Optical-thermal light-tissue interactions during photoacoustic breast imaging.

Light-tissue interactions during photoacoustic imaging, including dynamic heat transfer processes in and around vascular structures, are not well established. A three-dimensional, transient, optical-thermal computational model was used to simulate energy deposition, temperature distributions and thermal damage in breast tissue during exposure to pulsed laser trains at 800 and 1064 nm. Rapid and repetitive temperature increases and thermal relaxation led to superpositioning effects that were highly dependent on vessel diameter and depth. For a ten second exposure at established safety limits, the maximum single-pulse and total temperature rise levels were 0.2°C and 5.8°C, respectively. No significant thermal damage was predicted. The impact of tissue optical properties, surface boundary condition and irradiation wavelength on peak temperature location and temperature evolution with time are discussed.


Introduction
Photoacoustic imaging (PAI) has become an increasingly popular imaging modality due to its ability to overcome tissue scattering effects, which are a key limiting factor in optical imaging. Thus, PAI achieves increased penetration depth through the use of acoustic detection while maintaining the ability to provide spectroscopic information for biochemical analysis. As a result, PAI has the potential to improve capability for a wide range of applications from diagnosis and monitoring of breast cancer [1] to assessment of traumatic brain injury [2]. Macroscopic PAI typically involves the use of short-pulse (5-10 ns), low frequency (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) lasers to irradiate tissue, producing rapid thermoelastic expansion of tissue chromophores. This causes an emission of acoustic waves which are detected by an ultrasonic transducer. The aforementioned benefits of photoacoustics align particularly well with imaging of tissue vasculature, which contain highly absorbing endogenous chromophores at near-infrared (NIR) wavelengths -oxy and deoxy-hemoglobin. Furthermore, PAI can provide real-time structural and functional information without the need for ionizing radiation, thus making it a promising modality for imaging of breast vasculature in which angiogenic masses a few centimeters deep can dominate the tumor tissue. While numerous studies have introduced or improved PAI techniques for medical diagnostics, relatively little work has been done to elucidate temperature response during PAI procedures [3,4] and the light-tissue interaction mechanisms that influence the potential for laser-induced thermal injury.

Photothermal effects during PAI
Two studies of note -one theoretical and one experimental -have been published that address photothermal processes induced by PAI systems incorporating pulsed lasers. Wang et al. developed a numerical model combining a diffusion equation based optical component with a bioheat-Eq. (-)based thermal component [3]. This model was used to simulate temperature rise in a highly absorbing exogenous target, yet details regarding the methods and results were limited. Results included two-dimensional temperature distributions within the target that exhibit minimal effects from light scattering and a temperature rise of up to 70 °C with a single pulse. Experimental measurements of photothermal processes in tissue during PAI procedures based on 532 nm pulsed laser irradiation have also been performed [4]. This study involved temperature measurements in phantoms with embedded graphite particles and arterial tissue from a rabbit aorta. Single pulses with radiant exposures of 30 to 85 mJ/cm 2 produced temperature rises of up to 0.7 to 5.0°C in the phantom and 60 mJ/cm 2 pulses produced a temperature rise of up to 1.1°C in arterial tissue. While these studies indicate that PAI laser pulses can produce significant temperatures in the presence of exogenous absorbers, these results have limited relevance to endogenous breast tissue imaging.

Pulsed near-infrared photothermal modeling
Several Monte Carlo (MC) and heat transfer models have been developed to predict temperature variations and thermal damage during pulsed laser irradiation of tissue. Jaunich et al. performed an extensive study using different laser wavelengths (1064 nm and 1552 nm) to evaluate the temperature rise that occurred after irradiating human and mouse skin with collimated and focused laser diameters (less than 100 μm) [5]. The data obtained was also compared to available experimental data, which substantiated the temperature distributions that resulted from the MC simulations. Similarly, Fanjul-Velez and Arce-Diego used simulations to monitor temperature distributions in vocal cord tissue at 1064 nm during endoscopic thermotherapy [6]. Pfefer et al. developed a combined Beer's Law optical model and finite difference thermal model to simulate temperature and thermal damage during a single 250-µs-long Holmium:YAG laser pulse, which compared well with experimental measurements [7]. In addition, Milanic and Majaron investigated the features of energy deposition and temperature profiles of Nd:YAP (1342 nm) and Nd:YAG (1064 nm) lasers in skin [8]. In this study, the benefit of using focused laser heating on the dermis without causing thermal damage to the epidermis was investigated. Although these studies provide minimal information directly relevant to PAI, they illustrate the utility of numerical modeling in elucidating photothermal processes during pulsed laser irradiation of tissue.

Optical modeling for photoacoustics
A variety of models have been developed to study photoacoustic techniques. An analytical model was developed by Maslov et al. to investigate the effect of spectral variations in fluence on oxygen saturation imaging [9]. Finite element models based on the diffusion approximation to the transport equation have also been developed [10]. These studies include a model-based approach to reconstruct chromophore distributions based on photoacoustic signals and measure blood oxygenation and hemoglobin concentration [11]. Several other studies have used a MC approach to evaluate light-tissue interactions during photoacoustic procedures and validate or explain experimental observations. Khokhlova et al. investigated the optical penetration depth and contrast in order to identify its full range of applications including the potential for PAI to detect even larger tumors if used in combination with diffuse optical tomography [12]. MC approaches have also been used in evaluating photoacoustic transducers, specifically, the effect of their surface reflectivity on fluence distribution, particularly near the tissue surface [13] and to identify the optimal geometry for 3D PAI of breast tumors [14,15]. Other MC studies have involved an analysis of absorption distribution for photoacoustic-based glucose monitoring [16] and an investigation of fluence distributions during photoacoustic microscopy [17]. However, there is a lack of literature describing predicted energy absorption and temperature rise in biological tissue during PAI.

Purpose and goals
The purpose of this study was to improve the understanding of optical-thermal response in tissue during photoacoustic diagnostic procedures, with a focus on breast imaging. The study had three main goals related to development, validation and implementation of a numerical model. The first was to modify existing optical and thermal codes into a three-dimensional computational model -including a MC light propagation algorithm and a finite difference heat transfer routine -which could simulate a train of laser pulses in a geometry representative of breast tissue. The second goal was to validate the model against data from the literature. The third goal was to predict the optical and thermal response of tissue for exposure levels representing established safety limits, and evaluate the influence of illumination wavelength, as well as size and depth of blood vessels. The results of this work provide insight into the utility of our model as well as photothermal response and safety for photoacoustic diagnostic devices.
In the literature addressing the OPs of breast tissue, there was good consistency for µ a and µ s ' at both wavelengths. At 800 nm, mean values obtained for µ a and µ s ' were 0.05 and 10 cm −1 , respectively [12]. The calculated means of µ a and µ s ' at 1064 nm were 0.2 and 9.0 cm −1 [19]. For the OPs of human skin, there were significant discrepancies among values from different sources. Reported µ a and µ s ' of literature OPs values for epidermis and dermis varied by several orders of magnitude. At 800 nm, mean OP values were approximately 1.0 cm −1 and 23.8 cm −1 for µ a and µ s ', respectively [20,21]. It should be noted that a value of 21 cm −1 was used for µ s ' because papers that measured the range between 800 and 1064 nm found that there was at most a 30% difference between values at 800 nm and 1064 nm [21,22]. Although values for the epidermis were collected and analyzed, these were considered to be less significant since the dermis is much thicker. At 1064 nm, data for µ a had an average of 0.5 cm −1 and thus this value was used in our simulations [21,23]. Values for the anisotropy coefficient (g) and refractive index (n) were also collected when available from the sources studied. OP values for blood were consistent for most of the values collected and agreed with the generally accepted results summarized by Prahl [24]. The values chosen for µ a and µ s' at 800 nm were 5 and 19 cm −1 , respectively [20]. Values chosen at 1064 nm were 3 cm −1 for µ a and 16 cm −1 for µ s ' [15].

Laser exposure limits for PAI
A key concern for the clinical application of PAI is the determination of laser safety based on maximum permissible exposures (MPE) recommended by the American National Standards Institute (ANSI) and International Electrotechnical Commission (IEC) [28,29]. MPEs are dependent on pulse duration and energy density, repetition rate, and duration of the train of pulses applied as well as tissue type exposed (i.e. skin versus the eye). The pulsed laser MPEs for skin -which are equivalent for both ANSI and IEC standards -were calculated for a laser pulse duration of 5-10 ns over the wavelength range of 400 to 1200 nm (Fig. 2). The graph on the left shows the maximum per-pulse permissible radiant exposure based on 5-10 ns pulses.
The graph on the right shows the maximum permissible irradiance (the "repetitive-pulse limit"), which is based on exposure durations that are around 1 second and above. Since ANSI divides the exposure duration into 100 nanoseconds to 10 seconds and 10 seconds to 3x10 4 seconds, these same divisions were used to divide the relevant exposure durations found in the literature. Additional data points reflect the values cited in the literature as ANSI MPEs and the values actually used in those studies (Fig. 2, left). There was not enough evidence to provide information about the irradiance-based limits cited in literature, so only values cited explicitly were given (Fig. 2, right). There was great variation in radiant exposure and irradiance values above and below the restrictions specified by ANSI and IEC in PAI studies. Some sources cited incorrect values for MPE, and many did not always use the maximum MPE allowed for skin. It is possible that the ANSI safety standards are not clearly understood and/or exposure levels far below the safety limits are commonly used due to a limited confidence in these values stemming from a lack of published data on damage thresholds for photoacoustic systems. In addition to single-pulse MPEs, the ANSI standard limits the average irradiance of pulse trains (Table 2). For a train of 10 ns laser pulses at 800 nm lasting 10 seconds or longer, ANSI restricts the maximum average (as opposed to peak) irradiance to 0.317 W/cm 2 , whereas for a similar scenario at 1064 nm the maximum average irradiance allowable is 1 W/cm 2 [30].

Optical-thermal numerical model
The modeling algorithm employed in this study has been well documented previously and is shown below (Fig. 3) [52,53]. A 3D material grid was generated initially to establish the location of the vessel and the layers with appropriate OPs (Table 1). Figure 4 shows the organization of the material grid with the embedded blood vessel and tissue layers. The skin layer was designed to be the combined thickness of epidermis and dermis equal to 0.2 cm. The breast tissue layer was 5.0 cm. The blood vessel was simulated as a small, shallow vessel with multiple diameters and depths. Note that depth of vessel is measured from the skin surface to the top of the blood vessel. Due to the size of the vessel, voxel sizes were chosen to be 0.01 cm in the x, y and z (depth) directions. The total grid size was 3 cm x 3 cm x 3 cm (deep) with 300 voxels in every direction yielding a total of 27 million voxels. This material grid served as an input to the MC portion of the program which simulates light propagation through the medium. This program calculates energy deposition and fluence distribution based on the input irradiance. All simulations were run on a supercomputer composed of 110 An explicit finite difference approach was used to solve the Pennes bioheat equation which uses the energy deposition (S) calculated from the MC algorithm (modified as described below to account for the pulsing of the laser) to compute the transient temperature distribution: where ρ is density (kg/m 3 ), c is specific heat (J/kg-ºC), ω b is perfusion rate (1/sec), T is temperature (ºC), T a is arterial temperature (ºC), t is time (seconds), and k is thermal conductivity (W/m-ºC). The subscript b was used in Eq. (1) to denote properties of blood. For side boundary nodes, an adiabatic boundary condition was applied, whereas a free convection heat transfer boundary condition (h = 50 W/m 2 -K) was applied for the top surface voxels. Values for perfusion rate, ω b , and arterial temperature, T a , were chosen to be 1.63 x10 −3 s −1 [54] and 37°C [55], respectively. The thermal properties used were based on each voxel's tissue type (Table 3) [56][57][58]. The Arrhenius rate process integral was used to calculate thermal damage [56]: where R is the universal gas constant (8.314 x10 3 J/mol-K) and the thermal damage parameters -frequency factor (A = 3.1 x10 98 s −1 ) and activation energy (E a = 6.28 x10 8 J/mol) -were based on skin data determined by Henriques [59]. This analysis indicated that no significant levels of thermal damage were produced for any of the simulated cases. To simulate the conditions of PAI, the source term in the thermal model was set to zero during all time steps for which no laser pulse was emitted. The energy in each pulse was delivered in a single time step. A repetition rate of 10 Hz and pulse train duration of 10 seconds were used. A time step of 2.5 ms was chosen based on stability criteria; it is also short enough to accurately model the rapid temperature rise that occurs with each laser pulse before heat diffusion becomes significant. While this approach might not accurately simulate the highly dynamic heat transfer processes involved during pulsed laser irradiation of individual micro-or nano-particles, it provides a reasonable estimate of heat transfer due to blood vessels as well as longer-time-scale dynamics that are relevant to laser pulse trains.

Validation of MC and thermal models
To verify that the MC algorithm used in this study was accurate, results from previous modeling studies were replicated. A study completed by Nemati et al. in 1998 was used to compare the effectiveness of the model in generating energy deposition rate data for three laser sources: diode (850 nm), Nd:YAG (1064 nm) and argon (500 nm) lasers [60]. Nemati et al. used an MC model to simulate the amount of energy deposition through 4 layers of the eye. All optical and thermal properties given were matched for validation. A beam diameter of 600 µm was used and a tissue-air refractive index of 1.0 was used at the boundary of the tissue. Reflectance, absorption and transmittance data presented in this paper were compared to the output from our MC model.
A prior study by Barton et al. was used to validate the thermal model calculations based on the given simulation parameters [61]. In the prior paper, a single blood vessel embedded in dermis was modeled and imaged using an OCT system. A 0.1 cm spot size, 1.0 second exposure time, and 390 mW beam energy were used as parameters of the beam in our model. The size of the vessel used was 0.012 cm in diameter at a depth of 0.03 cm. Energy deposition and temperature rise data from our model were compared to those from Barton et al.

Variation of laser and tissue parameters
Simulations were performed to evaluate the photothermal effects of blood vessel diameter and depth at ANSI MPE-limited radiant exposure and irradiance levels. MC simulations were performed for blood vessel diameters of 0.05, 0.1, 0.2 and 0.5 cm at depths of 0.1, 0.2, 0.4, 0.6, 0.8, and 1.0 cm. Irradiance levels were maintained for a beam diameter of 2.0 cm. All simulation parameters remained constant and were the same as those shown in Table 1 and  Table 3.
Simulations were conducted to investigate the effect of blood perfusion on temperature using the Pennes bioheat equation. For conditions of no perfusion, the perfusion rate parameter was set to 0 instead of the value given. Relatively small and large vessel sizes (0.05 cm and 0.2 cm diameter vessels) were simulated at depths of 0.1 and 0.2 cm. Otherwise, simulation parameters were the same as those used in the effect of laser and tissue parameter simulations.

Model validation
The outputs from the MC model used in this study were compared with those in the Nemati et al. 1998 study [60]. Specular and diffuse reflection and transmission data were compared for the three laser sources. Differences between the Nemati et al. data and our MC model were calculated. Differences in specular reflection, diffuse reflection and absorption were small, the greatest of which was seen for the Nd:YAG source with 0.47% error in diffuse reflection and 0.26% error in absorption. Percent error in transmission data was also consistently low for all three laser sources, except in the case of the argon laser. With respect to Nemati et al., there was a 5% percent error in the transmission data of the argon source, likely due to differences in boundary conditions implemented in the MC algorithm. Calculated energy deposition rate data from our MC program showed some discrepancy for shallower depths (less than 0.02 cm deep); however, at greater depths the rates of heat generation are in good agreement.
The energy deposition and temperature outputs from the MC and thermal models in this study were compared with the results from Barton et al. [61]. A set of percent error calculations was used to compare pseudo-random data points between the energy deposition and temperature contour plots generated in this study and the Barton et al. study. The results show very strong agreement, with an average difference between energy deposition data of up to 8.5% and an average difference between temperature data of up to 6.8% in the x and y positions of the contour plots. Discrepancies between the Barton et al. results and our model are likely due to differences in boundary conditions implemented, though all other aspects of the inputs to the program are the same based on the information given in the study. The results of these calculations provide validation of our photon propagation and heat transfer algorithms for a single blood vessel embedded in tissue being irradiated by a laser.

Energy deposition distributions
Light propagation simulations were performed for various blood vessel sizes and depths using a 2.0 cm diameter laser beam at 1064 nm and at ANSI/IEC MPE limits (Table 4). Energy deposition per pulse (S) was plotted as a function of depth along the center of the tissue region, where x = 1.5 cm and y = 1.5 cm (Fig. 5). Several basic trends are apparent in these data. The level of S within the skin and adipose layers was largely unaffected by vessel geometry, with values in the skin showing higher levels as well as more rapid decay in S with depth. The effect of light attenuation with depth causes both the exponential decrease in maximum S values for each vessel, as well as the rapid decay in S within each vessel -most noticeable in larger vessels (Fig. 5(c) and 5(d)). While the former effect is likely due to both scattering and absorption, the latter is dominated by the high absorption coefficient in the blood vessels. Additionally, with increased vessel size came a decrease in peak S values, likely due to the greater volume over which photons are absorbed in the vessels.
Energy deposition per pulse results at 1064 nm in the form of a two-dimensional x-z cross section centered along the y-axis are shown in Fig. 6. The difference in S between each layer (skin versus adipose tissue) is clearly evident and indicates a higher absorption at the skin surface versus deeper tissue. There is clear contrast in the energy deposition between the blood vessel and surrounding tissue, and a similar relationship with depth as shown in Fig. 5. While variations in S across individual vessels are not significant for the smaller (0.05 cm diameter) vessel, the larger vessel cases exhibit distributions that vary with both depth and lateral position, forming crescent shaped isolevels ( Fig. 6(b), 6(d), 6(f)). These variations in S within the vessel are qualitatively similar to those seen in prior modeling studies of selective photothermolysis [62], and are due to the combined effect of high absorption within the vessel and scattering in the surrounding tissue. These distributions, however, do not appear to agree with the results for instantaneous cross-sectional temperature distribution in a 5-µmdiameter spherical target simulated in a prior study of photoacoustics.

Temperature distributions
For all simulations in this section, exposure levels were based on ANSI/IEC MPE limits at 800 nm and 1064 nm (Table 4) for a 10 second pulse train and repetition rate of 10 Hz. Simulated temperature distributions as a function of depth through the center of the blood vessel for the first five pulses delivered in the 1064 nm case are shown in Fig. 7. Four different vessel geometries, including two vessel diameters (0.05 and 0.2 cm) and two depths (0.1 and 0.4 cm) are included. The results show both a strong superpositioning effect from sequential pulses as well as an evolution in temperature profile at the blood vessel edge from a sharp gradient to a more gradual one, due to heat diffusion from the vessel into the surrounding tissue. Similarities with the energy deposition data in Fig. 5 are also apparent. For example, the smaller diameter vessel (d = 0.05 cm) showed a slightly higher first-pulse temperature rise than the larger vessel (d = 0.2 cm). However, after five pulses the maximum temperatures for these vessels was roughly equivalent, due to the difference in thermal relaxation time between the two vessel sizes. The greater rate of temperature rise in shallow vessels was due to the higher energy deposition levels within the vessel as well as in the perivascular dermis (as compared to the deeper vessels which have lower energy deposition levels and are surrounded by low-absorption adipose tissue). It is also notable that the firstpulse temperature in both deeper vessels was larger than in the corresponding dermis region, yet by the fifth pulse, the temperature in the dermis had surpassed that in the vessel. This is due to the smaller size (and geometry) of the vessels relative to the irradiated skin layer as well as the limitation in heat loss represented by the free convective surface boundary, over which relatively little heat transfer occurs compared to conduction within the tissue. Temperature versus depth plots along the vessel center after 10 to 100 pulses at 1064 nm are shown in Fig. 8. Substantial variations in thermal profiles with pulse train exposure time as well as vessel diameter and depth are apparent. Further evolution of temperature distributions away from the early pulse profiles that resembled the energy deposition distribution can also be seen (Fig. 5). Over time, the insulating effect of the convective surface boundary becomes increasingly significant, resulting in the near-surface temperature plateau in Fig. 8(a), and facilitating the large subsurface peak in Fig. 8(c). At the end of the pulse train, the large vessel case yields a higher peak temperature in comparison to the smaller vessel (42.8ºC compared to 41.4ºC), and a much more significant differential with the surface temperature. This indicates that for longer exposure durations (on the order of 1 sec and longer), larger vessel sizes will have a greater impact on the temperature rise and subsequent potential damage occurring at the location of the blood vessel. The deep vessel cases result in nearly identical surface temperatures, but greater temperatures are produced at the larger vessel (39.1ºC vs. 38.4ºC at laser shut-off) due to the longer thermal relaxation time for larger vessels. Temperatures at the end of the pulse train are shown as a function of depth for 800 nm and 1064 nm wavelengths in Fig. 9 and Fig. 10, respectively. These results include vessels of different depths (0.1, 0.2, 0.4, and 1.0 cm) and diameters (0.05, 0.1 and 0.2 cm). For the 800 nm cases (Fig. 9), a maximum of 2°C temperature rise was produced. At this wavelength it is difficult to discriminate the temperature peak of the shallowest vessels (z = 0.1 and 0.2 cm). Even for the largest vessel case, the additive thermal effect of the 0.1-cm-deep blood vessel is only about 1.0°C. These results demonstrate the strong effect of conduction away from the vessels as well as the significance of energy deposition in the dermis combined with the insulating effect of the surface boundary. At 1064 nm, the temperatures produced by individual vessels are more pronounced (up to 5.8°C rise). Large, shallow vessels (z = 0.1 cm) showed the greatest temperature rise, due to significant light absorption and limited heat diffusion across the tissue surface. These vessels also represent the only cases in which the location of maximum temperature occurred below the surface. It is notable that the additive effect of small, shallow vessels is limited to fractions of a degree despite the fact that energy deposition levels in these vessels were up to four times greater than that of the surrounding skin. The difference between this result and that for the largest diameter vessel is an indication of the strong effect of vessel size on thermal relaxation. The deepest peak simulated (at 1.0 cm) is difficult to distinguish from the background, indicating that negligible temperature rise -in terms of safety, not necessarily photoacoustic signal generation -is produced at this vessel depth.   Two-dimensional spatial distributions of temperature (Fig. 11) for 1064 nm irradiation are presented for two different vessel diameters (0.05 and 0.2 cm) at three depths (0.1, 0.2 and 0.4 cm) at an x-z cross section at y = 1.5 cm. These graphs show a region of increased temperature in the skin directly below the beam, corresponding to the region of increased energy deposition (Fig. 6). The shallowest vessels ( Fig. 6(a) and 6(b)) produced high temperatures extending from the vessel through the skin layer to the tissue surface. This seemingly directional propagation of heat was due to the limited heat transfer that occurred across the convective boundary, whereas conduction into the large region of cooler tissue in deeper regions minimized heat accumulation below the vessel. For the 0.2 cm diameter vessel, the region of substantial temperature increase due to the vessel in the skin layer was approximately 0.5 cm in width. The temperature difference between the center and outer regions of the skin layer decreased sharply with vessel depth. The effect of the small vessel became negligible at greater depths, whereas the effect of the larger vessel is apparent to a depth of 0.5 cm.
Surface transient temperature distributions and maximum vessel temperatures are shown in Fig. 12. These graphs present data for 1064 nm irradiation with 0.05 or 0.2 cm diameter vessels and z = 0.1, 0.2, 0.4 and 1.0 cm cases. Inset graphs document temperature variation over half a second of irradiation. In these graphs, the maximum vessel temperatures exhibit a saw-tooth shape due to the effect of conduction away from the vessel between pulses along with thermal superpositioning of sequential pulses. The thin vessel cases exhibit sharper temperature rise and more rapid thermal decay after each pulse, due to greater energy deposition and a shorter thermal relaxation time. While thicker vessels have a lower average energy deposition rate -and thus a lower per-pulse temperature rise -they show a higher mean rate of temperature increase due to their longer thermal relaxation time. For surface locations, a stair-step transient profile is seen due to the relatively slow dissipation of heat compared to vessel structures. Figure 12 also provides predictions of temperature decay after the end of the pulse train, indicating that different cooling phases exist: an initial phase in which vessel temperatures decay to the same level as non-vessel tissue regions, and a longer phase in which heat dissipation occurs through the broader tissue volume and across the tissue surface. In analyses of damage thresholds, this temperature decay rate may be significant, as thermal damage -which is an exponential function of temperature and linear function of time, according to the Arrhenius rate process equation [56] -may accumulate for several seconds after the end of a pulse train.

Conclusion
The results presented here provide novel quantitative insights into optical-thermal laser-tissue interactions during PAI. Using idealized tissue geometries in a three-dimensional model we have demonstrated the influence of irradiation wavelength and tissue geometry parameters (vessel diameter and depth). This work also illustrates key dynamic processes involved in irradiation with a train of laser pulses, including thermal relaxation and superpositioning, as well as the effect of the surface boundary. Maximum per-pulse temperature rise was 0.2°C and the overall maximum temperature predicted for a 10 second exposure was less than 42.8°C. Arrhenius calculations indicated no significant thermal damage. Finally, our findings illustrate the utility of computational modeling for elucidating processes relevant to the safety and effectiveness of this emerging technology. In the future, we will apply the model to investigate threshold damage cases and potential limitations of standards for photoacousticbased diagnostic devices.

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