Combining two excitation wavelengths for pulsed photothermal profiling of hypervascular lesions in human skin.

. When pulsed photothermal radiometry (PPTR) is used for depth proﬁling of hypervascular lesions in human skin, melanin absorption also heats the most superﬁcial skin layer (epidermis). Determination of lesion depth may be difﬁcult when it lies close to the epidermal– dermal junction, due to PPTR’s limited spatial resolution. To overcome this problem, we have developed an approximation technique, which uses two excitation wavelengths (585 and 600 nm) to separate the vascular and epidermal components of the PPTR signal. This technique permits a noninvasive determination of lesion depth and epidermal thickness in vivo , even when the two layers are in close physical proximity to each other. Such information provides the physician with guidance in selecting the optimal parameters for laser therapy on an individual patient basis.


Introduction
Time-resolved measurement of infrared (IR) radiant emission following pulsed laser irradiation, known as pulsed photothermal radiometry (PPTR), can be used to assess the longitudinal temperature profile induced in a layered sample (Tam and Sullivan 1983). Knowing the absorption properties of the sample chromophores, their depth distribution may then be determined (Long et al 1987, Crostack et al 1989. Such a PPTR technique was recently introduced for in vivo depth profiling of hypervascular lesions in human skin, such as port-wine stain (PWS) birthmarks (Jacques et al 1993, Milner et al 1995. PWS consists of an excess of ectatic blood vessels, usually fully contained within the most superficial millimetre of the dermis. PWS depth varies on an individual patient basis, but on average, the highest fractional blood content is found between 200 and 400 µm below the epidermal-dermal junction (Barsky et al 1980).
The ability of PPTR to correctly determine the depth of sub-surface chromophores in turbid media has been demonstrated previously by profiling layered tissue phantoms (Vitkin et al 1995, Milner et al 1996, and comparison with histological assessment of PWS depths (Milner et al 1996). However, when a visible laser pulse is used to increase the temperature of PWS blood vessels for the purpose of PPTR profiling in vivo, melanin absorption heats also the epidermis (50-150 µm thick superficial layer of skin). When the PWS lies in close proximity to the epidermis, determination of lesion depth may be difficult due to the inherently limited spatial resolution of PPTR (Milner et al 1995, Smithies et al 1998. To overcome this problem, we present an approximation technique that achieves improved selectivity by utilizing two excitation wavelengths. Such an approach enables in vivo determination of both PWS depth and epidermal thickness, which is required for optimization of laser therapy involving cryogen spray cooling on an individual patient basis (Anvari et al 1995a.

Experimental setup and theory
A PWS lesion on the arm of a volunteer patient was irradiated with two 1.5 ms duration pulses at 585 and 600 nm, delivered sequentially from a ScleroPLUS pulsed dye laser (Candela, Wayland, MA). At both wavelengths, the energy density at the centre of a 6 mm diameter laser spot was approximately 5 J cm −2 . The transient increase in IR radiant emission from the central 1.9 × 1.9 mm 2 area was recorded with an InSb focal-plane-array camera (Raytheon, Dallas, TX; detection band 3-5 µm) at a rate of 200 frames per second. After calibrating the response of the 64 × 64 array detector elements with a temperature stabilized blackbody, averaging over the array and subtracting the radiant emission level before the pulsed laser exposure, signals s 585 (t) and s 600 (t) were obtained (figure 1). These signals represent the radiometric temperature increase induced by pulsed exposure at 585 and 600 nm, respectively. The radiometric temperatures are given in degrees Celsius of the blackbody temperature increase. (Note, however, that they do not represent the skin surface temperature, due to the finite penetration depth of the detected IR radiation.) Reconstruction of the initial temperature profile from the PPTR signals is a severely ill posed inverse problem (Milner et al 1995, Prahl 1996. In our case, it is solved by a dedicated iterative algorithm using a nonnegative-constrained conjugate-gradient method (Milner et al 1995). As an example, consider the longitudinal temperature profile immediately after 585 nm excitation computed from signal s 585 (t) (figure 1), presented in figure 2(a). The three curves shown are iterative solutions, obtained with different degrees of regularization. In accordance with the discrepancy principle (Groetsch 1984), the iterative algorithm runs until the Euclidian norm of the residue reaches a level defined by a preset signal-to-error ratio (SER). At low values of SER, we obtain under-iterated solutions, which are blurred images of the actual temperature profile. By increasing SER, near optimal solutions that show more detail are obtained, eventually followed by over-iterated results. As discussed previously by Milner et al (1995), the latter often oscillate, as the algorithm attempts to fit mismatches between the experimental and theoretically predicted signals (dotted line). In this study, we avoid the issue of optimal regularization by presenting a series of iterative solutions for each example discussed. Since at high SER settings (SER = 50 in figures 2(a), (b)) the above criterion for terminating the iteration cannot be met, the iteration run is stopped after an arbitrarily chosen high number of iteration steps (n = 100, compared to n = 6 reached at SER = 30). Clearly, in the presented example, the temperature profile in the PWS layer cannot be resolved from the heated epidermis.

Combining two excitation wavelengths
The calibrated PPTR signals s(t) are linear functions of the longitudinal temperature distribution immediately following pulsed laser exposure (Milner et al 1995). Therefore, the superposition principle can be applied to express signal s 585 (t) as a sum of two signal components, originating from the heated PWS (x(t)), and epidermis (y(t)): (1) At 600 nm, the absorption and scattering properties of the epidermis and dermis are essentially equivalent to those at 585 nm (Wan et al 1981). As a result, the temperature profile in the epidermis and, consequently, the corresponding signal component, are nearly equal at both excitation wavelengths. In contrast, absorption by blood is significantly weaker at 600 nm than at 585 nm (van Kampen and Zijlstra 1965; see table 1). This results in a smaller contribution from the PWS to the PPTR signal obtained with 600 nm excitation. The latter can therefore be approximated by α and β are unknown positive constants. Based on the above described spectral properties of the tissue components, we expect their values to be α < 1 and β ≈ 1. Table 1. Absorption coefficients of oxygenated and deoxygenated human blood (hematocrit 40) at 585 nm, 600 nm, and the ratio of the two (from van Kampen and Zijlstra 1965).
Due to the difference in blood absorption, 600 nm laser radiation may penetrate deeper into the PWS compared to 585 nm. Consequently, the PWS temperature profiles induced by the 600 and 585 nm laser pulses are in general not exactly proportional. Nevertheless, the proportionality assumed in equation (2) is valid at least in a thin top layer of the PWS, where both temperature profiles can be linearized. The first-order approximation made in equation (2) is thus appropriate for reconstruction of the epidermal profile and top boundary of the PWS, as required for optimization of therapy, but can be expected to deteriorate at deeper depths. We discuss the limitations of such an approach in more detail in section 4. From equations (1) and (2), the PWS and epidermal components of s 585 (t) can be derived as: By applying our reconstruction algorithm to each of these components separately, the initial temperature profiles in the PWS and epidermis can be obtained independently. Since the values of α and β are not known, we estimate them as follows. First, we use the fact that the radiometric signal immediately following pulsed laser exposure results predominantly from the temperature rise within a few penetration depths of the detected IR radiation (40-50 µm) from the skin surface. Since the blood vessels are located deeper (>100 µm) in the skin, we require that the PWS signal component starts from x(t = 0) = 0, yielding β = s 600 (t = 0)/s 585 (t = 0). A signal, proportional to the PWS contribution x(t), can then be calculated as βs 585 (t) − s 600 (t) (see equation (3a)). The temperature profile reconstructed therefrom is proportional to the temperature increase in the PWS induced by 585 nm excitation.
Second, we know that reconstruction of a pure epidermal component should not contain any temperature increase deeper than 200 µm below the skin surface. Therefore, we calculate signals y(t) according to equation (3b) with increasing values of α, starting from 0, and reconstruct the corresponding temperature profile from each of these signals. This is repeated until the temperature increase deeper than 200 µm below the skin surface drops to zero. The value of α at which this happens is taken as the best estimate, and is used to normalize the amplitude of the previously obtained PWS temperature profile (by simply dividing it by (β −α), in accordance with equation (3a)).

Results
Figures 2(a) and 2(b) present temperature profiles for a PWS birthmark in vivo (on a patient's forearm), as reconstructed from PPTR signals s 585 (t) and s 600 (t) in figure 1, respectively. Without knowing the actual temperature profile, it is certainly somewhat ambiguous whether the solution with SER = 30 (solid line) is closer to optimal than that obtained with SER = 10 (dashed). Irrespective of that, these results convincingly demonstrate how, in the presented example, neither the PWS depth nor epidermal thickness can be assessed by reconstruction from a single PPTR signal. In addition, they illustrate the previously discussed absorption properties of melanin and blood by indicating a similar average temperature increase in the superficial layer (epidermis, containing melanin) but considerably lower temperature rise deeper in the skin with 600 nm excitation ( figure 2(b)), compared to 585 nm (figure 2(a)). Figure 3(a) presents a signal proportional to the PWS component x(t), calculated from the experimental PPTR signals as βs 585 (t)−s 600 (t). As described in the previous section, the value of β is adjusted to bring the first point of this signal to 0 (β = 1.06 for the presented example). The reconstructed temperature profile (figure 3(b)) is proportional to the temperature increase in the PWS layer, and clearly shows its top boundary. The solution obtained with SER = 30 can be disregarded as over-iterated based on its oscillatory shape, which is in agreement with the lower signal-to-noise ratio in the subtracted signal (figure 3(a)) compared to the original single-wavelength PPTR signals (see figure 1). The SER = 20 solution is thus considered as the closest available estimate of the initial temperature profile (solid line).
The signals y(t) calculated according to equation (3b) with α increasing from 0 to 0.50 (curves A-E) are presented in figure 4(a). Temperature profiles reconstructed from these signals (figure 4(b); SER = 50) show steadily decreasing temperatures at depths below 150-200 µm, with values of α increasing up to 0.40. At α = 0.45, the PWS contribution to the temperature profile practically disappears. In the most superficial 150 µm (epidermis), the temperature profile varies little from α = 0.20 to 0.45, indicating that this part of the solution is insensitive to small variations of α. While the PWS contribution is completely absent from the solution at α = 0.50, the abrupt change in width and height of the epidermal profile indicate that this value is most likely too high. A further discussion on determining the best choice of α is given in section 4. Figure 5 presents the final result, showing separately the temperature profiles in the PWS and epidermis (using α = 0.45), which are evidently in close proximity to each other. In fact, our result indicates an overlap of the two profiles, which could result from the uneven shape of the epidermal-dermal junction, but also from broadening of one or both profiles by the limited spatial resolution of the reconstruction algorithm.
In order to establish a direct correlation between our two-wavelength approximation algorithm and single-wavelength PPTR profiling, which has been thoroughly tested before (Vitkin et al 1995, Milner et al 1996, we present in figure 6(a) a similar analysis of another PWS lesion (located on a finger of the same patient). In the PPTR signal obtained with 585 nm excitation (curve A in figure 6(a)), the initial spike, resulting from the heated superficial layer, and the delayed contribution from the deeper lying PWS can be easily distinguished. This indicates that in this specific example, the PWS vascular cluster is spatially separated from the epidermis, which is confirmed by the initial temperature profiles reconstructed from this signal ( figure 6(b)). The signals in figure 6(a) also illustrate how the initial spike, resulting from epidermal heating, is reproduced in the signal obtained with 600 nm exposure (curve B), whereas the delayed contribution from subsurface PWS is considerably diminished.  The temperature profiles in the epidermis (SER = 30) as well as PWS (SER = 20) replicate very closely the ones determined by standard, single-wavelength PPTR profiling (figure 6(b)), up to a depth of ∼400 µm. The two heated layers are separated by approximately 60 µm, which enables the reconstruction algorithm to differentiate their contributions to the 585 nm signal, in contrast to the previous example ( figure 2(a)).

Discussion
The presented method is based on the principle of superposition, which relies on the linear relationship between the PPTR signals following laser exposure s(t > 0) and the induced temperature distribution T (z, t = 0) (equation (5) in Milner et al 1995). This linearity, which is to the best of our knowledge used in all related work thus far, arises from a power series expansion of the emitted infrared radiation intensity (Planck's law) around the starting temperature, of which only the linear term is preserved. The emitted radiation is therefore linear in the temperature distribution only for small temperature increases. For the discussed experiment, by taking into account the acquisition wavelength band of 3-5 µm and initial skin temperature of 35 • C, the actual intensity of the emitted radiation deviates from the corresponding linear approximation by 3.8% for a homogeneous temperature increase of 10 • C. It is very important to note, however, that the amplitudes of the PPTR signals used in the presented analysis have been calibrated by comparison with infrared radiation levels emitted from a homogeneously heated black body, which eliminates most, if not all, of this nonlinearity.
As previously mentioned, equation (2) is a first order approximation, which holds in the epidermis and most superficial layer of the PWS. At deeper depths, the validity of this approximation may deteriorate, depending on differences between the temperature profiles induced in the PWS with 585 versus 600 nm irradiation. The latter likely penetrates deeper into the lesion, since, according to published data on blood vessel size distribution in PWS (Barsky et al 1980) and absorption properties of blood (van Kampen and Zijlstra 1965), most vessels can be expected to behave as optically thin (Lucassen et al 1996). This is reflected in the lower PWS temperature increase observed with 600 nm, compared to 585 nm excitation (figure 2).
As a result, signal y(t) calculated using equation (3b) in general contains some contribution from deeper blood vessels, which can be expected to show up in the reconstructed temperature profiles. The 'epidermal' profile deeper than 200 µm in figure 5, is in our opinion such an artifact of the approximation method, and should not be interpreted as a melanin-mediated temperature increase. For the same reason, the presented PWS temperature profile (reconstructed from x(t) differs from the actual temperature profile induced in the PWS by 585 nm excitation at depths beyond ∼200 µm. The same effect can be observed by comparing the results in figures 6(b) and 6(d), which differ at depths beyond ∼400 µm. Nevertheless, as equation (2) is valid for shallow skin depths, down to the most superficial layer of the PWS, we can conclude that the temperature profiles reconstructed from x(t) and y(t) are representative for determination of PWS depth and epidermal thickness, respectively, as required to guide laser therapy.
When determining the value of α as described in section 2.2, it is instructive to monitor the behaviour of the residual norm. In the example presented in figure 4(b), increasing the value of α from 0.45 to 0.50 results in a 5% higher residual norm, supporting our conclusion that the latter value is likely too high. An overestimated value of α introduces a negative heat source at the PWS position, which cannot be accounted for by the positively constrained inversion algorithm. In the second example presented (figure 6(c)), using a value of α = 0.45 increases the residual norm by a factor of six, compared to α = 0.40 or 0.35, confirming the value of 0.40 as the best estimate. (In view of the inexact nature of our criteria, we made no attempt to determine α more accurately than to the closest 0.05.) In addition, we found that by adding the integrals of the PWS and epidermal temperature profiles, the integral of the profile obtained using 585 nm excitation alone is matched within a relatively narrow error margin (3.0% for figure 5 versus 2(a); 1.0% for figure 6(d) versus 6(b), as required by energy conservation. In both examples, using a larger value of α degraded this match.
PPTR profiling of four PWS sites on the same patient yielded average values ofᾱ = 0.41 (standard deviation s.d. = 0.07), andβ = 1.0 (s.d. = 0.1). The latter indicates that, on the average, the epidermal contributions to the PPTR signals obtained with 585 and 600 nm excitation are nearly equal. The occasionally observed differences between the amplitudes of the initial PPTR signal jump observed with the two excitation wavelengths can be attributed in part to random variations of the excitation pulse energy. In addition, due to strong scattering in dermis, the excitation fluence in epidermis may be somewhat affected by absorption in PWS blood (Verkruysse et al 1993). This effect would diminish the epidermal contribution to the PPTR signal following the 585 nm excitation with respect to 600 nm, in particular when the PWS lies close to the epidermal-dermal junction (as is the case in figure 1).
Although the ratio of PWS temperature increase with 600 versus 585 nm excitation does not depend exclusively on the blood absorption coefficients at these wavelengths, it is interesting to note that the obtained value ofᾱ resembles the absorption coefficient ratio for completely deoxygenated blood (µ 600 /µ 585 = 0.41) as compared to fully oxygenated blood (0.11; see table 1). This may indicate the effect of PWS blood deoxygenation during laser exposure, as a result of the impaired oxygen binding capacity of heamoglobin at increased temperatures (Kelman and Nunn 1966). Note that the temperature increase in the presented one-dimensional profiles reflects the average value at a given depth, whereas temperature rises in individual blood vessels are likely several times higher.
A considerable correction to the above rough estimates of the expected values of α would result from consideration of the absorption in bloodless dermis (µ D = 0.22 mm −1 ; Verkruysse et al 1993). By assuming the fractional blood content in the superficial part of the PWS equal to f = 0.06 (Barsky et al 1980), for example, the value of α would be predicted at (f µ 600 + µ D )/(f µ 585 + µ D ) = 0.26 for completely oxygenated, and 0.52 for deoxygenated blood. However, in view of the influence of other variable factors and effects, such as distribution of vessel diameters (Lucassen et al 1996, Verkruysse et al 1997 scattering in dermis (Verkruysse et al 1997), and dynamical changes in the optical properties of blood (Verkruysse et al 1998), a much more detailed study-possibly taking into account the exact three-dimensional geometry of a specific lesion-would be required in order to draw quantitative conclusions from the experimentally determined values of α.
In conclusion, the presented technique, which combines PPTR signals obtained with two different excitation wavelengths, enables determination of epidermal thickness and PWS depth in vivo with an accuracy sufficient to guide laser therapy, even when the two layers are in close physical proximity to each other. A direct comparison of our approach with standard, singlewavelength PPTR profiling, shows no significant difference in the epidermal profile nor PWS depth, when the two layers are separated by ∼60 µm. In ongoing experiments at our institution (BLIMC), we aim at improving the accuracy of PPTR profiling by using higher acquisition rates and reduced spectral detection band . We are also correlating the temperature profiles determined using the above presented approach with information obtained from non-invasive imaging techniques, such as optical Doppler tomography (Zhao et al 2000a, b). However, such comparisons, as well as those involving histological evaluation of PWS, are practically limited to correlations of epidermal thickness and PWS depth, since the relation between the geometry of the lesion and the laser-induced temperature profile is complicated by the nonhomogeneous distribution of the chromophores and strong scattering of the laser radiation in skin.