2.1.

Overview of Model

In Fig. 1, we present a block diagram of the mathematical model consisting of three components: a Monte Carlo light-transport model to estimate the energy deposition in response to laser irradiation,^30,31 finite-element model to compute the spatiotemporal temperature distribution based on the heat diffusion equation, and an Arrhenius rate process integral to quantify the resulting thermal damage. Each component of the model is described in the following sections.

Fig. 1

Block diagram of the mathematical model components.

2.2.

Model Geometry

We used two geometries to model the human skin with PWS. The first geometry simulated the skin and consisted of a $60\text{-}\mu \mathrm{m}$-thick epidermis and $1940\text{-}\mu \mathrm{m}$-thick dermis containing BVs (Fig. 2). The epidermis was composed of a $45\text{-}\mu \mathrm{m}$ melaninless layer and a $15\text{-}\mu \mathrm{m}$ melanocyte-filled layer located at the basal epidermis. BVs were assumed to be cylinders with diameters of $200\mu \mathrm{m}$, running parallel to the $y$-axis for the entire length of the geometry (1 mm). The top position of the vessel was located either at 500 or $800\mu \mathrm{m}$ below skin surface.

Fig. 2

Simulated PWS geometry.

In addition, we also constructed a PWS skin geometry from an image obtained by optical coherence tomography (OCT) of a PWS patient (Fig. 3).³² We first removed motion artifact associated with the image cube, 5 mm (length, in $x$-direction) $\times 5\mathrm{mm}$ (width, in $y$-direction) $\times 2.8\mathrm{mm}$ (height, in $z$-direction), by taking the Fourier transform of each two-dimensional (2-D) section ($5\mathrm{mm}\times 5\mathrm{mm}$) (axial resolution $=8\mu \mathrm{m}$) and applying a bandpass filter with cutoff normalized frequencies of 0.1 and 1.0, where 1.0 corresponds to half of the sampling frequency in the horizontal direction, and 0.0 and 0.01 in the vertical direction. We then took the inverse Fourier transform of each image and converted into binary values through thresholding. Finally, speckle noise was removed using a three-dimensional (3-D) median filter.

Fig. 3

Flowchart of processing an OCT image of PWS skin for use in mathematical model. With respect to the coordinate system shown in Fig. 2, the coordinate system here is rotated 90 deg counterclockwise around the $x$-axis. The images are horizontal cross-sections in the $x\text{-}y$ plane at depth of $z=680\mu \mathrm{m}$.

2.3.

Optical Properties of Human Skin

The baseline absorption coefficient for melaninless epidermis ${\mu }_{\mathrm{a},\text{base}}$ (${\mathrm{mm}}^{-1}$) and bloodless dermis was approximated by³³

For simulated single vessels, we accounted for attenuation of the incident light by absorption in the remaining PWS BVs by adjusting the absorption coefficient of the dermis (${\mu }_{\mathrm{a},\mathrm{der}}$) (Table 1) as³⁰

Table 1

Adjusted absorption coefficient of dermis used in this study.

The adjusted values of ${\mu }_{\mathrm{a},\mathrm{der}}$ at 585 nm vary with depth and the corresponding values of $r_{\mathrm{i}}$ and $f_{\mathrm{i}}$, whereas those for 755 nm are nearly independent of depth.

For OCT simulated vessels, ${\mu }_{\mathrm{a},\mathrm{der}}$ was expressed as

The scattering coefficients (${\mu }_{\mathrm{s}}$) (${\mathrm{mm}}^{-1}$) of the melaninless epidermis, epidermal basal layer, and dermis were estimated as³³

2.4.

Optical Properties of NETs and Blood Vessels

Spectrally dependent values of ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ for micron-sized NETs ($\mu \mathrm{NETS}$) and nano-sized NETs (nNETs) with respective mean diameters ($d_{\text{mean}}$) of $\approx 4\mu \mathrm{m}$ and 92 nm were previously estimated using an integrating sphere in conjunction with an inverse adding-doubling algorithm.²⁹ Values of ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}$ for blood with 45% hct and oxygen saturation of 70% were obtained from the literature.³⁷ We then determined the effective optical properties of BV as

Using Eq. (12), we determined [ICG] values of $\approx 108$, 286, 464, 642, 820, and $998\mu \mathrm{M}$ to produce the corresponding ${\mu }_{\mathrm{a},\mathrm{BV}}$ values of 1, 2, 3, 4, 5, and $6{\mathrm{mm}}^{-1}$. For example, values of $f_{\text{NETs}}=25\%$ and ${\mu }_{\mathrm{a},\mathrm{BV}}=18{\mathrm{mm}}^{-1}$ resulted in [ICG] = $1258\mu \mathrm{M}$. Values of the optical properties used in this study are provided in Table 2.

Table 2

Optical properties used in this study. Optical properties for blood are based on 45% hematocrit.

2.5.

Mathematical Model

The 3-D Monte Carlo model for light transport and energy deposition was developed earlier by Majaron et al.^30,31 Our simulations involved one million photons for 585- or 755-nm flat-top laser beams with diameter of 6 mm for simulated PWS geometry, and 8 mm for the skin model based on the PWS patient OCT record. With a 2.3-GHz central processing unit, each Monte Carlo simulation took $\approx 2$ to 11 h depending on the geometry and optical properties of the tissue. For example, the run time was $\approx 10.5\mathrm{h}$ for a simulated geometry containing nNETs ($f_{\text{NETs}}=10\%$, ${\mu }_{\mathrm{a},\mathrm{BV}}=6{\mathrm{mm}}^{-1}$), and lightly pigmented skin ($f_{\text{mel}}=4\%$) irradiated at 755 nm. For an OCT geometry, an example run time was $\approx 2.0\mathrm{h}$ for a moderately pigmented skin ($f_{\text{mel}}=15\%$) irradiated at 585 nm without NETs.

We used the heat diffusion equation to calculate the spatiotemporal temperature profiles in response to laser irradiation:

We assumed that a cryogen spurt was sprayed onto the skin surface immediately prior to the laser pulse.^39–43 To account for this type of skin cooling, we implemented a convective surface boundary condition as follows:

Table 3

Parameters for surface thermal boundary condition.

Thermal damage to the skin was quantified using the Arrhenius rate damage integral

3.1.

Simulated PWS Geometry

3.1.2.

Photothermal response of PWS blood vessels in the absence of NETs

The percent photothermal damage profiles to BVs without NETs for lightly ($f_{\text{mel}}=4\%$) pigmented skin at the $D_{\mathrm{th}}=8\mathrm{J}/{\mathrm{cm}}^2$ at 585 nm and $21\mathrm{J}/{\mathrm{cm}}^2$ at 755 nm are shown in Fig. 4. Complete damage to BVs without NETs was observed for BVs in response to 585-nm laser irradiation at $D_{\mathrm{th}}=8\mathrm{J}/{\mathrm{cm}}^2$ [Figs. 4(a) and 4(c)]. However, this vascular damage was also accompanied by damage to the surrounding dermis. For BVs without NETs irradiated at 755 nm, there was 79 and 50% damage to vessels at depths of 500 and $800\mu \mathrm{m}$, respectively, without thermal injury to perivascular dermis [Figs. 4(b) and 4(d)].

Fig. 4

Damage profiles shown in red ($\mathrm{\Omega }\ge 1$) for blood vessels located at (a, b) 500 and (c, d) $800\mu \mathrm{m}$ below skin surface for lightly pigmented skin ($f_{\text{mel}}=4\%$) in response to (a, c) 585 and (b, d) 755-nm laser irradiation without NETs.

For moderately pigmented skin ($f_{\text{mel}}=15\%$) in response to 585-nm irradiation at $D_{\mathrm{th}}=3\mathrm{J}/{\mathrm{cm}}^2$, % damage to the vessels at 500 and $800\mu \mathrm{m}$ were 34% and 11%, respectively (Fig. 5). In response to 755-nm irradiation at $D_{\mathrm{th}}=6\mathrm{J}/{\mathrm{cm}}^2$, there was no damage to the BVs at either depth. Lastly, for heavily pigmented skin ($f_{\text{mel}}=50\%$) in response to 585-nm irradiation at $D_{\mathrm{th}}=1\mathrm{J}/{\mathrm{cm}}^2$ and 755 nm irradiation at $D_{\mathrm{th}}=3{\mathrm{cm}}^2$, there was no damage to the vessels at either depth (results not shown). The decrease in % damage for blood vessels with moderately and heavily pigmented skin can be attributed to the decrease in $D_{\mathrm{th}}$, as well as increased light absorption within the basal epidermis.

Fig. 5

Damage profiles shown in red ($\mathrm{\Omega }\ge 1$) for blood vessels located at (a, b) 500 and (c, d) $800\mu \mathrm{m}$ below skin surface for moderately pigmented skin ($f_{\text{mel}}=15\%$) in response to (a, c) 585 and (b, d) 755-nm laser irradiation without NETs.

3.1.3.

Photothermal response of PWS blood vessels containing NETs

The percent photothermal damage profiles to blood vessels containing $\mu \mathrm{NETs}$ or nNETs ($f_{\mathrm{NETs}}=10\%$) for lightly pigmented skin ($f_{\text{mel}}=4\%$) in response to 755 nm irradiation at $D=21\mathrm{J}/{\mathrm{cm}}^2$ are shown in Fig. 6. There was 100% damage to blood vessels located at depths of 500 and $800\mu \mathrm{m}$ below skin surface containing $\mu \mathrm{NETs}$, or nNETs with ${\mu }_{\mathrm{a},\mathrm{BV}}$ of $1{\mathrm{mm}}^{-1}$ (Fig. 6). As the depth of the blood vessel increased from 500 to $800\mu \mathrm{m}$, there was a decrease in damage to the dermis, which was further reduced when using nNETs as compared to $\mu \mathrm{NETs}$. These results suggest PWS patients with light pigmentation and blood vessels as deep as 500 to $800\mu \mathrm{m}$ could potentially benefit from the delivery of $\mu \mathrm{NETs}$ or nNETs that yield ${\mu }_{\mathrm{a},\mathrm{BV}}=1{\mathrm{mm}}^{-1}$ to achieve photothermal injury to the blood vessels. This value of ${\mu }_{\mathrm{a},\mathrm{BV}}$ corresponds to $\mu \mathrm{NETs}$ or nNETs with ${\mu }_{\mathrm{a},\mathrm{NETs}}\approx 6{\mathrm{mm}}^{-1}$, which can be fabricated by using $\approx 108\mu \mathrm{M}$ ICG in the fabrication buffer [Eq. (12)].

Fig. 6

Damage profiles shown in red ($\mathrm{\Omega }\ge 1$) for blood vessels containing $\mu \mathrm{NETs}$, or nNETs at $f_{\text{NETs}}=10\%$ with ${\mu }_{\mathrm{a},\mathrm{BV}}=1{\mathrm{mm}}^{-1}$, and located at depths of (a, b) 500 and (c, d) $800\mu \mathrm{m}$ below skin surface. Light skin pigmentation ($f_{\text{mel}}=4\%$), $\lambda =755\mathrm{nm}$, and $D_{\mathrm{th}}=21\mathrm{J}/{\mathrm{cm}}^2$.

For moderately pigmented skin ($f_{\text{mel}}=15\%$), $f_{\text{NETs}}=10\%$, and 755-nm laser irradiation at $D_{\mathrm{th}}=6\mathrm{J}/{\mathrm{cm}}^2$, there was no damage to the blood vessels when using $\mu \mathrm{NETs}$ or nNETs that yielded ${\mu }_{\mathrm{a},\mathrm{BV}}=1{\mathrm{mm}}^{-1}$ [Fig. 7(a)]. For ${\mu }_{\mathrm{a},\mathrm{BV}}=3{\mathrm{mm}}^{-1}$, the blood vessel at depth of $500\mu \mathrm{m}$ showed 94 and 86% damage when containing $\mu \mathrm{NETs}$ or nNETs, respectively [Figs. 7(a) and 7(b)]. For this value of ${\mu }_{\mathrm{a},\mathrm{BV}}$, when the depth of the blood vessel was increased to $800\mu \mathrm{m}$, respective % damage values were reduced to 89% and 74% in the presence of $\mu \mathrm{NETs}$ or nNETs [Figs. 7(c) and 7(d)].

Fig. 7

(a) % Damage to blood vessels containing $\mu \mathrm{NETs}$ or nNETs ($f_{\text{NETs}}=10\%$) as a function of ${\mu }_{\mathrm{a},\mathrm{BV}}$ and ${\mu }_{\mathrm{a},\mathrm{NETs}}$ (markers) fitted with exponential or sigmoidal functions (solid curves). Damage profiles shown in red ($\mathrm{\Omega }\ge 1$) for blood vessels located at depths of (b, c) 500 and (d, e) $800\mu \mathrm{m}$ below skin surface containing $\mu \mathrm{NETs}$, or nNETs at $f_{\text{NETs}}=10\%$ with ${\mu }_{\mathrm{a},\mathrm{BV}}=3{\mathrm{mm}}^{-1}$. Moderate skin pigmentation ($f_{\text{mel}}=15\%$), $\lambda =755\mathrm{nm}$, and $D_{\mathrm{th}}=6\mathrm{J}/{\mathrm{cm}}^2$.

In general, for the case of the blood vessel containing $\mu \mathrm{NETs}$ at depth of $500\mu \mathrm{m}$, % damage to blood vessels followed an exponentially increasing behavior with ${\mu }_{\mathrm{a},\mathrm{BV}}$, and approached an asymptotic value of $\approx 95\%$ for values of ${\mu }_{\mathrm{a},\mathrm{BV}}\ge 3{\mathrm{mm}}^{-1}$, corresponding to ${\mu }_{\mathrm{a},\mathrm{NETs}}\ge 26{\mathrm{mm}}^{-1}$ [Fig. 7(a)]. For the blood vessel containing nNETs at depth of $500\mu \mathrm{m}$, and blood vessels containing $\mu \mathrm{NETs}$ or nNETs at depth of $800\mu \mathrm{m}$, the relationship between ${\mu }_{\mathrm{a},\mathrm{BV}}$ and % damage to blood vessels followed a sigmoidal behavior where below a certain threshold value of ${\mu }_{\mathrm{a},\mathrm{BV}}$ (and the corresponding ${\mu }_{\mathrm{a},\mathrm{NETs}}$) there was no damage to the vessel [Fig. 7(a)]. These results indicate that once ${\mu }_{\mathrm{a},\mathrm{BV}}$ exceeds $\approx 3{\mathrm{mm}}^{-1}$ with either $\mu \mathrm{NETs}$ or nNETs, % damage to blood vessels ranging in depth between 500 and $800\mu \mathrm{m}$ is maximized to the same level of $\approx 95\%$.

The therapeutic advantage of NETs in conjunction with 755-nm laser irradiation over current treatment at 585 nm without NETs was more evident with moderate skin pigmentation. For example, blood vessels with ${\mu }_{\mathrm{a},\mathrm{BV}}=6{\mathrm{mm}}^{-1}$, and containing $\mu \mathrm{NETs}$ or nNETs had $>98\%$ damage to vessels at either depths [Fig. 7(a)], whereas blood vessels without NETs irradiated at 585 nm had 34 and 11% damage to vessels at depths of 500 and $800\mu \mathrm{m}$, respectively (Fig. 5).

For heavily pigmented skin ($f_{\text{mel}}=50\%$), there was a dramatic decrease in damage to blood vessels containing NETs with ${\mu }_{\mathrm{a},\mathrm{BV}}=1$ to $6{\mathrm{mm}}^{-1}$ ($f_{\text{NETs}}=10\%$) in response to 755-nm laser irradiation at $D_{\mathrm{th}}=3\mathrm{J}/{\mathrm{cm}}^2$ (results not shown). When $f_{\text{NETs}}$ was increased to 25%, blood vessels located at depths of 500 and 800 μm showed 60 and 36% damage, respectively, in presence of $\mu \mathrm{NETs}$ (${\mu }_{\mathrm{a},\mathrm{BV}}=18{\mathrm{mm}}^{-1}$) [Figs. 8(a) and 8(c)]. At this value of $f_{\text{NETs}}$, blood vessels containing nNETs (${\mu }_{\mathrm{a},\mathrm{BV}}=18{\mathrm{mm}}^{-1}$) showed 36 and 27% damage to vessels at depths of 500 and $800\mu \mathrm{m}$, respectively [Figs. 8(b) and 8(d)]. For ${\mu }_{\mathrm{a},\mathrm{BV}}=18{\mathrm{mm}}^{-1}$, the corresponding ICG concentrations in the fabrication is $\approx 1258\mu \mathrm{M}$ [Eq. (12)].

Fig. 8

Damage profiles shown in red ($\mathrm{\Omega }\ge 1$) for blood vessels containing $\mu \mathrm{NETs}$, or nNETs at $f_{\text{NETs}}=25\%$ with ${\mu }_{\mathrm{a},\mathrm{BV}}=18{\mathrm{mm}}^{-1}$, and located at depths of (a, b) 500 and (c, d) $800\mu \mathrm{m}$ below skin surface. Heavy skin pigmentation ($f_{\text{mel}}=50\%$), $\lambda =755\mathrm{nm}$, and $D_{\mathrm{th}}=3\mathrm{J}/{\mathrm{cm}}^2$.

These results demonstrate that blood vessels containing $\mu \mathrm{NETs}$ had greater therapeutic efficacy as compared to nNETs. The increase in % damage to a blood vessel containing $\mu \mathrm{NETs}$ is due to higher energy deposition values deeper into the blood vessels resulting from greater amount of light scattered in the forward direction by $\mu \mathrm{NET}$ ($g=0.99$, Table 2) as compared to nNETs ($g=0.55$, Table 2). Given their larger diameter, the optical behavior of $\mu \mathrm{NETs}$ is consistent with Mie scattering,²⁹ allowing for higher forward scattering.

3.2.

PWS Geometry Based on Patient OCT Image

A 3-D rendering of the patient PWS geometry is shown in Fig. 9(a) (see also multimedia files). The PWS vessel diameters ranged from 60 to $650\mu \mathrm{m}$ with most around $200\mu \mathrm{m}$ and as deep as 1 mm below the skin surface. To test different skin pigmentations, epidermal layers were added to the geometry with light ($f_{\text{mel}}=4\%$), moderate ($f_{\text{mel}}=15\%$), and heavy ($f_{\text{mel}}=50\%$) pigmentations. Due to the greater therapeutic efficacy of $\mu \mathrm{NETs}$ for simulated PWS vessel geometries, we chose to use $\mu \mathrm{NETs}$ for patient PWS vessels with ${\mu }_{\mathrm{a},\mathrm{BV}}=6{\mathrm{mm}}^{-1}$ and $f_{\text{NETs}}=10\%$ for lightly pigmented skin ($f_{\text{mel}}=4\%$), and ${\mu }_{\mathrm{a},\mathrm{BV}}=18{\mathrm{mm}}^{-1}$ and $f_{\text{NETs}}=25\%$ for moderately ($f_{\text{mel}}=15\%$) and heavily ($f_{\text{mel}}=50\%$) pigmented skins. Damage profiles are shown for lightly, moderately, and heavily pigmented skin irradiated with 755 nm for PWS vessels with $\mu \mathrm{NETs}$, or 585 nm for PWS vessels without NETs [Figs. 9(b)–9(f)].

Fig. 9

3-D rendering of (a) human PWS obtained by OCT (Video 1, MPEG, 2.3 MB [URL: https://doi.org/10.1117/1.JBO.23.12.121616.1]) and (b–f) damage profiles to PWS blood vessels. Red regions correspond to values of $\mathrm{\Omega }\ge 1$. (b, c) Damage profiles in response to 585-nm laser irradiation without NETs for light ($f_{\text{mel}}=4\%$) (Video 2) and moderate ($f_{\text{mel}}=15\%$) (Video 3) pigmentation levels, respectively (Video 2, MPEG, 2.3 MB [URL: https://doi.org/10.1117/1.JBO.23.12.121616.2]); Video 3, MPEG, 2.3 MB [URL: https://doi.org/10.1117/1.JBO.23.12.121616.3]. (d–f) Damage profiles in response to 755-nm laser irradiation in presence of $\mu \mathrm{NETs}$ for light ($f_{\text{mel}}=4\%$) (Video 4), moderate ($f_{\text{mel}}=15\%$) (Video 5), and heavy ($f_{\text{mel}}=50\%$) (Video 6) pigmentation levels, respectively (Video 4, MPEG, 3.3 MB [URL: https://doi.org/10.1117/1.JBO.23.12.121616.4]); Video 5, MPEG, 3.3MB [URL: https://doi.org/10.1117/1.JBO.23.12.121616.5]; Video 6, MPEG, 3.3 MB [URL: https://doi.org/10.1117/1.JBO.23.12.121616.6]. Parameters for patient PWS blood vessels containing $\mu \mathrm{NETs}$ were ${\mu }_{\mathrm{a},\mathrm{BV}}=6{\mathrm{mm}}^{-1}$, $f_{\text{NETs}}=10\%$ for (d), and ${\mu }_{\mathrm{a},\mathrm{BV}}=18{\mathrm{mm}}^{-1}$, $f_{\text{NETs}}=25\%$ for (e, f).

The therapeutic effectiveness of NETs in conjunction with 755-nm irradiation over 585-nm irradiation without NETs can be seen from these results. We calculated the % damage for vessels up to the depth of $1000\mu \mathrm{m}$ below the surface on a pixel-by-pixel basis within the simulated 3-D PWS geometry obtained by OCT imaging. This was accomplished by comparing each pixel in the 3-D damage profile with that of the 3-D geometry. The number of pixels showing values of $\mathrm{\Omega }\ge 1$ were summed and divided by the total number of pixels in the geometry to obtain an estimate of % damage. Lightly, moderately, and heavily pigmented skins showed % damage of 88%, 30%, and 4%, respectively, in presence of $\mu \mathrm{NETs}$. For PWS vessels without NETs, there was 32 and 2% damage for lightly and moderately pigmented skins, respectively. In response to the irradiation parameters investigated, current therapeutic approach, based on 585-nm laser irradiation, is most effective in treating patients with light pigmentation by damaging blood vessels to a depth of $\approx 1.2\mathrm{mm}$ but still with some blood vessels remaining intact in the lateral direction [Fig. 10(b)]. Depth of damage is reduced to $\approx 0.8\mathrm{mm}$ and accompanied by a reduction in lateral vascular damage in moderately pigmented PWS skin [Fig. 10(c)].

Fig. 10

2-D $x\text{-}z$ cross section of (a) human PWS obtained by OCT and (b–f) damage to PWS blood vessels. Red regions correspond to values of $\mathrm{\Omega }\ge 1$. (b, c) Damage profiles in response to 585-nm laser irradiation without NETs for light ($f_{\text{mel}}=4\%$), and moderate ($f_{\text{mel}}=15\%$) pigmentation levels, respectively. (d–f) Damage profiles in response to 755-nm laser irradiation in presence of $\mu \mathrm{NETs}$ for light ($f_{\text{mel}}=4\%$), moderate ($f_{\text{mel}}=15\%$), and heavy ($f_{\text{mel}}=50\%$) pigmentation levels, respectively. Parameters for patient PWS blood vessels containing $\mu \mathrm{NETs}$ were ${\mu }_{\mathrm{a},\mathrm{BV}}=6{\mathrm{mm}}^{-1}$, $f_{\text{NETs}}=10\%$ for (d), and ${\mu }_{\mathrm{a},\mathrm{BV}}=18{\mathrm{mm}}^{-1}$, $f_{\text{NETs}}=25\%$ for (e, f).

Under the parameters investigated, laser irradiation at 755 nm in conjunction with $\mu \mathrm{NETs}$ can increase the damage depth to $\approx 1.4\mathrm{mm}$ and also induce complete damage to the vascular plexus in the lateral direction in patients with light pigmentation [Fig. 10(d)]. For patients with moderate and heavy pigmentation levels, blood vessels to depth of $\approx 1.2\mathrm{mm}$ can be damaged when using 755-nm laser irradiation in conjunction with NET, but the extent of lateral vascular damages decreases [Figs. 10(e) and 10(f)]. These results suggest that similar to the optical response of single blood vessel, there may be shadowing effects to reduce the energy deposited to deeper blood vessels.⁴⁹ Such effects can occur if vessels are as close as a few microns.⁵⁰ Optimizing the ICG concentration in NETs may provide a means to allow for more uniform light energy distributions.

Use of free ICG in conjunction with pulsed 808- and 810-nm laser irradiation for treatment of patients with PWS has been reported.^11,12 While promising clinical results have been reported in these studies, delivering NETs to PWS blood vessels is more advantageous than free ICG as it provides a method to increase the circulation time of ICG, and can consequently, elongate the therapeutic window of time over which laser irradiation can be performed. For example, nanoconstructs ($\approx 80\mathrm{nm}$ diameter) composed of poly (lactic-co-glycolic acid) core coated with erythrocyte-derived membranes were retained in blood for 3 days with circulation half-life of $\approx 8\mathrm{h}$ in mice.⁵¹ Piao et al.⁵² reported that the circulation half-life of gold materials cloaked with erythrocyte membranes ($\approx 90\mathrm{nm}$ diameter) was $\approx 9.5\mathrm{h}$. Increased circulation time of erythrocyte-coated particles can be attributed to the presence of “self-marker” membrane proteins to allow evasion by immune cells.^53,54 One important “self-marker” membrane protein on the surface of the erythrocytes is CD-47 glycoprotein, whose interaction with immunoreceptor signal regulatory protein alpha ($\mathrm{SIRP}\alpha$), expressed by macrophages, results in inhibition of phagocytosis.⁵⁵ We previously demonstrated that CD-47 remains on the surface of the NETs,⁵⁶ providing a mechanism for increased circulation time of NETs. Furthermore, NETs can serve as a biocompatible and nontoxic platform for delivery of ICG. In a recent study, Rao et al.⁵⁷ reported the absence of systemic toxicity at 15 days postintravenous injection of erythrocyte membrane-coated upconversion nanoparticles in mice.

Results of this theoretical study indicate that use of NETs in conjunction with pulsed 755-nm laser irradiation can provide a personalized approach for effective treatment of PWS blood vessels by customizing the optical properties of NETs to match the type of vascular plexus (e.g., depth, size, and distribution of blood vessels) and induce the necessary photothermal effects. The theoretical model presented in this study can be used in guiding the fabrication of NETs with an appropriate level of ICG and development of laser dosimetry parameters.