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Measurements of optical parameters of phantom solution and bulk animal tissues in vitro at 650 nm
ARTICLE IN PRESS Optics & Laser Technology 42 (2010) 1–7
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Review
Measurements of optical parameters of phantom solution and bulk animal tissues in vitro at 650 nm Ping Sun , Yu Wang Department of Physics, Beijing Normal University, Beijing Area Major Laboratory of Applied Optics, Beijing 100875, PR China
a r t i c l e in fo
abstract
Article history: Received 26 November 2007 Received in revised form 31 May 2009 Accepted 1 June 2009 Available online 18 June 2009
Optical parameters of bulk animal tissue in vitro, including absorption coefficient (ma), reduced scattering coefficient (m0 s) or scattering coefficient (ms), total attenuation coefficient (mt), anisotropy factor (g) and refractive index (n) are measured at wavelength of 650 nm. Clinical Intralipid-10% is diluted in distilled water into different concentrations to use as tissue phantoms. Four types of animal tissues in vitro are studied. The relationships among the optical parameters are analyzed systemically. For animal tissues, ma, m0 s or ms and n rely on muscle fiber orientations. ms and mt range from 10 to 20 mm1, ma from 102 to 103 mm1 and g from 0.95 to 0.99. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Turbid media Optical parameters Diffuse reflectance
Contents 1. 2.
3.
4.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1. Refractive index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2. Total attenuation coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.3. Absorption coefficient, reduced scattering coefficient and anisotropy factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.1. Refractive index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.2. Total attenuation coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.3. Absorption coefficient, reduced scattering coefficient and anisotropy factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Discussions and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1. Introduction Optical parameters of biological tissue, including absorption coefficient (ma), reduced scattering coefficient (m0 s) or scattering coefficient (ms), anisotropy factor (g) and refractive index (n) are essential for effective and safe applications in medical therapeutics [1,2]. Moreover, the optical parameters themselves can potentially provide enough information to monitor tissue metabolic status or diagnose disease, particularly cancer [3]. A wide variety of methods of measuring tissue optical parameters have
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E-mail address: [email protected] (P. Sun). 0030-3992/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2009.06.001
been developed recently. Many of them use light in the visible and near infrared wavelength range. Up to now experimental methods to determine ma and m0 s of tissues mostly are based on measurements of the diffuse reflectance or transmittance such as integrating sphere measurement [4,5], sized-fiber reflectometry [6], video reflectometer [7] and oblique-incidence optical fiber reflectometry [8,9]. In general, ma and m0 s are obtained by means of inverse algorithm e.g. diffusion approximation (DA) [8], Monte Carlo model (MC) [10], hybrid model of DA and MC [11] and adding-doubling method [12]. g can be measured by goniometry [13] or non-normal incident illumination [14]. However, it is more convenient to determine the value of g indirectly according to measurable parameters including ma, m0 s and total attenuation coefficient (mt) [15]. Recently, it is commonly acceptable to
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determine n with the method of total internal reflectance based on Fresnel formulae [16,17]. Above methods are well described in literature. However, it is still insufficient to study several optical parameters systemically for the same tissue sample. Especially, the published values of the parameter existed significant discrepancy. Therefore, further and systemic analyses of tissue optical properties are still necessary. The difficulties involved in determining the optical properties of tissue in vivo are well know: a lot of stochastic errors originating from temperature, pulsation, hydration, sweatiness and fluid blood have influences on measurements. Therefore, ex vivo measurement remains a good method of isolating particular tissue types. However, it is important to keep in mind issues of sample freshness, blood drainage and tissue hydration. Maintaining tissue viability under measurement conditions is also a necessary concern. The basic assumption in this study is that in vitro samples are a reasonable representation of the in vivo situation. The aim of this paper is to provide a more detailed quantitative measurement of optical parameters in different tissues and perform an extensive study. We selected Intralipid as the tissue phantom, because, like tissue, it was turbid at visible and near infrared wavelengths. Considering fiber orientations and haemoglobin content, we chose some bulk fresh animal tissues in vitro which were bovine adipose, bovine muscle, porcine adipose, porcine muscle, porcine kidney, porcine liver, mutton and chicken breast. Refractive indices were measured by total internal reflection. mt was obtained by a classical narrow-beam method. ma and m0 s were determined from diffuse reflectance profiles by use of oblique-incidence optical fiber reflectometry. g was determined indirectly. We have gained number of experimental data of Intralipid with different concentrations and some typically soft tissues. The main advantage of this study is that the full set of parameters (ma, m0 s, ms, g, n, mt) is obtained and their relationship is also set up. In addition, we demonstrate in detail that the approaches including experimental setups are relatively easy to construct and calibrate.
2. Methods 2.1. Refractive index The method of measuring the critical angle of total reflection has long been used to determine the refractive index of liquid and other samples interfacing with a high-index glass prism and has been extended to biological tissues. The method comes from the well-known classical laws of reflection and refraction. When total internal reflection occurs, the incident light does not interact with the second medium except in the region at the interface of
Fig. 1. Schematic diagram of experimental principle for determining refractive index.
thickness that is about the same order of magnitude as the wavelength. Note that the mean free path, which describes the characteristic distance between scattering and absorption events for photons in tissue, is about 100 mm for most tissue type. It is much longer than the wavelengths available [18]. Thus, when total internal reflection takes place, statistically significant scattering does not happen if tissue is used as the second medium. To determine the critical angle, the relationship between the internal reflectance and the incident angle has to be measured. Fig. 1 shows the schematic of principle of total internal reflection. A beam of collimated polarized light with incident angle of i irradiates the plane AB of a right-angle prism and then is refracted with refractive angle of i1. Then the light with incident angle of y irradiates the interface BC of prism and tissue. When y is equal to the critical angle yc, total reflection occurs at the interface. In this case, the incident angle is called critically incident angle ic. Light, at last, is refracted out of plane AC with total reflectance RT. In the case of total reflectance there are three equations sin ic ¼ ng sin i1 ,
yc ¼ i1 þ a, nt ¼ ng sin yc . We can deduce the refractive index of tissue qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi nt ¼ sin ic cos a þ sin a n2g sin2 ic ,
(1)
(2)
where ng and a are the refractive index and angle of prism respectively. According to Fresnel’s equations the reflectivity of plane AB for s-polarized incident beam can be given by sinði i1 Þ 2 . (3) RSAB ¼ sinði þ i1 Þ The reflectivity of plane BC and plane AC can also be given, namely RSBC and RSAC. The total reflectivity RST is calculated by RST ¼ ð1 RSAB ÞRSBC ð1 RSAC Þ.
(4)
From Snell’s law and simple geometric relationship, RST can be expressed by i, nt, ng and a. In the same way for p-polarized incident beam the total reflectivity RPT can also be calculated. The calculating results of RST and RPT demonstrate that the curve of RST vs. i displays an obvious peak at ic, however, changes are not substantially visible in the curve of RPT vs. i. Accordingly, it is more realizable to measure refractive indices of tissues utilizing s-polarized light. 2.2. Total attenuation coefficient The total attenuation coefficient is measured using the narrowbeam experiment shown in Fig. 2. In this experimental setup, the collimating apertures A1 and A2 with 1 mm diameter, which restricts the field of view of the photomultiplier tube (PMT), are
Fig. 2. Experimental setup used to measure total attenuation coefficient.
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necessary to prevent most of the scattered photons from reaching the detector. Also, the distance between the sample holder and PMT is long enough to reduce the scattered photons reaching the detector. A laser beam illuminates the front surface of a sample. mt is calculated from Lambert–Beer’s law
mt ¼ lnðI=I0 Þ=d,
(5)
where d is the geometrical path length, I the signal measured when light is transmitted through a sample holder and I0 the signal measured when light irradiates on the front surface of sample holder. For phantom solution, mt is proportional to concentration of solution. Therefore, mt is calculated by [19]
mt ¼ lnðI=I0 Þ=cd,
(6)
where c is the concentration of phantom solution. Usually, water is used in the measurement of phantom solution to compensate for specular reflection losses of the incident light off the sample holder interfaces. Thus, I0 is the signal measured when light transmitted through the sample holder filled with water. 2.3. Absorption coefficient, reduced scattering coefficient and anisotropy factor Our experiments utilize the method described in detail by Lin et al. [8], which is based on the two-source diffusion theory model of spatially resolved, steady-state diffuse reflectance [20]. This diffusion theory model is not accurate near the source; that is, reflectance that falls in the range of 1–2 transport mean free paths (mfp0 ) of the source. We make up this drawback by measuring the reflectance beyond the range 2–3 mfp0 . For normally incident light, one positive photon source located 1 mfp0 below the tissue surface and one negative image source above the tissue surface. For obliquely incident light as shown in Fig. 3, the positive source is buried at the same distance from the incident point, but with a depth modified by Snell’s law. The distance of the buried source to the entry point is most accurately determined by [8] 3D ¼ 1=ð0:35ma þ m0 s Þ,
(7)
where D is defined as the diffuse coefficient. Comparing with normal incidence, the positive point source of oblique incidence shifts a distance of Dx in x direction and Dx is
Dx ¼ 3D sin yt ,
(8)
3
where yt is the refractive angle of tissue. If incident angle, refractive index of tissue and ambient medium through which the light delivered are known, yt can be calculated according to Snell’s law. The diffuse reflectance profile for oblique incidence is centered about the position of the point source, so we can measure the shift Dx by finding the center of diffuse reflectance relative to the point of light entry. The two-source model gives the diffuse reflectance [20] 1 expðr1 meff Þ RðrÞ ¼ z0 meff þ r1 4pr21 1 expðr2 meff Þ þ ðz0 þ 2zb Þ meff þ , (9) r2 4pr22
meff, the effective attenuation coefficient, is defined as meff ¼ ðma =DÞ1=2 .
(10)
r1 and r2 are the distance from the two point sources to the point of interest, z0 ¼ 3D is the distance between the positive source and the tissue surface, zb ¼ 2AD is the distance between the extrapolated boundary and the surface of tissue and z0+2zb is the distance between the negative image source and the tissue surface. A is related to the internal reflection and has an empirical 1 value A ¼ (1+ri)/(1ri),where ri ¼ 1.440n2 rel +0.710nrel +0.668+ 0.0636nrel and nrel ¼ nt/na, named relative index of the tissue–air interface [20]. We search for the center of diffuse reflectance by interpolating between the raw data points taken several mfp0 from the source and perform a non-linear least-squares fit with the Levenberg– Marquardt method on Eq. (9) to determine meff. ma and m0 s are solved from the expressions ma ¼ m0 s ¼
m2eff Dx
,
(11)
sin yt 0:35ma . Dx
(12)
3 sin yt
We calculate g from the data of m0 s, mt and ma using the expression [13] g ¼1
m0 s . mt ma
(13)
ms is obtained from the relationship ms ¼ m0 s/(1g). 3. Experiments 3.1. Refractive index
Fig. 3. Positions of point sources in the diffusion theory model for oblique incidence.
In all experiments below, we used same semiconductor laser (20 mW; 65075 nm; beam divergenceo0.3 mrad) and performed at room temperature. In consideration of the assumption of m0 sbma acting on diffusion theory model, we did not add any chromospheres to the phantom. Fresh excised animal tissues were obtained from a local slaughterhouse within 1 h postmortem and transported in an ice-cooled container without any direct contact to ice. Transportation time, until preparation, was a mean of 40 min. The experimental setup is shown in Fig. 1. The s-polarized light was used to measure refractive index. The stock Intralipid-10% was diluted in distilled water into different concentrations consisting of 0.4%, 0.7%, 1.0%, 3.0% and 5.0%. The collimated laser beam irradiated one side of a right-angle prism (K9) through an s-polarizer, a collimating lens and an aperture with 1.5 mm diameter. A PMT accepted the light emitted out of another side of the right-angle prism. The prism attached to a rectangle cell
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Fig. 4. Comparison of experimental result and theoretical calculation of Intralipid0.4%.
Fig. 5. Experimental results of total attenuation coefficient of Intralipid solutions.
Table 1 Refractive indices of bulk animal tissues.
Table 2 Experimental results of total attenuation coefficient of bulk animal tissues.
sample
n7Dn
Sample
n7Dn
Sample
mt7Dmt (mm1)
Sample
mt7Dmt (mm1)
Chicken breastP Chicken breastV Porcine muscleP Porcine muscleV Porcine adipose Porcine kidney
1.39770.002 1.40770.003 1.38770.005 1.41870.003 1.38270.006 1.40070.002
Porcine liver Bovine muscleP Bovine muscleV Bovine adipose Mutton
1.40170.006 1.37770.003 1.41470.003 1.39670.004 1.40270.007
Chicken breast Porcine muscle Porcine liver Porcine kidney
7.64170.131 7.42170.210 13.62771.245 12.02271.132
Porcine adipose Bovine muscle Bovine adipose Mutton
11.06471.010 9.70470.325 6.47770.210 9.63970.561
*pparallel orientation; vvertical orientation.
rotated driven by a rotation stage with resolution of 20 . When the prism rotated, the PMT was sensitive to the maximum of signals resulted from ic. When the cell was filled with air, we obtained ng ¼ 1.513070.0022. a was known as 451. To calibrate the experimental apparatus, first, we measured the index of distilled water. The value was 1.329 that was close to Li and Xie’s work [18] (H2O, n ¼ 1.32270.006, 632.8 nm). Then, we measured the refractive index of Intralipid. The experimental results with uncertainties were 1.34070.002 (0.4%), 1.34270.003 (0.7%), 1.35270.004 (1.0%), 1.35970.002 (3.0%), 1.36670.004 (5.0%) and 1.37070.005 (10%), which are in agreement with theory. Take Intralipid-0.4% as an example shown in Fig. 4. We adopt the same experimental setup to measure the refractive indices of bulk animal tissues. The fresh animal tissues were first frozen for 15 min to facilitate preparation of thin section of 2 mm thickness, 10 mm width and 20 mm length. The surface of prism was daubed with animal adipose so as to contact tightly between the tissue and the surface of prism. The section was pressed on the surface of prism without cell. Table 1 shows the experimental results with measurement uncertainties. There are differences in refractive indices for different kinds of tissues. In addition, there are discriminations owing to the fiber orientation for one kind of tissue. In general, index probed at vertical orientation is larger than that probed at parallel orientation, which corresponds with others’ researches [18].
3.2. Total attenuation coefficient The apparatus used to measure mt is illustrated in Fig. 2. In Intralipid, the attenuation of a light beam is due to both
absorption and scattering (mt ¼ ms+ma). Intralipid solutions were filled in a cell with 1 mm thickness. The stock Intralipid-10% was diluted in distilled water into seven dilute solutions with low concentrations involving 0.25%, 0.4%, 0.5%, 0.55%, 0.7%, 0.8% and 0.9%. According to Eq. (6), the slope of a plot of ln(I/I0) vs. (cd) determines mt of Intralipid-10%. Fig. 5 shows the line fitted to raw data. mt of Intralipid-10% is 33.21 mm1 derived from the slope of the attenuation curve. Usually for Intralipid there is an assumption that mtEms [13,19]. We will test this assumption after measuring ma, m0 s and g. The tissue samples were those used above. For each experiment, a sample was placed between two pieces of thin glass pressed by two clamps. If loss due to specular reflections at air–glass interface is considered, the Lambert–Beer’s law is rewritten by I ¼ I0exp(mtd), where I0 is the light intensity without two pieces of glass and sample, T the transmittance of taking the loss into account and d the tissue thickness. We measured that T was 91.6% using the setup shown in Fig. 2. Table 2 shows the experimental results of mt of tissues with measurement uncertainty. Typical total attenuation coefficients of soft tissues cover the range 10–50 mm1 at visible and near infrared wavelengths [21]. Our results are in reasonable agreement, considering that the measurement techniques are very different and that the physiological conditions are not strictly comparable in different studies. 3.3. Absorption coefficient, reduced scattering coefficient and anisotropy factor The experimental setup was drawn schematically in Fig. 6(a) and the three-dimensional perspective view of tissue surface was shown in Fig. 6(b). A laser beam transmitted through an aperture, 1 mm in diameter, and then was collimated with a lens. Being
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reflected by a mirror the beam irradiated obliquely the surface of Intralipid with incident angle of 451. A cylindrical black vessel with 10 cm diameter and 10 cm height was filled with Intralipid solution. Diffuse reflectance of Intralipid solution was collected by a detecting fiber (600 mm; N.A.0.3; multimode) and then coupled to a PMT. An analog to digital converter (A/D) transformed the analog signals into digital signals. The detecting fiber fixed on a three-dimensional transform stage with the least step of 5 mm was driven to scan the surface of Intralipid solution along the x
5
direction. When the electric translation stage moved a step, a value of diffuse reflectance relative to a position was sampled; that was, the computer controlled that the moving of the electric translation stage and sampling occurred simultaneously. The reflectance was detected in a plane that was parallel to the incident plane, but offset in y direction by Dy ¼ Dy ¼ 1.370.3 mm. Fig. 7 shows curves of diffuse reflectance vs. x for Intralipid solutions. The raw data are fitted by a non-linear least-squares with Levenberg–Marquardt method according to Eq. (9). Table 3 contains the results of Intralipid including fitted Dx and meff and the final calculated values of ma, m0 s, g and ms. m0 s or ms is proportional to the concentration of Intralipid solution, no dramatic changes for g and no significant differences for ma are found. Only average values without measurement uncertainty are listed in Table 3. However, we will account for the uncertainty of each parameter at Section 4. The optical parameters of Intralipid have been reported differently for various techniques and particle sizes [13,15,19,22,23]. Consequently, it is difficult to judge the results above. Fortunately, we can estimate the values of ms and g quantitatively according to Staveren’s approximate equation [19] based on the Mie theory. For Intralipid-10%, we estimate that ms ¼ 44.99 mm1 and g ¼ 0.72 at wavelength of 650 nm. By comparison, we find that g agrees with the estimation but ms is underestimated. Nevertheless, ms is close to Moes’s result (38.6 mm1) [23] and Chen’s result (30 mm1) [24]. A possible
Table 3 Fitted values of Dx and meff and calculated values of ma, m0 s, g and ms for Intralipid. c (%) mt (mm1) Dx (mm) meff (mm1) ma (mm1) m0 s (mm1) g 0.4 1.33 0.7 2.32 1 3.32 3 9.96 5 16.61 10 33.21 Fig. 6. Schematic diagram of experimental system (a); and three-dimensional perspective view of tissue surface (b).
1.420 0.764 0.489 0.173 0.101 0.056
0.040 0.087 0.106 0.137 0.152 0.299
0.002 0.004 0.004 0.002 0.002 0.003
0.370 0.686 1.067 3.001 5.144 9.230
ms (mm1)
0.72 1.329 0.70 2.316 0.68 3.317 0.70 9.958 0.69 16.609 0.72 33.207
*mt was determined in 3.2.
Fig. 7. Curves of diffuse reflectance vs. x for Intralipid solution with different concentrations. The raw data are plotted with circle label and the fitted results generated by our algorithm are plotted with solid line.
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Table 4 Fitted values of Dx and meff and calculated values of ma, m0 s, g and ms for animal tissues in vitro. Animal tissues
Dx (mm) meff (mm1) ms0 (mm1) ma (mm1) g
ms (mm1)
Chicken breast P Chicken breast v Porcine muscle p Porcine muscle v Porcine adipose Porcine kidney Porcine liver Bovine muscle p Bovine muscle v Bovine adipose Mutton
4.816 3.257 2.321 2.042 1.034 1.090 0.923 2.011 1.794 0.803 1.620
7.769 7.929 7.409 7.417 11.024 11.960 13.500 9.800 9.810 12.400 9.700
0.026 0.036 0.190 0.221 0.244 0.475 0.451 0.201 0.233 0.180 0.141
0.101 0.111 0.163 0.178 0.452 0.299 0.378 0.196 0.206 0.620 0.291
0.002 0.003 0.055 0.065 0.040 0.162 0.133 0.053 0.065 0.017 0.021
0.99 0.99 0.98 0.98 0.96 0.98 0.97 0.98 0.98 0.95 0.97
*pparallel orientation; vvertical orientation.
Fig. 8. Spatial distributions of diffuse reflectance of chicken breast.
explanation for this difference might be a different kind of Intralipid. ma changes insignificantly at an order of 103 mm1, which is similar to the absorption coefficient of water [25]. We measured the absorption coefficient of water by use of the Moes’s method [23]. The value of dilute water is 0.003 mm1, which is in agreement with Yoon’s value [26]. Therefore, it is concluded that water mainly contributes the absorption of Intralipid. In particular, ma keeps unchanged if measuring errors are taken into consideration. Concluding the results of Intralipid, reliable measurement and algorithm of m0 s, ma and g of turbid materials are possible. We use the same experimental arrangement shown in Fig. 6 to determine ma, m0 s and g of animal tissues in vitro. Before being prepared section of 3 cm thickness, the fresh animal tissue was first frozen for 15 min. Instead of Intralipid solution the bulk animal tissue was stacked in the black vessel with the muscle fibers aligned. Measurements were performed with the probe oriented at parallel and vertical relative to the muscle fibers. In experiments, it was obvious that ma and m0 s of some tissues with coarse fibers were related to their fiber orientations such as bovine muscle, porcine muscle and chicken breast. But mutton was an exception. Take chicken breast as an example, Fig. 8 shows the spatial distributions of diffuse reflectance probed at parallel and vertical orientation, respectively. The fact that two centers shift apparently indicates that m0 s of different orientations is also different. Table 4 also shows the average values of experimental results of animal tissues. ma and m0 s are diverse for eight types of tissues and also discriminative due to the probe orientation for one type of tissue. As a rule, values of ma and m0 s or ms probed at vertical orientation are larger than those probed at parallel orientation, which are consistent with others’ studies [27,28]. Most importantly, our results of chicken breast are similar to Marquez’s [27], bovine adipose and bovine muscle to Kienle’s [29], and porcine muscle and porcine adipose to Xie’s [30]. There are some comparisons possible between our measured g values (0.95–0.99) and other data. Using goniometry technique in vitro at 633 nm, Flock et al. [13] have reported g values of 0.97, 0.95 for chicken muscle and bovine muscle, respectively. From angular intensity measurements in vitro, Zijp and Bosch [28] have found g values of 0.96 for bovine muscle. Using a double sphere system, Roggan et al. [31] have evaluated numerically g values of 0.95 for porcine liver. These data all explains that light in animal tissues shows characteristic of highly forward scattering.
4. Discussions and conclusions One issue of discussion is that of error. In experiments of measuring n, the deviation of incident angle i is 20 . Thus, the maximal error in n is 70.007. The line of ln(I/I0) vs. (cd) shown in Fig. 5 is fitted by least-squares method. The error in mt mainly depends on the accuracy of ln(I/I0). The error of mt of Intralipid10% is 71.33 mm1. The accuracy of ma and m0 s depend on the directly measured parameters of Dx and meff. ma ¼ Dm2eff, so the error in ma is of the same order of magnitude as the error in D (or x) plus twice the error in meff and can be derived by Dma/ma ¼ DD/ D+2Dmeff/meff. In contrast, the error in m0 s is of the order of the error in D (or Dx) [8]. Dx and meff are calculated by fitting the measured diffuse reflectance to Eq. (9). However, it is practicable under the assumption of m0 sbma. The error will be expanded if this assumption does not hold. To test this assumption, we measured the diffuse reflectance of Intralipid-0.1%. As a result, the solution tended to be divergent, which meant Eq. (9) was not suitable for Intralipid-0.1% by reason of its weakly scattering. Accordingly, errors in ma and m0 s of porcine kidney and porcine liver possibly are marked for their strong absorption originated from high haemoglobin content. Another issue is about the applicability of these methods as mentioned above. One important aspect is that tissue is highly inhomogeneously structured e.g. discrete absorption by haemoglobin. As a matter of fact, we lay stress on macro-optical properties of tissues. The optical parameters measured in this work are statistically average. There are some conclusions from the results above. First, n of Intralipid increases as increase of concentration. n of bulk tissue depends on its fiber orientation. In general, n probed at vertical orientation is larger than that probed at parallel orientation. Second, mt of dilute Intralipid is proportional to its concentration. Except porcine kidney and porcine liver, mt of other animal tissues are close to ms. Third, m0 s or ms of Intralipid is directly proportional to its concentration and ma is similar to that of water. Most interestingly, ma and m0 s of some bulk animal tissues in vitro rely on the fiber orientations. Usually, ma and m0 s probed at vertical orientation are larger than those probed at parallel orientation like the results of n. Finally, g is almost same for Intralipid with different concentrations. Large value of g (gZ0.95) of animal tissues accounts for the characteristic of highly forward scattering of biological tissues. In conclusion, this research has demonstrated the measuring methods and experimental results of optical parameters (ma, m0 s, ms, g, n, mt) of turbid medium and set up the relationships among six parameters. It should be noted that a possible drawback in this work is that the evaluated optical characteristics are of limited value since they were measured from ex vivo samples of animals,
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whereas researches in the field of biomedical optics have already been, and yet currently, focused on in vivo human tissues. In addition, tissue absorption properties change dramatically in vitro, due to blood leakage and alterations in oxygenation and scattering changes significantly after freezing and thawing. At any rate, to determine optical parameters of tissues in systemic viewpoint is one of the most significant endeavors and a challenge. This report presents an easy way with which optical parameters can be obtained in any research laboratory.
Acknowledgments I am grateful to the National Natural Science Foundation of China (Grant no. 60577011) and also thank professor T.C.Poon for his helpful discussions. References [1] Wilson BC, Patterson MS. The physics of photodynamic therapy. Phys Med Biol 1986;26:327–60. [2] Tromberg BJ, Svaasand LO, Fehr MK, Madsen SJ, Wyss P, Sasone B, Tadir YA. Mathematic model for light dosimetery in photodynamic destruction of human endometrium. Phys Med Biol 1996;41:233–7. [3] Fantini S, Walker SA, Franceschini MA, Kaschke M, Schlag PM, Moesta KT. Assessment of the size, position, and optical properties of breast tumors in vivo by noninvasive optical methods. Appl Opt 1998;37:1982–9. [4] Pickering JW, Prahl SA, Vanwieringen N, Beek JF, Sterenborg HJCM, Van Gemert MJC. Double-integrating-sphere system for measuring the optical properties of tissue. Appl Opt 1993;32:399–410. [5] Chen W, Liu R, Luo Y, Han Y, Xu K. Preliminary study of mechanism of noninvasive blood glucose measurement based on near-infrared diffuse reflectance. Proc SPIE 2005;5696:91–100. [6] Moffitt TP, Prahl SA. Determining the reduced scattering of skin in vivo using sized-fiber reflectometry. Proc SPIE 2002;4613:254–63. [7] Wang L, Jacques SL. Use of a laser beam with an oblique angle of incidence to measure the reduced scattering coefficient of a turbid medium. Appl Opt 1995;34:2362–6. [8] Lin SP, Wang L, Jacques SL, Tittel FK. Measurement of tissue optical properties by the use of oblique-incidence optical fiber reflectometry. Appl Opt 1997;36:136–43. [9] Naˆscimento OF, Villaverde AB, Zangaro RA, Pacheco MTT, Durrant SF. Optical fiber device and biological tissue phantoms for determination of optical parameters in the near-infrared region. Instrum Sci Technol 2004;32: 489–505. [10] Friebel M, Roggan A, Mu¨ller G, Meinke M. Determination of optical properties of human blood in the spectral range 250–1100 nm using Monte Carlo simulations with hematocrit-dependent effective scattering phase functions. J Bio Opt 2006;11:034012-1–9.
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[11] Zarembo MS, Golovin NN, Meshalkin YP. Iterative indirect methods for determination of optical parameters of biological tissues. Proc SPIE 2006;6163:1–15. [12] Prahl SA, Gemert MJC, Welch AJ. Determining the optical properties of turbid media by using the adding-doubling method. Appl Opt 1993;32:559–68. [13] Flock ST, Wilson BC, Patterson MS. Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm. Med Phys 1987;14:835–41. [14] Joshi N, Donner C, Jensen HW. Noninvasive measurement of scattering anisotropy in turbid materials by non-normal incident illumination. Opt Lett 2006;31:936–8. [15] Flock ST, Jacques SL, Wilson BC, Star WM, Van Gemert MJC. Optical properties of Intralipid: a phantom medium for light propagation studies. Lasers Surg Med 1992;12:510–9. [16] Ding HF, Lu JQ, Wooden WA, Kragel PJ, Hu XH. Refractive indices of human skin tissues at eight wavelengths and estimated dispersion relations between 300 and 1600 nm. Phys Med Biol 2006;51:1479–89. [17] Jin YL, Chen JY, Xu L, Wang PN. Refractive index measurement for biomaterial samples by total internal reflection. Phys Med Biol 2006;51:N371–9. [18] Li H, Xie S. Measurement method of the refractive index of biotissue by total internal reflection. Appl Opt 1996;35:1793–5. [19] Staveren HJ, Moes CJM, Van Marle J, Prahl SA, Van Gemert MJC. Light scattering in intralipic-10% in the wavelength range of 400–1100 nm. Appl Opt 1991;30:4507–14. [20] Farrell TJ, Patterson MSA. Diffusion theory model of spatially resolved steadystate diffuse reflectance for the noninvasive determination of tissue optical properties. Med Phys 1992;19:879–88. [21] Cheong WF, Prahl SA, Welch AJ. A review of the optical properties of biological tissues. IEEE: Quantum Electron 1990;26:2166–85. [22] Driver I, Feather JW, King PR, Dawson JB. The optical properties of aqueous suspensions of Intralipid, a fat emulsion. Phys Med Biol 1989;34:1927–30. [23] Moes CJM, Van Gemert MJC, Star WM, Marijnissen JPA, Prahl SA. Measurements and calculations of the energy fluence rate in a scattering and absorbing phantom at 633 nm. Appl Opt 1989;28:2292–6. [24] Chen C, Lu JQ, Ding HF, Jacobs KM. A primary method for determination of optical parameters of turbid samples and application to Intralipid between 550 and 1630 nm. Opt Express 2006;14:7420–35. ¨ sterberg UL, Paulsen KD. Absorbance of opaque [25] Pogue BW, White EA, O microstructures in optically diffuse media. Appl Opt 2001;40:4616–21. [26] Yoon G, Welch AJ, Motamedi M, Van Gemert MJC. Development and application of three-dimensional light distribution model for laser irradiated tissue. IEEE: J Quantum Electron 1987;23:1721–33. [27] Marquez G, Wang LV, Lin SP, Schwartz JA, Thomsen SL. Anisotropy in the absorption and scattering spectra of chicken breast tissue. Appl Opt 1998;37:798–804. [28] Zijp JR, Bosch JJ. Optical properties of bovine muscle tissues in vitro; a comparison of methods. Phys Med Biol 1998;43:3065–81. [29] Kienle A, Lilge L, Patterson MS, Hibst R, Steiner R, Wilson BC. Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue. Appl Opt 1996;35:2304–14. [30] Xie SS, Li H, Wei Z. Principle and techniques for measuring optical parameters of bio-tissue. Proc SPIE 1997;2887:92–102. [31] Roggan A, Schadel D, Netz U, Ritz JP, Germer CT, Muller G. The effect of preparation technique on the optical parameters of biological tissue. Proc SPIE 2001;4241:186–99.
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Review
Measurements of optical parameters of phantom solution and bulk animal tissues in vitro at 650 nm Ping Sun , Yu Wang Department of Physics, Beijing Normal University, Beijing Area Major Laboratory of Applied Optics, Beijing 100875, PR China
a r t i c l e in fo
abstract
Article history: Received 26 November 2007 Received in revised form 31 May 2009 Accepted 1 June 2009 Available online 18 June 2009
Optical parameters of bulk animal tissue in vitro, including absorption coefficient (ma), reduced scattering coefficient (m0 s) or scattering coefficient (ms), total attenuation coefficient (mt), anisotropy factor (g) and refractive index (n) are measured at wavelength of 650 nm. Clinical Intralipid-10% is diluted in distilled water into different concentrations to use as tissue phantoms. Four types of animal tissues in vitro are studied. The relationships among the optical parameters are analyzed systemically. For animal tissues, ma, m0 s or ms and n rely on muscle fiber orientations. ms and mt range from 10 to 20 mm1, ma from 102 to 103 mm1 and g from 0.95 to 0.99. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Turbid media Optical parameters Diffuse reflectance
Contents 1. 2.
3.
4.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1. Refractive index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2. Total attenuation coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.3. Absorption coefficient, reduced scattering coefficient and anisotropy factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.1. Refractive index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.2. Total attenuation coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.3. Absorption coefficient, reduced scattering coefficient and anisotropy factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Discussions and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1. Introduction Optical parameters of biological tissue, including absorption coefficient (ma), reduced scattering coefficient (m0 s) or scattering coefficient (ms), anisotropy factor (g) and refractive index (n) are essential for effective and safe applications in medical therapeutics [1,2]. Moreover, the optical parameters themselves can potentially provide enough information to monitor tissue metabolic status or diagnose disease, particularly cancer [3]. A wide variety of methods of measuring tissue optical parameters have
Corresponding author. Tel.: +86 10 58808026; fax: +86 10 58802204.
E-mail address: [email protected] (P. Sun). 0030-3992/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2009.06.001
been developed recently. Many of them use light in the visible and near infrared wavelength range. Up to now experimental methods to determine ma and m0 s of tissues mostly are based on measurements of the diffuse reflectance or transmittance such as integrating sphere measurement [4,5], sized-fiber reflectometry [6], video reflectometer [7] and oblique-incidence optical fiber reflectometry [8,9]. In general, ma and m0 s are obtained by means of inverse algorithm e.g. diffusion approximation (DA) [8], Monte Carlo model (MC) [10], hybrid model of DA and MC [11] and adding-doubling method [12]. g can be measured by goniometry [13] or non-normal incident illumination [14]. However, it is more convenient to determine the value of g indirectly according to measurable parameters including ma, m0 s and total attenuation coefficient (mt) [15]. Recently, it is commonly acceptable to
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determine n with the method of total internal reflectance based on Fresnel formulae [16,17]. Above methods are well described in literature. However, it is still insufficient to study several optical parameters systemically for the same tissue sample. Especially, the published values of the parameter existed significant discrepancy. Therefore, further and systemic analyses of tissue optical properties are still necessary. The difficulties involved in determining the optical properties of tissue in vivo are well know: a lot of stochastic errors originating from temperature, pulsation, hydration, sweatiness and fluid blood have influences on measurements. Therefore, ex vivo measurement remains a good method of isolating particular tissue types. However, it is important to keep in mind issues of sample freshness, blood drainage and tissue hydration. Maintaining tissue viability under measurement conditions is also a necessary concern. The basic assumption in this study is that in vitro samples are a reasonable representation of the in vivo situation. The aim of this paper is to provide a more detailed quantitative measurement of optical parameters in different tissues and perform an extensive study. We selected Intralipid as the tissue phantom, because, like tissue, it was turbid at visible and near infrared wavelengths. Considering fiber orientations and haemoglobin content, we chose some bulk fresh animal tissues in vitro which were bovine adipose, bovine muscle, porcine adipose, porcine muscle, porcine kidney, porcine liver, mutton and chicken breast. Refractive indices were measured by total internal reflection. mt was obtained by a classical narrow-beam method. ma and m0 s were determined from diffuse reflectance profiles by use of oblique-incidence optical fiber reflectometry. g was determined indirectly. We have gained number of experimental data of Intralipid with different concentrations and some typically soft tissues. The main advantage of this study is that the full set of parameters (ma, m0 s, ms, g, n, mt) is obtained and their relationship is also set up. In addition, we demonstrate in detail that the approaches including experimental setups are relatively easy to construct and calibrate.
2. Methods 2.1. Refractive index The method of measuring the critical angle of total reflection has long been used to determine the refractive index of liquid and other samples interfacing with a high-index glass prism and has been extended to biological tissues. The method comes from the well-known classical laws of reflection and refraction. When total internal reflection occurs, the incident light does not interact with the second medium except in the region at the interface of
Fig. 1. Schematic diagram of experimental principle for determining refractive index.
thickness that is about the same order of magnitude as the wavelength. Note that the mean free path, which describes the characteristic distance between scattering and absorption events for photons in tissue, is about 100 mm for most tissue type. It is much longer than the wavelengths available [18]. Thus, when total internal reflection takes place, statistically significant scattering does not happen if tissue is used as the second medium. To determine the critical angle, the relationship between the internal reflectance and the incident angle has to be measured. Fig. 1 shows the schematic of principle of total internal reflection. A beam of collimated polarized light with incident angle of i irradiates the plane AB of a right-angle prism and then is refracted with refractive angle of i1. Then the light with incident angle of y irradiates the interface BC of prism and tissue. When y is equal to the critical angle yc, total reflection occurs at the interface. In this case, the incident angle is called critically incident angle ic. Light, at last, is refracted out of plane AC with total reflectance RT. In the case of total reflectance there are three equations sin ic ¼ ng sin i1 ,
yc ¼ i1 þ a, nt ¼ ng sin yc . We can deduce the refractive index of tissue qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi nt ¼ sin ic cos a þ sin a n2g sin2 ic ,
(1)
(2)
where ng and a are the refractive index and angle of prism respectively. According to Fresnel’s equations the reflectivity of plane AB for s-polarized incident beam can be given by sinði i1 Þ 2 . (3) RSAB ¼ sinði þ i1 Þ The reflectivity of plane BC and plane AC can also be given, namely RSBC and RSAC. The total reflectivity RST is calculated by RST ¼ ð1 RSAB ÞRSBC ð1 RSAC Þ.
(4)
From Snell’s law and simple geometric relationship, RST can be expressed by i, nt, ng and a. In the same way for p-polarized incident beam the total reflectivity RPT can also be calculated. The calculating results of RST and RPT demonstrate that the curve of RST vs. i displays an obvious peak at ic, however, changes are not substantially visible in the curve of RPT vs. i. Accordingly, it is more realizable to measure refractive indices of tissues utilizing s-polarized light. 2.2. Total attenuation coefficient The total attenuation coefficient is measured using the narrowbeam experiment shown in Fig. 2. In this experimental setup, the collimating apertures A1 and A2 with 1 mm diameter, which restricts the field of view of the photomultiplier tube (PMT), are
Fig. 2. Experimental setup used to measure total attenuation coefficient.
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necessary to prevent most of the scattered photons from reaching the detector. Also, the distance between the sample holder and PMT is long enough to reduce the scattered photons reaching the detector. A laser beam illuminates the front surface of a sample. mt is calculated from Lambert–Beer’s law
mt ¼ lnðI=I0 Þ=d,
(5)
where d is the geometrical path length, I the signal measured when light is transmitted through a sample holder and I0 the signal measured when light irradiates on the front surface of sample holder. For phantom solution, mt is proportional to concentration of solution. Therefore, mt is calculated by [19]
mt ¼ lnðI=I0 Þ=cd,
(6)
where c is the concentration of phantom solution. Usually, water is used in the measurement of phantom solution to compensate for specular reflection losses of the incident light off the sample holder interfaces. Thus, I0 is the signal measured when light transmitted through the sample holder filled with water. 2.3. Absorption coefficient, reduced scattering coefficient and anisotropy factor Our experiments utilize the method described in detail by Lin et al. [8], which is based on the two-source diffusion theory model of spatially resolved, steady-state diffuse reflectance [20]. This diffusion theory model is not accurate near the source; that is, reflectance that falls in the range of 1–2 transport mean free paths (mfp0 ) of the source. We make up this drawback by measuring the reflectance beyond the range 2–3 mfp0 . For normally incident light, one positive photon source located 1 mfp0 below the tissue surface and one negative image source above the tissue surface. For obliquely incident light as shown in Fig. 3, the positive source is buried at the same distance from the incident point, but with a depth modified by Snell’s law. The distance of the buried source to the entry point is most accurately determined by [8] 3D ¼ 1=ð0:35ma þ m0 s Þ,
(7)
where D is defined as the diffuse coefficient. Comparing with normal incidence, the positive point source of oblique incidence shifts a distance of Dx in x direction and Dx is
Dx ¼ 3D sin yt ,
(8)
3
where yt is the refractive angle of tissue. If incident angle, refractive index of tissue and ambient medium through which the light delivered are known, yt can be calculated according to Snell’s law. The diffuse reflectance profile for oblique incidence is centered about the position of the point source, so we can measure the shift Dx by finding the center of diffuse reflectance relative to the point of light entry. The two-source model gives the diffuse reflectance [20] 1 expðr1 meff Þ RðrÞ ¼ z0 meff þ r1 4pr21 1 expðr2 meff Þ þ ðz0 þ 2zb Þ meff þ , (9) r2 4pr22
meff, the effective attenuation coefficient, is defined as meff ¼ ðma =DÞ1=2 .
(10)
r1 and r2 are the distance from the two point sources to the point of interest, z0 ¼ 3D is the distance between the positive source and the tissue surface, zb ¼ 2AD is the distance between the extrapolated boundary and the surface of tissue and z0+2zb is the distance between the negative image source and the tissue surface. A is related to the internal reflection and has an empirical 1 value A ¼ (1+ri)/(1ri),where ri ¼ 1.440n2 rel +0.710nrel +0.668+ 0.0636nrel and nrel ¼ nt/na, named relative index of the tissue–air interface [20]. We search for the center of diffuse reflectance by interpolating between the raw data points taken several mfp0 from the source and perform a non-linear least-squares fit with the Levenberg– Marquardt method on Eq. (9) to determine meff. ma and m0 s are solved from the expressions ma ¼ m0 s ¼
m2eff Dx
,
(11)
sin yt 0:35ma . Dx
(12)
3 sin yt
We calculate g from the data of m0 s, mt and ma using the expression [13] g ¼1
m0 s . mt ma
(13)
ms is obtained from the relationship ms ¼ m0 s/(1g). 3. Experiments 3.1. Refractive index
Fig. 3. Positions of point sources in the diffusion theory model for oblique incidence.
In all experiments below, we used same semiconductor laser (20 mW; 65075 nm; beam divergenceo0.3 mrad) and performed at room temperature. In consideration of the assumption of m0 sbma acting on diffusion theory model, we did not add any chromospheres to the phantom. Fresh excised animal tissues were obtained from a local slaughterhouse within 1 h postmortem and transported in an ice-cooled container without any direct contact to ice. Transportation time, until preparation, was a mean of 40 min. The experimental setup is shown in Fig. 1. The s-polarized light was used to measure refractive index. The stock Intralipid-10% was diluted in distilled water into different concentrations consisting of 0.4%, 0.7%, 1.0%, 3.0% and 5.0%. The collimated laser beam irradiated one side of a right-angle prism (K9) through an s-polarizer, a collimating lens and an aperture with 1.5 mm diameter. A PMT accepted the light emitted out of another side of the right-angle prism. The prism attached to a rectangle cell
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Fig. 4. Comparison of experimental result and theoretical calculation of Intralipid0.4%.
Fig. 5. Experimental results of total attenuation coefficient of Intralipid solutions.
Table 1 Refractive indices of bulk animal tissues.
Table 2 Experimental results of total attenuation coefficient of bulk animal tissues.
sample
n7Dn
Sample
n7Dn
Sample
mt7Dmt (mm1)
Sample
mt7Dmt (mm1)
Chicken breastP Chicken breastV Porcine muscleP Porcine muscleV Porcine adipose Porcine kidney
1.39770.002 1.40770.003 1.38770.005 1.41870.003 1.38270.006 1.40070.002
Porcine liver Bovine muscleP Bovine muscleV Bovine adipose Mutton
1.40170.006 1.37770.003 1.41470.003 1.39670.004 1.40270.007
Chicken breast Porcine muscle Porcine liver Porcine kidney
7.64170.131 7.42170.210 13.62771.245 12.02271.132
Porcine adipose Bovine muscle Bovine adipose Mutton
11.06471.010 9.70470.325 6.47770.210 9.63970.561
*pparallel orientation; vvertical orientation.
rotated driven by a rotation stage with resolution of 20 . When the prism rotated, the PMT was sensitive to the maximum of signals resulted from ic. When the cell was filled with air, we obtained ng ¼ 1.513070.0022. a was known as 451. To calibrate the experimental apparatus, first, we measured the index of distilled water. The value was 1.329 that was close to Li and Xie’s work [18] (H2O, n ¼ 1.32270.006, 632.8 nm). Then, we measured the refractive index of Intralipid. The experimental results with uncertainties were 1.34070.002 (0.4%), 1.34270.003 (0.7%), 1.35270.004 (1.0%), 1.35970.002 (3.0%), 1.36670.004 (5.0%) and 1.37070.005 (10%), which are in agreement with theory. Take Intralipid-0.4% as an example shown in Fig. 4. We adopt the same experimental setup to measure the refractive indices of bulk animal tissues. The fresh animal tissues were first frozen for 15 min to facilitate preparation of thin section of 2 mm thickness, 10 mm width and 20 mm length. The surface of prism was daubed with animal adipose so as to contact tightly between the tissue and the surface of prism. The section was pressed on the surface of prism without cell. Table 1 shows the experimental results with measurement uncertainties. There are differences in refractive indices for different kinds of tissues. In addition, there are discriminations owing to the fiber orientation for one kind of tissue. In general, index probed at vertical orientation is larger than that probed at parallel orientation, which corresponds with others’ researches [18].
3.2. Total attenuation coefficient The apparatus used to measure mt is illustrated in Fig. 2. In Intralipid, the attenuation of a light beam is due to both
absorption and scattering (mt ¼ ms+ma). Intralipid solutions were filled in a cell with 1 mm thickness. The stock Intralipid-10% was diluted in distilled water into seven dilute solutions with low concentrations involving 0.25%, 0.4%, 0.5%, 0.55%, 0.7%, 0.8% and 0.9%. According to Eq. (6), the slope of a plot of ln(I/I0) vs. (cd) determines mt of Intralipid-10%. Fig. 5 shows the line fitted to raw data. mt of Intralipid-10% is 33.21 mm1 derived from the slope of the attenuation curve. Usually for Intralipid there is an assumption that mtEms [13,19]. We will test this assumption after measuring ma, m0 s and g. The tissue samples were those used above. For each experiment, a sample was placed between two pieces of thin glass pressed by two clamps. If loss due to specular reflections at air–glass interface is considered, the Lambert–Beer’s law is rewritten by I ¼ I0exp(mtd), where I0 is the light intensity without two pieces of glass and sample, T the transmittance of taking the loss into account and d the tissue thickness. We measured that T was 91.6% using the setup shown in Fig. 2. Table 2 shows the experimental results of mt of tissues with measurement uncertainty. Typical total attenuation coefficients of soft tissues cover the range 10–50 mm1 at visible and near infrared wavelengths [21]. Our results are in reasonable agreement, considering that the measurement techniques are very different and that the physiological conditions are not strictly comparable in different studies. 3.3. Absorption coefficient, reduced scattering coefficient and anisotropy factor The experimental setup was drawn schematically in Fig. 6(a) and the three-dimensional perspective view of tissue surface was shown in Fig. 6(b). A laser beam transmitted through an aperture, 1 mm in diameter, and then was collimated with a lens. Being
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reflected by a mirror the beam irradiated obliquely the surface of Intralipid with incident angle of 451. A cylindrical black vessel with 10 cm diameter and 10 cm height was filled with Intralipid solution. Diffuse reflectance of Intralipid solution was collected by a detecting fiber (600 mm; N.A.0.3; multimode) and then coupled to a PMT. An analog to digital converter (A/D) transformed the analog signals into digital signals. The detecting fiber fixed on a three-dimensional transform stage with the least step of 5 mm was driven to scan the surface of Intralipid solution along the x
5
direction. When the electric translation stage moved a step, a value of diffuse reflectance relative to a position was sampled; that was, the computer controlled that the moving of the electric translation stage and sampling occurred simultaneously. The reflectance was detected in a plane that was parallel to the incident plane, but offset in y direction by Dy ¼ Dy ¼ 1.370.3 mm. Fig. 7 shows curves of diffuse reflectance vs. x for Intralipid solutions. The raw data are fitted by a non-linear least-squares with Levenberg–Marquardt method according to Eq. (9). Table 3 contains the results of Intralipid including fitted Dx and meff and the final calculated values of ma, m0 s, g and ms. m0 s or ms is proportional to the concentration of Intralipid solution, no dramatic changes for g and no significant differences for ma are found. Only average values without measurement uncertainty are listed in Table 3. However, we will account for the uncertainty of each parameter at Section 4. The optical parameters of Intralipid have been reported differently for various techniques and particle sizes [13,15,19,22,23]. Consequently, it is difficult to judge the results above. Fortunately, we can estimate the values of ms and g quantitatively according to Staveren’s approximate equation [19] based on the Mie theory. For Intralipid-10%, we estimate that ms ¼ 44.99 mm1 and g ¼ 0.72 at wavelength of 650 nm. By comparison, we find that g agrees with the estimation but ms is underestimated. Nevertheless, ms is close to Moes’s result (38.6 mm1) [23] and Chen’s result (30 mm1) [24]. A possible
Table 3 Fitted values of Dx and meff and calculated values of ma, m0 s, g and ms for Intralipid. c (%) mt (mm1) Dx (mm) meff (mm1) ma (mm1) m0 s (mm1) g 0.4 1.33 0.7 2.32 1 3.32 3 9.96 5 16.61 10 33.21 Fig. 6. Schematic diagram of experimental system (a); and three-dimensional perspective view of tissue surface (b).
1.420 0.764 0.489 0.173 0.101 0.056
0.040 0.087 0.106 0.137 0.152 0.299
0.002 0.004 0.004 0.002 0.002 0.003
0.370 0.686 1.067 3.001 5.144 9.230
ms (mm1)
0.72 1.329 0.70 2.316 0.68 3.317 0.70 9.958 0.69 16.609 0.72 33.207
*mt was determined in 3.2.
Fig. 7. Curves of diffuse reflectance vs. x for Intralipid solution with different concentrations. The raw data are plotted with circle label and the fitted results generated by our algorithm are plotted with solid line.
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Table 4 Fitted values of Dx and meff and calculated values of ma, m0 s, g and ms for animal tissues in vitro. Animal tissues
Dx (mm) meff (mm1) ms0 (mm1) ma (mm1) g
ms (mm1)
Chicken breast P Chicken breast v Porcine muscle p Porcine muscle v Porcine adipose Porcine kidney Porcine liver Bovine muscle p Bovine muscle v Bovine adipose Mutton
4.816 3.257 2.321 2.042 1.034 1.090 0.923 2.011 1.794 0.803 1.620
7.769 7.929 7.409 7.417 11.024 11.960 13.500 9.800 9.810 12.400 9.700
0.026 0.036 0.190 0.221 0.244 0.475 0.451 0.201 0.233 0.180 0.141
0.101 0.111 0.163 0.178 0.452 0.299 0.378 0.196 0.206 0.620 0.291
0.002 0.003 0.055 0.065 0.040 0.162 0.133 0.053 0.065 0.017 0.021
0.99 0.99 0.98 0.98 0.96 0.98 0.97 0.98 0.98 0.95 0.97
*pparallel orientation; vvertical orientation.
Fig. 8. Spatial distributions of diffuse reflectance of chicken breast.
explanation for this difference might be a different kind of Intralipid. ma changes insignificantly at an order of 103 mm1, which is similar to the absorption coefficient of water [25]. We measured the absorption coefficient of water by use of the Moes’s method [23]. The value of dilute water is 0.003 mm1, which is in agreement with Yoon’s value [26]. Therefore, it is concluded that water mainly contributes the absorption of Intralipid. In particular, ma keeps unchanged if measuring errors are taken into consideration. Concluding the results of Intralipid, reliable measurement and algorithm of m0 s, ma and g of turbid materials are possible. We use the same experimental arrangement shown in Fig. 6 to determine ma, m0 s and g of animal tissues in vitro. Before being prepared section of 3 cm thickness, the fresh animal tissue was first frozen for 15 min. Instead of Intralipid solution the bulk animal tissue was stacked in the black vessel with the muscle fibers aligned. Measurements were performed with the probe oriented at parallel and vertical relative to the muscle fibers. In experiments, it was obvious that ma and m0 s of some tissues with coarse fibers were related to their fiber orientations such as bovine muscle, porcine muscle and chicken breast. But mutton was an exception. Take chicken breast as an example, Fig. 8 shows the spatial distributions of diffuse reflectance probed at parallel and vertical orientation, respectively. The fact that two centers shift apparently indicates that m0 s of different orientations is also different. Table 4 also shows the average values of experimental results of animal tissues. ma and m0 s are diverse for eight types of tissues and also discriminative due to the probe orientation for one type of tissue. As a rule, values of ma and m0 s or ms probed at vertical orientation are larger than those probed at parallel orientation, which are consistent with others’ studies [27,28]. Most importantly, our results of chicken breast are similar to Marquez’s [27], bovine adipose and bovine muscle to Kienle’s [29], and porcine muscle and porcine adipose to Xie’s [30]. There are some comparisons possible between our measured g values (0.95–0.99) and other data. Using goniometry technique in vitro at 633 nm, Flock et al. [13] have reported g values of 0.97, 0.95 for chicken muscle and bovine muscle, respectively. From angular intensity measurements in vitro, Zijp and Bosch [28] have found g values of 0.96 for bovine muscle. Using a double sphere system, Roggan et al. [31] have evaluated numerically g values of 0.95 for porcine liver. These data all explains that light in animal tissues shows characteristic of highly forward scattering.
4. Discussions and conclusions One issue of discussion is that of error. In experiments of measuring n, the deviation of incident angle i is 20 . Thus, the maximal error in n is 70.007. The line of ln(I/I0) vs. (cd) shown in Fig. 5 is fitted by least-squares method. The error in mt mainly depends on the accuracy of ln(I/I0). The error of mt of Intralipid10% is 71.33 mm1. The accuracy of ma and m0 s depend on the directly measured parameters of Dx and meff. ma ¼ Dm2eff, so the error in ma is of the same order of magnitude as the error in D (or x) plus twice the error in meff and can be derived by Dma/ma ¼ DD/ D+2Dmeff/meff. In contrast, the error in m0 s is of the order of the error in D (or Dx) [8]. Dx and meff are calculated by fitting the measured diffuse reflectance to Eq. (9). However, it is practicable under the assumption of m0 sbma. The error will be expanded if this assumption does not hold. To test this assumption, we measured the diffuse reflectance of Intralipid-0.1%. As a result, the solution tended to be divergent, which meant Eq. (9) was not suitable for Intralipid-0.1% by reason of its weakly scattering. Accordingly, errors in ma and m0 s of porcine kidney and porcine liver possibly are marked for their strong absorption originated from high haemoglobin content. Another issue is about the applicability of these methods as mentioned above. One important aspect is that tissue is highly inhomogeneously structured e.g. discrete absorption by haemoglobin. As a matter of fact, we lay stress on macro-optical properties of tissues. The optical parameters measured in this work are statistically average. There are some conclusions from the results above. First, n of Intralipid increases as increase of concentration. n of bulk tissue depends on its fiber orientation. In general, n probed at vertical orientation is larger than that probed at parallel orientation. Second, mt of dilute Intralipid is proportional to its concentration. Except porcine kidney and porcine liver, mt of other animal tissues are close to ms. Third, m0 s or ms of Intralipid is directly proportional to its concentration and ma is similar to that of water. Most interestingly, ma and m0 s of some bulk animal tissues in vitro rely on the fiber orientations. Usually, ma and m0 s probed at vertical orientation are larger than those probed at parallel orientation like the results of n. Finally, g is almost same for Intralipid with different concentrations. Large value of g (gZ0.95) of animal tissues accounts for the characteristic of highly forward scattering of biological tissues. In conclusion, this research has demonstrated the measuring methods and experimental results of optical parameters (ma, m0 s, ms, g, n, mt) of turbid medium and set up the relationships among six parameters. It should be noted that a possible drawback in this work is that the evaluated optical characteristics are of limited value since they were measured from ex vivo samples of animals,
ARTICLE IN PRESS P. Sun, Y. Wang / Optics & Laser Technology 42 (2010) 1–7
whereas researches in the field of biomedical optics have already been, and yet currently, focused on in vivo human tissues. In addition, tissue absorption properties change dramatically in vitro, due to blood leakage and alterations in oxygenation and scattering changes significantly after freezing and thawing. At any rate, to determine optical parameters of tissues in systemic viewpoint is one of the most significant endeavors and a challenge. This report presents an easy way with which optical parameters can be obtained in any research laboratory.
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