Port wine stains (PWS) are progressive vascular lesions of the dermis affecting around 25 million people worldwide.1 They often constitute a significant cosmetic problem, and, if left untreated, are likely to develop nodular or hypertrophic areas which are prone to spontaneous or trauma-induced bleeding and consecutive infection.2,3 The long-term psychological effects of PWS are documented widely but have been shown to be mitigated significantly after treatment.4
Although flashlamp-pumped pulsed dye laser (PDL) treatments are widely considered the treatment of choice for PWS, fewer than 20% of patients experience complete lightening using this method, whereas 20% to 30% are considered “poor responders”.56.–7 It has been proposed that one reason for inadequate clinical results is that the laser parameters used are virtually identical for all PWS patients despite the commercial availability of laser systems with user-specific settings.8,9 In order that laser treatment may be optimized on an individual patient basis, the practitioner must be aware of the vascular architecture constituting each lesion, including the number, distribution and sizes of affected vessels.9 It is these characteristics, as well as the properties of overlying skin (such as epidermal melanin content) which constitute the color of PWS skin.10
The simplest method of assessing PWS color is through visual observation. However, this is both subjective and qualitative. Perceived color may be influenced by a number of factors such as ambient lighting conditions, colors surrounding the subject, eye adaptation prior to viewing and viewing geometry.7,11 Although photographic images have been applied to determine the efficacy of laser treatment for PWS, great care must be taken to minimize the effects of variations in patient positioning, camera sensitivity and lighting during acquisition, and the quality of printing or visual display of the image.12,13 To confound this further, communication of perceived color is difficult as, for example, most PWS skin may correctly be described as ‘red’ in color.
Quantitative, reproducible assessments of PWS lesions have been achieved using color measurements (for a full discussion, see Ref. 1). Color measurement devices consist of one or more optical fibers or integrating spheres which are placed in contact with the skin and through which incident and reflected light are passed. Data available from these devices may include spectral reflectance curves covering a broad spectrum, (Fig. 1), color co-ordinate values relating to human color perception or indices representing approximations of blood or melanin content. Once a technique restricted to the laboratory, modern hand-held devices are capable of collecting skin color data instantaneously. Although care must be taken to avoid blanching during contact and to replicate the positioning of the device between assessments, color measurements have been shown to produce excellent inter- and intra-user repeatability (Fig. 1),14,15 and have been applied successfully in the determination of laser treatment efficacy in PWS lesions.16
Clinically relevant, objective information may be determined from skin color measurements through the inverse application of a skin model. This method begins by creating a mathematical skin model through which light transport is simulated. Specific features of the model are then adjusted until its simulated color is in adequate agreement with the measured color of the patient’s skin. These adjusted features, such as concentrations and distributions of melanin and hemoglobin, can be used to inform diagnosis or treatment. Simulations of skin color require an understanding of the optical properties of skin,10 and must consider the prominent interactions of light. This article addresses the latter, presenting a comprehensive review and analysis of the approaches used to simulate light transport through PWS skin.
When skin is illuminated with a white light source, its color is determined by the spectral variation in reflected and backscattered light. The proportion of light reflected from the surface of skin has not been shown to vary substantially with wavelength or between individuals, and does not contribute appreciably to the color of skin.17,18 The remaining light may be absorbed within the skin or scattered back to the surface. The proportion of backscattered light varies considerably with wavelength, pigment content and scattering properties of the skin.10 Thus, it is this backscattered light which is predominantly responsible for the color of skin.
With regards to PWS skin, vessel number, mean diameter and depth have been shown to influence the color of the lesion.1920.21.–22 It has been suggested that equivalent colors can be obtained through different combinations of these parameters. For example, Barsky et al. carried out an investigation involving biopsy samples from 100 facial PWS lesions.19 They observed that the mean vessel area and total vascular area correlated strongly with color assessed using a visual comparison of the skin against a Pantone color chart. Thus, Barsky’s results suggest than skin color is derived from the quantity of blood in PWS skin, independent of its distribution through the dermis. Fiskerstrand et al.21 used the same methods of 3-mm punch biopsies on 30 patients and comparisons against a Pantene color chart. They also reported that skin color was dependent upon vascular area, but found that “pink and purple lesions were significantly deeper located than were the red lesions,” and larger diameter vessels corresponded with a darkening of PWS color, from pink to purple.20,21 Verkruysse et al. introduced a correction factor to investigate the effect of vessel diameter on PWS color through Monte Carlo simulations. They suggested that several small vessels, close to each other, may be optically equivalent to one large vessel over the yellow and blue regions of the visible spectrum. However, their simulated results showed that the proportion of red light reflected from the skin was influenced strongly when varying dermal blood fraction but only minimally when varying vessel diameter (Fig. 2).
Simulating PWS Skin Color
In order to accurately reproduce human skin color, and variations in color between individuals or regions, over time or as a result of a medical condition such as PWS, a simulation must account for the prominent interactions of light within skin. These interactions may be described using classical electromagnetics, based upon Maxwell’s equations, whereby light is treated as a wave containing an electric component and a magnetic component. When traveling through a medium such as skin, this wave causes elements of electric or magnetic charge (e.g., electrons) to oscillate and, in turn, the oscillating elements radiate electromagnetic waves. The observed transmitted or scattered wave is a result of the summation of each of these secondary waves. The secondary waves may not have the same phase or magnitude as the incident wave and some of the energy will be lost to the charged elements; further energy is lost to the medium through destructive interference of secondary waves.
An exact calculation of the resultant wave is exceedingly complex, as it relies not only on the precise position of each charged element in the medium, but also upon the local electromagnetic environment, which is continually altered by the interaction of the wave with the medium. Instead, specific solutions to Maxwell’s equations have been developed for simplified situations.
At the Skin Surface
The effects of surface topology on skin appearance are of considerable interest to the cosmetic23 and computed animation24,25 industries, as well as medicine.26,27 These investigations are primarily concerned with differences in appearance as a result of varying viewpoints or angles of illumination. However, the majority of studies into PWS skin color consider a simple approach to approximating surface reflection. By modeling the skin surface as a perfectly smooth interface, and by assuming the superficial region of the skin can be assigned a single value of refractive index for the wavelength or wavelength range considered, the Fresnel equation may be used to estimate the relative quantities of reflected () and transmitted () light:
Refraction occurs as light passes from air to skin, or between regions of the skin whose refractive indices differ. Simulations of skin optics which account for the effects of refraction generally do so through the application of Snell’s law:
Both Fresnel’s equation and Snell’s law require knowledge of the refractive indices of skin and the incident angle of light. Angles of incidence and transmission may be calculated simply for a skin model consisting smooth or flat interfaces. Refractive indices are generally obtained from direct measurements.10
Light Transport through Skin
The behavior of the remaining (transmitted) light is commonly simulated using radiative transfer theory (RTT).28 This considers the transport of light in straight lines (beams). Absorption is modeled as a reduction in the radiance of a beam and is dependent upon the absorption coefficient (). The degree of scattering is described by both the scattering coefficient (), which considers both a loss of radiance in the direction of the beam and a gain from beams in other directions, and the phase function (), which describes the distribution of scattering angles.
Due to the complex nature of skin, a general solution to the application of RTT is not available.29 Thus, a further approximation is required. There are two main approaches to approximating the application of RTT; those which use a deterministic approach, and those which employ a stochastic ‘ray tracing’ technique. In addition, Prahl described an ‘adding-doubling’ method in his PhD thesis and associated publications.28,30,31 This is a one dimensional iterative technique that uses RTT to estimate the transport of light through skin from the reflection and transmission of two or more mathematical ‘slabs’. Although relatively simple in principle, it has not been used greatly outside of Prahl’s work.
The Beer-Lambert law is a simple deterministic technique which has been applied to estimate the reflectance () from a skin model. Although empirically derived,32 this is essentially a solution to the application of RTT to the interaction of light with a static homogeneous absorbing (nonscattering) medium.
The Beer-Lambert law uses an estimate of the attenuation of light () obtained by measurements of on-axis transmission through thin samples of skin, and the optical path length ():3334.–35 These generally involve an additional exponential term to describe loss due to scattering and use an approximation of the mean optical path length , for example: 35 In skin, where areas of high scattering (e.g., deep epidermis) and high absorption (such as those found in PWS skin) exist, the Beer-Lambert Law is not appropriate. Furthermore, it is not possible to account for the effects of vascular architecture in PWS skin using this method alone. When compared to an alternative simulation method, Shimada et al.34 confirmed that the Beer-Lambert law is not sufficiently accurate for investigating human skin.
The diffusion approximation is described in detail elsewhere.28,38 In summary, it has a low demand for computing power and thus provides fast convergence for a wide range of applications. For example, it has been applied successfully to real-time light dosimetry during photodynamic therapy (PDT) of superficial skin cancers,39,40 differentiation between pigmented skin lesions (including malignant melanoma),41 and to determine blood oxygen saturation levels faster, and over a larger area than existing methods with equivalent reliability.42 However, it suffers from a number of limitations, in part because it relies upon approximate solutions to an equation that itself represents an approximation to the equation of RTT.43 For example, there is a requirement that scattering is dominant over absorption. This may be appropriate in clinically normal pale skin types, as the probability of scattering within the skin may be as high as twenty times that of absorption.10,44 However, absorption is much greater in the epidermis of darker skin types, the blood vessel plexi of the normal dermis, and within PWS lesions. Thus, the validity of this approximation is limited in such cases.34,43,4546.–47
These drawbacks have limited the application of the diffusion approximation to investigations of PWS skin. For example, Verkruysse et al.45 reported that data obtained from their two-layered skin model could be obtained quickly but compared poorly to measured spectra, resulting in an overestimation of blood volume fraction, oxygenation levels and melanin concentration in port wine stain (PWS) skin. Zhang et al.48 found similar problems when applying a genetic algorithm minimization procedure to their diffusion approximation results, as did Lakmaker et al.49 when investigating a method of predicting the maximal treatment depth response required for complete clearance of PWS lesions. Svaasand et al.50 applied a diffusion approximation to their model, predicting the effects on skin color resulting from changes in the depth and thickness of a PWS lesion. However, simulated spectral reflectance curves compared poorly to their single example of a measured dataset, suggesting that these predictions of skin color may not be applicable on an individual basis.
Monte Carlo Method
Monte Carlo simulations used in biomedical optics are simply ray-tracing procedures, where a statistical analysis is used to calculate, step-by-step, the movements of simulated photons or light beams through a mathematical skin model51 (see Fig. 3). This has been described as a discrete version of the radiative transport equation.52 The Monte Carlo method was first introduced to the field of skin optics by Wilson and Adam in 198353 and was developed further by a number of groups over the next decade.5455.56.57.–58 Although its use at this time was limited due to high demands in computing power, Monte Carlo methods are widely regarded as the most accurate simulations of light transport through skin,48 and, as a result of recent advances in computing hardware, they are now routinely used for the interpretation of spectral data.1
In 1989, Keijzer et al. published their Monte Carlo simulation, analyzing the effectiveness of vascular laser treatments.59 This program employs a two-layer skin model, and was developed for investigating PWS skin, in particular for determining the energy deposition within a single vessel during laser treatment. A pencil beam directed perpendicular to the surface of the skin model is initiated at a position randomly allocated within a circular region. The beam propagates through the skin model, undergoing absorption and scatter at events separated by a distance (), calculated, as follows:6):
Keijzer et al.’s program has the advantage of easy insertion of a sphere, ellipsoid or cylinder into the skin model, to simulate blood vessels for example, but lacks versatility as it uses a predetermined set of optical parameters determined from phantom measurements.
Keijzer et al.’s program was used by Lucassen et al.60 to study the effects of laser wavelength on the response of PWS skin to laser therapy. The simulation calculated the absorbed energy within a single straight blood vessel of varying diameters, a curved blood vessel and multiple straight blood vessels. A 585-nm laser beam was predicted to be more effective than a 577-nm beam. This is in agreement with the results found in clinical practice, as a transition of standard practice between these two wavelengths followed worldwide (prior to the shift from 585 to 595 nm), as did the introduction of epidermal cooling during laser therapy, also recommended in Lucassen et al.’s study. Verkruysse et al.61 also used Keijzer et al.’s simulation to study the influence of PWS anatomy on skin color. They created five models consisting of varying blood layers containing homogenous distributions of blood, with a correction factor to account for reduced light absorption when blood is contained within vessels. Verkruysse et al. commented that their simple skin model failed to take into account the effects of high epidermal scattering, even though they were able to model a diffuse irradiance of photons. Predicted changes of skin color with the removal of superficial vessels did not correspond with the reported clinical response.
In 1992, Wang and Jacques (the latter of which was listed as an author on the previously discussed paper by Keizer et al.) published a Monte Carlo simulation of steady-state light transport in multi-layered tissue using the ANSI Standard C computing language.55,62 This program is freely available on the internet,55 and allows users to create a two-dimensional skin model by inputting custom values of absorption coefficients, scattering coefficients, refractive indices and (Henyey-Greenstein) anisotropy factors for any number of layers. Like the program produced by Keijzer et al., the simulation begins with an infinitely narrow beam incident normal to the skin surface whose path through the skin is governed by Eqs. (5) and (6). A convolution algorithm may then be applied retrospectively to simulate a light source of finite size, such as a laser beam. This effectively repeats the results from the infinitely narrow beam over a finite area without performing any further simulations.
Mantis and Zonios63 developed a two-layer mathematical skin model to estimate the thickness and absorption coefficient of a superficial absorbing layer using Wang and Jacques’ Monte Carlo program. They inputted reflectance values obtained from a fiber optic spectrophotometer setup and compared them to the results simulated from an infinitesimally narrow incident laser beam. Nishidate et al.64 applied the same program to a skin model consisting of an epidermis, dermis and local blood region. The depth and thickness of the simulated local blood region was adjusted until the simulated reflectance was in adequate agreement with a measured spectrum, forming an estimate of these parameters in the measured sample. They inputted measurements from a tissue phantom using a diffuse illuminant and a charge coupled device camera setup. Both studies reported absorption and reduced scattering coefficients with errors of around 10% compared to values expected from their skin phantoms. Considering the addition of uncertainty and optical inhomogeneity in a genuine skin sample, these errors are considerable. In fact, the study by Nishidate et al.64 used the same method to estimate the depth of in vivo human veins. They reported errors of up to 0.6 mm for the depth and 0.2 mm for the thickness of veins when compared to ultrasound measurements. Again, these errors are large when considering normal skin thickness.65
Other research groups have developed Monte Carlo simulations for use in biomedical optics. Graaf et al. produced a condensed Monte Carlo simulation based upon the same governing equations [Eqs. (5) and (6)], but utilizing the derived relationship between simulated reflectance and albedo. In detail, the same simulated diffuse reflectance may be obtained by increasing the scattering coefficient and simultaneously decreasing the absorption coefficient, maintaining a fixed value of albedo (a dimensionless coefficient defined as the ratio of scattering coefficient to the sum of absorption and scattering coefficients).66 To demonstrate the effects of varying absorption and scattering coefficients whilst maintaining a fixed albedo, we applied the following parameters to a simulation of 1 million photon packets, carried out using Wang and Jacques’ program.55 The skin model consisted of a single layer with an effectively infinite depth () (Table 1).
Results from a simulation of 1 million photons. Values are presented for a simulation carried out using the Wang and Jacques Monte Carlo program (MCML)62 with a simple, single-layered skin model of 1×108 cm depth; values of g=0.9, refractive index=1.3, and pencil beam irradiation used throughout (simulated by the first author, T. Lister).
|Absorption coefficient (cm−1)||Scattering coefficient (cm−1)||Albedo||Calculated diffuse reflectance (MCML) (%)|
This technique vastly improved simulation time for a uniform skin model and was shown to determine skin optical coefficients consistent with other studies.10,67 This work was later extended by Wang et al.68 who considered the effects of varying the diameter of the source. Wang et al. also demonstrated superior calculation times whilst maintaining good agreement with a standard Monte Carlo simulation.
Meglinski and Matcher’s program47,69 involved a seven layered skin model to simulate the reflectance spectrum of human skin, as measured using a fiber optic probe setup. Path lengths were calculated according to Eq. (7), and absorption coefficients were applied separately [Eq. (8)]:70,71
Meglinski and Matcher found good agreement between their calculated reflectance and a single example of measured reflectance between 450 and 600 nm wavelengths, although the skin properties used outside of this wavelength range did not appear to provide a good agreement. This shortcoming may have been as a result of the constant scattering properties applied to the skin model over the entire wavelength range investigated. When applying the coefficients used by Meglinski and Matcher to Wang and Jacques’ Monte Carlo program, Maeda et al.72 reported a “rather strange spectral curve that had much worse agreement with measured results than (another set of coefficients),” demonstrating a clear discrepancy between the two programs.
In summary, Monte Carlo simulations have contributed substantially to the field of skin optics since their introduction in 1983.53 Initial development by Keijzer et al.59 and later by Wang and Jacques55 facilitated a number of studies into the color of PWS skin. More recent work has demonstrated gradual development in Monte Carlo techniques for the simulation of PWS skin color and with continuing advancements in computing power available to the researcher, and an ever increasing interest in skin optics, such advances are likely to continue into the foreseeable future.
The color of PWS skin depends primarily upon the number, depth, and sizes of affected vessels. Thus, by measuring skin color, it may be possible to inform a better knowledge of these characteristics for an individual lesion, providing essential information for the optimization of laser treatment. The most common approach to extracting information from a measurement of skin color is through the inverse application of a skin model, whereby a simulation of light transport based upon RTT is performed.
Due to its low demand for computing power, the diffusion approximation has been applied widely in the field of skin optics. However, its limitations, along with the availability of increased computing power, have resulted in an increase in popularity of Monte Carlo simulations. Keijzer et al.’s and Wang and Jacques’ Monte Carlo programs employed implicit capture to increase the speed of their simulations. These simulations have contributed significantly to the field of biomedical optics. However, recent developments have improved upon these, to provide faster and more accurate simulations of light transport through skin. As the scope for applying such techniques continues to broaden, with the possibility of introducing such a technique into routine clinical practice and with the continuing increase in computing power available to the researcher, further developments should be investigated to overcome the shortcomings of the studies presented here.