2.1.

The UCL Optical Tomography System

A 32-channel time resolved system for optical tomography developed at UCL has been described in depth elsewhere.²² It consists of a portable fiber laser (IMRA Inc., USA) that produces pulses $\sim 2\mathrm{ps}$ in duration at $780\mathrm{nm}$ and $815\mathrm{nm}$ , interlaced with an overall repetition rate of $80\mathrm{MHz}$ . These pulses are transmitted through a 32-way optical switch that illuminates each source fiber in sequence. Each source fiber is integrated along the axis of a detector fiber bundle. Combining the sources and detectors in this way reduces the number of connection points on the tissue being imaged, and facilitates a straightforward method of calibrating the temporal characteristics of the system.³¹ The detector fiber bundles collect the light that has traveled through the breast and transmit it to four 8-anode microchannel-plate photomultiplier tubes (MCP-PMTs). The MCP-PMTs produce an electronic pulse for each photon detected and are protected from over exposure by a series of programmable variable optical attenuators.

The detector electronics consists of 32 parallel channels which measure the times taken for photons to travel between each source and detector relative to a reference pulse generated by the laser, and produce a series of time-of-flight histograms known as temporal point spread functions (TPSFs). Datatypes such as integrated intensity, mean flight time, and temporal variance are typically extracted from the measured TPSFs. The use of such datatypes decreases the computational time and memory requirements of the reconstruction algorithm as compared to calculating the entire TPSF. Intensity and meantime were used here as these have proved to be the most robust and the most effective at separating scatter and absorption.³²

2.2.

The Liquid-Coupling Interface

The coaxial source∕detector bundles are attached to the exterior of an opaque plastic hemispherical cup, $165\mathrm{mm}$ in diameter with a thickness of $5\mathrm{mm}$ (EMA model supplies, Shepperton, UK). Thirty-one bundles are distributed over the surface of the cup as illustrated in Figs. 1(a) and 1(b) . The bundles are spaced at regular intervals within three horizontal planes, providing a reasonably even distribution across the surface of the hemisphere. Holes were drilled in the opaque cup, and optically scattering windows were attached to the inner surface to form a watertight seal across each hole. Each window was made from a mixture of epoxy resin and titanium dioxide particles, providing highly scattering properties to create a diffuse source.³³ The fiber bundles are held in position using short plastic tubes attached to the external surface of the cup.

Fig. 1

The hemispherical cup developed for breast imaging: (a) a photograph showing 31 fiber bundles attached; (b) the arrangement of sources∕detectors as seen from above; (c) a side view of the cup and the vertical extension used for reference measurements.

The remaining space between the breast and the cup is filled with a suitable coupling liquid. In the study performed with a similar device by the Philips group,²⁸ the optical properties of the coupling fluid were selected to match the average optical properties of the breast. This offers two obvious advantages. First, the reconstruction algorithm is not required to iterate too far from a uniform initial guess corresponding to those average optical properties, and is therefore more likely to converge to a correct solution. Second, contrast in the reconstructed images will be dominated by the features of interest within the breast, instead of by the differences between the breast and fluid properties. A further consideration is that the coupling fluid must be harmless to skin contact. For the purposes of this preliminary investigation the cup was filled with a solution of intralipid,³⁴ dye, and distilled water with properties of absorption coefficient ${\mu }_a=0.0070\pm 0.00035{\mathrm{mm}}^{-1}$ and reduced scattering coefficient ${\mu }_s^{\prime }=0.80\pm 0.04{\mathrm{mm}}^{-1}$ . These values were chosen as being representative of the average properties of the breast^{35, 36} and are consistent with those used in previous breast phantom studies at UCL.³⁷ These properties also ensured that the signal acquired for the largest source-detector separation (corresponding to the full diameter of $165\mathrm{mm}$ ) produced a measured photon count rate of around 50 to 100 photons per second, sufficient to obtain useful datatypes for image reconstruction.

Throughout this study a so-called difference imaging approach was performed. Difference imaging involves reconstructing the changes in optical properties between the cup containing both the coupling fluid and the breast, and those of a suitable reference medium. The advantage of using difference imaging as opposed to absolute imaging is that systematic errors inherent in the measurement largely cancel. For this application, difference imaging eliminates the effect of uncertainty and variability in the surface coupling, allowing use of intensity measurements. Disconnecting and reconnecting the fiber bundles to the cup has shown that the coupling can vary, and therefore absolute imaging would require the coupling to be measured empirically for each scanning session. The disadvantage of difference imaging is that errors will occur if the reference medium is poorly matched to the breast and its properties are not known exactly.³² The ideal reference is a homogeneous medium with known optical properties and external geometry, which are the same as the object under investigation. Such a reference can be created for this system by filling the cup with the coupling fluid described above.

Initial experiments with the cup revealed that measurements recorded with sources and detectors located near to the top of the hemisphere are highly sensitive to the proximity of the top surface of the liquid.³⁸ Furthermore, to provide a reasonable reference for patient studies (since detected photons can travel into and out of the chest wall) it is necessary to extend the height of the reference medium. Various alternative methods of extending the height have been explored.³⁸ The two most successful are the addition of an extra volume of coupling liquid, and the use of a solid cylindrical slab of tissue-equivalent phantom material placed in contact with the top surface of the liquid. The former was achieved by attaching a cylindrical plastic extension, $50\mathrm{mm}$ in height, to the top of the hemisphere as illustrated in Fig. 1(c). The height of liquid necessary to avoid significant loss of detected light from the top surface was established empirically.³⁸ The disadvantages of this method are that it requires several additional minutes to attach and fill the plastic extension, and it is difficult to maintain a reusable watertight seal. The cylindrical block was made from epoxy resin with a diameter of $200\mathrm{mm}$ and a thickness of $65\mathrm{mm}$ . The optical properties of the block are ${\mu }_a=0.007{\mathrm{mm}}^{-1}$ and ${\mu }_s^{\prime }=2.0{\mathrm{mm}}^{-1}$ . The scatter coefficient was chosen to represent the anticipated higher scattering within the chest wall, such as due to bone. The cylindrical block method is much easier to employ, although there is a concern how a mismatch in refractive index between the resin block (1.56) and the coupling fluid (1.33) may affect the reconstruction.³⁹

The repetition rate of the laser (two interlaced trains of pulses at $40\mathrm{MHz}$ ) dictates that the maximum temporal window for each TPSF is $12.5\mathrm{ns}$ . However, the large diameter of the cup and the optical properties of the coupling fluid cause some photons for the largest source-detector separations to be detected with flight times in excess of the window width. As a consequence it is necessary to acquire data at the two wavelengths successively rather than simultaneously, enabling a temporal window of $25\mathrm{ns}$ to be used. In the experiments reported below, data were only acquired at a single wavelength of $815\mathrm{nm}$ .

2.3.

Perturbation Experiments

To quantify the spatial resolution, localization accuracy, and contrast across the volume of the cup, two epoxy resin cylindrical targets with length and diameter of $10\mathrm{mm}$ were constructed. The optical properties of these are as follows. Target A: ${\mu }_a=0.07{\mathrm{mm}}^{-1}(10\times \text{background}{\mu }_a)$ and ${\mu }_s^{\prime }=0.8{\mathrm{mm}}^{-1}$ , and target S: ${\mu }_a=0.007{\mathrm{mm}}^{-1}$ and ${\mu }_s^{\prime }=8{\mathrm{mm}}^{-1}(10\times \text{background}{\mu }_s^{\prime })$ , respectively. The targets were each placed at 15 positions within one half-plane of the fluid filled cup as illustrated in Fig. 2 . These positions form a grid of equilateral triangles.

Fig. 2

The positions of the targets within a half-plane of the cup.

Each target was suspended in turn on the end of a thin wire supported by a frame mounted on vertical and horizontal translation stages. The target was initially placed in the center of the top ring of fiber bundles and was translated relative to this point. Data were acquired for $11\min$ at each position with an acquisition time of $10\mathrm{s}$ per source. Reference data sets were acquired with the target removed at the end of each row in Fig. 2, as well as prior to and following the experiment.

2.4.

Patient Interface

A patient-supporting table was built to enable the system to be evaluated on volunteers. The cup is attached to a plastic ring secured firmly into an aperture in the table as illustrated in Fig. 3 . A channel is cut into the ring, which allows coupling fluid that overflows from the cup to return via plastic tubing to the fluid reservoir. The cup is filled with fluid from below using a peristaltic pump, which then circulates fluid continuously and slowly to sustain a constant level of fluid. The addition of a heating element to the fluid reservoir will ultimately enable the liquid to be maintained at a constant, comfortable temperature. The table is covered with a layer of foam, and a pillow and towels are provided.

Fig. 3

A schematic of the breast imaging table and liquid-circulating mechanism.

2.5.

Preliminary Studies on Healthy Volunteers

Initial studies have been performed on several healthy volunteers. Prior to the investigation, the coupling fluid was prepared at an ambient room temperature of $23°\mathrm{C}$ . Data were acquired on each of the volunteer’s breasts for a total scan time of $11\min$ , or $10\mathrm{s}$ per source. To enable difference measurements to be used in the reconstruction, two different references were used and compared. One volunteer was also scanned a second time with the high-absorbing target (described above in Sec. 2(C)) attached to the surface of her breast with Micropore (3M) paper tape.

2.6.

Image Reconstruction

Images were generated from the data using the TOAST reconstruction package developed at UCL.⁴⁰ TOAST employs the finite element method (FEM) to model the propagation of light through tissue using the diffusion approximation to the radiative transfer equation. TOAST reconstructs 3D images of scatter and absorption coefficients. Image reconstruction involves iteratively adjusting the optical properties assigned to the FEM mesh to optimize the match of the model to the data.

A 3D finite element mesh was constructed with a Delaunay triangulation method to be used in reconstruction of the data obtained using the hemispherical cup.⁴¹ The mesh, shown in Fig. 4 , was generated as a hemisphere with a $50\text{‐}\mathrm{mm}$ cylindrical extension to the top. The mesh consists of 23,156 tetrahedral elements with quadratic interpolation functions and 35,233 nodes. The mesh has a greater density at the positions of the source detector bundles, where the rate of change of light intensity is greater.

Fig. 4

The finite-element mesh used for image reconstruction.

The image reconstruction was performed using a conjugate gradient solver and Robin boundary conditions. In all cases, the 15th iteration was analyzed as this was found to be the number beyond which no further improvement to the images was observed. Each iteration required $48\min$ on a $2.2\mathrm{GHz}$ Xeon processor and used approximately $800\mathrm{MB}$ of RAM.

2.7.

Analysis

The contrast, spatial resolution, and localization accuracy were determined from images obtained for all the 15 positions indicated in Fig. 2. The contrast $C$ is calculated using:

The localization accuracy was determined from the differences between the positions of the peak value within the images and the expected positions of the target. The position of the peak value was obtained by taking the mean $x$ , $y$ , and $z$ values for the nodes in the mesh that correspond to values above 95% of the maximum value. Any difference between the expected positions and the true positions (due to error in the initial positioning of the targets) was removed by subtracting the mean expected values and the mean measured values from the corresponding values of $x$ , $y$ , and $z$ . Any difference between the expected and measured values is then only due to the reconstruction error we wish to quantify.

Each 3D image may be considered to represent the target distribution convolved with a 3D point spread function (PSF). It is conventional to characterize spatial resolution in terms of the width of the PSF. For the analysis presented here, however, we elect to characterize spatial resolution in terms of the volume of the PSF. Since the volume of the images of the targets are much greater than that of the targets themselves, we make the approximation that the PSF volume is equal to the volume of the reconstructed target. The “volume resolution” presented here has been calculated as the volume of the mesh that encompasses all nodes associated with a value greater than or equal to 50% of the maximum value in the image. We call this parameter the full volume at half maximum (FVHM).

The PSF is assumed to have a Gaussian profile. When the volume occupied by the feature in the image becomes greater, the peak value (and therefore the contrast) will be reduced. Hence a decrease in spatial resolution will lead to a direct decrease in contrast, which can be expressed as:

3.1.

Perturbation Experiments

Figure 5 shows typical images reconstructed from the data acquired for the (a) absorbing and (b) scattering targets in position 11 in Fig. 2. These images represent $x\text{‐}z$ and $x\text{‐}y$ slices [see Fig. 1(c)] through the 3D images, intersecting the peak produced by the target. In each case the 15th iteration is shown. Although the targets are displayed in the expected location, we observe significant crosstalk between absorption and scatter. The TOAST algorithm has interpreted the difference data for both types of target as a perturbation in both parameters, although the largest perturbation is identified in the correct parameter (see discussion in Sec. 4).

Fig. 5

The reconstructed absorption (left) and scattering (right) images of (a) absorbing target A placed at position 11, and (b) scattering target S at position 11.

Plots of the variation in contrast, localization accuracy, and FVHM (as defined in Sec. 2(G)) with distance from the coordinate origin [position O in Fig. 1(c)] are shown in Figs. 6, 7, 8 , respectively. A linear trend line was fitted to each set of data using a least-squares regression. All three plots show strong dependency on the position of the cylinder from the edge of the cup. A plot of the adjusted contrast $(V_i{C}_i∕V_t)$ against distance from the coordinate origin is shown in Fig. 9 . As discussed in Sec. 4 below, the values obtained are significantly closer to the true contrast of 9, suggesting that such a method could be useful for improving the quantitation accuracy of optical tomography.

Fig. 9

Values of contrast following compensation for the partial volume effect for (a) target A and (b) target S plotted against distance from the center of the cup. The dashed lines represent the true contrast value.

Fig. 8

The full volume at half maximum for (a) target A and (b) target S plotted against distance from the center of the cup (using the 15th iteration).

Fig. 7

The localization accuracy for (a) target A and (b) target S plotted against distance from the center of the cup (using the 15th iteration).

Fig. 6

The contrast of (a) target A and (b) target S plotted against distance from the center of the cup (using the 15th iteration).

3.2.

Initial Images Using the System on a Healthy Volunteer

The reconstructed absorption and scatter images of a $69\text{‐}\text{year}$ -old healthy volunteer’s left breast are shown in Fig. 10(a) . In this case, the reference data was acquired using the additional height of coupling fluid. Reassuringly, an image acquired using the solid resin block on the top surface of the cup (not shown) was almost identical, both qualitatively and quantitatively, despite the refractive index mismatch for the resin block. The absorption and scatter images both exhibit reasonable contrast, although the scatter images generally show greater heterogeneity. Meanwhile, Fig. 10(b) shows the images of the same breast with the absorbing target attached to the surface of the breast (near position 5 in Fig. 2). The vertical $\left(x\text{‐}z\right)$ and horizontal $\left(x\text{‐}y\right)$ slices in Fig. 10(b) correspond to the planes through the apparent center of the absorbing target, and the same planes are selected for Fig. 10(a). The contrast of the target (in both absorption and scatter images) is entirely consistent with that shown for the isolated target in a similar position in Fig. 5(a). Allowing for some slight movement of the breast between the two measurements, the appearance of the breast in Fig. 10(b) is very similar to that shown in Fig. 10(a). The uncertainty in the nominal optical properties of the coupling fluid is roughly 5%, so the boundary between the breast and fluid is difficult to determine in terms of optical properties alone. Nevertheless, the images suggest that while the breast is generally more absorbing than the fluid, the breast contains regions which are evidently less scattering than the fluid. This may be indicative of regions of adipose tissue, which is expected to be lower scattering than other tissues and more dominant in the older, postmenopausal breast.⁴²

Fig. 10

The reconstructed absorption (left) and scattering (right) images of (a) a healthy $69\text{‐}\text{year}$ -old volunteer, and (b) the same volunteer with an absorbing target attached to the surface of her breast. The arrows indicate the height of the corresponding circular cross-sections.