1. Introduction

Diffuse optical tomography (DOT), emerging as a novel optical imaging technology, has exhibited a high potential for the noninvasive diagnostic imaging applications such as breast cancer detection [1, 2, 3] and functional brain imaging [4, 5, 6] as it uses non-ionizing radiation, has a large penetration depth, and provides functional information associated with the optical properties. For the implementation of the DOT system, most frequency-domain DOT systems use one or several frequency components as the modulating signals and measures the amplitude/phase changes caused by heterogeneities [7, 8]. The continuous-wave DOT uses a constant power laser for tissue illumination and detects the magnitude attenuation [8, 9]. The time-domain DOT, however, can provide full time spectra of diffusive light from which optical properties can be more accurately reconstructed. Therefore, the time-domain DOT can discriminate smaller variations of the optical properties among tissue types by image reconstruction [10, 11]. Among most of the developed time-domain DOT systems [12, 13, 14, 15, 16, 17], an ultrashort pulse laser (typically in several hundred picoseconds) is utilized as the light source to illuminate the tissue sample. The temporally dispersed photons are detected by either a streak camera [16, 17] or a time-correlated single photon counter (TCSPC) [12, 13, 14, 15]. The systems using streak camera are limited by small photon collection area, small dynamic range, and temporal nonlinearity. The TCSPC-based systems are more popular for its large dynamic range, high temporal linearity, and high temporal resolution. The bench top phantom-based experiments and the diagnostic trials on the breast cancer detection and the functional brain imaging have yielded good results [1, 2, 12, 13, 14]. However, the performance of the TCSPC-based system is usually limited by a slower data acquisition speed which is subjected to the photon counting rate. This problem will become pronounced when multiple source-detector channels are involved. For example, for a 32-channel time-domain DOT system reported in [8], one complete data acquisition usually takes 10–20 minutes. Clinically, the long data acquisition time will limit the range of applications of DOT. In addition, the TCSPC system should work under an extremely dark circumstance to achieve the best performance. This requirement is hard to be satisfied in practical situations. Last but not least, the ultrashort pulse laser and TCPSC (or the streak camera) usually lead to a high system cost and a complex system structure. For the case where multiple channels are involved, the cost and complexity may become prohibitive.

In this article, we report a novel time-domain DOT design which can achieve faster data acquisition speed than the conventional ones. The calibration results show a system impulse response with a full width at half maximum (FWHM) about 800 ps and a rapid data acquisition speed (<5 s) for 9 sources and 4 detectors. In addition, the design features a relative insensitivity to the environmental illumination as well as a high signal-to-noise ratio.

2. Method

2.1. Architecture

In our previous study, we have mathematically predicted the feasibility to realize a time-domain DOT by using pseudorandom bit sequence (PRBS) and reported a prototype time-resolvedDOT system with a temporal resolution of a few nanoseconds [18, 19]. However, to obtain more accurate dynamics of the photon migration in the tissue, a sub-nanosecond temporal resolution is highly desired.

In this article, we report a novel sub-nanosecond PRBS-based design for the first time. The schematic is shown in Fig. 1. A PRBS analyzer transmitter (ME3620A, Anritsu) continuously generates a high bit rate (2488 Mbit/s) PRBS signal. The pattern length of 2⁹-1 bits leads to a signal repetition time of 205.78 ns. A radio frequency (RF) power splitter (ZFSC-2-2500+, mini-circuits) evenly distributes this PRBS signal into branch A and branch B. Branch A is reserved as a reference signal for demodulation. Branch B is delayed in steps of 40 ps when going through a programmable digital delay line (PDDL5, GigaBaudics). A low power (5 mW) near-infrared (NIR) laser with a wavelength of 780 nm is used as the light source. An external intensity modulator (AZ-OK1-10-PFU-SFU-780-S, EOSPACE) modulates the intensity of this NIR light with the PRBS signal carried by branch B. The modulated light is multiplexed into 9 source fibers and guided to illuminate the tissue-like phantom from a handheld probe. Figure 2(a) shows the geometry of the handheld probe. The 9 fibers are switched on and off sequentially. The 4 fiber-bundles on the probe collect the light emitted from the phantom surface and are individually coupled to 4 high speed avalanche photodiodes (APDs, S2383-20, Hamamatsu). Each APD has a cut-off frequency around 650 MHz. The optoelectronic signal is amplified 42-dB by the RF amplifier before feeding into the mixer (SYM-2500, mini-circuits). The mixer demodulates this signal with respect to the reference signal (branch A). Since the mixer actually is not an ideal multiplier, the down-converted intermediate frequency (IF) signal contains not only the desired demodulation signals but also the undesired DC offset and the system noise. In order to get rid of the DC offset and reduce the noise level, a square wave with a frequency of 2.5 kHz is superimposed on the modulating PRBS signal and fed into the intensity modulator. Consequently, the demodulation results yield an IF signal of 2.5 kHz, which is further amplified 60-dB by a series of operational amplifiers. A personal computer acquires this signal via a data acquisition card (DAQ, PCI-6251, National Instruments). The sampling rate is 250 kS/s and the integration time is 4 ms for each temporal sampling point. Similarly, by correlating this signal with another 2.5 kHz square wave, the DC offset can be thoroughly eliminated and the system noise level is significantly reduced. The amplitude of the 2.5 kHz IF signal represents the detected light intensity at a specific time delay in response to a pulsed illumination. The entire temporal point spread function (TPSF) is obtained by scanning the time delay at a scan interval as small as 40 ps. In order to compromise the data length for the data acquisition speed, all TPSF curves were truncated at 5120 ps, or 128 temporal sampling points with a scan interval of 40 ps. The acquisition time for a TPSF of 128 points is 128×4 ms=512 ms. For 9 sources switched on sequentially, it needs a total of 4608 ms to acquire all the waveforms. The dead-time for 9 fibers switching is 20 ms×9=180 ms. Thus one complete scan can be finished in 5 s. The data acquisition time can be significantly reduced with a larger scan interval of, e.g., 200 ps. A scan interval of 40 ps is used in the current configuration as the acquisition speed is acceptable for our phantom experiments and the oversampled data set can be used explore different post-processing approaches such as deconvolution and Fourier analysis.

 

Fig. 1. Schematic of the fast time-domain DOT. The thick arrows represent the PRBS transmission path. The dashed arrows represent the optical signal path and the thin arrows represent the control signal.

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It should be noted that the APDs are temperature sensitive components. The optoelectronic efficiency will degrade as the component’s temperature increases. In order to keep the photon sensitivity stable over a long running time, 4 temperature controllers (TEC) are used to limit the temperature fluctuation of the APDs within ±0.03 C^°. In addition, because the performance of the intensity modulator is subject to its inherent photorefractive effect, the modulation depth and the amplitude of the measured TPSFs may not be repeatable. To keep the modulation depth constant, an automatic bias tracking and control module based on the addictive dither technique is implemented to set the working point (i.e. the positive quadratic point) of the intensity modulator ahead of each scanning.

2.2. Calibration

In order to characterize the system’s impulse response (SIR), we place a piece of diffusive white paper at an 18 cm distance from the handheld probe. Since the light beam from an optical fiber is diverging and the reflection from the white paper is diffusive, the 18 cm distance chosen for the SIR measurement provides appropriate attenuation of the light intensity arriving at the photodetectors. Figure 3(a) representatively plots one of 36 SIRs together with the theoretical prediction, i.e., the PRBS autocorrelation. The measured SIR has a FWHM approximately of 800 ps and the rise time (10%–90%) is about 600 ps. These values are slightly larger than the theoretical prediction with FWHM of 402 ps and the rise time of 360 ps. This signal integrity degradation is mainly caused by the junction capacitance (≈6 pF) of the APDs and the insufficient bandwidth of the components along the PRBS signal transmission path. If all components in the system have an adequate bandwidth, the shape of the measured SIRs should be approaching to the triangle shape of prediction. The error bars in Fig. 3(a) represent the standard deviation of the measured SIR among different channels, which suggests a very good uniformity.

 

Fig. 2. (a) Configuration of the reflection-mode handheld probe. The 4 big circles represent the detection fiber-bundles and the 9 small circles represent the source fiber. (b) Illustration of the experimental setup with the absorbing targets included. P1 and P2 represent the target positions. The coordinates of P1[x, y, z] and P2[x, y, z] are [0, 0, 2]cm and [1.5, 0, 2]cm, respectively.

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3. Experiments and results

To evaluate our design in terms of sensitivity and imaging capability, we conducted phantom-based experiments. The Lipofundin lipid emulsion (B. Braun, MCT/LCT 20%) with a concentration of 0.6% was chosen as the tissue-like phantom. This kind of solution had similar optical properties (absorption coefficient µ a≈0.02 cm^-1, reduced scattering coefficient µ′_s≈6.0 cm-1) as the normal human breast tissue [20, 21, 22]. The Lipofundin solution with a volume of 17 cm (length)×15 cm (width)×10 cm (depth) can be regarded as an infinite background medium. Besides, we use small cylindrical plastic absorbers (diameter=7 mm, length=10 mm, µa≈0.06 cm^-1, µ′_s≈6.0 cm^-1) to mimic tumors. These home-made cylindrical absorbers mainly consisted of epoxy-resin, resin harder, titanium dioxide (TiO ₂) and India ink. The TiO₂ powders provided scattering and India ink provided absorption. For the phantom fabrication and machining, we followed the recipe recommended by [22] due to its simplicity and low cost. In the experiments, the handheld probe just contacted to the surface of the medium. The cylindrical tumor-like phantom (target) was immersed in the Lipofundin solution (background) at depth of 2 cm. The axial directions of these targets were oriented in parallel to the X-axis (P1 and P2 in Fig. 2(b)). The TPSFs acquired from the liquid phantom with and without absorber immersed were respectively regarded as the homogeneous TPSF and the heterogeneous TPSF. Because the system contains 9 source fibers and 4 detection fiber-bundles, one full scan generates 36 TPSFs. Figure 3(b) plots one homogeneous TPSF as well as a corresponding heterogeneous TPSFs obtained from the same channel where the source-to-detector (S-D) distance is 3.3 cm. The TPSF peak intensity was attenuated by 5.9% and the mean time-of-flight of photons was reduced by 28.57 ps with the absorber embedded.

The signal-to-noise ratio (SNR) plays a key role in the DOT system because it determines the detection depth and the image quality. Hence a higher SNR is always desired. Our design demonstrates a noise level with a root of mean square voltage of 3.2 mV when room light is switched on and 2.7 mV when room light is switched off. Figure 3(c) compared the measured TPSFs with and without room light. The difference between each other is negligible which demonstrates that out design is relatively insensitive to the environmental light. This feature has a practical significance for the clinical applications. In addition, the SNR is also related to the S-D distance. The probe has a variable S-D distance from the minimum of 15 mm to the maximum of 43 mm. Correspondingly, the power ratio of the noise to the integral of the TPSF varies from 0.00028% to 1.9%, or equivalently from 56-dB to 18-dB. Essentially, the noise mainly comes from the amplified electronic circuit noise (e.g. the noise from the RF amplifier), which means there is still much room to improve the SNR before reaching the shot noise floor. Also, we can increase the SNR approximately 20 dB by increasing the light power we are using (1.25 mW) at present by a factor of 10. The laser power with the range of 12–15 mW is still safe for clinical breast tissue illumination. Moreover, the geometrical arrangement of the source fibers and the detection fiber-bundles on the handheld probe is optimized by the simulation in order to balance the detection area (determined by the largest S-D distance) and the SNR.

 

Fig. 3. (a) The measured SIRs (blue solid line) vs. the theoretical prediction (red dashed line). The measured SIR is slightly wider than the predicted one. The error bars represent the standard deviation of the measured SIR. (b) The homogeneous TPSF (blue solid line) obtained from the homogeneous Lipofundin solution and the heterogeneous TPSF (red dashed line) obtained from the heterogeneous solution for a channel where the source-to-detection distance is 3.3 cm. (c) The comparison of the TPSFs with the room light on (red circles) and off (blue line). The source-to-detector distance is 3.3 cm.

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4. Image reconstruction

For the image reconstruction, we only concern the distribution of the absorption coefficient. As the handheld probe works in a reflection mode, a semi-infinite boundary condition is used together with the diffusion equation as the forward model for photon migration through the tissue-air interface. Born approximation based perturbation method is adopted to calculate the Jacobian Matrix that relates the measured perturbations in TPSF to local changes in the absorption coefficient linearly [23, 24, 25]. To reconstruct the spatial variation of the optical properties, we applied a simultaneous iterative reconstruction technique (SIRT), a slightly modified algorithm of algebraic reconstruction technique (ART) to achieve a fast imaging speed. In addition,

Table 1. Analysis of the reconstructed absorption coefficient µ_a.

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the positivity constraint is imposed on the absorption heterogeneity during iteration. Figure 4 illustrates the two-dimensional images of the absorption coefficient. Each figure covers a cross sectional area of 50 mm×25 mm.

 

Fig. 4. The reconstructed image of the absorption coefficient based on the SIRT. (a–c) represent the cross sectional view where y equals to 0, 0.25 and 0.5 cm, respectively. The target (absorber) is located at position P1 [0.0, 0.0, 2.0]. (d–f) represent the cross sectional view where y equals to 0, 0.25 and 0.5 cm, respectively. The target is shifted 1.5 cm along x-axis from P1 to P2 [1.5, 0.0, 2.0].

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The target is placed at P1(0.0, 0.0, 2.0) and then P2(1.5, 0.0, 2.0) in the experiments. The depth remains the same at 2 cm. Figure 4(a–c) shows the case where the target is located at P1 and Fig. 4(d–f) shows the case where the target is moved to P2. From these figures, we can rather accurately determine the target’s position and size. For example, in the first case (Fig. 44 (a–c)), the recovered position of the absorber is ([x, y, z]=[0.013, 0, 1.918]cm), which is slightly different from the true position ([x, y, z]=[0, 0, 2]cm). In the second case (Fig. 44 (d–f)), the recovered position of the absorber is ([x, y, z]=[1.506, 0, 1.958] cm), which is slightly different from the true position ([x, y, z]=[1.5, 0, 2] cm). Table 1 provides the quantitative analysis of the reconstructed absorption coefficient. The mean and standard deviation are calculated with the reconstructed distribution within the true target region. It is evident that the reconstructed values are rather close to the true value. The total image reconstruction took about 3–5 s on a MATLAB platform including core 2 dual CPU at 1.8 GHz and 2 GB RAM. It is worthy of notice that our handheld probe is optimized for 2D cross-sectional imaging and 2.5D imaging in which a few slices in the Y-dimension can be obtained. For 3D imaging, we need to reconfigure the source and detector deployment. More sources and detectors may be necessary for high quality 3D imaging.

5. Summary

To summarize, we have developed a fast time-domain DOT prototype which features many advantages over the conventional time-domainDOT systems. The high speed on TPSF acquisition and system SNR, relatively simple system structure and low cost are also realized. To further strengthen these advantages, we expect to develop a real-time high resolution DOT system in the near future. We would like to thank the following for their funding support: Office of Life Science (R397-000-615-712), National University of Singapore and A*STAR/SERC (P-052 101 0098).