a
hockey stick linear array transducer on the palmar side of the PIP joint. (
identical, ergonomic hand and arm rest in the same height to
allow for identical positioning of the patient’s arm and hand.
2) Optical Imaging Protocol: Before the measurement was
started, the fingers were marked with a small black dot on the
back of the finger in the sagittal plane, 17 mm distal from the
PIP joint. This mark was used to position the finger identically
in both the tomographic and laser scanner unit. Once the finger
was placed inside the tomographic unit on a hand rest, the laser
beam was moved to the marked position. The finger axis was
aligned with the scanning plane of the laser. Then, the laser
moved to the first tomographic source position, 10 mm distal
from the PIP joint and subsequently scanned over a range of
20 mm. Images were acquired at 11 equally spaced source po-
sitions. At every source position the oscillation was sampled in
16 phase steps with an exposure time of 80 ms each. The scan
was performed twice, at first in the forward direction with mod-
ulation frequency of 600 MHz, and then in the reverse direction
with a frequency of 300 MHz.
Fig. 3. Setup of tomographic scanning unit, (a) schematic and (b) photograph.
The hardware parts shown are the (1) laser diode, (2) laser diode driver, (3,7)
signal generator, (4) finger, (5) focusing lens, (6) ICCD camera, (8) high rate
imager, and (9) computer.
We scanned three fingers from the hand of each patient; the
index, middle, and the ring finger (PIP II to PIP IV). To avoid
movement artifacts in the image reconstruction, the examiner
controlled the correct position of the finger again after the to-
mographic scan was finished. Acquisition time for one finger
including laser movement, image acquisition, and data storage
was about 35 s for one frequency. Positioning of the finger av-
eraged another 80 s. Thus, the complete tomographic scanning
time needed for six fingers and two modulation frequencies was
about 15 min.
out by using the mark on the finger as a reference. An additional
laser line, across the finger as a pilot beam, helps to find the
correct axial position for the mark. The finger is angled parallel
to the scanning direction. The scan starts approximately 3 mm
before the mark and ends after a distance of 40 mm on both
sides. One step of the stepping motor yields a step of the laser
line on the finger surface of approximately 0.05 mm and takes
about 10 ms. Both cameras are in a free running mode and take
images with 30 frames/s. A waiting time of 20 ms is inserted
between the steps to get approximately one step per frame. The
scanning over 40 mm takes about 25 s, positioning averages
another 60 s. Thus the complete time for scanning six fingers
is about 7 min.
HIELSCHER et al.: FREQUENCY-DOMAIN OPTICAL TOMOGRAPHIC IMAGING OF ARTHRITIC FINGER JOINTS1729
Fig. 4. (a) Surface registration and (b) 3-D mesh generation. The surface scan-
ning unit detects the shape of the laser line on the finger surface and determines
the 3-D-surface coordinates while the laser line is scanned over the finger. The
background serves for calibration of the camera coordinate system. Surface reg-
istration and 3-D mesh generation. (a) 3-D laser scanning to obtain a finger joint
geometry and (b) 3-D finite volume mesh generated using the laser scanned sur-
After acquisition, the raw imaging data was processed. In
every stack of images a fast Fourier transformation (FFT) was
performed through the stack in every pixel. The FFT yielded
values for the amplitude, phase and the dc components. By this
means 2-D dc, amplitude and phase images were calculated for
every distinct source position.
3) OpticalTomographicReconstruction: Three-dimensional
image reconstructions were performed using the PDE-con-
strained reduced-Hessian SQP method , that solves the
forward and inverse problems simultaneously. As a forward
model this code employs the frequency-domain equation of
radiative transfer (FD-ERT) , 
is the complex-valued radiance in unit
andare the absorption and scattering
coefficients, respectively, in units of
source modulation frequency,
the medium, and
is the scattering phase function
that describes scattering from incoming direction
. In this work we employed the widely used
Henyey–Greenstein phase function with
Furthermore, to be able to consider the refractive index mis-
match at air-tissue interface , , we implemented a par-
tially-reflective boundary condition
,is the external
is the speed of light inside
sity due to the external source function, subscript
the boundary surface of the medium, and
vector pointing outwards at the boundary surface.
Given the spatial distribution of optical properties inside the
medium, we solve the radiative transfer equation [(1)] with
a discrete ordinates method , which provides the predic-
tion of measurements obtained on the surface of the medium
is the reflectivity at Fresnel interface from di-
to direction,is the radiation inten-
is the unit normal
. Hereis the measurement
operator that projects the radiance vector
forward model onto the image plane of a CCD camera.
In PDE-constrained optimization, an image reconstruction
problem is to find the radiation intensity vector
and the optical property vector
for measurements and predictions,
surements and the predictions for source-detector pairs
and the operatordenotes the complex conjugate of the com-
Given the current estimate of forward and inverse variables
, the rSQP scheme makes the new iterate for both for-
ward and inverse variables
andare the numbers of sources and detectors used
, andare the mea-
where a step length
merit function, and a search direction
obtained by solving the quadratic programming problem
provides a sufficient decrease in the
1730IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO. 10, OCTOBER 2011
(or approximations) of the Lagrangian function
gradients. A detailed description on the rSQP algorithm can be
found in .
The code also incorporated the 3-D surface data obtained for
each finger, described in Section II-C-1 (also Fig. 4). Using
this data, we generated a 3-D finger joint mesh identical to
the actual geometry of each finger of interest. A typical 3-D
volume mesh was composed of about 30000 tetrahedron ele-
ments. All reconstructions were started with an initial estimate
mesh points. Typically, the total reconstruction time was ap-
proximately 1–2 h on a computer with an Intel Xeon 3.3 GHz
denotes the gradient of , denotes the full Hessian
D. Data Analysis
1) RegionofInterest(ROI)andFeatureExtraction: Afterre-
scattering coefficients, a 3-D region of interest (ROI) was deter-
mined for each finger. In particular, only mesh points that were
at least 2 mm away from a tissue boundary were considered to
eliminate any reconstruction artifacts that are at times visible
near tissueboundaries.Furthermore,onlymesh pointsthatwere
within the lateral extent of the light illumination points were in-
cluded in the ROI. Only within this range do the measurements
provide useful information for the reconstruction code. An ex-
ample of a reconstructed finger and the resulting ROI is shown
in Fig. 5. For better orientation, we also show a photograph and
an MRI image that covers approximately the same area of the
joint and finger.
From each 3-D ROI we extracted various feature parameters
that we subsequently used for our computer-aided diagnostics.
These feature parameters included the maximum
and, within the ROI. Furthermore, we calculated the ratio
of the minimum and maximum ratio=min/max , and the mean
across all pixels in each 3-D volume.
Medical experts diagnosed each RA patient using MRI and
ultrasound diagnosis as described in Section II-B, and each
volumetric image with derived feature parameters (
, and) was subsequently labeled as “affected” by RA
(group A) or “unaffected” by RA (group U). A third group
(group H) was formed, which consists of fingers of healthy
persons. In total we had 81 fingers in group A, 18 fingers in
group U, and 120 fingers in group H.
2) Classification Methods: The goal of the classification
method is to determine if an optical tomographic image belongs
to a healthy person or a person with RA. In this study we used
the image features described in the Section II-D-1 to make this
determination. When only one feature was considered [e.g.,
, or], we calculated the mean and variance
across images of the joints of healthy volunteers (group H)
and of joints affected by RA (group A). Using a student -test
-values for each image feature and determined
if a statistically significant difference between affected and
Fig. 5. (a) Photograph showing the approximate range of finger for which the
mesh was generate that was used to reconstruct the optical tomographic image.
(b) Example of a 2-D cross-section through a 3-D reconstruction of the distri-
bution of the absorption coefficients in a finger joint. Also shown is a selected
region of interest (ROI), for which various optical parameters were determined.
The ROI was limited to regions at least 2 mm away from boundaries and within
the lateral extent of the source and detector placement. (c) For further orienta-
tion the corresponding sagittal representation of the MR image is shown.
healthy fingers existed, concerning a particular image feature.
In addition, we generated receiver operating characteristic
(ROC curve) for all imaging parameters. Therefore, assuming a
certain threshold, for example
that all images with
volunteers, while all other images belong to a person affected
Based on this classification, we calculated the number
of true positive
, true negative
, and false negative
MRI- and US-based ground truth. Given these numbers, we
determined the clinically significant values for sensitivity
By varying the threshold values from 0 to the largest values
, we obtained a series of
are plotted as a ROC curve, which shows
for the different threshold values. This curve itself
can further be described by the area under the curve
and the Youdenindex, which is equivalent to the threshold
for, we say
belong to healthy
, false positive
classification using our
and values that
as a function of
HIELSCHER et al.: FREQUENCY-DOMAIN OPTICAL TOMOGRAPHIC IMAGING OF ARTHRITIC FINGER JOINTS 1731
Fig. 6. Examples of (a) 2-D and (b) 3-D feature parameter distributions. The
features plotted are
andin three dimensions. Joints affected by RA are shown
in red, while healthy joints are plotted in blue. The classification methods used
to calculate the line (plane) of separation is LDA.
in two dimensions and,
image features (e.g.,
of these individual parameters. To do so we employed 2-D,
3-D, and 4-D linear discriminant analysis (LDA) , .
This method creates a separation hyperplane that allows for
the classification of a given data point (image) into one of the
two classes: here healthy or affected. The classification is made
based on the location of a data point relative to the decision
boundary (Fig. 6). The calculation of the decision plane in LDA
relies on the distance between a given data point and the class
centroids. For example, in the 2-D case, where we considered
a combination of two image parameters (
in Fig. 6), LDA produces a line as the decision plane [Fig. 6(a)].
Increasing the number of dimensions (i.e., number of image pa-
rameters considered) increases the dimensionality of the deci-
sion hyperplanes. References for the theoretical development
and implementation of LDA can be found in  and .
plemented the leave-p-out technique for training the classifier
throughout this work). This process requires
that we randomly selected
culate the separation line (or hyperplane) as shown in Fig. 6.
of data points are subsequently classified by
,, andderived from combining two or more
of the data set to cal-
,,, and values. In this
joints and (b) joints affected by RA, showing the spatial distribution of
Imaging was performed with a source modulation frequency of 600 MHz.
studyweperformedthisprocedure100 timesfor eachset offea-
tures; therefore, 100 times we randomly selected
of the data to calculate the
, andvalues. We report the performance of the algorithm
by the average values for
, andover all 100 iterations.
We start by showing examples of 2-D cross-sections through
our 3-D tomographic reconstructions of optical properties of
healthy fingers and finger affected by RA. Fig. 7 shows images
of the absorption coefficient,
performedusing measurementdataobtainedat 600 MHzsource
modulation frequency. In these images the most striking feature
is that fingers from healthy volunteers [Fig. 7(a) and Fig. 8(a)]
to images of fingers from patients affected by RA [Fig. 7(b) and
Fig. 8(b)]. One can also see that images of healthy joints seem
, and Fig. 8 shows images of
1732IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO. 10, OCTOBER 2011
joints and (b) joints affected by RA, showing the spatial distribution of
Imaging was performed with a source modulation frequency of 600 MHz.
to show lower
especially in the region of the joint cavity, in the center of the
images. This is in agreement with the well-known fact that the
erties in patients with RA , . The inflammatory process
starts in the synovium, leading to changes in tissue architecture
and cell structure. Cell proliferation can be observed and the ap-
pearance of the synovial fluid changes from a clear, yellowish
substance to a turbid, gray-yellowish substance. The number of
leukocytes per mL increases from 100–200 in healthy condi-
tions to 1000–100000 during stages 1 and 2 of the disease. This
have a diameter of approximately 7–20
a considerable effect on the scattering coefficient. Furthermore,
the protein content in the synovial fluid approximately triples
from 10–20 g/L to 30–60 g/L , .
To further quantify these findings we started by calculating
the mean and standard deviation
The results are summarized in Table I. We found that indeed
and values than joints affected by RA,
and therefore have
MEAN VALUES AND STANDARD DEVIATIONS OF INDIVIDUAL FEATURES
Mean and standard deviations of features extracted from OT images
of finger joints from groups H and A.
Fig. 9. ROC curves for the features
images obtained at 600 MHz.
,,, and extracted from
the differences between healthy and affected joints in
, and are statistically significant, with -values
terestingly all features show statistically significant differences
between images of healthy and affected joints, ex-
Clinically more relevant is an ROC curve analysis. Fig. 9
shows the ROC curves for
. However,yields a slightly higher Youden
-dependent features (not shown) results in somewhat lower
). A similar analysis for
B. Use of Multiple Parameters
In previous studies we showed that it could be advantageous
summarizes the results for absorption and scattering derived
image features. Shown are the
culated with the LDA method for all possible combinations
of parameter pairing. The numbers in bold text indicate the
, , and values observed for both absorption and
which is higher than if
is used on its own, for which we
,and values as cal-
) (Fig. 9). When all
HIELSCHER et al.: FREQUENCY-DOMAIN OPTICAL TOMOGRAPHIC IMAGING OF ARTHRITIC FINGER JOINTS 1733
LDA CLASSIFICATION RESULTS WITH 600 MHz DATA
Summary of classification results using image features derived
anddistributions obtained with imaging data gener-
ated at 600 MHz source modulation frequency. The numbers in
bold indicated largest values observed.
four parameters are combined a higher specificity of
is achieved using LDA, however,
Combining scattering derived image features resulted ineven
,, and values. For example, we observed that
Youden index of
as well as the largest
. The highest sensitivity
is combined with
drops to 0.80, yielding the
yields the largest
is reached if
C. Influence of Source-Modulation Frequency
To test the influence of the source modulation frequency on
the classification results, we performed the same analysis dis-
cussed in Section III-B with data gathered at 0 and 300 MHz.
The results are shown in Tables III and IV, respectively. As
can be seen for all parameter combinations, the
values are considerably lower when 0 MHz data is used as
compared to 300 or 600 MHz data. This clearly supports the
hypothesis that frequency-domain data yields better classifica-
tion results than steady-state data.
Comparing the classification results obtained with the 300
and 600 MHz data, we found that overall
are higher when 600 MHz data is used. (The only exception
is the combination of
300 MHz is
, while at 600 MHz it is
is in agreement with our previous findings, which were based
on numerical simulations and phantom experiments, that at
source modulation frequencies in the range of 400–600 MHz
the signal-to-noise level is highest and the resulting image
reconstruction are the best for geometries encountered in finger
imaging , .
and , for which at
LDA CLASSIFICATION RESULTS WITH 300 MHz DATA
Summary of classification results using image features derived
anddistributions obtained with imaging data gener-
ated at 300 MHz source modulation frequency. The numbers in
bold indicated largest values observed.
LDA CLASSIFICATION RESULTS WITH 0 MHz DATA
Summary of classification results using image features derived
and distributions obtained with imaging data gen-
erated at 0 MHz source modulation frequency. The numbers in
bold indicated largest values observed.
D. Comparison of Healthy Joints With Unaffected Joints of
So far we have compared images of joints from healthy vol-
unteers and images of affected joints from patients with RA.
There is a third group of images, which are images of fingers
that belong to patients diagnosed with RA, but that do not show
1734 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO. 10, OCTOBER 2011
Fig. 10. Mean values with 95% confidence interval of various features extracted from optical tomographic images (600 MHz) of healthy fingers (H), fingers of
RA patients that are affected by RA (A), and fingers of RA patient that are unaffected by RA (U) as determined by MRI and US imaging. The left column depicts
values extracted from
images, while the column on the right shows values extracted from
between the unaffected group U and the affected group A or the healthy group H. If there is no overlap, then the mean of the given feature is different from the
other means at statistically significant levels
images. The dashed line was plotted to show if there is overlap
any symptoms of RA as determined with MRI and US. There-
fore, when MRI or US imaging is performed these fingers look
like fingers from healthy persons. To determined how these fin-
viously discussed image features from optical tomographic im-
ages of these joints and calculated their respective means, stan-
dard errors and 95% confidence intervals. The results are shown
in Fig. 10.
Fig. 10 shows the mean and 95% confidence intervals (calcu-
lated with an imbalanced one-way ANOVA and using Tukey’s
test in a multiple comparison procedure) for the means of six
different features [
and ] for the healthy joints (H), affected joints
of patients with RA (A), and joints not yet affected by RA (U)
as determined by MRI and US imaging. We observe that for
all features the mean values of the group U lie between the
values determined for healthy joints and joints affected by RA.
In several cases, the differences are statistically significant.
For example for
group U differs significantly from the mean of group H; and
,, the mean of
and group A. ROC analysis for this case yields a sensitivity
and specificity of
that optical tomographic methods may not only be capable of
distinguishing between healthy joints and joints of RA patients
that are affected by RA, but it may also be more sensitive than
MRI or US to see very early changes in joints that do not yet
appear to be affected by RA.
Fig. 11 provides another look at this issue. Here we have
plotted the combined image features of
for fingers of healthy volunteers (blue dots), finger of RA pa-
tients that are affected by RA (red dots), and fingers of RA pa-
tients that are not yet affected by RA (white circles), as deter-
mined by MR and US imaging. As mentioned before affected
joints show smaller variations and maximum absorption coef-
ficient and hence can be predominately found in the lower left
corner of this plot, while healthy joints tend to appear in the
upper right corner of this plot. Joints of RA patients determined
to be yet unaffected (using MRI and US imaging) have a mean
that lies between these two classes. Indeed looking at the plot
there is a significant difference between group U
. This suggests
HIELSCHER et al.: FREQUENCY-DOMAIN OPTICAL TOMOGRAPHIC IMAGING OF ARTHRITIC FINGER JOINTS 1735
Fig. 11. Distribution of optical tomographic image features found in fingers of
healthy volunteers (blue dots), fingers of RA patients that are affected by RA
(red dots), and fingers of RA patients that are not yet affected by RA (white
circles), as determined by MR and US imaging. The bars show the standard
error with respect to
and , respectively, for each group.
we can see that some joints are clearly with the group of healthy
joints, while others fall within the group of affected joints. The
later patients may be recommended to start treatment of RA, if
studies with a larger number of patients validate these findings.
IV. CONCLUSION AND SUMMARY
In this study we used a new frequency-domain (FD) op-
tical tomography system in conjunction with reduced-spaced
quadratic programming algorithm to generate 3-D reconstruc-
tions of the optical property distribution in finger joints of
healthy volunteers and patients with RA. For a total of 219
fingers we generated 3-D volumetric images of the absorption
, and scattering coefficients,
mental data obtained with source modulation frequencies of 0
(continuous wave), 300, and 600 MHz. From each image we
extracted various image features such as the largest or smallest
coefficients, the ratio of these parameters and variance across
the image [
magnetic resonance (MR) images as gold standard, the 219
fingers were assigned to three different cohorts, including a
group of healthy fingers (group H),one groupsof jointsaffected
by rheumatoid arthritis (group A), and one group of fingers of
RA patients that appeared to be unaffected by RA (group U).
Applying classical classification algorithms such as ROC curve
analysis and LDA, we explored which image features yield the
highest sensitivities and specificities.
In general we found that images generated with 600 MHz
data result in better joint classification (higher
than images generated with continuous wave data (0 MHz) or
300 MHz. This is in agreement with our previous numerical
studies that identified modulation frequencies in the range of
400–600 MHz as optimal for finger joint geometries. Further-
more, we found that combining several image features leads
,andvalues as compared to using only a
single feature.For example,combining
. In general it appears that scattering-de-
rived features perform slightly better than absorption-derived
, using experi-
]. Using ultrasound (US) and
is reached ifis com-
features in these multidimensional feature classifications. Fur-
thermore, we observed that the mean of many optical features
of joints of patients with RA that seemed to be yet unaffected
as determined by US and MR imaging, lies in between values
of healthy joints and joints affected by RA. This suggests that
optical methods may be useful in diagnosing very early signs
of RA in these joints. Larger clinical trials will be necessary to
conclusively support this hypothesis.
prospective clinical trials, optical tomographic imaging could
play a substantial role in clinical management of RA. Optical
tomography has several advantages over MRI as well as US
imaging. While MR imaging can provide anatomical features
in great detail, it is not typically used for monitoring of RA.
The cost related to MR imaging are relatively high and the use
of gadolinium as contrast agents is contraindicative in several
risk of various kidney diseases. This is a particular problematic
can have serious nephrotoxic effects by themselves –.
participated in their study presented some kidney disease.
tact free. This appears to be an advantage given the increased
sensitivity to touch of joints affected by RA and the resulting
discomfort experience by patients. Furthermore, the sensitivi-
ties and specificities reported in our study compare favorably
to a recent finding by Freeston et al. , who found a sensi-
tivity of 0.71 and specificity of 0.82 using double ultrasound in
a study involving 50 patients with RA. Furthermore, it should
be noted that in current day-to-day clinical practice, medical
findings. Neither MRI nor US have been elevated to standard of
carebythe ACR or theEULAR.It remains to be seen if OT
can breach that gap. But given the low cost, relatively high sen-
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