System Calibration with Tissue Simulating Phantoms

For any medical imaging method, the use of tissue-simulating phantoms to evaluate and calibrate the system is central to achieving a useful device. In our studies, we have developed several different types of tissue phantoms, as discussed below.

In all imaging situations, we insert a homogeneous phantom into the fiber array to provide a homogeneous field in which to test the system response and the ability of our finite element code to match the measured data.

Figure 4. Table-top system (top) whose schematic is shown in Figure 3. In the three photographs at bottom, the first-generation clinical system (schematically similar to the table-top system) is shown with its fibers opened to three different diameters. Each fiber is adjusted one tooth at a time through a mechanical gearing system that simultaneously moves all fibers radially inwards or outwards.

Figure 4. Table-top system (top) whose schematic is shown in Figure 3. In the three photographs at bottom, the first-generation clinical system (schematically similar to the table-top system) is shown with its fibers opened to three different diameters. Each fiber is adjusted one tooth at a time through a mechanical gearing system that simultaneously moves all fibers radially inwards or outwards.

Measurements of phase shift and AC amplitude are taken for the intensity-modulated light that is transmitted through the phantom. These values are averaged for all source positions, assuming that the response at each of the 15 detectors will be the same as the source is rotated (i.e., as each fiber is used in turn as the source). Using this averaged data set, the finite element diffusion simulation is calculated and its absorption and scattering values systematically updated until the best possible approximation is found. In our estimation algorithm, phase shift is treated as a linear function of distance from the source and the slope of this linear relationship is extracted. The same process is completed for the logarithm of the AC amplitude versus distance from the source. These two slopes have been found from both phantoms and tissues to be very robust, and so provide a stable way to fit the

Figure 5. Second-generation system with parallel detection and three layers of optical fibers. The fiber translation array system (top left) drives three layers of fibers (top center) to accommodate radial and vertical positioning relative to the pendant breast. The computer control panel and data acquisition system (right) and the exam table with optical array (bottom left) are also shown. The array of photomultiplier tubes that is translated to multiplex to each of the three layers of 16 detection fibers is immediately below the table.

Figure 5. Second-generation system with parallel detection and three layers of optical fibers. The fiber translation array system (top left) drives three layers of fibers (top center) to accommodate radial and vertical positioning relative to the pendant breast. The computer control panel and data acquisition system (right) and the exam table with optical array (bottom left) are also shown. The array of photomultiplier tubes that is translated to multiplex to each of the three layers of 16 detection fibers is immediately below the table.

homogeneous estimates of the bulk optical properties. The fitting of the slopes of phase versus distance and log AC amplitude versus distance is accomplished by a Newton-Raphson algorithm. Estimates of the absorption and reduced scattering coefficients are typically obtained in less than ten iterations. These data are then used in a diffusion-model simulation, along with calculated offsets in AC amplitude and phase shift at zero distance. The best estimate of the simulated data is subtracted from the actual set of measured data and this difference residual is subtracted from all future measurements recorded during the same session. The calibration process provides a correction for interfiber variations in phase and amplitude as well as for any coupling errors. It is important to note that this calibration routine is not equivalent to what is sometimes called "difference imaging" relative to the phantom, because in both cases we match the simulation to the data; hence, the absolute absorption and scattering coefficients are recovered.

We have systematically examined the impact of the properties and size of the homogeneous calibration phantom on image quality by calibrating with different homogeneous phantoms before repeatedly imaging the same heterogeneous phantom. We developed a heterogeneous phantom with a cavity that could be filled with a mixture of water, Intralipid, and blood at varying concentrations, allowing a direct measure of an object with well-established optical properties. Photographs of one heterogeneous phantom and six homogeneous calibration phantoms are shown in Figure 6. The heterogeneous phantom is 84 mm in diameter, with a single, 20 mm-diameter hole parallel to the depth-axis of the cylinder. This hole was filled with different ratios of water, Intralipid, and blood to provide a target with variable contrast. The human blood used in the experiment was kept in a 7 ml tube with liquid additive to reduce the clotting of the platelets (volume, 0.07ml of 15% solution [buffered]; weight: 10.5 mg EDTA[k3]). The total hemoglobin content in these samples of blood was 140 g/dL as measured spectropho-tometrically in a clinical co-oximeter system. The blood was then aliquoted into a water-Intralipid solution to make specific concentrations of blood solution as needed.

Figure 6. Heterogeneous target phantom (left) and a representative set of homogeneous calibration phantoms (right). The target phantom has a diameter of 84 mm and height of 55 mm, with a cylindrical hole of diameter 20 mm. The homogeneous calibration phantoms labeled P1, P2 and P3 are all 55 mm high but are 73 mm, 84 mm, and 92 mm in diameter, respectively. The average optical property coefficients of PI, P2 and P3 are fl, = .005 mm"1 and n's = 1.0 mm"1 for PI; = .005 mm"1 and H's = 1.3 mm-1 for P2; and ¡J.a = .004 mm"1 and fl's = 1.1 mm-' for P3. Both P4 and P5 were 82 mm in diameter and had = .004 mm"1 and fl's = 1.6 mm-1. The P6 phantom is approximately breast-shaped and constructed of a soft, RTV-based material. The bottom diameter and the height of P6 are 82 mm and 78 mm, respectively, and its optical properties are = .0046 mm-1 and (Xs = 1.2 mm"1.

Figure 6. Heterogeneous target phantom (left) and a representative set of homogeneous calibration phantoms (right). The target phantom has a diameter of 84 mm and height of 55 mm, with a cylindrical hole of diameter 20 mm. The homogeneous calibration phantoms labeled P1, P2 and P3 are all 55 mm high but are 73 mm, 84 mm, and 92 mm in diameter, respectively. The average optical property coefficients of PI, P2 and P3 are fl, = .005 mm"1 and n's = 1.0 mm"1 for PI; = .005 mm"1 and H's = 1.3 mm-1 for P2; and ¡J.a = .004 mm"1 and fl's = 1.1 mm-' for P3. Both P4 and P5 were 82 mm in diameter and had = .004 mm"1 and fl's = 1.6 mm-1. The P6 phantom is approximately breast-shaped and constructed of a soft, RTV-based material. The bottom diameter and the height of P6 are 82 mm and 78 mm, respectively, and its optical properties are = .0046 mm-1 and (Xs = 1.2 mm"1.

The phantom's optical properties were measured before the hole was drilled. It was found to have an absorption coefficient (¡da) of 0.0064 mm'1 and a reduced scattering coefficient (//') of 1.0 mm-1, respectively, at a wavelength of 785 nm. The hole was filled with an Intralipid and ink solution which matched the background reduced scattering coefficient and had a slightly higher absorption (0.00643 mm-1) before different concentrations of blood were added. This type of phantom is constructed using the methods described by Firbank et al. [107]. Specifically, 330 grams of resin (GY502 Ar-aldite resin, D. H. Litter, Elmsford, NY) are mixed with 99 grams of hardener (HY832, D. H. Litter), 1.4 g of titanium dioxide, and 0.5 ml of a 2% ink solution. The ingredients are carefully mixed, then degassed in a large bell jar before being moved to an evacuation fume hood to cure for several days. When this process is complete, the phantom is finished by machining (on a lathe) to reduce its diameter to the desired size. Machining is also a good way to reduce the superficial sticky layer that remains after curing. The final product has a solid, smooth surface and is easily handled in the lab.

Measurements from six homogenous phantoms were used to calibrate data recorded from the target heterogeneous phantom. The first three calibration phantoms (P1, P2, and P3 in Figure 6) were constructed from the resin composition discussed above and were similar in composition to the heterogeneous phantom used in this study.

A second kind of phantom was also investigated—a "soft" phantom that provides an elastic property similar to most breast tissue. Coupling of the optical fibers to harder phantoms is never achieved with complete and even contact because the surface is curved and rigid, whereas the ends of the fibers are large and flat. It was, therefore, hypothesized that a softer phantom would provide better contact and thus mimic imaging of the actual breast. A soft, RTV-based material was used to make three soft calibration phantoms (P4, P5, and P6 in Figure 6). These phantoms were fabricated by using 500g Sili-cone (RTV141, Medford Silicone, Medford, NJ) mixed with 17 g of hardener (comes with RTV141), 1.7 g of titanium dioxide, and 0.8 ml of a 2% ink solution.

Following measurements on all of these phantoms, images of the single inhomogeneous phantom were reconstructed. The absorption coefficient was varied for the inhomogeneous phantom by varying the blood concentration. Values for the slope of absorption coefficient versus blood concentration of an embedded inclusion at a wavelength of 785 nm were compared between data sets reconstructed with calibration phantoms of different stiffness, size, shape, and optical properties. Figure 7 shows plots of the estimated maxi mum ¿ua within the blood region the of target phantom versus blood concentration, with each line of data corresponding to a different homogeneous calibration phantom. The blood concentration was varied from 0% to 1%, as shown on the horizontal axis.

Figure 7. Estimated fit versus blood concentration. The lines LPi through Lp^ are linear regression fits to the values of maximum fia within the blood region for phantoms P1 through P6 (see Fig.6). The equations in the lower right-hand corner show the slopes of the fitted lines.

The standard deviation of the slopes of the lines in Figure 7 was 8% of the average slope. If reconstructions from data calibrated using the hard phantom with a diameter of 73 mm (P1) were omitted, the standard deviation was less than 3%. For the variations in the reconstructed absorption coefficient for the same blood concentration, the variations in the reconstructed absorption coefficient for the same blood concentration were within 2% when ignoring the P1 phantom. This shows that the effect of using different calibration phantoms is small as long as all of the source and detector fibers remain in good contact with the target (not the case with P1). Considering the tradeoff between detector size and the curvature of the reference phantom surface, 80-90 mm diameter phantoms with optical properties similar to those of the normal breast appear to produce the best image quality for the 6 mm diameter fiber bundles currently in use within our imaging system. In addition, it can be seen that the ¡J.a corresponding to the breast-shaped calibration phantom (P6) is approximately the same as the data corresponding to the soft phantom P4, which has the same diameter and similar optical properties and height.

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