Abstract. A thermal model of blood vessel damage during the laser treatment of port-wine stains. (PWS) is presented. The model depends on the heat generation ...
Lasers in Medical Science 1996, 11-177-180
Thermolysis of Port-wine-stain Blood Vessels: Diameter of a Damaged Blood Vessel Depends on the Laser Pulse Length
J.F. DE BOER, G.W. LUCASSEN, W. VERKRUYSSE, M.J.C. VAN GEMERT Amsterdam Laser Centre, Academic Medical Centre, University of Amsterdam, Amsterdam, The Netherlands Correspondence to M. J. C. van Gemert, Amsterdam Laser Centre, Academic Medical Centre, Meibergdreef 9, 1105 A2 Amsterdam ZO, The Netherlands Paper accepted 17 July 1996
A b s t r a c t . A thermal model of blood vessel damage during the laser treatment of port-wine stains (PWS) is presented. The model depends on the heat generation in a blood vessel caused by the absorption of laser light and the thermodiffusion of that heat through the dermis. The criterion of vessel injury adopted was an average vessel temperature of 70 ~ Results show that for a chosen combination of pulse length and radiant exposure, only blood vessels within a certain diameter range will be injured. This is in agreement with the pulse length selective photothermolysis criteria suggested previously by Anderson and Parrish (1). The Anderson and Parrish model relies on the cooling behaviour of instantaneously heated vessels, whereas the present study utilizes the heating of the vessel by a Gaussian temporal laser pulse profile. Predictions based on one blood vessel were verified in a skin model with multiple blood vessels by simulating vessel coagulation with a single laser treatment. The diameter of the blood vessels that are damaged during laser treatment of PWS depends on the laser pulse length.
INTRODUCTION The laser settings of pulse length, radiant exposure and wavelength are important in determining clinical results in the laser treatment of port-wine stains (PWS). Generally, parameters used clinically are: wavelengths between 577 599 nm, radiant exposure 3-10 J cm-2, and 0.1-10 ms pulse length. Most PWS patients undergo multiple laser treatments with almost identical laser settings, where the radiant exposure is the only variable. Why some PWS patients respond better to laser treatment than others is not understood. It is believed that PWS patients with small ectatic vessels respond poorly (2). Monte Carlo (MC) calculations are helpful in gaining insight into the problem. The progress mode in modelling the processes during laser treatment allows for the simulation of laser treatment by MC calculations for skin modules with multiple vessels of different sizes. In these calculations, the laser settings can be varied so as to study the effect of these 0268-8921/96/030177+04 $12.00/0
parameters. This study concentrates on the effect of the pulse length and radiant exposure, with all other parameters being held constant. It is generally accepted t h a t the choice of laser pulse length should match the thermal relaxation time, x, of blood vessels as derived by Anderson and Parrish (1). This derivation is based on the cooling behaviour of the blood vessel in response to instantaneous heating by a line source located in the centre of the blood cells. From the assumed symmetric Gaussian spatial temperature profile in the blood vessel, with full width at half maximum 2a equal to the vessel diameter d, the well-known relation 9 =d2/16 z is derived, with X as the thermal dif[usivity of blood. In this study, the radiant exposure threshold required to heat up the vessel to a critical average temperature of 70 ~ as a function of blood vessel diameter and laser pulse duration is studied. The authors emphasize t h a t the criteria of irreversible vascular damage are arbitrary [for instance, one could have adopted a temperature at the vessel wall (2)], but general trends 9 1996 W.B. Saunders Company Ltd
178
J.F. de Boer, G.W. Lucassen, W. Verkruysse, M.J.C. van Gemert
Table 1. Optical properties of tissue as used in the Monte Carlo calculations at 2=585 nm
Epidermis Dermis Blood
Za (cm-1)
~ts (cm 1)
g
18 0.25 191
470 131 467
0.79 0.79 0.995
,
'
/~a, absorption coefficient; /~s, scattering coefficient; g, anisotropy factor. will be valid even for different c r i t e r i a of i r r e v e r s i b l e v a s c u l a r damage. 17
METHOD
The MC m e t h o d was used to c a l c u l a t e the spatial deposited e n e r g y f r a c t i o n d i s t r i b u t i o n in a skin model consisting of a 0.05 mm epid e r m a l l a y e r and a 1.0mm dermal layer. Details of the MC p r o g r a m m e are described e l s e w h e r e (3). In this experiment, a threed i m e n s i o n a l MC c a l c u l a t i o n was c a r r i e d out. Since the system c h o s e n is t r a n s l a t i o n a l l y i n v a r i a n t in the y-direction, the p h o t o n density is p r o j e c t e d on the (x-z) plane and the deposited e n e r g y f r a c t i o n s DE (x,z) are s t o r e d (grid size 2 x 2/~m). F u r t h e r m o r e , periodic b o u n d a r y c o n d i t i o n s were applied in the x-direction. The optical p r o p e r t i e s of epiderm i s , dermis and blood were as defined by V e k r u y s s e et al (4) and are p r e s e n t e d in Table 1. The MC p r o g r a m m e was r u n for a single c y l i n d r i c a l blood vessel of d i a m e t e r d r a n g i n g from 0.01 to 0.2 mm, with the vessel c e n t r e at z=0.25 mm in an a r e a of 1 x 1 mm 2 at wavel e n g t h of 585 nm. Next, the deposited e n e r g y fractions for a skin model w i t h multiple vessels were calculated. Nine vessels in t h r e e layers were defined (depth 0.25, 0.5 and 0.75 mm) with diameters of 10, 20 and 60/~m in a l t e r n a t i n g order. The a r e a was 0.75 mm in the x-direction x 1 mm in the z-direction w i t h an e p i d e r m a l layer of 50 p m (Fig. 1). T h e deposited energies were fed into the h e a t diffusion p r o g r a m m e w h i c h calcul a t e d the a v e r a g e m a x i m u m t e m p e r a t u r e rise in a blood vessel with different pulse lengths with the same t o t a l r a d i a n t exposure. This p r o g r a m m e solves t h e h e a t diffusion e q u a t i o n n u m e r i c a l l y using the second-order m e t h o d of finite differences (5). The h e a t diffusion e q u a t i o n is given by:
Fig. 1. Skin model as used in the Monte Carlo calculations with multiple vessels, consisting of a 0.05 mm epidermal layer and a 1.0 mm dermal layer. The width (x-direction) was 0.75 mm. Nine vessels are defined in three layers at z=0.25 mm, z=O.5 mm and z=0.75 mm with diameter a = l O , 20 and 60/.zm.
9C 5T (x,z,t) = Q(x,z,t) 5t + ~ ( 5 2 T ( x , z , t) 5X 2
52T(x,z,t)) ~
5Z 2
(1)
w h e r e P is the density 0.998 x 1 0 - 6 (kg m m - 3), C is the specific h e a t c a p a c i t y 4.05 x 103 [J(kg ~ and )~ is the h e a t c o n d u c t i o n coefficient 0.45 x 10 - 3 [W(mm ~ - 1]. The thermal diffusivity Z is )~/pC. Since the system is t r a n s l a t i o n a l l y i n v a r i a n t in the y-direction, t h e r e is no g r a d i e n t in the y-direction. Hence, E q u a t i o n 1 is r e d u c e d to a two-dimensional diffusion equation. The h e a t r a t e s o u r c e Q[x,z,t] is given by: Q[x,z,t]=E'DE(x,z).P(t)
( W m m -3)
(2)
w h e r e E is ( J m m -2) the r a d i a n t exposure, DE(x,z) ( l m m -3) is the MC r e s u l t for the deposited e n e r g y f r a c t i o n s and P(t) (s - 1) is the t e m p o r a l G a u s s i a n pulse profile: P(t)
1 aL~exp
[
(t-to)2 ~ 2c~ J
(s-
1) (3)
w h e r e t o r e p r e s e n t s the time of the pulse maximum, and (~L is the s t a n d a r d d e v i a t i o n of the G a u s s i a n distribution, w h i c h is r e l a t e d to the full-width at half-maximum F W H M = ~ L = 2(~L~/2l~~ . Values of the pulse l e n g t h ZL r a n g e d from 225/~s to 9.6 ms, with time steps of
Thermolysis of PWS Blood Vessels
179
Table 2. Radiant exposure (J cm-2) to heat up the vessel to a temperature of 70 ~ tabulated for different pulse length at depth z and diameter O of the vessel in the multiple vessel geometry shown in Fig. 1
2.0
1.5
Pulse length 1.0
0.5 0
I ~ ] ~ I ~ I , I , 20 40 60 80 100 120 140 160 180 200 Blood vessel diameter (/~m)
z = 250 Fm
(ms)
O=10~m
O=20#m
O=60#m
0.45 0.90 1.80'
1.59 2.43 3.85
0.91 1.24 1.79
0.76 0.86 1.02
z=500Fm
Fig. 2. The threshold radiant exposure to raise the average temperature of a single blood vessel to 70 ~ as a function of vessel diameter and pulse length. The wavelength was 585 nm, and the centre of the vessel was at a dermal depth of 250Fm. The area of the dermis with the single blood vessel was 1 mm by 1 mm. *, 9.2 ms; t , 3.6 ms; V, 1.8 ms; A, 900/~s; 0 , 4 5 0 / ~ s ; I , 225/~s.
5-20/~s. I n all c a l c u l a t i o n s , t h e t o t a l r a d i a n t e x p o s u r e w a s 1 J c m - 2 , a n d t e m p e r a t u r e rise of i n d i v i d u a l vessels w a s c a l c u l a t e d . Since the t e m p e r a t u r e rise is l i n e a r w i t h t h e r a d i a n t e x p o s u r e for a c e r t a i n pulse length, r a d i a n t e x p o s u r e s are easily d e r i v e d t h a t lead to a t e m p e r a t u r e rise of 33 ~ for a pulse l e n g t h a n d vessel d i a m e t e r .
RESULTS
The e s t i m a t e d r a d i a n t e x p o s u r e n e e d e d to r e a c h a n a v e r a g e t e m p e r a t u r e of 70 ~ in a single b l o o d vessel of d i a m e t e r d a n d v a r y i n g l a s e r pulse l e n g t h a r e p r e s e n t e d in Fig. 2. T h e s e r e s u l t s are s i m i l a r to r e s u l t s p r e s e n t e d r e c e n t l y b y S v a a s a n d et al (2) b a s e d on a n a n a l y t i c a l m o d e l w h i c h c a l c u l a t e s t h e temp e r a t u r e rise in t h e vessel due to h e a t conduct i o n f r o m t h e h o m o g e n o u s l y h e a t e d vessel. As c a n be seen, t h e t h r e s h o l d e n e r g i e s are l o w e s t for t h e s h o r t e s t p u l s e b e c a u s e t h e s m a l l e s t a m o u n t of e n e r g y h a s l e a k e d out of t h e b l o o d vessel b y t h e r m o d i f f u s i o n o v e r the d u r a t i o n of the pulse. F o r t h e s m a l l e s t vessels, the t h r e s h o l d e n e r g y rises s h a r p l y as the p u l s e length increases because considerable a m o u n t s of e n e r g y l e a k o u t of the b l o o d vessel d u r i n g the l a s e r pulse. T h e i n c r e a s e in t h r e s h o l d e n e r g y for r e l a t i v e l y l a r g e vessels is due to t h e i n c r e a s e of t h e a r e a t h a t is to be h e a t e d up. The d e e p e s t vessels t h a t c a n be damaged with a given pulse length have a d i a m e t e r at w h i c h t h e t h r e s h o l d r a d i a n t expo-
0.45 0.90 1.80
2.40 3.65 5.78
1.30 1.78 2.58
1.08 1.22 1.45
z = 750 pm 0.45 0.90 1.80
3.68 5.59 8.86
2.06 2.81 4.08
1.70 1.91 2.26
sure h a s a m i n i m u m , ie O = 3 0 ~ m for a pulse l e n g t h of 225 #s. F i g u r e 1 shows the m u l t i p l e vessel g e o m e t r y . In T a b l e 2, the r a d i a n t exposures n e c e s s a r y for e a c h b l o o d vessel to r e a c h a n a v e r a g e t e m p e r a t u r e of 70 ~ for pulse l e n g t h s of 0.45, 0.9 a n d 1.8 ms a r e s h o w n . I n Fig, 3, the effect of a l a s e r pulse w i t h 3 J cm 2 r a d i a n t e x p o s u r e a n d v a r y i n g pulse l e n g t h is depicted g r a p h i c a l l y . F o r the s h o r t e s t pulse, only the s m a l l e s t vessel in t h e deepest l a y e r survives. F o r t h e 0.9 ms pulse, t h e s m a l l e s t vessel in t h e two d e e p e s t layers survives. F o r t h e l o n g e s t p u l s e (1.8 ms), t h e s m a l l e s t vessels a n d the 20/~m d i a m e t e r vessels in the deepest l a y e r survive.
DISCUSSION
It h a s b e e n s h o w n t h a t the l a s e r t r e a t m e n t of PWS c a n be s i m u l a t e d u s i n g s k i n g e o m e t r y w i t h m u l t i p l e vessels. The e x a c t p a r a m e t e r s r e q u i r e d for i r r e v e r s i b l e v a s c u l a r d a m a g e are n o t k n o w n . A n a v e r a g e t e m p e r a t u r e of 70 ~ h a s b e e n a s s u m e d as b e i n g a r e a s o n a b l e criterion. C h a n g e s in t h e o p t i c a l p r o p e r t i e s of skin w i t h t e m p e r a t u r e h a v e n o t b e e n t a k e n into c o n s i d e r a t i o n as t h e s e are l a r g e l y
J.F. de Boer, G.W. Lucassen, W. Verkruysse, M.J.C. van Gemert
180
(a)
(b)
X
x 9
zI
O
9
(c)
O
p r e s e n c e of m a n y small blood vessels. Therefore, the r e s p o n s e m a y be i m p r o v e d by c h o o s i n g a s h o r t e r pulse length. F o r all vessel diameters, these c a l c u l a t i o n s suggest t h a t the s h o r t e s t pulse l e n g t h has the lowest r a d i a n t e x p o s u r e t h r e s h o l d to r e a c h the d a m a g e criteria. H o w e v e r , a c o u s t i c s h o c k waves are n o t c a l c u l a t e d by the model and it is n o t k n o w n h o w this will affect the results. I n c o n c l u s i o n , t h e m e a s u r e m e n t or calculation of realistic d a m a g e criteria is needed to improve the p r e d i c t i o n of MC calculations.
ACKNOWLEDGEMENTS
x
The authors would like to thank L. Svaasand and S. Nelson for stimulating discussions. This work was funded by the Dutch Technology Foundation (STW, Grant AGN 33.2954).
0
9
REFERENCES
Fig. 3. The remaining blood vessels after a single laser treatment of the skin geometry in Fig. 1 with radiant exposure 3 J cm -2. Only vessels that have not reached an average temperature of 70 ~ are shown. (a) Pulse length 0.45 ms. (b) Pulse length 0.90 ms. (c) Pulse length 1.8 ms.
u n k n o w n . One of the most i m p o r t a n t findings from these t h e o r e t i c a l c a l c u l a t i o n s is t h a t b l o o d vessels with different sizes can be damaged selectively by c h o o s i n g a p p r o p r i a t e laser pulse lengths, as was suggested by A n d e r s o n a n d P a r r i s h (1). The judicious choice of b o t h r a d i a n t exposure levels and pulse l e n g t h m a k e s it possible to spare the small vessels t h a t h a v e r e p l a c e d the ectatic vessels des t r o y e d d u r i n g p r e v i o u s laser t r e a t m e n t . A possible e x p l a n a t i o n for the p o o r response to laser t r e a t m e n t in some p a t i e n t s m i g h t be the
1 Anderson RR, Parrish JA. Mierovasculature can be selectively damaged using dye lasers: A basic theory and experimental evidence in human skin. Lasers Surg Med 1981, 1:293-76 2 Svaasand LO, Fiskerstrand EJ, Norvang LT, Stopps EKS, Nelson JS, Berns MW. On the damage to microvessels during pulsed laser treatment of port-wine stains. Lasers Med Sci (submitted) 3 Lucassen GW, Verkruysse W, Keijzer M, van Gemert MJC. Light distributions in a port wine stain skin model containing multiple cylindrical and curved blood vessels. Lasers Surg Med 1996, 18:345-57 4 Verkruysse W, Pickering JW, Beek JF, Keijzer M, van Gemert MJC. Modelling the effect of wavelength on the pulsed dye laser treatment of port wine stains. Appl Optics February 1993, 32:39~8 5 Carslaw HS, Jaeger JC. Conduction of Heat in Solids. Oxford: Clarendon Press, 1986. Key words: Port-wine stain; Photothermolysis; Laser
treatment; Vascular injury; Laser pulse length; Blood vessel diameter
