Determination of parameter β for dual-wavelength pulsed photothermal profiling of human skin

~ Presented on 24 June 2002 ! In pulsed photothermal proﬁling of human skin, subsurface blood vessels may be difﬁcult to resolve due to nonselective absorption in the overlying epidermis. The dual-wavelength excitation ~ DWE ! technique solves this problem by exploiting spectral differences between the epidermal melanin and blood hemoglobin. An improved approach to determination of DWE-speciﬁc parameter b for depth proﬁling of port wine stain birthmarks in vivo using the 585 and 600 nm wavelengths is discussed. © 2003 American Institute of Physics. @ DOI: 10.1063/1.1517186 #


I. INTRODUCTION
2][3] However, due to melanin absorption in the epidermis ͑50-150 m thick superficial layer of skin͒ and inherent limitations of PPTR, 2,4,5 PWS blood vessels may not be resolved from epidermal heating when they lie in close proximity to the epidermal-dermal ͑ED͒ junction.
The dual-wavelength excitation ͑DWE͒ approach solves this problem by exploiting spectral differences between the melanin and blood hemoglobin. 6We describe an improved approach to determination of DWE-specific parameter ␤, which controls the removal of epidermal contribution to PPTR signals in depth profiling of PWS.The same approach was recently applied to three-dimensional PPTR imaging of in vivo PWS. 7

II. MATERIALS AND METHODS
A PWS lesion on the forearm of a volunteer patient was irradiated with 1.5 ms pulses from a flashlamp-pumped dye laser ͑ScleroPLUS, Candela, Wayland, MA͒, at wavelengths of 585 and 600 nm and a subtherapeutic radiant exposure (5 -6 J/cm 2 ).Infrared ͑IR͒ radiant emission from the central 1.9ϫ1.9mm 2 area was recorded by an InSb focal-planearray camera ͑Galileo, Raytheon, Dallas, TX͒ at a rate of 700 frames per second.A narrow detection band ͑4.5-5 m͒ was used to reduce the spectral variation of the IR absorption coefficient. 8PPTR signals were prepared by calibrating the system response with a computer-controlled blackbody, averaging the used subset of array elements (64ϫ64), and subtracting the background signal level.
Within the customary assumptions and approximations, 2,4,8 PPTR signal ͓S(t)͔ is related to the initial temperature profile ͓⌬T(z,tϭ0)͔ as In the present study, we apply the kernel function K(z,t) derived by Milner et al. 2 and the same tissue parameters as used in Ref. 8. From signals S(t), represented by 400 measured values, temperature profiles ⌬T(z,0) in the most superficial millimeter of skin are reconstructed at 64 equidistant points using a non-negatively constrained conjugategradient algorithm, regularized by early termination. 2igure 1 presents ⌬T(z,0) in in vivo PWS, reconstructed from a PPTR signal S 585 (t), acquired after 585 nm exposure ͑Fig.2͒.The solid line is a near-optimal solution according to L-curve analysis 2 ͑iteration number nϭ5), dashed and dotted lines are under-(nϭ2) and overiterated solutions (n ϭ10), respectively.The latter is featuring characteristic oscillations. 2The PWS temperature profile cannot be resolved from the heated epidermis, as the two layers lie in close proximity to each other.

III. DUAL-WAVELENGTH EXCITATION
Due to linearity of Eq. ͑1͒, S 585 (t)ϭx(t)ϩy(t), where x(t) and y(t) mark the contributions from PWS vessels and the epidermis, respectively.At 600 nm, hemoglobin absorption is several times weaker than at 585 nm, 9 while the absorption and scattering properties of the epidermis and dermis are equivalent at either wavelength. 10As a result, the PPTR signal after the 600 nm excitation has a smaller PWS contribution, while the epidermal signal component is very similar.As a first-order approximation, we can write From in Eq. ͑2͒, the PWS and epidermal contributions to S 585 (t) are The corresponding temperature profiles can be reconstructed separately after the parameters ␣ and ␤ are determined.
The value of ␣ is determined based on prior anatomical knowledge that no melanin is present below the ED junction.The temperature profiles reconstructed from y(t) with increasing values of ␣ differ very little in the epidermal region, while the temperature rise deeper in skin decreases monotonically.6 The lowest ␣ that yields a zero temperature rise below the ED junction is selected as optimal.At larger values of ␣, the epidermal temperature profile degrades and the norm of the residue increases.The described approach is theoretically sound and very reliable.In the present example, ␣ϭ0.45.
Similarly, ␤ can be determined by utilizing the fact that no blood vessels are found in the epidermis.Since PPTR senses the tissue temperature only within a few penetration depths of the detected radiation, the PWS contribution im-mediately after laser exposure was assumed to be zero in our original report on DWE profiling of human skin. 7Such logic results in a simple formula, ␤ Ϫ1 ϭS 585 (tϭ0)/S 600 (tϭ0), which yields ␤ Ϫ1 ϭ0.83 in the present example.The corresponding signal x(t) is plotted in Fig. 2.

IV. IMPROVED DETERMINATION OF PARAMETER ␤
Since the IR penetration depth in our system is ϳ40 m, 8 and blood vessels may be found 50-100 m below the skin surface, the hemoglobin contribution to the PPTR signal may jump instantly to a nonzero value upon laser exposure.The above assumption ͓i.e., x(tϭ0)ϭ0] is therefore not generally valid, and a more careful approach to determination of ␤ is warranted.
In Eq. ͑3͒, the epidermal contribution to S 585 (t) is removed by subtracting a suitably sized signal S 600 (t).Similar to the above-described determination of ␣, we reconstruct the temperature profiles from x(t) with increasing values of ␤ Ϫ1 ͑Fig.3͒.The lowest value yielding a zero temperature rise in the superficial 50 m ͑epidermis͒ is selected as optimal (␤ Ϫ1 ϭ0.77; solid line͒.The corresponding x(t) differs significantly from that obtained using the earlier approach ͑Fig.2͒.
At lower than optimal values of ␤ Ϫ1 , some epidermal contribution is noted in the resulting temperature profiles, but the PWS component is essentially unaffected ͑Fig.3͒.At higher values, in contrast, the top boundary of the PWS is ''pushed'' deeper into the skin.At ␤ Ϫ1 ϭ0.83, as obtained using the original formula, the PWS depth is overestimated by ϳ30 m ͑Fig.3, dash-dot-dot͒.This is reasonable in view of the underlying assumption that no IR radiation from the PWS transpires directly to the skin surface.
Figure 4 presents the quadratic norm of the residue ͑i.e., difference between the measured signal and that predicted from the solution͒ as a function of iteration number, for the reconstructions leading to Fig. 3.With ␤ Ϫ1 р0.77 ͑solid and short-dashed lines͒, the residual norm reaches the same value as for the signal S 585 (t) alone ͑dotted line͒.This suggests that the quality of the reconstructed PWS temperature profiles is not affected by the remaining epidermal contribution.With higher than optimal ␤ Ϫ1 values, however, the ultimate FIG. 3. ⌬T(z,0) as obtained from x(t) with increasing values of ␤ Ϫ1 .The lowest value yielding a zero temperature increase in the epidermis is selected as optimal (␤ Ϫ1 ϭ0.77; solid line͒.At higher values of ␤ Ϫ1 , the PWS profile is ''pushed'' deeper into the skin ͑all curves: nϭ20) residual norm increase by 39% at ␤ Ϫ1 ϭ0.80, and by a factor of 4.4 at ␤ Ϫ1 ϭ0.83.This happens because an overestimated ␤ Ϫ1 defines a PPTR signal corresponding to a negative temperature change in the epidermal region, which cannot be accounted for by the positively constrained reconstruction algorithm.
In Figs.5͑a͒ and 5͑b͒, respectively, we compare temperature profiles reconstructed from x(t) with ␤ Ϫ1 ϭ0.83 ͑according to the original formula͒, and ␤ Ϫ1 ϭ0.77.With the latter, convergence of the reconstruction is significantly improved, allowing a much more reliable assessment of PWS depth and peak temperature.While the PWS depth, as determined at half-height of the temperature profiles in Fig. 5͑a͒, is relatively stable ͑100 and 110 m at nϭ10 and 20, respec-tively͒, these values differ considerably from 82 m in the improved results ͓Fig.5͑b͔͒.
To complement the final result, Fig. 5͑b͒ includes a profile reconstructed from y(t) ͑dash-dotted line; ␣ϭ0.45, n ϭ10).Note that the two solutions ͑solid and dash-dotted lines, respectively͒ represent correctly the temperature rise in PWS and epidermis at depths up to ϳ0.2 mm, where the deeper part of the latter solution starts.͑A detailed discussion of this artifact can be found in Refs.6 and 8.͒

V. DISCUSSION
In comparison with the earlier approach, the improved determination of parameter ␤ results in: ͑a͒ more accurate determination of the PWS depth ͑Fig.3͒; ͑b͒ improved quality of the result ͑Fig.4͒; and ͑c͒ improved convergence of the iteration, allowing a more reliable assessment of the optimal solution ͑Fig.5͒.These effects can be used as additional indicators in determination of optimal ␤.The largest improvement will result in shallow PWS, where the assumption of the earlier approach is most likely violated.
As seen in Fig. 3, variations in ␤ only marginally influence the PWS profile, as long as the optimal value of ␤ Ϫ1 is not exceeded-analogous to determination of ␣ in our earlier report.6 The values of ␣ and ␤ affect the PWS and epidermal temperature profiles also through the nominators in Eqs.͑3͒ and ͑4͒.Since the area under the PPTR-determined temperature profiles correlates accurately with deposited laser energy, 4,5 this provides an additional check on the selected values.The sum of areas under the final profiles in Fig. 5͑b͒ is within 1.5% of that obtained from S 585 (t) alone ͑Fig.1͒.
The overlap of the epidermal and PWS temperature profiles in Fig. 5͑b͒ is consistent with uneven shape of the ED junction in human skin.However, it may in part result from broadening of the two profiles due to inherent limitations of PPTR profiling. 2,4,5IG. 4. Residual norm as a function of the iteration number (n), illustrating the convergence and quality of reconstructions with different values ␤ Ϫ1 .With ␤ Ϫ1 ϭ0.77 ͑solid line͒ and lower, the norm reaches the same value as for the signal S 585 alone (␤ Ϫ1 ϭ0, dotted line͒.At higher ␤ Ϫ1 values, the residual norm is increasingly higher.FIG. 5. ⌬T(z,0) obtained using: ͑a͒ ␤ Ϫ1 ϭ0.83, and ͑b͒ the optimal value ␤ Ϫ1 ϭ0.77.Convergence of the iterative reconstruction is significantly improved in the latter example.The dash-dotted line in ͑b͒ is the profile reconstructed from y(t).͑See the text for details.͒