Depth determination of chromophores in human skin by pulsed photothermal radiometry.

We report on the application of pulsed photothermal radiometry 1 PPTR 2 to determine the depth of in-vitro and in-vivo subsurface chromophores in biological materials. Measurements provided by PPTR in combination with a nonnegative constrained conjugate-gradient algorithm are used to determine the initial temperature distribution in a biological material immediately following pulsed laser irradiation. Within the experimental error, chromophore depths 1 50–450 µm 2 in 55 in-vitro collagen phantoms determined by PPTR and optical low-coherence reﬂectometry are equivalent. The depths of port-wine-stain blood vessels determined by PPTR correlate very well with their locations found by computer-assisted microscopic observation of histologic sections. The mean blood-vessel depth deduced from PPTR and histologic observation is statistically indistinguishable 1 p . 0.94 2 .


Introduction
In recent years, a number of investigators have studied various techniques to image the internal structure of human skin. [1][2][3] Many of these studies have been motivated by efforts to improve diagnosis and treatment of various skin pathologies. The increased use of lasers for medical treatments that rely on a photothermal-damage mechanism has heightened interest in infrared diagnostic methods. In many cases, information deduced from an infrared diagnostic measurement can be applied directly for improved therapeutic results.
Pulsed photothermal radiometry 1PPTR2 is a noncontact technique that utilizes an infrared detector to measure temperature changes induced in a test material exposed to pulsed radiation. Heat generated as a result of light absorption by subsurface chromophores in the test material diffuses to the surface and results in increased infrared emission levels. By the collection and concentration of the emitted radiation onto an infrared detector, a PPTR signal is obtained that represents the time evolution of temperature near the test-material surface. Useful information regarding the test material may be deduced from analysis of the PPTR signal; reported applications include 112 evaluation of surfacecoating thickness in industrial components, 4 122 identification of subsurface microcracks in aircraft structures, 5 132 determination of the optical absorption coefficients in human artery 6 and biliary calculi, 7 and 142 characterization of vascular lesions in human skin, such as port-wine stain 1PWS2 birthmarks. 8 Various investigators have reported mathematical and physical methods to deduce the optical and thermal properties of a laser-irradiated test material from a PPTR measurement. By using tissue phantoms that permit the independent variation of the optical absorption µ a and scattering µ s coefficients, Anderson et al. 9 found that heating of superficial layers increases when µ s is greater. Prahl et al. 10 derived an analytic expression for the PPTR signal amplitude in terms of the optical and thermal properties of the irradiated test material and obtained estimates of µ a and µ s . Vitkin et al. 11 extended the analysis of Prahl et al. 10 to a generalized two-layer model and applied their results to PWS diagnostics. Milner et al. 12 used a numerical-inversion algorithm to compute the initial temperature distribution in a test material from a PPTR signal recorded immediately following pulsed laser irradiation.
In this paper we report the results of an experimental investigation to determine the depth of in-vitro and in-vivo subsurface chromophores in biological materials from measurements provided by PPTR. An in-vitro phantom that makes use of thin, type I collagen films is used to simulate a subsurface chromophore positioned at various depths in human skin. The recorded PPTR signal amplitude in combination with a nonnegative constrained conjugategradient inversion algorithm is used to deduce the chromphore depth in the phantom and is compared with locations measured by the use of optical lowcoherence reflectometry 1OLCR2.
In human skin, heat generated from the absorption of laser radiation by melanin and hemoglobin diffuses to the surface and results in increased infrared emission levels. In experiments similar to those using collagen phantoms, the recorded PPTR signal amplitude in combination with the nonnegative constrained conjugate-gradient inversion algorithm is used to deduce the depth of dermal PWS blood vessels and is compared with values deduced from a computer-assisted microscopic examination of histologic sections.

Theory
When the diameter of the laser-irradiation spot is much larger than the thermal-diffusion length, heat transport in the test material along the z axis is well approximated by a one-dimensional model 1Fig. 12. In this case, the measured PPTR signal amplitude DS1t2 is related to the initial temperature distribution DT1z, t 5 02 in the test material immediately following pulsed laser irradiation by a Fredholm integral equation of the first kind, Eqs. 112 12 : DS1t2 5 e z DT1z, t 5 02K1z, t2dz 1 n1t2, K1z, t2 5 µ ir 2 exp12z 2 @4Dt2 h@k 2 µ ir 3 3erfcx1u 1 2 2 erfcx1u 1 24 6 .

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Here, erfcx1u2 5 3exp1u 2 243erfc1u24 is the exponential complementary error function; high-accuracy 118 dig-its2 computation of erfcx1u2 is possible by the use of a Chebyshev approximation. 13 Both DS1t2 1in degrees Celsius2 and DT1z, t 5 02 1also in degrees Celsius2 represent temperature increases relative to their respective background levels just before laser irradiation, i.e., DS1t2 5 S1t2 2 S1t 5 0 2 2 and DT1z, t 5 02 5 T1z, t 5 02 2 T1z, t 5 0 2 2, where t 5 0 2 is the time just before laser irradiation. K1z, t2 is the kernel of the integral equation, n1t2 represents system noise, and u 6 and u 1 are defined as respectively, where D 1mm 2 @s2 is the thermal diffusivity of the irradiated test material, µ ir 1mm 21 2 is the infrared absorption coefficient, k 1W@mm 2 K2 is the thermal conductivity, and h 3in watts per 1millimeters squared times degrees kelvin24 is the heat-loss coefficient at the air-material boundary. Given a measured PPTR signal DS1t2, a unique solution for DT1z, t 5 02 does not exist because the Fredholm integral equation is severely ill posed. 14 Equivalently, the kernel K1z, t2 strongly blurs the initial temperature distribution, so that accurate reconstruction of DT1z, t 5 02 from the measured PPTR signal amplitude DS1t2 requires an unrealistically-large signal-to-noise ratio. Inasmuch as a temperature change in response to light absorption is always positive, improved solution estimates are obtained by the imposition of a nonnegativity constraint 3i.e., DT1z, t 5 02 $ 04.
When finding a solution estimate for the initial temperature distribution DT1z, t 5 02, the Fredholm integral equation 3Eqs. 1124 is linearized, and one seeks to minimize a regularized norm: 132 Here DS and DT are linearized vector quantities representing the PPTR signal amplitude DS1t2 and the initial temperature distribution DT1z, t 5 02, respectively. The linearized kernel of the integral equation is represented by the matrix K. A regular- Fig. 1. Three-dimensional phantom geometry approximated as a one-dimensional model with the initial temperature distribution DT1z, t 5 02. The oval shaded region represents the laserirradiation spot.

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APPLIED OPTICS @ Vol. 35, No. 19 @ 1 July 1996 ization term, 14 L 6 DT6 2 , is added to the squared norm of the residual 6 KDT 2 DS6 2 to penalize large solution estimates. We apply a nonnegative constrained conjugate-gradient algorithm to the unaugmented problem 1L 5 02 of Eq. 132, starting with DT 5 0, and then regularize by early termination. 12,15 In the chemometrics literature this method is called the partial least-squares technique and has been given a sound theoretical basis. 16,17 Although the best iterate can be selected by the use of ordinary or generalized cross validation, 18 in our analysis both the discrepancy-principle 14 and the L-curve methods 19 are used to determine the best iterate.

Methods and Materials
We have developed an in-vitro model using thin, type I collagen films consisting of variable amounts of organic absorbing dye to simulate multilayered composite PWS skin 1Fig. 12. The collagen films were prepared to different thicknesses and optical absorptions to simulate a PWS. We constructed each phantom by staining a single collagen film with triphenylmethane dye 1Brilliant Blue, Aldrich Chemical Company2 which absorbs optimally at a wavelength of 585 nm. We prepared each phantom by first placing a stained film on a 10-mm-thick collagen substrate to simulate the optical and thermal properties of the dermis and second by positioning a variable number 11-42 of unstained films over the stained layer to simulate a PWS with blood vessels at various depths 150-450 µm2. Before and after each PPTR measurement, the depth of the stained collagen film was determined by means of OLCR. The physical principles underlying OLCR have been described previously by many investigators [20][21][22] and are not given here. Briefly, OLCR utilizes a low-coherence Michelson interferometer to measure the backscattered-light amplitude at discrete user-specified depths within a turbid material. Each OLCR scan of the collagen phantom measured the amplitude of the backscattered light at increasing depths. Because of a discontinuity in the refractive index, the boundaries between adjacent collagen films were detected in the OLCR scan as peaks in the backscattered-light amplitude. Knowledge of the group refractive index of collagen and the position of the backscattering peaks permitted accurate depth determinations of the stained collagen film.
In experiments involving phantoms, light emitted by a flash-lamp-pumped, pulsed dye laser 10.45 ms, E p 5 0.5 J, l 5 585 nm2 was imaged from a 1-mm core-diameter multimode optical fiber onto the collagen surface at 30°from the sample normal to form a 25-mm 2 elliptically-shaped irradiation spot. A 25mm-diameter f@1 germanium lens stopped down to 5 mm was positioned 50 mm in front of the detector to provide the unit magnification 1Fig. 22. Infrared radiation emitted from the phantom was amplitude modulated 13.9 kHz2 by a mechanical chopper posi-tioned at the 5-mm-diameter aperture and imaged onto a 1-mm 2 liquid-nitrogen-cooled HgCdTe detector optically filtered at the cold stop for sensitivity in the 10-14-µm spectral range. The detected signal was demodulated by a lock-in amplifier 1Model SR850, Stanford Research Systems2, recorded by a digital oscilloscope 1Model DSA 601, Tektronix2, and transferred to a magneto-optic storage disk.
Following University of California internal review board approval, informed consent to participate in the study was given by three PWS patients undergoing laser therapy at the Beckman Laser Institute and Medical Clinic. In experiments involving PWS's, light emitted by a flash-lamp-pumped, pulsed dye laser 10.45 ms, E p 5 1.5 J, l 5 585 nm2 was imaged from a 1-mm core-diameter multimode optical fiber at 30°from the normal to form a 25-mm 2 elliptically shaped irradiation spot on the skin surface. Infrared emission from the PWS was imaged onto a liquid-nitrogen-cooled 128 3 128 InSb infrared focal-plane array 1IR-FPA2 camera 1Model AE 4128, Amber Engineering2. The camera optics consisted of an f@3 multi-element infrared lens and filter positioned at the cold stop to limit the sensitivity to the 3-5-µm spectral range. The PWS was held stationary against the insulated back surface of a 20-mm-diameter iris diaphragm positioned 190 mm from the lens objective to yield an image-to-object linear magnification of 0.4. PWS sites ranging in appearance from light red or pink to purple were selected for laser irradiation; an adjacent normally pigmented skin site was also irradiated and served as the control. Immediately following the pulsed laser irradiation, 140 infrared emission images were recorded 1217 frames@s2 and transferred to a magnetooptic storage disk. From the more than 50 recorded PPTR signals of PWS's, patient consent permitted the biopsy of seven skin sites.
Immediately after surgical removal from the skin, tissue samples were fixed for 24 h in a phosphate buffer 1pH 7.42, 10% formalin solution. Each tissue sample was sequentially dehydrated in 10 solutions of increasing ethanol:water concentrations, cleared 1Histoclear, National Diagnostics2, and then infiltrated with paraffin in an automated processor 1Model 166 MP, Fisher Scientific2. After the tissue samples were embedded in 1-cm 3 paraffin blocks, 6-µm-thick serial sections were cut and placed on a clean glass slide. Sections were cleared of paraffin, stained with hematoxylin and eosin, and protected with a coverglass.

Results and Discussion
The nonnegative constrained conjugate-gradient inversion algorithm was used to analyze PPTR signals recorded from collagen phantoms and PWSs; the value of thermal diffusivity for each inversion was 0.11 mm 2 @s. 23 When working with collagen phantoms, we took the magnitude of the infrared absorption coefficient 1100 mm 21 2 from the values for water 24,25 and collagen, 26 averaged over the spectral response of the HgCdTe detector 1i.e., 10-14 µm2. Air currents generated by the mechanical chopper required the use of a nonzero heat-loss coefficient. A value of h 323 W@1m 2 K24 as determined by the computation of a least-squares fit to the tail of the recorded PPTR signals was consistent with values for forced-air convective cooling. 27 After a number of computer experiments with the simulated data, a criterion was derived 3see Eq. 1424 to locate the position z c of the upper surface of the stained collagen film from DT1z, t 5 02: where DT max is the maximum temperature of DT1z, t 5 02. For each collagen phantom, the PPTR signal amplitude 3Fig. 31a24 was used to compute z c by the application of the nonnegative constrained conjugate-gradient inversion algorithm 3Fig. 31b2, DT1z, t 5 024 and the criterion in Eq. 142. With the group refractive index of collagen 1n g 5 1.432, 28 z c was determined from OLCR measurements. Of the 55 collagen phantoms tested, the standard deviation of the difference between values of z c deduced by the use of the two methods was 2 µm 1Fig. 42. PPTR signals representing the thermal response of normal and PWS skin were derived from recorded infrared emission images by the computation of the average temperature within a 3-mm-diameter circular area centered in the elliptical-shaped irradiation spot. For inversions involving human skin, the infrared absorption coefficient 135 mm 21 2 was deduced from the values for water 24,25 and collagen 26 averaged over the spectral response 1i.e., 3-5 µm2 of the IR-FPA camera. Because PPTR measurements of PWS's with the IR-FPA did not require a mechanical chopper, heat loss at the skin surface was dominated by unforced air convection 3h 5 1 W@1m 2 K24. 27 Tested skin sites were categorized according to appearance into one of three types: I, a deep red or purple PWS; II, a light red PWS; and III, natural or normal pigmentation.
Recorded PPTR signals representative of each skin type 3Fig. 51a24 indicate differences in the thermal response following pulsed laser irradiation. As noted previously, 8 the initial thermal response of skin immediately following pulsed laser irradiation is dominated by epidermal melanin heating. A delayed thermal wave caused by heat deposited in deeper chromophores diffuses to the skin surface and produces increased temperatures. We expect, and our measurements confirm, that heat deposited 1a2 1b2 Fig. 3. Representative signals from an in-vitro collagen phantom: 1a2 PPTR signal amplitude DS1t2, and 1b2 computed initial temperature distribution DT1z, t 5 02, with z c 5 0.33 mm.

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APPLIED OPTICS @ Vol. 35, No. 19 @ 1 July 1996 in dermal PWS blood vessels results in an increased PPTR signal amplitude at later times 1,0.7 s2. At these times, the recorded amplitude from type I sites is greatest; in contrast, the amplitude of type III sites decays more rapidly and attains the smallest relative magnitude at later times. The initial temperature distribution DT1z, t 5 02 corresponding to each laser-irradiated and biopsied skin site was computed by the application of the nonnegative constrained conjugate-gradient inversion algorithm. Distinct regions of increased temperature in the epidermis and dermis are evident and indicate light absorption by melanin and hemoglobin, respectively, contained within the PWS blood vessels. The computation of DT1z, t 5 02 for the three representative PPTR signals illustrated in Fig.  51a2 indicates that heat generated in dermal PWS blood vessels is greatest in type I sites and decreases monotonically for skin types II and III 3Fig. 51b24. Over the seven biopsied skin sites, the mean peak temperature increases of the subsurface blood vessels for skin types I, II, and III are 34, 27, and 8°C, respectively.
Microscopic observation of the histologic sections permitted the comparison of PWS blood-vessel locations with their corresponding initial temperature distributions, DT1z, t 5 02. An electronic camera 1Model 2250, Cidtec2 in combination with a low-power 11032 microscope 1Model BH-2, Olympus2 were used to record digital images 1512 3 512 pixels2 of 20 equal-spaced tissue sections taken from each skin biopsy. With a computer-assisted analysis of the recorded histologic images, the 1x, z2 coordinates representing the periphery of each PWS blood vessel were identified by a manual trace of a closed geometric curve coincident with the venule boundary. The depth of each PWS blood vessel was taken to be the distance along a line segment connecting the center position 1x c , z c 2 to the nearest point on the skin surface, as given by For each biopsied skin site a histogram representing the hemoglobin distribution was generated by the computation of the fractional occurrence of blood vessels 1h i 5 n i @N T 2 at each depth interval Dz i 5 1z i 2 D@2, z i 1 D@22. In our analysis z i 5 iD 1in millimeters2, where i 5 1, 2, 3, . . . , 20, D 5 0.05 mm, n i is the number of blood vessels counted in the depth interval Dz i , and N T is the total number of blood vessels observed in all histologic sections at a skin site. A representative histogram of a type I skin site 1Fig. 62 shows good correlation in the dermis 1z . 0.05 mm2 between the hemoglobin distribution h i deduced from microscopic observation of histologic sections and the corresponding initial temperature distribution DT1z, t 5 02.
For the quantitative comparison of histologic observations with computed initial temperature distributions, algebraic terms representing light absorption by melanin 3DT m 1z, t 5 024 in the epidermis and hemoglobin within the dermal PWS blood vessels 3DT b 1z, t 5 024 are identified by Representative signals from three skin types exposed to equivalent laser irradiance: solid curves, type I skin; dashed curves, type II skin; short-dash-long-dash curves, type III skin. The plots show the 1a2 PPTR signal amplitude DS1t2, and 1b2 computed initial temperature distribution DT1z, t 5 02. 172 The mean depths 3Eqs. 1824 computed from hemoglobin 1z h 2 and thermal 1z b 2 distributions are compared by the use of Student's paired t-test 29 ; for each biopsied skin site z h and z b are essentially indistinguishable 1 p . 0.942: The square root of the standard variance 3s, Eq. 1924 between h i and b i is computed for each biopsied skin site; for type I and type II sites s was 0.03 and 0.08, respectively, as given by .

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Many factors are relevant when comparing hemoglobin h i and thermal b i distributions. First, because the light-fluence distribution decreases at deeper skin positions, 30 we expect values of h i to exceed those of b i at greater depths 1see e.g., Fig. 62. Second, one is not able to exclude a number of potential artifacts in h i . These artifacts include: 112 vessels that are counted during the computation of h i may be empty of blood during laser irradiation and thus may not contribute to b i ; 122 the hemoglobin content may not scale uniformly with the number of blood vessels at various depths; and 132 fixing, dehydrating, and embedding the biopsies may introduce tissue shrinkage. In view of these considerations, the correlation found between h i and b i in this study is satisfactory. Hence the use of state-of-the-art tissue-processing techniques 1e.g., plastic embed-ding2 in combination with novel diagnostic methods 31 may provide a basis for an accurate and objective evaluation of PPTR for the characterization of biological materials.