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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 5, Iss. 3 — Mar. 1, 2014
  • pp: 832–847
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Optical-thermal light-tissue interactions during photoacoustic breast imaging

Taylor Gould, Quanzeng Wang, and T. Joshua Pfefer  »View Author Affiliations


Biomedical Optics Express, Vol. 5, Issue 3, pp. 832-847 (2014)
http://dx.doi.org/10.1364/BOE.5.000832


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Abstract

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.

© 2014 Optical Society of America

1. Introduction

1.1 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

3. Z. Wang, S. Ha, and K. Kim, “Evaluation of finite element based simulation model of photoacoustics in biological tissues,” Proc. SPIE 8320, 83201L (2012). [CrossRef]

]. 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

4. S. Sethuraman, S. R. Aglyamov, R. W. Smalling, and S. Y. Emelianov, “Remote temperature estimation in intravascular photoacoustic imaging,” Ultrasound Med. Biol. 34(2), 299–308 (2008). [CrossRef] [PubMed]

]. 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/cm2 produced temperature rises of up to 0.7 to 5.0°C in the phantom and 60 mJ/cm2 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.

1.2 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

5. M. Jaunich, S. Raje, K. Kim, K. Mitra, and Z. Guo, “Bio-heat transfer analysis during short pulse laser irradiation of tissues,” Int. J. Heat Mass Transfer 51(23-24), 5511–5521 (2008). [CrossRef]

]. 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

6. F. Fanjul-Vélez and J. L. Arce-Diego, “Modeling thermotherapy in vocal cords novel laser endoscopic treatment,” Lasers Med. Sci. 23(2), 169–177 (2008). [CrossRef] [PubMed]

]. 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

7. T. J. Pfefer, K. F. Chan, D. X. Hammer, and A. J. Welch, “Dynamics of pulsed holmium:YAG laser photocoagulation of albumen,” Phys. Med. Biol. 45(5), 1099–1114 (2000). [CrossRef] [PubMed]

]. 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

8. M. Milanič and B. Majaron, “Energy deposition profile in human skin upon irradiation with a 1,342 nm Nd:YAP laser,” Lasers Surg. Med. 45(1), 8–14 (2013). [CrossRef] [PubMed]

]. 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.

1.3 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

9. K. Maslov, H. F. Zhang, and L. V. Wang, “Effects of wavelength-dependent fluence attenuation on the noninvasive photoacoustic imaging of hemoglobin oxygen saturation in subcutaneous vasculature in vivo,” Inverse Probl. 23(6), S113–S122 (2007). [CrossRef]

]. Finite element models based on the diffusion approximation to the transport equation have also been developed [10

10. B. T. Cox, S. R. Arridge, K. P. Köstli, and P. C. Beard, “Two-dimensional quantitative photoacoustic image reconstruction of absorption distributions in scattering media by use of a simple iterative method,” Appl. Opt. 45(8), 1866–1875 (2006). [CrossRef] [PubMed]

]. These studies include a model-based approach to reconstruct chromophore distributions based on photoacoustic signals and measure blood oxygenation and hemoglobin concentration [11

11. J. Laufer, C. Elwell, D. Delpy, and P. Beard, “In vitro measurements of absolute blood oxygen saturation using pulsed near-infrared photoacoustic spectroscopy: accuracy and resolution,” Phys. Med. Biol. 50(18), 4409–4428 (2005). [CrossRef] [PubMed]

]. 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

12. T. D. Khokhlova, I. M. Pelivanov, V. V. Kozhushko, A. N. Zharinov, V. S. Solomatin, and A. A. Karabutov, “Optoacoustic imaging of absorbing objects in a turbid medium: ultimate sensitivity and application to breast cancer diagnostics,” Appl. Opt. 46(2), 262–272 (2007). [CrossRef] [PubMed]

]. 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

13. B. Tavakoli, P. D. Kumavor, A. Aguirre, and Q. Zhu, “Effect of ultrasound transducer face reflectivity on the light fluence inside a turbid medium in photoacoustic imaging,” J. Biomed. Opt. 15(4), 046003 (2010). [CrossRef] [PubMed]

] and to identify the optimal geometry for 3D PAI of breast tumors [14

14. S. A. Ermilov, M. P. Fronheiser, H. P. Brecht, R. Su, A. Conjusteau, K. Mehta, P. Otto, and A. A. Oraevksy, “Development of Laser Optoacoustic and Ultrasonic Imaging System for breast cancer utilizing handheld array probes,” Proc. SPIE 7177, 717703 (2009). [CrossRef]

, 15

15. M. A. Yaseen, S. A. Ermilov, H.-P. Brecht, R. Su, A. Conjusteau, M. Fronheiser, B. A. Bell, M. Motamedi, and A. A. Oraevsky, “Optoacoustic imaging of the prostate: development toward image-guided biopsy,” J. Biomed. Opt. 15(2), 021310 (2010). [CrossRef] [PubMed]

]. Other MC studies have involved an analysis of absorption distribution for photoacoustic-based glucose monitoring [16

16. Z. Zhao and R. A. Myllyla, “Photoacoustic blood glucose and skin measurement based on optical scattering effect,” Proc. SPIE 4707, 153–157 (2002). [CrossRef]

] and an investigation of fluence distributions during photoacoustic microscopy [17

17. Z. Xie, L. V. Wang, and H. F. Zhang, “Optical fluence distribution study in tissue in dark-field confocal photoacoustic microscopy using a modified Monte Carlo convolution method,” Appl. Opt. 48(17), 3204–3211 (2009). [CrossRef] [PubMed]

]. However, there is a lack of literature describing predicted energy absorption and temperature rise in biological tissue during PAI.

1.4 Purpose and goals

2. Methods

2.1 Tissue optical properties (OPs)

In the literature addressing the OPs of breast tissue, there was good consistency for µa and µs’ at both wavelengths. At 800 nm, mean values obtained for µa and µs’ were 0.05 and 10 cm−1, respectively [12

12. T. D. Khokhlova, I. M. Pelivanov, V. V. Kozhushko, A. N. Zharinov, V. S. Solomatin, and A. A. Karabutov, “Optoacoustic imaging of absorbing objects in a turbid medium: ultimate sensitivity and application to breast cancer diagnostics,” Appl. Opt. 46(2), 262–272 (2007). [CrossRef] [PubMed]

]. The calculated means of µa and µs’ at 1064 nm were 0.2 and 9.0 cm−1 [19

19. A. Pifferi, J. Swartling, E. Chikoidze, A. Torricelli, P. Taroni, A. Bassi, S. Andersson-Engels, and R. Cubeddu, “Spectroscopic time-resolved diffuse reflectance and transmittance measurements of the female breast at different interfiber distances,” J. Biomed. Opt. 9(6), 1143–1151 (2004). [CrossRef] [PubMed]

]. For the OPs of human skin, there were significant discrepancies among values from different sources. Reported µa and µs’ 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 µa and µs’, respectively [20

20. I. Fredriksson, M. Larsson, and T. Strömberg, “Measurement depth and volume in laser Doppler flowmetry,” Microvasc. Res. 78(1), 4–13 (2009). [CrossRef] [PubMed]

, 21

21. E. Salomatina, B. Jiang, J. Novak, and A. N. Yaroslavsky, “Optical properties of normal and cancerous human skin in the visible and near-infrared spectral range,” J. Biomed. Opt. 11(6), 064026 (2006). [CrossRef] [PubMed]

]. It should be noted that a value of 21 cm−1 was used for µs’ 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

21. E. Salomatina, B. Jiang, J. Novak, and A. N. Yaroslavsky, “Optical properties of normal and cancerous human skin in the visible and near-infrared spectral range,” J. Biomed. Opt. 11(6), 064026 (2006). [CrossRef] [PubMed]

, 22

22. C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, “Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique,” Phys. Med. Biol. 43(9), 2465–2478 (1998). [CrossRef] [PubMed]

]. 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 µa had an average of 0.5 cm−1 and thus this value was used in our simulations [21

21. E. Salomatina, B. Jiang, J. Novak, and A. N. Yaroslavsky, “Optical properties of normal and cancerous human skin in the visible and near-infrared spectral range,” J. Biomed. Opt. 11(6), 064026 (2006). [CrossRef] [PubMed]

, 23

23. J. M. Schmitt, “Optical Measurement of blood oxygenation by implantable telemetry,” (1986).

]. 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

24. S. Prahl, “Optical Absorption of Hemoglobin,” http://omlc.ogi.edu/spectra/hemoglobin/index.html2013.

]. The values chosen for µa and µs’ at 800 nm were 5 and 19 cm−1, respectively [20

20. I. Fredriksson, M. Larsson, and T. Strömberg, “Measurement depth and volume in laser Doppler flowmetry,” Microvasc. Res. 78(1), 4–13 (2009). [CrossRef] [PubMed]

]. Values chosen at 1064 nm were 3 cm−1 for µa and 16 cm−1 for µs’ [15

15. M. A. Yaseen, S. A. Ermilov, H.-P. Brecht, R. Su, A. Conjusteau, M. Fronheiser, B. A. Bell, M. Motamedi, and A. A. Oraevsky, “Optoacoustic imaging of the prostate: development toward image-guided biopsy,” J. Biomed. Opt. 15(2), 021310 (2010). [CrossRef] [PubMed]

].

2.2 Laser exposure limits for PAI

2.3 Optical-thermal numerical model

The modeling algorithm employed in this study has been well documented previously and is shown below (Fig. 3
Fig. 3 MC and thermal code processes including inputs (in white), outputs (in gray), and parts of the algorithm (in black).
) [52

52. T. J. Pfefer, J. K. Barton, D. J. Smithies, T. E. Milner, J. S. Nelson, M. J. C. van Gemert, and A. J. Welch, “Modeling laser treatment of port wine stains with a computer-reconstructed biopsy,” Lasers Surg. Med. 24(2), 151–166 (1999). [CrossRef] [PubMed]

, 53

53. T. J. Pfefer, D. J. Smithies, T. E. Milner, M. J. C. van Gemert, J. S. Nelson, and A. J. Welch, “Bioheat transfer analysis of cryogen spray cooling during laser treatment of port wine stains,” Lasers Surg. Med. 26(2), 145–157 (2000). [CrossRef] [PubMed]

]. A 3D material grid was generated initially to establish the location of the vessel and the layers with appropriate OPs (Table 1). Figure 4
Fig. 4 MC model structure including vessel and incident laser beam.
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 IBM System x3650 M2 8-core diskless computer nodes, 170 TB of shared network hard drive space and 10 Gbps Ethernet inter-node communications. The approximate model run times were 2-4 hours for the optical model (20 million photons) and 24-28 hours for the thermal model.

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:

ρcTt=k(2Tx2+2Ty2+2Tz2)+ωbcbρb(TaT)+S
(1)

where ρ is density (kg/m3), c is specific heat (J/kg-ºC), ωb is perfusion rate (1/sec), T is temperature (ºC), Ta 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/m2-K) was applied for the top surface voxels. Values for perfusion rate, ωb, and arterial temperature, Ta, were chosen to be 1.63 x10−3 s−1 [54

54. J. Jiao and Z. Guo, “Thermal interaction of short-pulsed laser focused beams with skin tissues,” Phys. Med. Biol. 54(13), 4225–4241 (2009). [CrossRef] [PubMed]

] and 37°C [55

55. H. H. Pennes, “Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm,” J. Appl. Physiol. 1(2), 93–122 (1948). [PubMed]

], respectively. The thermal properties used were based on each voxel’s tissue type (Table 3

Table 3. Thermal properties used in simulations

table-icon
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) [56

56. A. R. Moritz and F. C. Henriques, “Studies of Thermal Injury: II. The Relative Importance of Time and Surface Temperature in the Causation of Cutaneous Burns,” Am. J. Pathol. 23(5), 695–720 (1947). [PubMed]

58

58. F. A. Duck, Physical Properties of Tissue: A Comprehensive Reference Network (Academic Press, London, 1990).

].

The Arrhenius rate process integral was used to calculate thermal damage [56

56. A. R. Moritz and F. C. Henriques, “Studies of Thermal Injury: II. The Relative Importance of Time and Surface Temperature in the Causation of Cutaneous Burns,” Am. J. Pathol. 23(5), 695–720 (1947). [PubMed]

]:
Ω(t)=A0teEa/RT(τ)dτ
(2)
where R is the universal gas constant (8.314 x103 J/mol-K) and the thermal damage parameters - frequency factor (A = 3.1 x1098 s−1) and activation energy (Ea = 6.28 x108 J/mol) – were based on skin data determined by Henriques [59

59. F. C. Henriques Jr., “Studies of Thermal Injury; The predictability and the significance of thermally induced rate processes leading to irreversible epidermal injury,” Arch. Pathol. (Chic) 43(5), 489–502 (1947). [PubMed]

]. 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.

2.3.1 Validation of MC and thermal models

A prior study by Barton et al. was used to validate the thermal model calculations based on the given simulation parameters [61

61. J. K. Barton, A. Rollins, S. Yazdanfar, T. J. Pfefer, V. Westphal, and J. A. Izatt, “Photothermal coagulation of blood vessels: a comparison of high-speed optical coherence tomography and numerical modelling,” Phys. Med. Biol. 46(6), 1665–1678 (2001). [CrossRef] [PubMed]

]. 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.

2.3.2 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.

3. Results and discussion

3.1 Model validation

The outputs from the MC model used in this study were compared with those in the Nemati et al. 1998 study [60

60. B. Nemati, A. Dunn, A. J. Welch, and H. G. Rylander, “Optical model for light distribution during transscleral cyclophotocoagulation,” Appl. Opt. 37(4), 764–771 (1998). [CrossRef] [PubMed]

]. 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

61. J. K. Barton, A. Rollins, S. Yazdanfar, T. J. Pfefer, V. Westphal, and J. A. Izatt, “Photothermal coagulation of blood vessels: a comparison of high-speed optical coherence tomography and numerical modelling,” Phys. Med. Biol. 46(6), 1665–1678 (2001). [CrossRef] [PubMed]

]. 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.

3.2 Energy deposition distributions

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
Fig. 6 Energy deposition per pulse distributions (y-z cross sections) at ANSI MPE limits for 1064 nm irradiation. Graphs show two different vessel diameters of 0.05 cm (a, c, and e) and 0.2 cm (b, d, and f) at depths of 0.1 (a and b), 0.2 cm (c and d), and 0.4 cm (e and f).
. 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

62. D. J. Smithies, M. J. van Gemert, M. K. Hansen, T. E. Milner, and J. S. Nelson, “Three-dimensional reconstruction of port wine stain vascular anatomy from serial histological sections,” Phys. Med. Biol. 42(9), 1843–1847 (1997). [CrossRef] [PubMed]

], 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-µm-diameter spherical target simulated in a prior study of photoacoustics.

3.3 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
Fig. 7 Temperature with depth for first five pulses delivered to tissue for the 1064 nm perfusion case. Data shown for two different vessel diameters of 0.05 cm (a and b) and 0.2 cm (c and d) at two different depths of 0.1 cm (a and c) and 0.4 cm (b and d). Plots correspond to Media 1 through 4: Media 1 corresponds to plot a, Media 2 corresponds to plot b, Media 3 corresponds to plot c, and Media 4 corresponds to plot d.
. 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 first-pulse 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
Fig. 8 Temperature as a function of depth at various pulses leading up to laser shut-off (10 seconds, 100 pulses) at ANSI MPE limits under perfusion conditions at 1064 nm. Data shown for two different vessel diameters of 0.05 cm (a and b) and 0.2 cm (c and d) at two different depths of 0.1 cm (a and c) and 0.4 cm (b and d). Plots correspond to Media 5 through 8: Media 5 corresponds to plot a, Media 6 corresponds to plot b, Media 7 corresponds to plot c, and Media 8 corresponds plot d.
. 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
Fig. 9 Temperature distributions at termination of the 10 second pulse train at ANSI/IEC MPE limits for an irradiation wavelength of 800 nm. Profiles through the center of the tissue for vessel depths of 0.1, 0.2, 0.4, and 1.0 cm. Vessel diameters include a.) 0.05 cm, b.) 0.2 cm and c.) 0.5 cm.
and Fig. 10
Fig. 10 Temperature distributions at termination of the 10 second pulse train at ANSI/IEC MPE limits for an irradiation wavelength of 1064 nm. Profiles through the center of the tissue for vessel depths of 0.1, 0.2, 0.4, and 1.0 cm. Vessel diameters include a.) 0.05 cm, b.) 0.2 cm and c.) 0.5 cm.
, 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
Fig. 11 X-z cross-sections of temperature distributions at the center of the beam at laser shut-off (1064 nm). Graphs show vessel diameters of 0.05 cm (a, c, and e) and 0.2 cm (b, d, and f) at depths of 0.1 (a and b), 0.2 (c and d) and 0.4 cm (e and f). Colorbar on the right-hand side of each graph shows temperature-based color range. Plots correspond to Media 9 through 14: Media 9 corresponds to plot a, Media 10 corresponds to plot b, Media 11 corresponds to plot c, Media 12 corresponds to plot d, Media 13 corresponds to plot e, and Media 14 corresponds to plot f.
) 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
Fig. 12 Transient temperature distributions for a.) 0.05 cm and b.) 0.2 cm blood vessel cases at a variety of depths (0.1, 0.2, 0.4 and 1.0 cm) at 1064 nm. Temperature at the tissue surface and maximum temperature in the vessel are shown. Insets highlight results for the 0.1 and 0.2 cm deep vessels during the initial 0.5 s of exposure.
. 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

56. A. R. Moritz and F. C. Henriques, “Studies of Thermal Injury: II. The Relative Importance of Time and Surface Temperature in the Causation of Cutaneous Burns,” Am. J. Pathol. 23(5), 695–720 (1947). [PubMed]

] - may accumulate for several seconds after the end of a pulse train.

4. 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 photoacoustic-based diagnostic devices.

Disclaimer

The mention of commercial products, their sources, or their use in connection with material reported herein is not to be construed as either an actual or implied endorsement of such products by the Department of Health and Human Services.

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OCIS Codes
(140.3360) Lasers and laser optics : Laser safety and eye protection
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.3830) Medical optics and biotechnology : Mammography
(170.5120) Medical optics and biotechnology : Photoacoustic imaging
(350.5340) Other areas of optics : Photothermal effects

ToC Category:
Photoacoustic Imaging and Spectroscopy

History
Original Manuscript: December 13, 2013
Revised Manuscript: January 26, 2014
Manuscript Accepted: January 29, 2014
Published: February 24, 2014

Citation
Taylor Gould, Quanzeng Wang, and T. Joshua Pfefer, "Optical-thermal light-tissue interactions during photoacoustic breast imaging," Biomed. Opt. Express 5, 832-847 (2014)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-5-3-832


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References

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  20. I. Fredriksson, M. Larsson, and T. Strömberg, “Measurement depth and volume in laser Doppler flowmetry,” Microvasc. Res.78(1), 4–13 (2009). [CrossRef] [PubMed]
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