In this study, a three-dimensional skin tissue model was constructed and used to evaluate the effect of HbV administration on skin laser treatment for PWS. Light propagation simulations and thermal conduction analyses were performed, and the resulting tissue damage was measured. The model considered two vascular networks located within the dermis, with straight blood vessels placed at depths corresponding to these networks. To account for the axial migration of RBCs, the vascular cross-section was divided into two regions: the RBC core and a surrounding plasma layer. HbVs, which do not exhibit axial migration, were assumed to be uniformly distributed within a surrounding cell-free layer. This modeling approach facilitated the numerical investigation of the influence of HbV administration during PDL irradiation and showed that HbV administration reduced the heterogeneity of hemoglobin distribution across the vascular cross-section, enhancing the efficacy of laser treatment for PWS.

HbV-free (Case 1) and HbV-treated (Case 2) scenarios were compared. In the light propagation simulations, the relative absorption energy in the entire subpapillary vessel region was significantly higher in Case 2 than in Case 2 owing to the presence of absorbers distributed within the cell-free layer. In the subcutaneous vessels, the absorption energy was also increased in the cell-free layer, resulting in overall improvements in laser absorption and enhanced heat delivery to the vessel walls. Thermal conduction analysis revealed that an increase in laser energy fluence elevated intravascular temperatures and caused a corresponding increase in the thermal damage index. HbV administration further elevated intravascular temperatures and thermal damage at the same energy fluence, enhancing therapeutic efficacy. Consequently, as comparable effects are achieved at lower energy levels in the presence of HbV, this approach may help to minimize damage to the tissues surrounding PWS. These findings suggest the potential therapeutic benefits of developing patient-specific treatment protocols to optimize laser therapy for PWS.

The present analysis was compared with existing in vitro experimental results regarding HbV administration. Rikihisa et al. [5] presents an animal study using a PWS model to evaluate the photosensitizing effect of HbVs on photothermal coagulation. At fluences of 4 and 5 J/cm², there were no appreciable differences in vascular damage between samples with and without HbV. However, at a fluence of 6 J/cm², photocoagulation was clearly enhanced in HbV-treated samples. Our numerical simulation also revealed a similar trend. As shown in Fig. 7, the thermal damage index was more substantially increased in the presence of HbV administration than in the control at the same fluence, reflecting the enhanced optical absorption attributable to improved intravascular hemoglobin distribution. This agreement between computational results and experimental observations provides further support of the validity of the numerical framework developed in this study.

In the presence of HbVs, laser absorption by subpapillary vessels increased, resulting in fewer photons reaching the underlying subcutaneous vessels. Consequently, energy absorption at the center of subcutaneous vessels was lower in Case 2 than in Case 1, indicating that laser absorption in deeper vessels is strongly influenced by absorption in overlying superficial vessels. In subcutaneous vessels, heat diffusion occurred predominantly in a concentric manner from the vessel center. In contrast, in regions containing closely spaced subpapillary vessels, thermal diffusion from neighboring vessels contributed to sustained elevated temperatures within the intervascular tissue. As a result, closely packed vascular structures may lead to increased thermal damage in the intervening skin tissue. These findings demonstrate that vascular arrangement plays a critical role in determining laser treatment outcomes. Moreover, in densely vascularized regions, sufficient thermal damage may be achieved at lower laser fluences.

This study also investigates the influence of laser pulse duration on vessel-wall temperature. When the pulse duration is shorter than the thermal relaxation time, laser irradiation terminates before substantial heat diffusion occurs. As a result, absorbed laser energy is converted to heat primarily within the optical penetration depth, confining the temperature rise to the targeted region and limiting collateral thermal damage. In contrast, when the pulse duration exceeds the thermal relaxation time, heat diffuses into deeper tissue layers, producing thermal effects over a broader spatial extent. Accordingly, for small-diameter blood vessels, shorter pulse durations may restrict thermal injury to localized regions, whereas for larger vessels, longer pulse durations may promote more uniform heating across the vessel wall. Laser treatment experiments using rabbit auricles showed that thrombus formation occurred predominantly in the upper regions of blood vessels, with HbV administration leading to increased thrombus area [43]. Consistent with these observations, Fig. 6 shows that the heat flux at the vessel wall was greater in the upper vessel regions in Case 2. Together, these results suggest that thermal injury is likely initiated at the upper portion of the vessel wall.

In this study, the thermal response of skin tissue under laser irradiation was analyzed using a transient heat conduction equation without explicitly incorporating a blood perfusion term. Since laser pulses were of short duration (on the order of milliseconds), thermal conduction was considered the dominant mechanism, and convective heat transfer due to blood flow was assumed to be negligible. Furthermore, the vessels modeled were small venules and capillaries with diameters below 100 μm, in which bulk perfusion typical of larger vessels is minimal. Under these conditions, heat conduction can reasonably be considered the primary mode of thermal transport. However, neglecting blood flow may lead to an overestimation of local temperature rise because the convective cooling effect of circulation is not accounted for. For steady-state or long-duration heating, the effect of blood perfusion becomes significant, and Pennes’ bioheat equation is commonly used to model such scenarios [45]. In recent years, modified forms of Pennes’ bioheat equation have been developed to incorporate heterogeneous or anisotropic blood perfusion, providing a more accurate representation of spatial variability in vascular density and local cooling capacity [46]. Although the present study did not consider such heterogeneous perfusion, this factor is particularly relevant in congenital vascular malformations such as PWS. In PWS lesions, irregularly dilated capillaries are non-uniformly distributed within the dermis, and this structural and hemodynamic heterogeneity strongly affects local heat diffusion, leading to selective photothermal responses. Future studies should incorporate spatially heterogeneous blood flow models to achieve a more physiologically realistic understanding of laser-induced thermal behavior in PWS treatment.

The reported thermophysical properties of biological tissues vary among literature sources [47, 48]. These discrepancies are primarily thought to arise from differences in tissue water content, lipid composition, measurement techniques, and temperature ranges. Such variations highlight the need for the careful selection of appropriate parameters relevant for the target tissue and irradiation conditions. Nevertheless, these variations are not expected to significantly impact the overall trends or the main conclusions of this study; specifically, the findings related to the enhancement of optical absorption achieved with HbV-assisted therapy are unaffected.

In this analysis, as shown in Fig. 1(b), the cell-free layer thickness across the vessel cross-section was assumed to be constant. However, in vivo, the vessels of microvascular networks branch intricately, causing RBCs to shift to one side of the wall after bifurcation. This results in a non-uniform thickness of the cell-free layer, which may result in uneven vessel damage during laser irradiation [49]. Therefore, the administration of HbV may mitigate the spatial unevenness of the damage, even when using short-pulse lasers. Vascular arrangements were found to influence both laser absorption and heat diffusion. Further insight into the variation in laser absorption among different vessels could be obtained by constructing skin models with randomly distributed vessels within the vascular network region.

The thermal damage index Ω provides a quantitative measure of cumulative protein denaturation based on Arrhenius kinetics. In this study, a threshold value of Ω = 1 was used to indicate irreversible thermal damage, consistent with the conventional criterion that approximately 63% of native proteins are denatured when Ω reaches unity, resulting in loss of cellular viability and structural integrity [44]. However, this model represents an idealized approximation and does not capture complex biological repair and regenerative mechanisms. In living tissue, continuous oxygen and nutrient supply via arterial blood can enable partial recovery from sublethal heating (Ω < 1), while immune responses at the interface between healthy and damaged regions may limit excessive damage accumulation. As these physiological processes are not included in the current conduction-based model, it may overestimate irreversible injury under quasi-static or repetitive heating conditions. Incorporating tissue perfusion dynamics and regeneration kinetics into a modified Arrhenius framework [50] will be an important objective for future studies.

In this study, the extent of thermal damage in skin tissue was quantified using the classical Arrhenius model. This formulation assumes that thermal injury follows a single-step, temperature-dependent reaction, a widely adopted approach for modeling tissue coagulation under laser or radiofrequency heating. However, recent studies, such as Singh et al. [51]., have reported that at relatively low temperatures (~ 43 °C), protein denaturation exhibits a temperature-dependent time delay, which reduces the required heating duration compared with traditional Arrhenius predictions. In contrast, the PDL treatments simulated here involved short pulses on the order of milliseconds, during which local temperatures in target vessels rapidly exceeded 50–55 °C. Under these transient, high-temperature conditions, the low-temperature delay described by Singh et al. is negligible, and the conventional Arrhenius integral remains appropriate for predicting irreversible protein denaturation and endothelial damage. For future applications involving lower-temperature or longer-duration exposures, incorporating temperature-dependent delay kinetics could enhance predictive accuracy and expand the applicability of thermal modeling frameworks.

The present findings also indicate potential clinical relevance. Although we present numerical simulations, the proposed approach may offer a theoretically grounded, effective new option for treatment-resistant PWS cases in which conventional PDL therapy has failed to achieve sufficient blanching after multiple attempts. By improving the homogeneity of hemoglobin distribution and enhancing the optical absorption efficiency of microvessels, the proposed method may increase the selectivity and efficacy of laser-induced photothermolysis. Moreover, in less clinically severe cases, the obtained improvements in absorption efficiency could facilitate effective therapy at a lower laser fluence, thereby reducing the occurrence of unnecessary thermal injury to surrounding tissues. This would enhance treatment safety, extend the lifespan of the laser system, and reduce running costs (notably, dye cartridge replacement would occur less often). As the underlying principle remains consistent with that of conventional PDL therapy, clinicians could implement this approach as a natural extension of existing practice, without the need for new devices or additional training. Thus, this work provides a theoretical basis for the development of safer and more effective clinical laser treatment strategies.

In this study, blood vessels were modeled as straight cylindrical tubes with uniform intravascular distributions. While this simplification allows systematic evaluation of the thermal effects of HbV administration, it does not fully capture the geometric and hemodynamic complexity of real PWS vasculature. Clinical and computational studies indicate that actual PWS lesions exhibit irregular vessel dilation, curvature, and branching, which can induce asymmetric RBC distributions—for instance, preferential RBC accumulation along one side of the vessel wall following a bifurcation—resulting in heterogeneous hemoglobin distributions [52]. Such nonuniformities can alter local optical absorption and, consequently, the thermal response to PDL irradiation. Although HbV administration may partially mitigate these intrinsic heterogeneities by homogenizing intravascular absorption, this effect should be validated using models incorporating realistic three-dimensional vascular architectures. In addition, patient-specific anatomical factors, including skin thickness, vascular density, perfusion heterogeneity, and variability in PWS lesion depth and severity, were not incorporated into the present model. Accurately reproducing in vivo vascular morphology and blood flow patterns remains computationally challenging in silico. Therefore, the results of this study should be interpreted as a proof-of-concept demonstration rather than a direct prediction of patient-specific therapeutic outcomes. Future studies should integrate patient-specific vascular models and more detailed hemodynamic characteristics to improve the clinical relevance of HbV-assisted PDL treatment simulations.

In general, laser devices are not optimized for long-pulse irradiation, and high-power operation is associated with increased cost and reduced device lifespan. HbV administration has the potential to homogenize vascular damage and reduce the required energy fluence, thereby alleviating the burden on laser equipment. In clinical practice, epidermal cooling is routinely applied during PDL treatment to minimize thermal injury to the epidermis and enhance safety. Cooling modalities, such as cryogen spray [48, 53, 54], can significantly lower surface temperature before and during laser exposure, altering the thermal response of superficial tissues. Although the present model does not explicitly include epidermal cooling, incorporating such effects in future simulations would provide more clinically realistic predictions of temperature evolution in HbV-assisted PDL therapy. Accounting for cooling may yield more accurate insights into the balance between enhanced intravascular absorption from HbVs and the protection of surrounding tissues during laser treatment.