Optical properties of ocular tissues in the near infrared region

Transcription

1 Lasers Med Sci (2007) 22: DOI /s y ORIGINAL ARTICLE Dhiraj K. Sardar. Guang-Yin Swanland. Raylon M. Yow. Robert J. Thomas. Andrew T. C. Tsin Optical properties of ocular tissues in the near infrared region Received: 13 April 2006 / Accepted: 19 September 2006 / Published online: 2 December 2006 # Springer-Verlag London Limited 2006 Abstract Near infrared characterization of optical properties of aqueous humor and vitreous humor of healthy human and bovine eyes has been performed. The indices of refraction (n) of these ocular tissues were determined using a Michelson interferometer. The total diffuse reflection (R d ) and total transmission (T t ) measurements had been taken for individual ocular tissue by using a double-integrating sphere setup and infrared laser diodes. The inverse adding doubling (IAD) computational method based on the diffusion approximation and radiative transport theory was applied to the measured values of n, R d, and T t to calculate the optical absorption and scattering coefficients of the human and bovine ocular tissues. The scattering anisotropy value was determined by iteratively running the IAD method program and a Monte Carlo simulation of light tissue interaction until the minimum difference in experimental and computed value for T t was realized. A comparison between the optical characterization of human and bovine ocular samples was also made. Keywords Human ocular tissues. Bovine ocular tissues. Optical properties. Infrared laser wavelengths D. K. Sardar (*). G.-Y. Swanland. R. M. Yow Department of Physics and Astronomy, The University of Texas at San Antonio, San Antonio, TX , USA dsardar@utsa.edu Tel.: Fax: R. J. Thomas Air Force Research Laboratory, Brooks City-Base, TX , USA A. T. C. Tsin Department of Biology, The University of Texas at San Antonio, San Antonio, TX , USA Introduction Almost immediately after the advent of the first laser in 1960, the medical applications of optical radiation, especially for diagnosis and treatment of ocular diseases, had begun. The use of various lasers in medical applications has steadily increased over the past several years. The fundamental optical properties such as scattering, absorption, and refractive index of tissues influence the distribution and propagation of photons in laser-irradiated tissues. Therefore, understanding the fundamental optical properties of tissues has become imperative. There had been some studies in the past on ocular tissues [1 9]. However, to the best of our knowledge, a systematic investigative comparison of the optical properties of human and bovine ocular tissue components has not been performed, particularly, in the near infrared region where the eye changes from strongly transmissive to strongly absorbing [7]. Construction of diagnostic or imaging devices for ocular diseases in the spectral range of interest will require a detailed knowledge of optical parameters to predict performance and effectiveness. Also, the prediction of safe exposure limits requires a quantitative knowledge of these parameters for predicting damage thresholds to various components of the eye [10 12]. In this article, we therefore present a characterization and a comparison of the refractive indices and the optical absorption and scattering properties of aqueous humor and vitreous humor from a healthy human eye and healthy bovine eye. Due to the complex nature of the biological tissues, both the absorption and scattering properties of ocular tissues must be understood thoroughly for laser dosimetry and medical applications of lasers. The quantitative distribution of light intensity in biological media can be obtained from the solution of the Chandrasekhar s radiative transport equation [13]: Z diðr; s Þ ds ¼ ðμ a þ μ s ÞIðr; s Þþ μ s 4π 4π ps; ð s 0 ÞIðr; s 0 ÞdΩ 0 ; (1)

2 where I(r,s) is the intensity per unit solid angle at the target location r in the direction s (s is the directional unit vector), μ a and μ s are the absorption coefficient and scattering coefficient, respectively, p(s,s ) is the phase function, representing scattering contribution from the direction s to s,and Ω is the solid angle. The first term on the right-hand side of Eq. 1 represents the loss in intensity per unit length in direction s due to absorption and scattering, while the second term denotes the gain per unit length due to scattering from direction s. An analytical solution to Eq. 1 has been difficult to achieve due to the complex nature of biological media and their inherent inhomogeneities and irregularities in the physical shape. However, an approximate solution can be obtained by assuming homogeneity and regular geometry of the medium. Although the functional form of the phase function in biological media is generally unknown for many practical applications, the Henyey Greenstein formula, Eq. 2, provides a good approximation of the phase function for turbid media [14]: pðνþ ¼ 1 1 g 2 ; (2) 4π ð1 þ g 2 3=2 2gνÞ where ν=cos(θ), and θ is the angle between s and s. The Henyey Greenstein phase function depends only on the scattering anisotropy coefficient g, which is defined as the mean cosine of the scattering angle and expressed as follows: R 4π g ¼ p ð ν Þν dω0 R 4π pðν : (3) ÞdΩ0 The value of g ranges from 1 for the complete backward scattering to +1 for the complete forward scattering. The anisotropy value of 0 corresponds to isotropic scattering. The phase function, p(ν), is normalized so that its integral over all directions becomes unity. Recently, Prahl et al. [14] have introduced an important numerical approach known as the inverse adding doubling (IAD) method to solve the transport equation, Eq. 1. The IAD method [14] in conjunction with the Monte Carlo (MC) simulation technique [15 17] is currently being used to obtain a more accurate estimate of optical properties of turbid media such as biological samples. Details of the IAD method have been previously provided by Prahl et al. [14]. Nonetheless, to maintain continuity in this article, a short synopsis of the IAD model is provided in this study. Two dimensionless quantities used in the entire IAD method are albedo (a) and optical depth (τ), which are defined as follows: a ¼ μ ðμ s þ μ a Þ (4) and where t is the physical thickness of the sample measured in centimeter. Values of n, g, R d,andt t are input to the IAD computer program which returns the values of a and τ. The values of these dimensionless quantities are then applied to Eqs. 4 and 5 to solve for μ s and μ a of the human and bovine ocular tissues. Further details of the IAD method can be found in the work of Prahl et al. [14]. According to Prahl et al. [14], the validity of the IAD method for samples with comparable absorption and scattering coefficients is especially important because other methods based on only diffusion approximation are inadequate [18]. They have also stated that because both anisotropy phase function and Fresnel reflection at boundaries are accurately approximated, the IAD method is well suited to optical measurements for biological materials sandwiched between two glass slides. The values of the absorption, scattering, and scattering anisotropy coefficients are needed for the approximate solution to the transport equation. Therefore, appropriate experimental methods are necessary to measure n, R d,and T t that in turn produce the values of absorption, scattering, and scattering anisotropy coefficients. In this article, we present a characterization of optical properties of human and bovine ocular tissues at 980, 1,310, and 1,530 nm. Materials and methods Procurement of human and bovine eyes 47 One pair of whole human eyes was provided by the National Disease Research Interchange (NDRI #55305, Philadelphia, PA, USA) for optical measurements. This pair of eyes was enucleated from a 74-year-old Caucasian male at 4.7 h postmortem and was shipped fresh on ice to the research laboratory within 24 h. Ocular tissues were evaluated by the Southern Eye Bank using Medical Standards of the Eye Bank Association of America, eye banking standards approved by the American Academy of Ophthalmology. The tissue evaluation report from the Southern Eye Bank indicated that both left and right corneas had intact epithelium and clear stroma and both left and right lens were phakic. Visual inspection showed clear aqueous and vitreous humor at the time when optical measurements were conducted. One pair of bovine eyes was provided by Wiatreks (Poth, TX, USA). This pair of eyes was enucleated fresh, packed on ice, and immediately transported to the research laboratory (within 1 h). Visual inspection showed clear aqueous and vitreous humor at the time when optical measurements were conducted. Immediately upon arrival to the research laboratory, fresh (not frozen) whole eyes were dissected on ice to remove aqueous and vitreous humor for optical measurements with methods detailed below. τ ¼ tðμ s þ μ a Þ ; (5)

3 48 Preparation of aqueous humor One milliliter of aqueous humor was removed from both the human and bovine eyes using a 1-cm 3 tuberculin syringe with a fine needle inserted into the anterior chamber of the eye. Aqueous humor was then introduced into a sample holder constructed with two glass slides, sealed by epoxy to form a chamber with a thickness of approximately 1 mm. Preparation of vitreous humor Approximately 2 ml of vitreous humor was removed from both the bisected human and bovine eyes using a 1-cm 3 tuberculin syringe sans the fine needle. Vitreous humor was then introduced into a sample holder constructed with two glass slides, sealed by epoxy to form a chamber with a thickness of approximately 2 mm. Measurement of index of refraction The refractive indices, n, of the aqueous and vitreous humor samples were determined using a Michelson-type transillumination interferometer. Light from light emitting diodes (LEDs) (centered at 462, 560, 590, 654, and 947 nm) with an approximate power of 10 mw each was used for the measurement of n. The coherence length of each of the LEDs was less than 25 μm. The index of refraction was determined from the optical path difference, ε, and the sample thickness, d, by the following relation: n ¼ " þ 1:0003 (6) d where is the average index of refraction of air in the spectral region of interest. The measured values of the refractive index were least-square-fitted to Sellmeier s equation, Eq. 7, yielding the coefficients S and l 0 : (Thorlabs model L9805E2P5 and Mitsubishi ML725B8F, respectively) coupled to collimators (Thorlabs model F220FC-C) and controlled by a Thorlabs (model LDC 2000) laser driver. The laser beam diameter at 1/e 2 of the peak intensity was 1.97 mm, and the beam divergence was about The 1530-nm wavelength was supplied by a pig-tailed erbium-fiber-amplified stimulated emission module (NP Photonics model ASE SMP-4010) coupled to a collimator (Thorlabs model F220FC-1550) and controlled by NP Photonics supplied software. The laser beam diameter at 1/e 2 of the peak intensity was 2.07 mm, and the beam divergence was about The average output power was kept at about 0.25 mw for all optical measurements. The schematic of the experimental setup for measuring the total diffuse reflectance and total transmittance is shown in Fig. 1. The laser beam was directed into the entrance port A of integrating sphere 1, whose exit port was coupled with the entrance port of integrating sphere 2; the sample was mounted at the coupling port C situated in between the two integrating spheres. The exit port B of integrating sphere 2 was covered with a cap with a reflective surface identical to that of the integrating spheres. The diameter of each sphere was 150 mm, and each port had an aperture of 11 mm in diameter. Light leaving the sample reflected multiple times from the inner surfaces of the spheres before reaching the detectors. Baffles within the spheres shielded the detectors from receiving the direct reflected light from inside the sphere. The reflected and transmitted light intensities were detected by two identical infrared detectors (Judson model J16-D); these were attached to the two measuring ports of the integrating spheres 1 and 2. The detector signal was sent to identical preamplifiers (Judson model PA-9) powered by a common power supply (Pasco model 8000). Signals from the detectors were measured by a digital oscilloscope (Tektronix model TDS3054B). The measured light in- Oscilloscope n 2 ¼ 1 þ Sλ2 λ 2 λ 2 0 (7) The Sellmeier s coefficients S and l 0 were then used to determine the desired values of n. Measurement of diffuse reflectance and transmittance The total diffuse reflectance and total transmittance were measured using two identical integrating spheres (Oriel model 70451). The tissue sample was placed in a specially designed holder that coupled the two integrating spheres. The measurements were performed on the human and bovine aqueous humor and the vitreous humor prepared samples at 980, 1,310, and 1,530 nm. The 980- and 1,310- nm wavelengths were supplied by pig-tailed diode lasers Laser Light A Preamplifiers Det. 1 Det. 2 C Integrating Sphere 1 Integrating Sphere 2 Fig. 1 Experimental schematic for the measurement of total diffuse reflectance (R d ) and total transmittance (T t ) B

4 49 Table 1 Measured refractive indices of human and bovine aqueous humor and vitreous humor; Sellmeier s coefficients S and λ 0 Wavelength (nm) Measured refractive index Human Bovine Aqueous humor Vitreous humor Aqueous humor Vitreous humor S λ 0 (nm) tensities were then utilized to determine the total diffuse reflectance R d and total transmittance T t by the following expressions: R d ¼ X R C R Z R C R (8) and T t ¼ X T C T Z T C T (9) where X R is the reflected light intensity detected by Det.1 with the sample at C, Z R is the incident intensity detected by Det.1 with no sample at C, and a reflective surface at the exit port of integrating sphere 1, X T is the transmitted light intensity detected by Det.2 with the sample at C and a reflective surface at B, and Z T is the incident light intensity detected by Det.2 with no sample at C and with a reflective surface at B. C R is the correction factor for the stray light measured by Det.1 with no sample at C and the exit port of sphere 1 uncovered and sphere 2 removed. C T is the correction for Det.2 measured with no sample or light entering the sphere 2. That is, C R is the correction for light diffusion as it enters the experimental setup and detected by Det.1, and C R is the dark current correction for Det.2. There is no need to measure dark current for Det.1 because it would cancel out in Eq. 8. Inverse adding doubling method To solve the radiative transport equation, the IAD computer program [14] must be supplied with the experimental values of total diffuse reflectance (R d ) and total transmittance (T t ) along with values of index of refraction (n) and scattering anisotropy (g) of the sample. The IAD program Fig. 2 Measured refractive index vs wavelength and dispersion curves representing the best fit to Sellmeier s equation for aqueous humor and vitreous humor Sellmeier's Equation Experimental value for bovine aqueous humor and vitreous humor Experimental value for human aqueous humor Experimental value for human vitreous humor Refractive Index Wavelength (nm)

5 50 Table 2 Absorption coefficient (μ a ), scattering coefficient (μ s ), total attenuation coefficient (μ t ), albedo (a), and optical depth (τ) as determined by IAD using the measured diffuse reflectance (R d ), total transmittance (T t ), index of refraction (n), and reservoir thickness (t) with anisotropy coefficient (g) of human and bovine aqueous humor and vitreous humor at 980, 1,310, and 1,530 nm Wavelength (nm) Sample Measured Computed IAD t (cm) n R d T t g a τ μ a (cm 1 ) μ s (cm 1 ) μ t (cm 1 ) 980 Human aqueous humor Human vitreous humor Bovine aqueous humor Bovine vitreous humor ,310 Human aqueous humor Human vitreous humor Bovine aqueous humor Bovine vitreous humor ,530 Human aqueous humor Bovine aqueous humor guesses a set of optical properties (a and τ) and then calculates values for R d and T t. This process is repeated until the calculated and measured values of R d and T t are within a specified tolerance. Values of a and τ provided by the IAD method are used to calculate the absorption coefficient (μ a ) and the scattering coefficient (μ s ) for individual tissue using Eqs. 4 and 5. Monte Carlo simulation Measurements of the total diffuse reflectance (R d ) and total transmittance (T t ) used in the IAD method to determine the optical absorption coefficient (μ a ) and the scattering coefficient (μ s ) are modeled by the MC simulation technique, which uses a stochastic simulation of light interaction with biological media [15 17]. The values of μ a and μ s determined by the IAD method, along with the values of n, sample thickness (t), and g, are input into the MC simulation model which in turn determines R d and T t. Results and discussion The refractive indices (n) of the human aqueous and vitreous humor samples were measured with a Michelsontype interferometer at 590, 654, and 947 nm (462 and 560 nm LEDs were not on hand at the time of the measurement). The measurements were performed with the samples at room temperature; owing the low power of the LEDs, the temperature of the samples was assumed to remain at room temperature during the experiment. The measured n values varied from to and are given in Table 1. The indices of refraction (n) of the bovine aqueous and vitreous humor samples were measured with the same Michelson-type interferometer at 462, 560, 590,654, and 947 nm and at room temperature. The measured n values varied from to and are also given in Table 1. Measured refractive indices for human and bovine aqueous and vitreous humor are shown in Fig. 2, along with the best fit to the Sellmeier s dispersion equation. These indices of refraction are in good agreement Table 3 Diffuse reflectance (R d ) and total transmittance (T t ) determined by experimental and Monte Carlo techniques for human and bovine aqueous humor and vitreous humor at 980, 1,310, and 1,530 nm Wavelength (nm) Sample Experimental MC R d T t R d T t 980 Human aqueous humor Human vitreous humor Bovine aqueous humor Bovine vitreous humor ,310 Human aqueous humor Human vitreous humor Bovine aqueous humor Bovine vitreous humor ,530 Human aqueous humor Bovine aqueous humor

6 51 with the dispersion relationships in the paper of Hammer et al. [19]. The average scattering anisotropy coefficient (g) of the tissues was determined by iteratively running IAD and MC methods, with g ranging from 0.86 to 0.99 at 0.01 intervals, and choosing g based on the best agreement between the measured and computed values of the total transmittance (T t ). The difference between the measured and computed T t was chosen as the measure to minimize because for any given sample, the intensity of the total transmittance was several orders of magnitude greater than the diffused reflectance. The anisotropy values for all samples varied from 0.97 to 0.99 and are given in Table 2. These anisotropy values of near unity are in good agreement with the values reported in the work of Hammer et al. [20]. The total diffuse reflectance (R d ) and total transmittance (T t ) were measured on human and bovine aqueous and vitreous humor samples at 980, 1,310, and 1,530 nm from diode lasers. The power of each of the diode lasers was approximately 0.2 mw. All measurements were performed on tissue samples at room temperature; owing the low power of the diode lasers, the temperature of the samples was assumed to remain at room temperature during the experiment. Values of R d and T t for human and bovine ocular tissue samples are given in Table 2. The R d values for both human and bovine vitreous humor at 1,530 nm were too small to measure accurately and have thus been excluded from the analysis. The R d and T t values in Table 2, along with the index of refraction and estimated values of the scattering anisotropy coefficient, were input into the IAD program. The output of the IAD program were the dimensionless quantities a and τ defined by Eqs. 4 and 5, respectively. The absorption and scattering coefficients were then calculated from the values of a and τ and the thickness t of the sample. The absorption coefficient (μ a ), scattering coefficient (μ s ), total attenuation coefficient (μ t ¼ μ a þ μ s ), penetration depth (1/μ t ), albedo (a), and optical depth (τ) for the human and bovine ocular tissues are given in Table 2. The experimental values of total diffuse reflectance (R d ) and total transmittance (T t ) used to obtain the absorption coefficient (μ a ) and the scattering coefficient (μ s ) from the IAD have been compared with those generated by the MC simulation technique. These values are given in Table 3 for the human and bovine tissue samples at three wavelengths. Differences in R d and T t determined by experimental and MC techniques can be considered reasonable considering the experimental uncertainties in the measurements, as well as the complex nature of tissue samples. Table 2 shows that the absorption and scattering coefficients for the bovine ocular tissues have the same order of magnitude as those for human ocular tissues. The calculated absorption and scattering coefficients for bovine and human ocular samples are comparable at 1,310 nm. The largest discrepancy between the reported bovine and human absorption coefficients is observed at 980 nm, where the absorption coefficient for the bovine vitreous humor is about twice that of human. Also, the difference in the reported scattering coefficients at 1,530 nm between human and bovine aqueous humor may be due to experimental uncertainty in the measured diffused reflectance, which is small and thus difficult to measure. Nonetheless, the absorption coefficients for all samples are comparable to values reported for rhesus monkey in the study of Maher [7]. In conclusion, the values of the absorption and scattering coefficients for ocular samples reported in this study could have significant importance for modeling light transport in the eye to predict ocular damage during exposure to laser light. Acknowledgments This work was supported in part by the Air Force Research Laboratory Human Effectiveness Directorate HBCU/ MI grant FA , Wright Patterson Air Force Base, Dayton, Ohio, and the NSF-sponsored Center for Biophotonics Science and Technology at UC Davis under Cooperative Agreement No. PHY The authors would like to thank Eileen Vidro and Albert Muniz for preparing the ocular tissue samples and Joshua Dickerson for developing the automated interferometer used in this work. The authors would also like to thank Scott Prahl (Oregon Medical Laser Center) for the use of the IAD source code and Steven L. Jacques (Oregon Medical Laser Center) and Lihong Wang (Texas A&M University) for the use of the source code for the MC model. The source codes for both of these programs are available at: omlc.ogi.edu/software/. References 1. 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