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1 November 2009 Quantitative three-dimensional photoacoustic tomography of the finger joints: an in vivo study
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Abstract
We present for the first time in vivo full three-dimensional (3-D) photoacoustic tomography (PAT) of the distal interphalangeal joint in a human subject. Both absorbed energy density and absorption coefficient images of the joint are quantitatively obtained using our finite-element-based photoacoustic image reconstruction algorithm coupled with the photon diffusion equation. The results show that major anatomical features in the joint along with the side arteries can be imaged with a 1-MHz transducer in a spherical scanning geometry. In addition, the cartilages associated with the joint can be quantitatively differentiated from the phalanx. This in vivo study suggests that the 3-D PAT method described has the potential to be used for early diagnosis of joint diseases such as osteoarthritis and rheumatoid arthritis.

1.

Introduction

Photoacoustic tomography (PAT), also referred as optoacoustic tomography (OAT), is an emerging nonionizing, noninvasive imaging modality, which combines both high optical contrast and high ultrasound resolution in a single modality.1, 2, 3 Thus far, PAT has shown its potential to detect breast cancer, to assess vascular and skin diseases, and to image epilepsy in small animals.4, 5, 6, 7, 8, 9, 10, 11, 12, 13 By combining a light transport model with conventional PAT method,14, 15, 16, 17, 18 the utility of PAT has now been extended significantly to provide quantitative tissue absorption coefficient and physiological/functional information including hemoglobin concentration, blood oxygenation, and water content. These intrinsic tissue properties may be important for accurate diagnostic decision-making.

Diseases related to bones and joints are a major cause of morbidity in the population over 50year old and affect millions of people over the world, early detection of which is infeasible with traditional methods such as x-ray radiography, computed tomography (CT), and ultrasonography. Magnetic resonance imaging (MRI) represents a powerful tool for imaging joint diseases, but it is costly and cannot be used for frequent monitoring of the progressive joint diseases. Diffuse optical tomography (DOT), an emerging all-optical imaging modality, has been studied for joint imaging.19, 20, 21 Significant absorption contrast between diseased and normal joints has been observed in the hand with osteoarthritis22, 23 and rheumatoid arthritis.24, 25 For example, for an osteoarthritic joint, the ratio of its cartilage absorption coefficient to that of the associated bone is increased by 40% relative to the healthy joints.22 Since the same high absorption contrast is available to PAT, we expect that PAT may represent another optical-based modality for joint imaging with improved spatial resolution.

Wang 26 have recently presented high-resolution two-dimensional (2-D) photoacoustic images of the proximal interphalangeal (PIP) and distal interphalangeal (DIP) joints from a cadaver human finger. In vivo joint imaging represents a challenge because unlike the joint from a cadaver finger, an in vivo joint has abundant blood vessels located along the skin that strongly absorb light. The strong absorption from the blood vessels and bones give rise to significantly reduced signal-to-noise ratio (SNR) in an in vivo setting. In addition, both light and acoustic propagation in tissue are 3-D in nature. In particular, the joint structures are highly heterogeneous, which makes a full 3-D volumetric image reconstruction necessary.

Herein, in this study, we present an in vivo full 3-D PAT study of the DIP joint in a human subject using a Ti:Sapphire laser–based photoacoustic system in a spherical scanning geometry. Photoacoustic images containing major features/components in the finger joint as well as the absorption coefficient profiles of these joint structures are successfully achieved.

2.

Methods

The finite-element-based 3-D PAT reconstruction algorithm and its enhancement for extracting quantitative absorption coefficient used in this study have been described in detail previously and validated using considerable phantom experiments.15, 27, 28 (We found that the accuracy for obtaining absorption coefficient from the phantom experiments is typically within 20% relative to the exact values.) Basically, the reconstruction method includes two steps. The first step is to obtain the 3-D images of absorbed optical energy density through the conventional 3-D PAT reconstruction algorithm that is based on finite element solution to the photoacoustic wave equation in the frequency-domain subject to the second-order absorption boundary conditions:27

Eq. 1

2P(r,ω)+k02P(r,ω)=ik0c0βϕ(r)Cp,

Eq. 2

Pn̂=MP,
where P is the pressure wave; k0=ωc0 is the wave number described by the angular frequency, ω and the average speed of acoustic wave in the tissue, c0 ; β is the thermal expansion coefficient; Cp is the specific heat at constant pressure; and ϕ is the absorbed light energy density. M is a differential operator defined as the function of the mean and Gaussian curvatures at a point along the boundary surface.

The reconstruction algorithm assumes a homogeneous acoustic speed c0 , which is an approximation to the possible heterogeneous acoustic media seen in the experiments. Newton method combined with Marquardt and Tikhonov regularizations is used to iteratively update an initial (guess) absorbed optical energy density distribution so that an object function composed of a weighted sum of the squared difference between computed and measured acoustic pressures for all acoustic frequencies can be minimized.

The second step is to recover the optical absorption coefficient using the absorbed optical energy density, ϕ reconstructed in the first step and the following photon diffusion equation as along with the Robin boundary conditions:15

Eq. 3

D(r)[Ψ(r)]μa(r)Ψ(r)=S(r),

Eq. 4

DΨ(r)n̂=αΨ(r),
where Ψ(r) is the photon density, Ψ(r)=ϕ(r)μa(r) , μa(r) is the optical absorption coefficient, D(r) is the diffusion coefficient, D=1[3(μa+μs)] and μs is the reduced scattering coefficients, α is a boundary condition coefficient related to the internal reflection at the boundary, and S(r) is the incident point or distributed source term.

To recover the optical absorption coefficient from the reconstructed absorbed optical energy density ϕ from an initial distribution of μa(r) , the optical fluence Ψ(r) and the absorbed energy density ϕ(c) are iteratively calculated through the photon diffusion equation and ϕ(c)=μa(r)Ψ , respectively. If the error between ϕ and ϕ(c) is not small, then μa(r) is updated by μa(r)=ϕΨ , and the preceding procedure is repeated until a small error between ϕ and ϕ(c) is reached, resulting in a stable quantitative distribution of μa(r) .

3.

System and Experiments

The in vivo finger joint experiment was conducted with our 3-D PAT imaging system, as shown in Fig. 1 . The Ti:Sapphire laser (LOTIS, Minsk, Belarus) generates a pulsed beam with a repetition rate of 10Hz and a pulse width <10ns . The wavelength of the laser is tunable from 600to950nm and was locked at 820nm in this study for deep tissue penetration. The light beam is delivered via an optical fiber to the bottom of the water tank and expanded by a lens and a ground glass before reaching the finger so that the DIP joint can be uniformly illuminated by an area source of light. The laser energy at the DIP joint was controlled around 10mJcm2 , which is far below the safety standard of 22mJcm2 .

Fig. 1

Schematic of the 3-D spherical scanning PAT system for finger joint imaging. L: lens; T: detector/transducer; R1/R2: rotary stages.

064002_1_003906jbo1.jpg

The DIP joint of the left index finger from a female healthy volunteer was photoacoustically examined, and the palmar side of the finger faced up during the examination, allowing the finger joint to be illuminated from the dorsal side of the finger. Our experience indicates that this way of light illumination can give us maximized tissue penetration. To secure the position of the finger, rubber bands were applied to the distal tip and the proximal end of the examined finger.

To detect the acoustic field generated by the pulsed laser, 1-MHz transducer (Valpey Fisher, Hopkinton, Massachusetts) was optimally chosen based on considerable phantom experiments. 28 The transducer has a bandwidth of 80% at 6dB and an aperture size of 6mm . To overcome the directivity limitation and aperture size effect of transducer, we adopted a spherical scanning configuration. Both the transducer and the finger were immersed in the water tank for minimized ultrasound attenuation. As can be seen from Fig. 1, the transducer was attached to the rotary stage R2 whose position was controlled by the rotary stage R1. During the examination, the finger was placed at the center of the two rotary stages. The detected acoustic signals were amplified and filtered by a Pulser/Receiver 5058PR (Panametrics, Waltham, Massachusetts). Labview software was used to control the entire data acquisition procedure.

The collection of acoustic signals along a spherical scanning surface was realized through the combined rotations of rotary stages R1 and R2. (Note that R1 and R2 were attached to the same L-shape arm; see Fig. 1.) As shown in Fig. 2, the examined finger joint was aligned in the direction of y axis, and located at the rotation center, O. In the scanning, the transducer was first rotated by R1 to a position along the circular locus L1 and then rotated by R2 along the circular locus L2 [Fig. 2a]. This process was repeated until the spherical scanning was completed. Since the finger/hand blocked the scanning of the transducer in certain angles, the scanning along L1 and L2 covered only 240deg and 252deg , respectively [Figs. 2b and 2c]. A complete scanning allowed the collection of signals at 387 positions along the spherical surface which took about 40min .

Fig. 2

Schematic of the spherical scanning geometry (a), circular locus L1 (b), and L2 (c).

064002_1_003906jbo2.jpg

4.

Results and Discussion

In this section, we present the in vivo 3-D reconstruction results and make observations based on these results. The 3-D images were reconstructed using a finite element mesh of 41,323 tetrahedral elements and 7519 nodes, which required 120min per iteration, for a total of 10 iterations on a parallel computer with 10 processors. Each of the processors worked at 2.2GHz with 2-GB memory.

A coronal section of the reconstructed 3-D image (absorbed energy density) is shown in Fig. 3a, while a similar section of the DIP joint from a typical human finger by MRI is given in Fig. 3b for comparison. As can be observed from Fig. 3a, the cartilage/joint space is well differentiated from the adjacent distal phalanx (DP) and intermediate phalanx (IP). The recovered absorption coefficient image and the absorption coefficient profile along a transect x=2mm corresponding to the coronal slice shown in Fig. 3a are displayed in Figs. 4a and 4b, respectively. We see that the absorption coefficient values of the phalanxes and cartilage/joint space are quantitatively consistent with that reported in the literature.22, 23 By estimating the full width at half maximum (FWHM) of the absorption coefficient profiles, the recovered thickness of cartilage/joint space was found to be 1.6mm , which is in agreement with the actual size.

Fig. 3

Selected coronal section from the reconstructed 3-D image (absorbed energy density) at z=5mm (a), and MRI (coronal section) from a similar joint (b). DP: distal phalanx; IP: intermediate phalanx; DIP: distal interphalangeal joint.

064002_1_003906jbo3.jpg

Fig. 4

Selected coronal section from the recovered absorption coefficient image at z=5mm (a), and its profile along the cut line x=2mm (b).

064002_1_003906jbo4.jpg

Figure 5a presents a cross section of the reconstructed 3-D image (absorbed energy density). Again, a similar cross section of the DIP joint from a typical human finger by MRI is shown in Fig. 5b for comparison. Comparing both Figs. 5a and 5b, it appears that several joint tissue types are visible including phalanx (PX), lateral artery (LA), median artery (MA), and tendon (TE). The recovered absorption coefficient image and the absorption coefficient profiles along two transects are displayed in Figs. 6a, 6b, 6c . The first transect [line 1 in Fig. 6a] goes through the phalanx and tendon, while the second one [line 2 in Fig. 6a] crosses the tendon and two arteries. The recovered absorption coefficients of the phalanx, tendon, median and lateral arteries were found to be 0.07mm1 , 0.074mm1 , 0.064mm1 , and 0.058mm1 , respectively. Again, these values are generally consistent with that reported in the literature.21, 22 We note that blurs around the two blood vessels are noticeable [Fig. 5a] largely due to the relatively low-frequency (1MHz) transducer used in this study. We believe the resolution can be enhanced with a wideband transducer having higher frequency (e.g., 5to10MHz ), which will make the millimeter- to submillimeter-sized arteries accurately imaged.

Fig. 5

Selected cross section from the reconstructed 3-D image (absorbed energy density) at y=7mm (a), and MRI (cross section) from a similar joint (b). PX: phalanx; MA: median artery; TE: tendon; LA: lateral artery.

064002_1_003906jbo5.jpg

Fig. 6

Selected cross section from the recovered absorption coefficient image at y=7mm (a), and its profile along cut lines 1 (b) and 2 (c), respectively.

064002_1_003906jbo6.jpg

To view the volumetric structures of the tissues around the joint, a series of cross- and coronal-section images are displayed in Figs. 7 and 8 , respectively. As shown in Figs. 7a, 7b, 7c, 7d, 7e, 7f, the phalanx is clearly visible in all the cross-section images from the proximal end (y=2.5mm) to the distal end (y=9mm) . The tendon is differentiated from the phalanx [Figs. 7a, 7e, 7f]. The lateral artery is visible almost in all the cross section images except for that shown in Fig. 7f at the distal end of the finger. The median artery is seen in Figs. 7e and 7f and weakly visible in Fig. 7d. Other joint structures including the phalanges (DP and IP) and the cartilage (CL) are clearly imaged from the coronal section images close to the dorsal side of the finger [Figs. 8a and 8b]. Close to the palmar side of the finger, the tendon and two arteries begin to show up [Fig. 8c], and the two arteries become clearly visible eventually [Fig. 8d]. Negative values are also observed in the reconstructed absorbed energy density images. This is likely due to the homogenous acoustic approximation (constant acoustic speed) to the actual heterogeneous acoustic media of the finger joints and limited signal-to-noise ratio because of the strong light scattering of joint tissues.

Fig. 7

Cross-section images (absorbed energy density) at y=2.5mm (a), y=0mm (b), y=3mm (c), y=5mm (d), y=7mm (e), and y=9mm (f). PX: phalanx; MA: median artery; TE: tendon; LA: lateral artery.

064002_1_003906jbo7.jpg

Fig. 8

Coronal-section images (absorbed energy density) at z=5mm (a), z=3.5mm (b), z=1mm (c), and z=4.5mm (d). DP: distal phalanx; IP: intermediate phalanx; CL: cartilage; PX: phalanx; MA: median artery; TE: tendon; LA: lateral artery.

064002_1_003906jbo8.jpg

In summary, we have presented a 3-D PAT technique that is able to image finger joints in vivo. Although it seems impossible for PAT to provide image quality (in terms of spatial resolution) comparable to MRI for joint or breast imaging, PAT is capable of obtaining absorption coefficient or functional information. In addition, PAT is portable and low in cost. While our current experimental setup is not optimized, it allows us to demonstrate the possibility of 3-D in vivo joint imaging for the first time. The results obtained indicate that major joint structures and their absorption coefficients can be quantitatively reconstructed using our 3-D PAT approach. We plan to improve our imaging system for optimized performance. For example, we will implement an excitation configuration that allows light illumination of the entire finger joint, which would then permit the use of higher frequency transducers for enhanced resolution due to the significantly improved signal-to-noise ratio. We also plan to perform in vivo 3-D PAT studies in human subjects with hand osteoarthritis or rheumatoid arthritis in the near future.

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©(2009) Society of Photo-Optical Instrumentation Engineers (SPIE)
Yao Sun, Eric S. Sobel, and Huabei Jiang "Quantitative three-dimensional photoacoustic tomography of the finger joints: an in vivo study," Journal of Biomedical Optics 14(6), 064002 (1 November 2009). https://doi.org/10.1117/1.3257246
Published: 1 November 2009
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