Lasers in Surgery and Medicine 16:147-155 (1995)
Wavelengths for Laser Treatment of Port
Wine Stains and Telangiectasia
Martin J.C. van Gemert, A.J. Welch, John W. Pickering, Oon Tian Tan, and
Geert H.M. Gijsbers
Laser Centre, Academic Medical Center, Amsterdam, The Netherlands (M.J. C.v.G.,
J. W.P., G.H.M.G.);Biomedical Engineering Program, University of Texas,
Austin (A.J. W.); Deparfment of Comparative Medicine, Tufts University,
Boston, Massachusetts (0.T. T.)
Background and Objective: This report presents analytical modelling of the influence of wavelength on the amount of volumetric
rate of heat produced in dermal blood vessels by millisecond laser radiation.
Study designlMaterials and Methods: A new anatomical model is
proposed that represents port wine stains as well as telangiectatic lesions. It consists of a target blood vessel, representing the
deepest dermal blood vessel that requires irreversible injury, and
a layer of whole blood, representing all other dermal blood vessels above the target vessel. The laser light that interacts with the
blood vessels is assumed to be diffuse. Selective photothermolysis is the basis for the analysis. We consider wavelengths between
577 nm and 600 nm, the argon laser wavelengths at 4881515 nm,
and the frequency doubled NdYAG laser wavelength at 532 nm.
Results: The rate of volumetric heat production of absorbed laser
light in the target blood vessel is expressed analytically as a function of blood absorption, the concentration of additional dermal
blood, and the depth of the target vessel.
Conelmion: The model explains why 585 nm is a good compromise for treating port wine stains that vary widely in number of
dermal blood vessels. It predicts that wavelengths between 577
nm and 582 nm are excellent for the treatment of port wine stains
in young children, and it suggests a possible explanation as to
why the argon laser is sometimes said to be capable of treating
dark mature port wine stains. The copper vapour laser wavelenght at 578 nm, and the frequency doubled Nd:YAG laser wavelength at 532 nm, are predicted to be suitable for the treatment of
port wine stains that contain, respectively, a small to moderate
and a moderate number of dermal blood vessels. When laser
beam spotsize becomes smaller, the best wavelength for producing maximal rate of heat in the target vessel is predicted to shift
t0 577 nm. Q 1995 Wiley-Liss, Inc.
Key words: port wine stain, telangiectasia, modelling, laser wavelengths, 577 nm,
585 nm, millisecond pulses, argon laser at 4881515 nm, frequency
doubled Nd:YAG laser wavelength at 532 nm, copper vapour laser
wavelength at 578 nm, beam diameter, concentration of dermal blood
Accepted for publication May 20, 1994.
Address reprint requests to Martin J.C. van Gemert, Laser
Centre, Academic Medical Centre, Meibergdreef 9, 1105 AZ
Amsterdam, The Netherlands.
0 1995 Wiley-Liss, Inc.
Geert H.M. Gijsbers is now at the Laser Laboratory, Thorax
Center, Dijkzicht Hospital, Rotterdam, The Netherlands.
This work was presented during the Second International
Laserfair Conference, Edinburgh, 16-17 October, 1992.
148
van Gemert et al.
INTRODUCTION
Many laser systems have been judged suitable, at different times and by different groups,
for removing the abnormally ectatic blood vessels
in port wine stains (PWS). These include the
ruby, argon, argon pumped dye, flashlamp pulsed
dye, copper vapour, Nd:YAG, frequency doubled
Nd:YAG and CO, lasers. Each of these systems
has its own unique properties of wavelength, exposure time, and power [1,21. It is not surprising
that such a wide range of wavelengths (48810,600 nm), exposure times (40 ns to continuous
wave), powers (1Watt to several kWatt), and spotsizes (0.1-7 mm) have resulted in confusion as to
what the “ideal” combination of laser parameters
might be that would selectively and effectively
destroy the abnormal blood vessels in these birthmarks without adversely altering adjacent nonvascular tissues.
One set of laser parameters consisting of a
combination of wavelength (585 nm), pulse duration (0.45 ms), fluence (5-8 J/cm2), and spotsize
(3-5 mm) has been shown to produce selective
vascular injury using the flashlamp pulsed dye
laser [31. The question might then be: Are all of
the laser parameters used in this combination
equally important t o achieve this vascular selectivity or are certain of these parameters more important than others? Because of the complexity of
PWS pathology [41 and, until recently, the paucity of histologic data documenting the sequence
of pathological events occurring following exposure of the skin to laser irradiation, it has been
difficult to assess the response of PWS blood vessels t o the different laser systems and to compare
the effectiveness of these systems.
The most important parameter for achieving
vascular selectivity is wavelength. The absorption spectral peak of oxyhemoglobin, at 577 nm,
has been demonstrated by several investigators t o
produce vascular-specific injury [5]. Tan et al. [6]
have demonstrated that replacement of the 577
nm wavelength by 585 nm (almost two times less
absorption in blood) increased the average dermal
depth of vascular injury of the laser light in six
adult PWS patients from 0.72 mm from the
dermo-epidermal junction to 1.2 mm. A possible
explanation of these clinical findings has been recently published [7]. This explanation is based
upon the concept that the penetration depth is
reduced through absorption of the scattered light
by dermal red blood cells. The explanation requires sufficiently short irradiation times (be-
tween 0.1 ms and 10 ms [8,91) to confine the thermal injury to the blood vessel walls, and a spotsize
that is sufficiently large (>3 mm) to produce the
deepest possible tissue penetration of the light per
unit of irradiance [81.
In this report, the differential effect of wavelength upon volumetric heat production in blood
vessels of PWS and telangiectasia is described assuming the conditions for selective photothermolysis t o apply, i.e., pulse durations in the order of
ms, and 577 nm as the best wavelength to injure
an isolated blood vessel [lo]. The model is simple,
analytically solvable, and depends only on the coefficient of blood absorption, the dermal depth of
the deepest vessel that requires injury (the target
vessel), and the concentration of dermal blood
above the target vessel. It provides guidelines for
the choice of laser parameters that might suitably
be used for conducting comparative clinical studies on PWS and telangiectasia.
THE MODEL
Consider Figure 1A where one (target) blood
vessel of a certain diameter located parallel t o the
air-tissue interface is embedded in the dermis at
a certain depth. This model has been widely used
to represent the vasculature of a PWS [8-101, and
it is obviously an excellent representation of a
telangiectatic lesion. The photons, a-d, represent
four out of a huge number of photons within the
laser beam spotsize that will reach the target vessel.
A more realistic model of a PWS vasculature
is shown in Figure 1B. Other blood vessels are
added in addition t o the target vessel. Again, the
blood vessels are chosen parallel to the air-tissue
interface. The same photons, a-d, as in Figure 1A
are shown, but these photons now cross blood vessels numbered 1 and 3, respectively. As absorption of photons by a chromophore has a certain
probability, represented by the absorption coefficient of the chromophore (blood), it is assumed
here that photon a is absorbed by blood vessel 1
but that photon d is not absorbed by blood vessel
3 and that its direction of propagation is unchanged. The point of Figure 1B is to suggest that
all blood vessels in the irradiated volume of the
dermis have a certain probability of absorbing
scattered photons that cross the blood vessels and
that would otherwise reach the target vessel. It is
obvious that the larger the absorption coefficient
of blood, the more these scattered photons are ab-
Laser Wavelengths for Port Wine Stains
sorbed, and the fewer of them will reach the target vessel.
The target vessel as well as the other vessels
are chosen sufficiently deep inside the dermis
that only scattered photons can reach them. We
emphasize that for the wavelengths of interest,
between 488 nm and 600 nm, scattering dominates over absorption in skin tissue [ill. Hence
the average pathlength that a photon can propagate in the (bloodless) dermis between two scattering events (-0.1 mm) is much shorter than the
average pathlength between two absorption
events (-10 mm). As a consequence, the laser
a
b
a
d
C
b
C
d
-
149
light that reaches the blood vessels is diffuse (photons have scattered several times).
We hypothesize that the dermal blood vessels above the target vessel can be represented as
a layer of blood located in the dermis between the
air-skin interface and the target vessel (Fig. lC>.
The dermal depth of this layer is arbitrary as it is
assumed to be deep enough to have only interaction with diffuse light. However, it is highly
likely that our model of Figure 1C is not an exact
representation of that of Figure 1B.
The thickness of the layer D in Figure 1C is
directly proportional to the amount of dermal
blood above the target vessel. That is, it is directly
proportional to the volumetric concentration of
blood C, (volume of blood per volume of dermis)
and t o the dermal depth over which these additional vessels occur, which is assumed here to be
the depth of the target vessel z,. Hence,
Assuming values of z, vary between 0.5 mm for
young children and 1mm for adults [12], and values of C, between 0 and 10% [131, D varies between 0 and 0.1 mm.
We emphasize that lesion colour correlates
with the total amount of dermal blood present
113,141 and, hence, with D (Fig. 1C). Unfortunately, a quantitative correlation between colour
and D is unknown, although we assume that
small values of D will represent pink lesions,
I 1
1
EPIDERMIS
TRANSMITTED
PHOTON
PHOTON I
;
B
A
EPIDERMIS
DERMIS
1
LAYER OF
BLOOD
c
--@%-
VESSEL
TARGET
lzv
Fig. 1. A. Model of a vascular skin leasion that consists of one
ectatic target blood vessel located in the dermis at dermal
depth z, and directed parallel to the air-epidermis interface.
Four photons are shown, labelled a, b, c, and d, out of a huge
number of photons incident on the epidermis that reach the
target vessel. B. A more realistic model of a PWS, consisting
of the target vessel (as in A, but representing here the deepest
ectatic dermal blood vessel that requires irreversible injury)
and, e.g., three additional ectatic blood vessels, numbered 1,
2, and 3, which are located elsewhere in the dermis and which
are all directed parallel to the target vessel. For simplicity,
the additional vessels are assumed to have the same diameter
as the target vessel. Photon a is assumed to cross blood vessel
1 and t o be absorbed by the blood in that vessel. Photon d is
assumed to cross blood vessel 3 without any interaction,
reaching the target vessel. C. The final model used here, consisting of a layer of whole blood representing all dermal blood
vessels anterior to the target vessel, and the target vessel
located below the layer of blood at dermal depth z,. The thickness D of the blood layer is such that it contains the same
amount of red blood cells per volume of skin as the anterior
vessels. This requires Eq. (1) to be valid.
van Gemert et al.
150
path length L in blood layer D, where L(D) depends on D. It is assumed to follow Beer's law as
Ab(A,D) = exp[- pa,b(h)L O 1
(34
When the light is collimated and normal t o the
layer D, then L = D, and A,(A,D) = expi- p,,b(h)Dl.
However, if the light is diffuse, the average pathlength is equal to L = 2D [15]. Even more complicated is the resulting angular distribution of diffuse light that propagated through an absorbing
layer of thickness D. The average pathlength that
results under such circumstances represents an
500
550
WAVELENGHT b m ) 6oo
interesting question that we do not consider here
as it does not affect the argument of this report.
Fig. 2. Absorption coefficient of whole blood as used here H
~we ~ ~ that
, the average path length for
(from ref.8). Wavelengths >577 nm that have equal blood
diffuse
light,
L,
is
twice the geometrical pathabsorption coefficients as 4881515 nm and 532 nm are indiSo,
L=2D,
and hence
length
D
[151,
cated (respectively, 586.61587.4 nm and 583 nm).
/
I
I
1
L
I
8
I
f
I
I
A,(A,D) = exp[-pa,b(A) 2 Dl
(3b)
whereas large
Of
represent purple The rate of volumetric heat production (Watt/cm3)
lesions.
at the top of the target vessel lumen at dermal
we now examine the rate Of heat production depth z,, Q(A,z,,D), is well known to be the prodin the
at the
Of the target
lumen, uct of fluence rate and blood absorption coeffiwhich is proportional to the amount of available cient
local light intensity and the absorbing properties
of blood. The light intensity at wavelength A,
Q(h,z,,D) = +(h,z,,D) pa,b(h)
(4)
reaching the top of the blood vessel lumen at dermal
V
'
is the light fluence rate +(A,z~,D)For the short pulse durations considered, of -1
(Watt/cm'). Values of the blood absorption coeffi- ms, the temperature rise achieved at the end of
cient pa,b(A)> which
with wave- the laser pulse is in good approximation proporlength L8] are graphed in Figure 2* In the wave- tional to Q. Using Eqs. (2) and (3b), Eq. (4) belength band considered in this report (488-600 comes
nm), the maximum blood absorption coefficient is
35.4 mmpl at 577 nm.
Q(A,z,,D) = E Ae,d exp[-p,,,b(A) 2 Dl ka,b(h) ( 5 4
When E is the laser beam irradiance (Watt/
cm2) incident on the air-skin interface, the flu- In this report, we do not specify Ae,d any further
rate at
V
'
is
to
as we want only to study the wavelength depenPlied
two factors that account for Propagation dence of the rate of heat production in the target
through,
the bloodless skin (ePider- vessel at a fked, although unspecified value of z,.
mis-dermis, represented by a factor Ae,J and the
we therefore divide
in Eq. (5) by &(A =
layer of blood (represented by a factor Ab)
577nm,z,,D = 01, which represents the maximum
possible rate of heat prodiction in the target ves(2) sel
The actual value of Ae,ddepends on the epidermal
and dermal absorption and scattering coefficients,
the laser spotsize diameter, and the dermal depth
of the target vessel z,. A good approximation is t o
assume that Ae,dis independent of wavelength in
the wavelength band of 577-600 nm.
Propagation of light through the layer of
blood is a function of wavelength A and average
Q(h,zV,D)/Q(577nm,z,,D= 0) =
exp[- pa,b(h) 2 D1Fa,b(h)/35.4
(5b)
Equation (5b) is the final result of our model. It
represents the rate of volumetric heat produced in
blood at the top of the target vessel lumen and
relates this with laser wavelength, dermal location of the target vessel, and amount of dermal
Laser Wavelengths for Port Wine Stains
blood. Blood absorption coefficient pa,b(X) is the
factor that varies with wavelength X, Figure 2, and
D is the factor that varies with z, and cb, Eq. (I).
The model does not explicitly account for factors
such as epidermal pigmentation or laser beam
spotsize. This would require computation of Ae,din
Eqs. (2) and (5a)by using photon propagation models te.g., Monte Carlo numerical methods).
151
RESULTS
A plot of Q(A,z,,D), divided by Q(X =
577nm,z,, D = 01, Eq. (5b), is given in Figure 3 as
a function of wavelength h, and for various values
of blood layer thickness D. The values of Q at
D=O represent the rate of volumetric heat production at the top of a telangiectatic blood vessel
lumen at dermal depth z,, which are proportional
to the blood absorption coefficient. Note that the
maximum value of Q(A,z,,D = 0 ) is proportional t o
the maximum value of the blood absorption coefficient p,,b(h), which is at h = 577 nm. This implies that a single isolated dermal ectatic vessel
at (any) dermal depth z, can best be injured by a
laser pulse at 577 nm, in accordance with the concept of selective photothermolysis [lo] that we
adopted here. Figure 3 shows that addition of a
small amount of dermal blood (values of D up to
0.0141 mm, obtained from pa,,(577nm)2D = 1,see
Appendix) lowers the amount of heat that can be
produced in the target vessel, but retains 577 nm
as the best wavelength for irreversible injury (see
Appendix). Further addition of dermal blood vessels is predicted not only to lower the amount of
heat that can be deposited in the target vessel,
but also t o shift the “best” wavelength for heat
production to larger values than 577 nm. Note,
e.g., that for D = 0.04 mm, there is a 2.2 times
greater rate of heat production at 586.9 nm
(wavelength of maximum heat production) than
at 577 nm.
The “optimal” wavelength, ,X, where the volumetric rate of heat production in the target vessel is maximal, see Figure 3 and Eq. (7) of Appendix, and those wavelengths >577 nm where 80%
and 90% of the maximum heat is produced, are
plotted in Figure 4 as a function of blood layer
thickness D. This figure shows that the “best”
wavelength is 577 nm when D 5 0.0141 mm; it
changes abruptly to wavelengths longer than 577
nm when D > 0.0141 mm. Figure 4 predicts that
when 80% of the maximum rate of heat production is considered adequate, wavelengths longer
than 582 nm can handle more and more dermal
0.3
0.2
570
580
590
Boo
WAVELENGTH (nm)
Fig. 3. Relative rate of volumetric heat production at the top
of the target vessel lumen, as a function of wavelength, for
various values of D. The model predictions are according to
Eq. (5b). The wavelength of maximum heat production (A,) is
indicated (see Appendix).
blood (larger D values). Figure 4 also predicts
that wavelengths between 577 nm and 582 nm
produce virtually the same rate of heat in the target vessel for values of D<0.03 mm. This prediction correlates surprisingly well with results by
Tan et al. 1161who showed in albino pigs virtually
identical dermal vascular injury for h = 572 nm
(with identical blood absorption as 581 nm, Fig.
2), 577 nm and 580 nm, for incident energy densities between 5 and 10 J/cm2.
In Figure 5 , the maximum rate of volumetric
heat production is shown at optimal wavelength
X, (see Appendix), and at a fixed albeit unspecified depth z,, relative to the maximum possible
rate of heat production at z, (which is at 577 nm
and for D = 0 mm) as a function of D. From Eq.
(5b) this is given by
van Gemert et al.
152
-1
t
"A
e---___
I
If
I
0.0141
I
0.1
l
0.0141
I
I
0.05
0.1
0.05
0 (mm)
0 (mm)
Fig. 4. Wavelength of maximum heat production, A,, and
wavelengths at which 80% and 90% of the maximum heat is
produced, as a function of D. (For details, see Appendix.) The
wavelengths longer than 577 nm that have equal blood absorption as the argon and frequency doubled Nd:YAG laser
wavelengths are also indicated (the dashed lines at 586.6/
587.4 nm and 583 nm, respectively). We assume that values of
D that are very small correspond to pink PWS and values of
D that are large correspond to purple PWS.
Figure 5 shows that a substantial reduction in
rate of heat production occurs at the target vessel
when the dermal blood concentration increases,
even for irradiation with optimal wavelength A,.
In the Appendix it is derived that Eq. (6) shows a
rapidly decreasing behaviour as exp(-35.4 2 D)
= exp(-70.8 D) for D between 0 and 0.0141 mm,
and a much slower decrease as pa,b(&)j/(35.4
e) =
pa,b(Ao)/96.2, which equals 1/(192.45 D), for
DB0.0141 mm. As an example, for D = 0.035
mm, only 15% of the maximum possible heat is
produced in the target vessel at dermal depth z,
compared to a single telangiectatic vessel (D = 0
mm) at the same depth.
DISCUSSION
The Model
The model is based upon three assumptions.
First, selective photothermolysis [lo1 is the basis
for the analysis. This implies (1)577 nm is the
best wavelength for injury of an (isolated) blood
vessel, irrespective of the size of the vessel, and
(2) ms pulse durations, implying that influences
of cooling the target by heat conduction, and by
blood flow of the dermal vessels [171 can be neglected. Second, the light surrounding all blood
vessels is diffuse. The influence of the additional
blood vessels, in terms of attenuating the diffuse
photons that are bound to reach the target vessel,
is represented by one single layer of whole blood.
The thickness D of that layer is directly related t o
Fig. 5. Relative maximum volumetric rate of heat production, according to Eq. (6) and Figure 3, as a function of D
(mm). (For details, see Appendix.) Dashed line: continuation
of exp(-70.8D) beyond D = 0.0141 mm.
the product of the dermal concentration of additional blood (vessels) and to the dermal depth over
which these vessels occur (which is here assumed
to be the depth z, of the target vessel), Eq. (1).
Attenuation of diffuse light by the layer of blood
is assumed to follow Beer's law. The use of 2D as
the effective thickness of the layer is an approximation, most likely valid only for small values of
D, that is for ~ , , ~ ( h ) 2 D < < For
l . large values of D,
nonzero transmission of the diffuse light through
the layer occurs mainly at (near) perpendicular
incidence. Under such conditions of large D values, the factor pa,b(h)L in Eq. (3a) should most
likely become close to p.,,b(h)D. In this work, we
use the factor of 2 in Eq. (3b) for convenience, but
it must be kept in mind that this factor is expected to be between 2 and 1, depending upon
whether D is small or large. Third, it is tacitly
assumed that once the target vessel is injured all
other anterior vessels are injured, too. It is also
assumed that the absorption coefficient of blood
remains constant during the laser pulse. The use
of one layer of blood to represent volumetrically
distributed dermal vessels may not be exact, but,
unfortunately, its verification requires an optical
model that contains a distribution of blood vessels
comparable to "real" PWS skin. Nevertheless, the
advantage of the present model is its simplicity,
as expressed by Eq. (5b). Obviously, such an approach can only be useful when relative behaviour is studied, such as shown in Figures 3-5.
Another advantage of the present model is that it
has been made independent of the actual absorption and scattering behaviour of skin tissues by
normalizing the rate of heat production to the
maximum possible rate of heat production in the
target vessel (at 577 nm, and D = 01, Eq. (5b). It
Laser Wavelengths for Port Wine Stains
153
only depends on the absorption coeffkient of amount of dermal blood equivalent t o about D <
whole blood. Fortunately, this latter parameter is 0.03 mm (at least 80% of the maximum rate of
well known, whereas the optical parameters for heat production). For children having a dermis of
epidermis and dermis are not yet available with -0.5-0.7 mm thickness 1121, D<0.03 mm corregreat accuracy.
sponds to dermal blood concentrations C,<6%.
The present anatomical model combines two The present analysis, therefore, predicts 577-582
previously used PWS models: the layer of blood nm to be excellent laser wavelengths for the
118,191, and the target vessel [9,10]. The layer of treatment of PWS in very young children. Alblood accounts here for the attenuation of diffuse though this speculation must still be tested clinlight by all blood vessels that are present in the ically, it is supported by an earlier publication of
dermis (in addition to the target vessel) instead of Tan et al. [201, who described excellent clinical
representing the vascular target itself [18,191. In results of PWS in children using 577 nm.
this way our model accounts for the competition
A quantitative comparison between the arthat occurs between absorption of photons by the gon, frequency doubled Nd:YAG, and copper
additional dermal blood vessels and absorption of vapour laser wavelengths and the flashlamp
photons for producing heat in the target vessel: a pulsed dye laser is difficult to make as the former
large (small) blood absorption coefficient produces lasers can produce only a fraction of the power of
correspondingly a large (small) attenuation coef- the flashlamp pulsed dye laser. Consequently,
ficient. At 577 nm the model predicts that for these lasers operate with longer irradiation times
D>0.0141 mm of additional blood content (e.g., z, and/or smaller beam spotsizes and are theoreti= 0.5 mm and 2.82% blood concentration, or z, = cally less optimal for PWS treatment [2,S] be1mm and 1.41%blood concentration) attenuation cause they easily cause nonspecific dermal injury.
by the other blood vessels becomes the limiting In addition, blue-green and green wavelengths
factor in the production of heat by preventing too are expected to have smaller skin penetration
many photons from reaching the target and pro- depths than yellow wavelengths due to larger epiducing heat. A reduction in blood absorption, by dermal and dermal absorption and scattering
shifting the wavelength to larger values than 577 (smaller A,, values). Furthermore, copper vapour
nm, results in so much more light fluence rate at and the new frequency doubled Nd:YAG lasers
the top of the target vessel lumen that the rate of have short pulses, high peak powers per pulse,
heat production increases again despite the re- but such a high repetition rate that these lasers
are considered to operate as “quasi continuous
duction in (target) blood absorption.
wave.” In this report, a qualitative comparison is
Wavelengths
made by considering wavelengths between 577
From Figures 3 and 4, it can be assessed that nm and 600 nm that have equal blood absorption
585 nm produces at least 80% of the maximum coefficients as the argon, frequency doubled Nd:
possible volumetric rate of heat in the target ves- YAG, and copper vapour laser wavelengths (Fig.
sel for values of D between 0.012 mm and 0.049 21, but that have otherwise identical pulse duramm, with a maximum at D = 0.026 mm. A t D = tions and beam spotsizes as the flashlamp pulsed
0 mm, 585 nm still produces 54%of the maximal dye laser (typically -1 ms and 3 to 5 mm, respecpossible rate of heat (maximum at h, = 577 nm), tively).
Consider, first, the argon blue-green laser
whereas at D = 0.07 mm, this is 50% (maximum
at X, = 589.8 nm). Our model clearly predicts 585 lines at 488/515 nm. The wavelengths of equal
nm to be a good compromise in producing optimal blood absorption are 586.61587.4 nm and our
volumetric rate of heat in the target vessel for a model predicts that they produce maximum voluwide range of dermal blood layer thicknesses and metric heating of the target vessel when D =
hence for a wide range of PWS anatomies and 0.03810.045 mm. The range of D values where at
colours. However, our model also predicts that least 80% of the maximal possible rate of heat is
585 nm is not the single best wavelength for treat- produced is between 0.017 mm and 0.081 mm. Asing PWS, but that other wavelengths can perform suming for adults the deepest target vessel is at z,
equally well, or even better, depending upon the -1 mm, such values of D represent a dermal conamount of dermal blood present [7,81. An inter- centration of blood vessels that correspond to the
esting speculation is based on the observation in darker types of PWS [13,14]. Although blue-green
Figure 4 that wavelengths between 577 nm and light from an argon laser has a well-documented
582 nm are excellent to treat PWS with an limited depth of vascular injury [211, usually non-
van Gemert et al.
specific, it is a noteworthy coincidence that the length for producing heat in dermal blood vessels
argon laser is claimed to do well in dark, mature is discussed in some detail and is related to the
PWS [2,22]. Second, the 532 nm green wave- amount of blood present in the dermis and, hence,
length of a frequency doubled Nd:YAG laser has a to the colour of the lesion. This sort of information
blood absorption that is equal to that at 583 nm may be of particular value when, in the near fu(Fig. 2). This latter wavelength is predicted to ture, comparative trials may be designed in which
produce maximum heating for D = 0.019 mm, the influence of different wavelengths on the clinand at least 80% of the maximum for D between ical outcome will be studied. Our analysis also
0.005 and 0.035 mm corresponding, respectively, points out the need of characterizing the vascuto light to darker PWS (for a baby, z, = 0.5 mm larization of a PWS prior to treatment. Although
and Cb is between 1%and 7%; for an adult, z, = possible methods for such a characterization are
1 mm and Cb is between 0.5% and 3.5%).Third, currently not established, several of them have
our model predicts that the 578 nm copper vapour been summarized by Pickering et al. [251. An inlaser wavelength is optimal (producing at least teresting and promising new approach, using fast
80% of the maximum possible rate of heat at the pulsed photothermal thermography imaging [261,
target vessel) for D between 0 and 0.026 mm, with was recently presented at the 14th Annual Meeta maximum for D = 0.0141 mm which corre- ing of the American Society for Laser Medicine
sponds to a lighter PWS.
and Surgery (Toronto, Ontario, Canada, April
8-10, 1994).
Laser Beam Diameter
In Eq. (I), it is tacitly assumed that laser
spotsize is much larger than the average dermal ACKNOWLEDGMENTS
distance between blood vessels (e.g., a 5 mm spotDiscussions with Dr. Steven L. Jacques
size vs. 0.1 mm to 0.4 mm distance between ves- (Houston) are gratefully acknowledged.
sels). When the spotsize becomes so small that
A.J.W. is a Marion E. Forsman Centennial
only a few, or even single, vessels are being irra- Professor of Electrical and Computer Engineering
diated (for spotsizes smaller than 0.5 mm, say), C, and Biomedical Engineering.
in Eq. (1)becomes a function of spotsize, usually
being smaller for smaller spotsizes, and will become zero when only the target vessel is irradi- REFERENCES
ated. Clinically, therefore our model predicts that
1. Gemert MJC van, Welch AJ, Tan OT, Parrish JA. Limilaser treatment of telangiectatic lesions, or laser
tations of carbon dioxide lasers for the treatment of
treatment of PWS according to Scheibner and
portwine stains. Arch Derm 1987; 123:71-73.
Wheeland [23] using CW argon dye lasers should 2. Gemert MJC van, Carruth JAS, Shakespeare PG. Laser
treatment of portwine stains: newer lasers bring better
preferably be performed with 577 nm. We recall,
treatments. Br Med J 1993; 306:4-5.
however, that the concept of selective photother3. Tan OT, ed. “Management and Treatment of Benign Cumolysis is the basis for our model. That is, we
taneous Vascular Lesions.” Philadelphia: Lea & Febiger,
have assumed ms laser pulse durations and that
1992.
an isolated (target) blood vessel can be optimally 4. Mulliken JB, Young AE. “Vascular Birthmarks: Hemangiomas and Malformations.” Philadelphia: Saunders,
injured by the laser wavelength of maximum absorption in the red blood cells (at 577 nm), irre- 5. 1988.
Tan OT, Stafford TJ. Treatment of portwine stain at 577
spective of the size of the vessel. Some modelling
nm: clinical results. Med Instr 1987; 21:218-221.
suggests vessel size influences the optimum 6. Tan OT, Morrison P, Kurban AK. 585 nm for the treatment of portwine stains. Plastic Reconstr Surg 1990; 86:
wavelength for injury of that vessel because of the
1112-1117.
quantity of blood within the vessel [241. However,
7.
Pickering
JW, Gemert MJC van. 585 nm for the treatno conclusive clinical or histological information
ment of portwine stains: a possible explanation. Lasers
is currently available that shows a relationship
Surg Med 1991; 11:616-618.
between optimal wavelength for irreversible in- 8. Gemert MJC van, Pickering JW, Welch AJ. Modeling
jury and vessel size.
laser treatment of portwine stains. In Tan OT, ed. “Management and Treatment of Benign Cutaneous Vascular
In conclusion, the present model is simple,
Lesions.” Philadelphia: Lea & Febiger, 1992, pp 24-47.
analytically tractable, and, hence, as transparent
9. Pickering JW, Butler PH, Ring BJ, Walker EP. Comas possible to understand better the interactions
puted temperature distributions around ectatic capillarbetween laser light and benign vascular skin leies exposed to yellow (578 nm) laser light. Phys Med Biol
sions. In particular, the choice of laser wave1989; 34:l-11.
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Laser Wavelengths for Port Wine Stains
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experimental evidence in human skin. Lasers Surg Med
1981;1263-276.
11. Gemert MJC van, Jacques SL, Sterenborg HJCM, Star
WM. Skin optics, IEEE-Trans BME 1989;36:1146-1154.
12. Tan CY, Stratham B, Marks R, Payne PA. Skin thickness
measurement by pulsed ultrasound its reproducibility,
validation and variability. Br J Dermatol 1982;106:657667.
13. Barsky, SH,Rosen S, Geer DE, Noe JM. The nature and
evolution of port wine stains: A computer-assisted study.
J Invest Dermatol 1980;74:154-157.
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the color perception of port wine stains related to blood
vessel depth. Lasers Surg Med 1993;13219-226.
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light-scattering materials. Part I. J Opt Soc Am 1948;
38:448-457.
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Dermatol 1989;92868-871.
17. Welch AJ, Wissler EH, Priebe LA. Significance of blood
flow in calculations of temperature in laser irradiated
tissue. IEEE Trans Biomed Eng 1980;27:164-166.
18. Gemert MJC van, Kleijn WJ de, Hulsbergen Henning JP.
Temperature behaviour of a model port-wine stain during
argon laser coagulation. Phys Med Biol 1982;27:10891104.
19. Miller ID,Veith AR. Optical modelling of light distributions in skin tissue following laser irradiation. Lasers
Surg Med 1993;13565-571.
20. Tan OT, Sherwood K, Gichrest BA. Treatment of children
with portwine stains using the flashlamp-pulsed tunable
dye laser. N Engl J Med 1989;320:416-421.
21. Neumann FtA, Knobler RM, Leonhartsberger H, BohlerSommeregger K, Gebhart W. Histochemical evaluation of
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APPENDIX
The wavelength of maximum rate of heat
production, A,, follows from the first derivative of
Q(A,z,,D), Eq. (5a),with respect to A and solving A
from equating this derivative to zero. Unfortunately, an analytic relation between Q and A is
not available. Therefore, we first solve for the optimum blood absorption coefficient k,,b(hO), by requiring the first derivative of Q of Eq. (5a) with
respect to Pa,b(A)to be zero, yielding
~.,,b(Ao) = 1/(2D)
(7)
and using Figure 2 t o convert p,,b(Ao) to the corresponding A,. As Fa,b(A) is at most 35.4 mm-l
(Fig. 21, values of D that are smaller than 1/[2
&,b&)] = 1/(2*35.4) = 0.0141 mm refer to A, =
577 nm.
The relative maximum volumetric rate of
heat production has been expressed as a function
of blood absorption coefficient and dermal blood
layer thickness in Eq. (6). For D I0.0141 mm,
i.e., when A, = 577 nm and Fa,b(Ao)= 35.4 mm-l,
the relative maximum rate of heat production
equals exp(-35.4*2*D) = exp(-70.8 D). For D >
0.0141 mm, i.e., when P,,b(ho) 2 D = 1,Eq. (71, the
relative maximum rate of heat production equals
p,,b(A0)/(35.4e) = p,,b(A0)/96.2 = 1/(96.2*2*D) =
U(192.4 D). The two descriptions exp(-70.8 D)
and U(192.4 D) are smoothly continuous at D =
0.0141 mm. That is, the functions, as well as the
derivatives with respect to D, are equal at D =
0.0141 mm.
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