2.1.

Fiber Design and Prototype

The side-firing fiber was custom designed as shown in Fig. 1(a) and described in our previous publication.³² A multimode 1-mm core diameter optical fiber (Thorlabs, Newton, New Jersey) with a numerical aperture (NA) of 0.39 was polished at a 45 deg angle. This angle directed a fraction of the light 90 deg to the fiber axis using principles of total internal reflection. To collect and reuse the remaining light directed at an angle $<90\mathrm{deg}$ to the fiber axis, a mirror was constructed from a metal rod polished to a 45 deg angle. The fiber and mirror were inserted into opposite ends of a quartz tube and oriented with their polished faces coincident to each other. The tube had an outer diameter of 2 mm. Epoxy was used to permanently fix the fiber and mirror in this orientation inside the quartz tube and create the side-firing fiber prototype shown in Fig. 1(b). An external marker was placed to visually track the direction of the laser beam. Visible 635-nm light was coupled to the free end of the fiber to display the profile of light that exits the fiber. The area of the emitted light on the surface of the quartz tube was estimated by resting a white sheet of paper on the tube, directing light toward this sheet, and observing the projection of this light onto the sheet, as shown in Fig. 1(c).

Fig. 1

(a) Design components of the side-firing fiber and photographs of (b) a custom-built fiber prototype and (c) the laser spot size projection on a sheet of paper resting on the surface of the quartz tube. The dashed ellipse was drawn to scale on the photograph to show the perimeter of the surface area calculated with Eq. (4) and the design parameters listed in Table 1. The scale has units of millimeter.

2.2.

Surface Area and Energy Density Calculations

The laser spot size on the surface of the quartz tube can be approximated as an ellipse with a long axis $\ell$ and short axis $S$, as illustrated in Fig. 2(a). The long and short axes were derived by considering the longitudinal and axial cross-sectional views shown in Figs. 2(b) and 2(c), respectively. Fundamental principles of geometrical optics, with assumptions that all light is redirected 90 deg to the fiber axis, the fiber and tube are concentric, and the air gap between them is negligible, yield the following equations:

Fig. 2

(a) Schematic diagram showing the dimensions of the laser spot size on the surface of the quartz tube. Dimensions of the light emitted in (b) longitudinal and (c) axial cross-sections of the fiber are related to the fiber design parameters.

Given the similarity of Eq. (3) to the critical angle for total internal reflection in the fiber [i.e., $\gamma ={\sin }^{-1}(n_{\text{air}}/n_{\text{glass}})$],³⁵ ${\gamma }_e$ can be thought of as the effective critical angle of the light after passing through the quartz tube. Inserting Eqs. (1) and (2) into the equation for the area of an ellipse yields the following equation:

The design parameters for the side-firing fiber shown in Fig. 1 are reported in Table 1. Inserting these parameters into the above equations yields $\ell =1.8\mathrm{mm}$, $S=1.2\mathrm{mm}$, and $\text{Area}=1.7{\mathrm{mm}}^2$, which are reasonable estimates, as indicated by the ellipse with these dimensions, superimposed on the laser spot photograph in Fig. 1(c). Equations (1)–(4) were used to estimate surface areas and corresponding energy densities for a range of NA values, fiber diameters, and tube diameters, and to determine the initial light profile for the simulations described in Sec. 2.4. In addition, the energy limit, $E_{\lim }$, for a particular energy density limit, $U_{\lim }$, was determined by combining the definition of energy density with Eq. (4) to achieve the following equation:

Table 1

Summary of side-firing fiber design parameters.

2.3.

Phantom Experiments

The side-firing fiber prototype was coupled to a 1064-nm Q-switched Nd:YAG laser (Phocus InLine, Opotek, Carlsbad, California) with a 5 ns pulse duration and 10 Hz repetition rate. The resulting pulse energy was measured with and without the fiber inserted into a 16-Fr silicone urinary catheter (Model 1658-16 Bardex®, Bard Medical Division, Covington, Georgia). Energy losses due to the presence of the catheter were minimal.

A $4\mathrm{cm}\times 2\mathrm{cm}\times 10\mathrm{cm}$ plastisol phantom was drilled with a 4-mm-diameter hole to accommodate a 14-Fr urinary catheter and a 2-cm-diameter hole to insert the transrectal US probe. The relationship between the holes mimicked the relationship between the urethra and rectum. Decayed brachytherapy seeds (TheraSeed, Theragenics Corporation, Buford, Georgia) were inserted using a standard 18 G brachytherapy needle at radial distances of 0.5, 1, 2, and 3 cm from the center of the 4-mm hole, which corresponds to distances of 1.7, 2.3, 2.9, and 5.0 cm from the closest outer edge of the 2-cm hole, respectively. The seeds were cylindrical shells with an outer diameter of 0.8 mm and a long axis of 4.5 mm, coated with black India ink to increase optical absorption.³⁶ For clinical implementation, a biocompatible coating with similar optical absorption to India ink would be more suitable, which is a reasonable modification for seeds purposely designed for photoacoustic imaging considering that similar enhancement coatings are common in brachytherapy.³⁷

After placing the catheter and probe in their respective holes, the side-firing fiber was inserted through the urinary catheter and rotated to visualize each seed individually, as illustrated in Fig. 3(a). A photograph of the actual phantom appears in Fig. 3(b), showing the holes for the probe and catheter as well as the implanted seeds. The average energy per pulse used to visualize the seeds was $\sim 2\mathrm{mJ}$, which corresponds to an energy density of $111\mathrm{mJ}/{\mathrm{cm}}^2$ at the surface of the quartz tube.

Fig. 3

(a) Schematic diagram showing the phantom design with labels representing distances of the seeds from the light source. The light is directed toward the seed located 1 cm from the light source (i.e., 2.3 cm from the probe), and it was rotated to visualize the other seeds. (b) Photograph of phantom.

A photoacoustic imaging system consisting of a US scanner (SonixTouch, Ultrasonix, Richmond, BC, Canada), transrectal US probe with dual linear and curvilinear arrays (BPL9-5 and BPC8-4, Ultrasonix), data acquisition unit (SonixDAQ, Ultrasonix), and the 1064-nm Phocus InLine Nd:YAG laser was utilized to acquire photoacoustic data. The laser was coupled to the free end of the side-firing optical fiber. Prebeamformed photoacoustic images were displayed in real time at a rate of 3 to 5 frames per second to assist with seed localization. The software framework for real-time photoacoustic imaging with this system was described in a previous publication,³⁸ while the commercial SonixTouch US system and software were utilized to acquire linear and curvilinear US images (i.e., images acquired with the linear and curvilinear arrays, respectively). The sampling rate for data acquisition was 40 MHz, and the bandwidths of the linear and curvilinear arrays were 4 to 8 MHz and 5 to 9 MHz, respectively.

2.4.

Monte Carlo Simulation

To investigate light propagation beyond the urethral walls in an optically scattering medium, a 3-D Monte Carlo simulation³⁹ was performed with a $1\mathrm{cm}\times 1\mathrm{cm}\times 1\mathrm{cm}$ cubic voxel of prostate tissue and a resolution cell of $50\mu \mathrm{m}$ in each dimension. The light source incident on the urethral wall (i.e., centered on one surface of the prostate voxel) was a $1.2\mathrm{mm}\times 1.8\mathrm{mm}$ ellipse with a focus located 2.1 mm from the prostate tissue (i.e., inside the urethra), which corresponds to the geometrical dimensions of the elliptical light cone produced by our fiber prototype. A 0.1-mm air interface separated the light source from the urethra.

The prostate contained three $0.8\mathrm{mm}\times 4.5\mathrm{mm}$ cylindrical targets (i.e., brachytherapy seeds) at radial distances of 5.0, 5.4, and 5.8 mm from the center of the light source incident on the urethra. The circumference of the seeds intersected the $x\text{-}z$ plane, and the length of the seeds was coincident with the $y\text{-}z$ plane. To demonstrate the expected differences in light distribution with the implantation of additional seeds, a fourth seed was added with its center offset by 0.3 mm from the $x=0$ plane at a radial distance of 3 mm from the center of the light source incident on the urethra. The run times for the three- and four-seed simulations were 20 and 8 min, respectively, resulting in a total of $\sim 1.3\times {10}^6$ photons launched for each simulation.

Optical properties were modeled at a laser wavelength of 1064 nm, using the values for canine prostates⁴⁰ and 100% India ink⁴¹ reported in Table 2. Note that the optical absorption of India ink is similar (within an order of magnitude) to that of stainless steel brachytherapy seeds.¹¹

Table 2

Optical parameters for three-dimensional Monte Carlo simulation.

2.5.

Canine Experiments

Two canine prostates were implanted with cylindrical (0.8 mm outer diameter, 4.5 mm long axis), decayed, coated brachytherapy seeds under transrectal US guidance, as approved by the Johns Hopkins Animal Care and Use Committee. The abdomen of each dog was opened to access the prostate and insert the urinary catheter. For the first dog, seeds were implanted transperineally, similar to a human procedure, prior to the abdominal surgery. For the second dog, the seeds were inserted directly into the prostate after the surgery with an orientation similar to a human procedure. This approach enabled precise targeting of difficult-to-image regions of the prostate.^42,43 A 16-Fr (i.e., 5.3 mm outer diameter) silicone urinary catheter (Model 1658-16 Bardex®) was inserted through an incision in the bladder to avoid the curvature of the urethra near the canine’s pubic bone, which is more pronounced than that of humans. The side-firing fiber was inserted into the open end of the catheter to image the implanted brachytherapy seeds.

Using the US and photoacoustic imaging systems described in Sec. 2.3, the first prostate was imaged in the native tissue environment, 1 to 2 h after euthanasia. The average energy per pulse was 6.7 mJ, which corresponds to an energy density of $370\mathrm{mJ}/{\mathrm{cm}}^2$ at the surface of the quartz tube. The radial distance between the center of the urethra and the three seeds that were imaged was $6$ to 9 mm, as measured in the curvilinear US image. The second prostate was imaged in vivo with an average energy per pulse of 7.5 mJ, which corresponds to an energy density of $414\mathrm{mJ}/{\mathrm{cm}}^2$ at the surface of the quartz tube. The radial distance between the center of the urethra and the seed was $1\mathrm{cm}$.

The locations of implanted seeds were confirmed with intraoperative US images and postoperative computed tomography (CT) images. The transrectal US probe was locked in place with a brachytherapy stepper (Nucletron, Veenendaal, The Netherlands) to acquire coregistered US and photoacoustic images.

2.6.

Beamforming Photoacoustic Data

A conventional delay-and-sum (DAS) beamformer and a coherence-based short-lag spatial coherence (SLSC) beamformer^28,44 were applied to the zero-mean radiofrequency (RF) photoacoustic signals received by the transducer. Received signal time delays were calculated with 33-element subapertures to limit off-axis acoustic clutter. Hanning apodization was applied to the delayed signals for DAS beamforming with no apodization applied for SLSC images. The parameters for SLSC imaging were adjusted to optimize seed visualization as described in previous publications,^18,28 where $M$, the short-lag value for integration of coherence functions, was equal to 10 for curvilinear images and 4 for linear images (i.e., 30 and 12% of the active receive aperture, respectively). The correlation kernel length was equivalent to the smallest wavelength within the bandwidth of the linear array (i.e., 0.308 mm). The beamformed photoacoustic data were envelope-detected, normalized to the brightest image pixel, and log compressed. In addition, images acquired with the curvilinear array were scan converted. No aperture growth, RF frame averaging, nor compensation for optical attenuation was implemented for either beamformer.

To assess image quality, the contrast of seed signals in DAS and SLSC photoacoustic images were calculated using the definition, $\text{Contrast}=20{\log }_{10}(S_i/S_o)$, where $S_i$ and $S_o$ are the means of the envelope-detected RF data within regions of interest (ROIs) located inside and outside of a brachytherapy seed. Comparative lateral resolutions were measured as the full width at half maximum (FWHM) of line plots passing through the center of seed signals. US and photoacoustic image processing and image analyses were performed with MATLAB® software (The MathWorks, Inc., Natick, Massachusetts), while CT image analyses were performed with ImageJ software.⁴⁵

3.1.

Design Parametrization

Equations (1) and (2) show that the minor and major axes of the elliptical light profile depend on the NA of the fiber, the tube inner and outer diameters, the fiber diameter, and the minimal air gap spacing between the fiber and tube. The latter parameters are related through the expression $R_{\text{tube}}-R$, which represents the combined tube thickness and air gap spacing. As illustrated in Fig. 4(a), increasing these parameters increases the surface area.

Fig. 4

(a) Elliptical surface area as the tube diameter and $R_{\text{tube}}-R$ (i.e., the combined tube wall thickness and air gap between fiber and quartz tube) are varied. The black $\mathbf{x}$ denotes parameters of the custom-built prototype. (b) Energy limits were calculated for various numerical aperture values given the fiber and tube radii corresponding to the prototype ($R=0.5\mathrm{mm}$ and $R_{\text{tube}}=1.0\mathrm{mm}$, respectively), a tube radius corresponding to the urinary catheter ($R_{\text{tube}}=2.65\mathrm{mm}$), and a larger fiber radius ($R=0.75\mathrm{mm}$).

Figure 4(b) shows the energy limits required to satisfy the $100\mathrm{mJ}/{\mathrm{cm}}^2$ safety limit for skin exposure at a wavelength of 1064 nm,⁴⁶ as the NA was varied from 0.1 to 0.5. Results are shown for optical fibers with 1 and 1.5 mm core diameters (i.e., $R=0.5$ and 0.75 mm, respectively), tube diameters of 2.0 and 5.3 mm (i.e., $R_{\text{tube}}=1.0$ and 2.65 mm, respectively), and the remaining parameters listed in Table 1. These calculations indicate that the energy limit increases with larger NAs, fiber diameters, and tube diameters, due to the larger surface area of the laser beam that exits the fiber. This result can be modified for different fiber parameters, using Eq. (5) to determine the energy limits required to remain below any given energy density limit.

Limits to the maximum achievable surface area and energy limit in Figs. 4(a) and 4(b), respectively, include the size of the urethra and the inner diameter of the catheter when present (e.g., 6 and 2 mm, respectively), as well as additional mechanical design constraints (e.g., minimum required bending radius, stresses applied during fiber insertion) and ergonomic considerations (e.g., patient comfortability with large catheters), which are beyond the scope of this paper.

3.2.

Beamformer Comparisons

A cross-sectional schematic of the phantom design and curvilinear US and photoacoustic images created with the DAS and SLSC beamformers are shown in Fig. 5. The fiber was rotated to visualize each seed located at distances of 0.5 to 3 cm from the catheter. The mean contrast of DAS images varied from 20 dB for the seed located 0.5 cm from the light source to 9 dB for the seed located 2.8 cm from the light source. Seeds located 2 to 3 cm from the catheter were better visualized with the SLSC beamformer, which provided a 12 to 29 dB mean contrast improvement over the DAS images, as shown in Fig. 6(a).

Fig. 5

Phantom schematic diagram and curvilinear ultrasound (US) image of the phantom are shown on the left. Delay-and-sum (DAS) (top) and short-lag spatial coherence (SLSC) (bottom) photoacoustic data were created after the fiber was rotated toward each seed. The distances between the light source and seed are indicated in the schematic diagram and above each image. The far right displays results after summing eight DAS (top) and SLSC (bottom) images from each fiber rotation. The scales on the left images have units of millimeter and correspond to all photoacoustic images, which are all shown with 15 dB dynamic range, as indicated by the colorbar on the right.

Fig. 6

(a) Contrast, (b) line profiles, with values in the legend representing distances from the light source to the seed, and (c) full width at half maximum (FWHM) measurements from DAS and SLSC photoacoustic images acquired with the curvilinear array.

Eight images of each seed were summed and shown with a 15 dB dynamic range in the last column of Fig. 5. The seeds farthest from the light source are more difficult to locate in the combined DAS image due to the decreasing contrast with distance. However, the combined SLSC image (bottom right) shows a clear map of the location of the four implanted seeds, regardless of distance from the light source, and it closely resembles the US image (bottom left). The SLSC image also amplifies the coherent photoacoustic artifacts associated with the urinary catheter location. One solution to minimize these artifacts is to limit the dynamic range of the SLSC image, which would not affect seed visualization, as the seeds are more coherent than the artifacts. On the other hand, increasing the dynamic range of the combined DAS image would enhance visualization of the farthest seed but increase the background noise in the image.

Examples of line profiles passing through the seeds located at 0.5 and 3 cm from the urinary catheter are displayed prior to scan conversion (i.e., as a function of azimuthal angle) in Fig. 6(b). The line profiles for the seed located at 0.5 cm from the catheter in DAS and SLSC images were taken from the same image depth (i.e., 1.7 cm from the probe) and displayed with the maximum signals aligned. The coherent background signals observed to the left and right of the seed closest to the catheter (located 0.5 cm away) is likely due to clutter, electronic noise, and the off-axis spatial coherence of catheter signals. These line plots demonstrate that the background noise in SLSC images has more variance, which causes the larger standard deviations for SLSC contrast measurements. In addition, note that the contrast measurement is dependent on the location of the noise ROI relative to the surrounding clutter.

The line profiles in Fig. 6(b) and similar line profiles for each seed were used to measure the FWHM of the seed signals and obtain comparative estimates of lateral resolution. These measurements were performed on prescanconverted images, converted from degrees to distance, and reported as a function of distance from the probe in Fig. 6(c). Results show the mean measurements from eight images for each $\text{seed}\pm \text{one standard deviation}$. The actual seed width is 0.8 mm in this dimension, which both beamformers overestimate.

Two of the same seeds visualized with the linear array are shown in Fig. 7(a). The distance between the light source and seeds is indicated in the US image (left) and above each photoacoustic image created with DAS (top) and SLSC (bottom) beamformers. The width of the phantom is 2 cm in the lateral image dimension, and the air tracks created from seed insertion appear to the left of the seeds in the US image. Similar to the curvilinear results, photoacoustic images created with the SLSC beamformer have 10 to 27 dB higher contrast than images created with the DAS beamformer, particularly when the seeds are located 2 to 3 cm from the light source.

Fig. 7

(a) The linear US image on the left shows seeds in the phantom located at 1 and 3 cm from the catheter. DAS (top) and SLSC (bottom) photoacoustic data were created after the fiber was rotated toward each seed. The distances between the light source and seed are indicated above each image. The scales on the left images have units of millimeter and correspond to all photoacoustic images, which are all shown with 15 dB dynamic range, as indicated by the colorbar on the right. (b) $\text{Mean}\pm \text{one standard deviation}$ of the lateral FWHM of all seeds in the phantom.

For the seed located 1 cm from the light source, SLSC images have more apparent clutter compared to the DAS image, which is similarly true for the curvilinear image of this seed. In both cases, light was directed toward the probe, causing less sound attenuation by the air inside the catheter. The increased potential for multiple acoustic reflections among the seed, probe, and catheter boundary strongly indicates the source of this additional clutter. Figure 7(b) shows the mean lateral FWHM measurements from eight images for each $\text{seed}\pm \text{one standard deviation}$. The actual seed length (4.5 mm) is underestimated for the seeds located closer to the probe.

These beamforming results demonstrate that multiple seeds at a range of distances from the light source in curvilinear images can be visualized with similar contrast and no attenuation compensation required for the SLSC beamformer. On the other hand, seeds in linear images affected by multiple clutter sources (e.g., proximity to the light source, acoustic reverberations within the catheter, and acoustic reflections between the catheter and probe) are better visualized with the DAS beamformer, which is less sensitive to low-amplitude, spatially coherent clutter. These observations determined the beamformer choice for displaying the remaining photoacoustic images.

3.3.

Light Delivery in Scattering Media

The normalized fluence distribution of light from an elliptical surface area source is shown for three seed-like targets in Fig. 8 (left), representing cross-sectional views that might be obtained with the curvilinear and linear arrays (top and bottom, respectively). As expected, the targets farthest from the light source experience the least fluence, with at most $10\mathrm{J}/{\mathrm{cm}}^2\mathrm{per}\mathrm{J}$ experienced by the closest seed, as depicted in the $z\text{-}y$ plane. When a fourth seed was added to the simulation (Fig. 8, right), representing a partially out-of-plane seed for the linear array, light distribution to the original three seeds was reduced by one to two orders of magnitude, which indicates the difficulty with using fixed light attenuation models to improve target visualization with the DAS beamformer. In both simulations, the fluence delivered within a 1 cm radius from a light source was two to four orders of magnitude lower than the maximum fluence observed in the prostate tissue.

Fig. 8

Cross-sectional views of normalized fluence beyond the urethral wall in prostate tissue containing three (left) and four (right) seed-like targets in log compressed units of ${\mathrm{cm}}^{-2}$ [i.e., ${\log }_{10}$ ($\mathrm{J}/{\mathrm{cm}}^2\mathrm{per}\mathrm{J}$) of energy delivered].

A postoperative CT image of three brachytherapy seeds implanted in one canine prostate with geometry similar to the three-seed simulation is shown in Fig. 9 (top left). Seeds #2 and 3 are separated by $<2\mathrm{mm}$. A corresponding curvilinear US image is shown in Fig. 9 (top center). The urethra containing the 16-Fr urinary catheter is outlined with a circle. This catheter causes a shadow artifact in the curvilinear US image (i.e., the dark region extending from the urethra). Seeds #1 and 2, located at radial distances of 6 to 9 mm from the center of the urethra, are visible in this US image. A single SLSC photoacoustic image (top right) reveals the three implanted seeds, along with photoacoustic signals that correspond to the catheter location. The seed farthest from the light source (#1) was not visualized in the matching DAS image (not shown).

Fig. 9

Postoperative computed tomography (CT) image of three brachytherapy seeds in a canine prostate and corresponding US and photoacoustic SLSC and DAS images of the seeds, acquired after euthanasia. The photoacoustic images were overlaid on the US images and share the same scale indicated in the corresponding curvilinear or linear US image.

The three seeds are visualized in the linear US image of the same prostate, as shown in Fig. 9 (bottom left). In this image, seeds #2 and 3 are closely spaced and appear in the same plane, while seed #1 is partially outside of the image plane. When light was directed toward the in-plane seeds (#2 and 3), these seeds were more visible than the out-of-plane seed (#1) with DAS beamforming, as shown in Fig. 9 (bottom middle). When light was directed toward the out-of-plane seed, both this seed and the nearby in-plane seed (seeds #1 and 2, respectively) appeared in the DAS photoacoustic image (Fig. 9, bottom right). These results indicate that the side-firing fiber combined with amplitude-based beamforming can be used to selectively differentiate closely spaced targets.

The postoperative CT image of a brachytherapy seed implanted in the second canine prostate is shown in Fig. 10 (top left). The catheter in the urethra appears as a faint circle in the CT image, while the seed appears as a bright spot. The seed was implanted in the apex of the prostate, which is known to be difficult to visualize in the sagittal view of transrectal ultrasound images,^42,43 as demonstrated in the US image of Fig. 10, where the arrow points to the seed. The corresponding photoacoustic image, overlaid on the US image, contains the seed as well as signals in the urethra and associated reverberation artifacts. The comet-tail-like reverberation artifacts were less prevalent in matched DAS images (not shown) and not present in SLSC images when the fiber tip was outside of the image plane, as demonstrated in Figs. 5 and 9. Note that these reverberation artifacts (likely caused by the metal tip) have a different characteristic appearance from the catheter-related clutter in Fig. 5. The shadow artifact in the corresponding US image (i.e., the dark region caused by poor acoustic penetration through the catheter) was used to create a mask and set a threshold for signal rejection, resulting in a seed that is clearly differentiated from its surroundings. A similar mask may be used to hide the less prominent photoacoustic signals originating within the catheter (e.g., Fig. 9). The linear US image in Fig. 10 (bottom left) shows a longitudinal view of the same seed, which is better visualized and more easily distinguishable in the corresponding photoacoustic image (Fig. 10, bottom right).

Fig. 10

In vivo CT, US, and photoacoustic SLSC and DAS images of a brachytherapy seed in the apex of the prostate. The photoacoustic images were overlaid on the US images and share the same scale indicated in the corresponding curvilinear or linear US image.

4.1.

Considerations for Transurethral Illumination

To demonstrate the feasibility of transurethral photoacoustic imaging, brachytherapy seeds were visualized in a plastisol phantom and in two canine prostates with $2\mathrm{mJ}$ and 6 to 8 mJ per pulse, respectively, at distances of 5 to 30 mm and 6 to 9 mm from the light source, respectively. The two canine prostates were imaged in their native tissue environments, in the presence of competing endogenous and in vivo chromophores, such as blood, proteins, water, and lipids, indicating that a similar performance can be expected with transurethral photoacoustic imaging of tumors and contrast agents.

Monte Carlo simulations performed by El-Gohary et al.³³ revealed that the optimal optical beam geometry for imaging spherical tumors with a diameter of 2 to 10 mm was a $4\mathrm{mm}\times 20\mathrm{mm}$ rectangle. Figure 4(a) shows that the corresponding surface area ($80{\mathrm{mm}}^2$) is not practical with the design herein, given the physical constraints of catheter size, urethra diameter, tube wall thickness, fiber size, and a fixed NA of 0.39. In spite of these constraints, sufficient fluence was delivered to smaller targets ($0.8\mathrm{mm}\times 4.5\mathrm{mm}$ cylinders), as confirmed with our simulations and canine experiments. If larger surface areas are required, a light delivery mechanism similar to our prototype can be translated or rotated within the urethra and the resulting images may be compounded (as demonstrated in Fig. 5) to fully visualize the larger targets.

Several side-firing fiber prototypes have been designed and built for photoacoustic imaging by manipulating the fiber tip (e.g., relying solely on total internal reflection to direct light through the side of a fiber or adding an external mirror to an end-firing fiber) and fixing the modified fiber relative to a US transducer.^35,47 Our design differs from these approaches by combining the effects of internal and external reflection and separating the light delivery mechanism from the US transducer. Benefits of this novel design include directing light 90 deg to the fiber axis with minimal energy lost to significantly smaller or larger angles, utilizing more than one pieozoelectric element to receive photoacoustic signals, and obviating the need to maintain a fixed overlap between light emission and sound reception. This design is challenged by reverberation artifacts caused when the metal tip intersects the image plane, which is potentially useful for identifying the fiber tip inside the urethra. After tip identification, the artifacts could be removed with an image mask as demonstrated in Fig. 10 or mitigated by preventing intersection with the image plane as in Figs. 5 and 9.

The reported energy densities at the tube surface in the canine experiments (Figs. 9 and 10) exceeded the safety limit for skin (i.e., $100\mathrm{mJ}/{\mathrm{cm}}^2$ with a 1064 nm wavelength⁴⁶), but the main safety concern should be the energy density at the first laser-tissue contact interface (i.e., the urethra), which is likely lower than the reported values. Assumptions to achieve more relevant estimates include negligible energy loss between the quartz tube and catheter, negligible spacing between the fiber and catheter (and, therefore, negligible light diffraction in the urine), no deformation of the cylindrical catheter, and similar light refraction in the catheter and quartz tube given the similar refractive indices of their constituents (i.e., silicone and silicon dioxide, respectively^48,49). Based on these assumptions and Eq. (4), the energy density incident on the urethra with a 0.49 NA, 1 mm core diameter fiber, and 5.3 mm tube diameter (i.e., the outer diameter of the catheter) is 88 to $99\mathrm{mJ}/{\mathrm{cm}}^2$, which is within the limit for skin exposure. In addition, Fig. 4(b) shows that the energies used in the canine experiments would have been $<75\%$ of the safety limit if the fiber diameter were 1.5 mm instead of 1 mm. Moreover, the prostate and urethra could potentially withstand higher energy densities than the existing limit for skin.¹¹ The derived equations enable nonempirical surface area estimates that can be used to further explore safety limits and photon transport with Monte Carlo simulations.

4.2.

Importance of the Image Reconstruction Method

Consistent with previous results achieved with interstitial transperineal light delivery,^17,28 the contrast of DAS images generally decreased with increasing distance from the light source, a direct effect of the decreasing incident fluence, which produces lower photoacoustic signal amplitudes. Rotating the direction of the light source and combining the resulting SLSC photoacoustic images acquired with the curvilinear array is an alternative to depth-dependent optical attenuation compensation, which requires an optical distribution model that is subject to change with the implantation of additional brachytherapy seeds (e.g., Fig. 8). This model is difficult to develop when the target locations are unknown (e.g., tumors) or dynamic (e.g., brachytherapy seed implantation).

Thus, coherence-based beamforming is an essential component of the proposed photoacoustic system because it allows target locations to be directly compared with postoperative CT and curvilinear US B-mode images, without application of a light distribution model. Although more advanced summation approaches may be applied to improve the combined DAS images, they are not required for SLSC imaging as demonstrated in Fig. 5. Once targets have been located with the SLSC beamformer, the DAS beamformer would be more advantageous for providing isolation and discrimination of in-plane or out-of-plane targets relative to the US probe and near or far targets relative to the light source, as demonstrated in Fig. 9.

4.3.

Optical and Acoustic Resolution Limits

Comparative resolution was assessed with FWHM measurements, revealing minimal (0 to 3 mm) differences in target size with the DAS and SLSC beamformers. In curvilinear images, the seed diameter increased with distance from the probe [Fig. 6(c)] likely because of the increase in lateral beam width. The measured diameter was generally larger than the actual diameter because of the finite acoustic aperture size and the optical diffraction limited resolution. In linear images, the seed appeared longer with distance from the probe [Fig. 7(b)] likely because of the absence of aperture growth in the receive beamformer or the increasing area of light illumination incident on the seed as distance increased. This relationship between the optical illumination area and the displayed seed length, particularly within 0.5 to 1 cm from the urethra [Fig. 7(b)], is mitigated with optical scattering in tissue, as shown in the simulation (Fig. 8) and canine images (Figs. 9 and 10).