Numerical simulation of heating blood vessel using various lasers

  1. A.E. Pushkareva1,
  2. I.V. Ponomarev2 and
  3. S.B. Topchiy2

1Department of Laser Technologies, Saint Petersburg National Research University of Information Technologies, Mechanics and Optics; 49, Kronverkskiy Prospect, Saint Petersburg, 197101, Russian Federation
2 Department of quantum radiophysics, P.N. Lebedev Physics Institute, 53, Leninsky Prospect, Moscow, 119991, Russian Federation

  1. Corresponding author email

Advanced Modelling and Simulation 2018, 1, 1–6. doi:10.26705/advmodsim.2018.1.1.1-6
Received 26 March 2018, Accepted 10 April 2018, Published 19 April 2018

Abstract

The relevance of laser treatment of skin vessel lesions was proved demonstratively to be dependent on the appropriate choice of settings of laser systems. Up now there was clearly accepted the algorithm for the determination of both most relevant and safe modes of laser treatment considering features of the vessel angioarchitectonics of the dysplastic vessel to be targeted with laser irradiation. The relevance of different most used laser systems as pulsed dye laser ( PDL), copper vapor laser (CVL), diode laser and Nd:YAG laser was compared, and the limits of phototherapeutic ranges for each laser system were determined by means of numerical simulation of selective skin vessel heating for various combinations of vessel diameters and the distance of the targeted vessel from the skin surface. The fluences band for selective vessel heating with different laser systems appeared to amount to 6-17, 7 J/cm2 for the CVL, 2-6 J/cm2 for the PDL, 40-100 J/cm2 for the diode laser and 80-170 J/cm2 for the Nd: YAG laser. When using the fluence values exceeding this limit, photodestruction becomes nonselective.

Keywords: Copper vapor laser, pulsed dye laser, skin vascular lesions, vessel heating

Introduction

For the time present lasers and intense pulsed light sources enable physicians to treat vascular skin lesions previously appeared to be untreatable. Currently, the preferable method of treating the vascular lesions is accepted to be selective photodestruction technique based upon selective heating of dysplastic vessels. This technique demands for the set of the appropriate mode of laser exposure by choosing of wavelength, fluence and pulse width of laser exposure to target hemoglobin within dilated blood vessels selectively without damaging the surrounding derma.

In 1981, Anderson and Parrish proposed the selective photothermolysis concept concerning the capability of the laser light with the wavelength of 577 nm to selectively target skin blood chromophores to give rise in photoobstruction of dysplastic blood vessel due to thermal blood coagulation during proper short laser pulses. To prevent overheating of surrounding tissue, the laser exposure time should be less than the vessel thermal relaxation time (TRT) [1].

The extent of laser heating of blood vessels was shown to be tightly depended on both of the vessel diameter and the distance from the skin surface. In venous capillary malformation the diameter of the dysplastic vessel is shown to vary from 30 up to 300 microns in the port-wine spots and from 0,1 to 1,0 mm in telangiectasias along with limits of depth range from 200 to 800 mm [2].

Therefore, the problem of simulation of vessel heating due to laser exposure generated by different laser systems appears to be actual [1, 3, 4].

Model

Numerical simulation of the dynamics of optical and thermal processes under the laser exposure of skin vessels was carried out on the basis of the theory of radiation transfer (in the diffusion approximation), and the theory of thermal conductivity in frameworks of as the further development of the work on the modeling reported previously [5-6]. For calculations, there was created a mathematical model including optical and physical properties of the object (skin and vessels) (Figure 1). In the model, the skin is represented by a multi-layer structure consisting of the epidermis, in which there was isolated a basal layer containing melanin proved to be one of the main skin chromophores and dermis. In the dermis, there are located blood vessels of various diameters and depth of location. For calculations the thickness of the epidermis was chosen to be equal to 70 μm, the thickness of the basal layer was accepted to be of 15 μm.

[2456-279y-1-1-1]

Figure 1: The scheme of skin model used for calculation (1 - vessel top, 2 — vessel axis, 3 — vesselbottom, 4 - vessel side, 5 - basal layer)

[2456-279y-1-1-2]

Figure 2: Absorption spectra of skin components, taken into account

The tissue is considered as a plane parallel structure of the finite width and infinitely extended in the direction transverse to the direction of the laser pulse. Diameters of blood vessel were accepted to range from 7.5 μm to 500 μm. The vessel is a cylinder of infinite length, located parallel to the skin surface. The blood was assumed to be immobile during the laser pulse [7]. The optical properties of all considered structures were assumed to depend on the wavelength (Figure 2) and are homogeneous. This model does not take into account changes in the optical and physical properties of the bio-object due to coagulation, temperature changes, etc., as well as the dynamic cooling device of the skin during PDL treatment.

In order to calculate the temperature distribution in the skin, the thermal conductivity equation (1) was used:

[2456-279y-1-1-i1]
(1)

where: ρ- density, c — thermal capacity, t - time, κ=α.ρ.c- thermal conductivity and α-thermal diffusivity.

The value [Graphic a] as the bulk density of heat sources in a medium was calculated as follows (2):

[2456-279y-1-1-i2]
(2)

where: µa- absorption coefficient, [Graphic b]- total illuminance at the point [Graphic c] , including both the collimated and diffusion components, and Е0- radiation energy density (Fluence)

The collimated illuminance component was decaying in accordance with the exponential law due to absorption and scattering (3):

[2456-279y-1-1-i3]
(3)

Here [Graphic d] is the intensity at the point [Graphic e] in the absence of the medium (dermis), [Graphic f] - the direction of the propagation of the primary beam, µt = µa + µs- total attenuation coefficient and l - depth of the propagation of nonscattered photons in dermis from the skin surface and the point [Graphic e] is related to the volume element under consideration.

To solve the thermal conductivity equation, it is required to know the illuminance distribution in the medium, which was calculated using the equation of radiation transfer in the diffusion approximation (4):

[2456-279y-1-1-i4]
(4)

where: [Graphic b] is the illuminance diffusion component at the point [Graphic e] , μa - absorption coefficient, μs-scattering coefficient, [Graphic b] - attenuation transfer coefficient and g — average cosine of the scattering angle (scattering anisotropy factor).

The values of the optical (See Figure 2) and thermophysical properties were taken from [8-16]. The model takes into account the specific pulsed nature of the copper vapor laser (CVL) radiation, which emits a train of 15 ns micropulses at 16.6 kHz reprate.

In order to ensure the simulation procedure, the Matlab mathematical simulation software and applications thereof for solving differential equations in the Femlab partial derivatives and using the Finite Element Method were introduced.

Laser settings used for the calculation were taken from [2-4] are presented in Table 1.

Table 1: Laser systems settings used in calculations

  CVL PDL Diode Nd:YAG
Wavelength, nm 578 585 980 1064
Average power, W 0.6 - - -
Laser energy density (fluence) F, (J/cm2 ) 5-20 3-7 50-150 50-200
Duration of the exposure, msec 200 3 200 200
Duration of a single laser pulse, tp 15 ns 0,45 mseс - -
The interval between laser pulses, tpause 60 msec - - -
Number of pulses per exposure 3332 1 1 1
Blood absorption coefficient, mm-1 26.5 16.9 0.51 0.2
Basal absorption coefficient, mm-1 2.28 2.195 0.28 0.167

Results and Discussions

To calculate the dependence of wavelength, vessel depth, and vessel diameter on the deposited energy in the blood vessel, we introduce geometry for multiple vessels in dermis, as shown in Figure 3.

[2456-279y-1-1-3]

Figure 3: Geometry with 9 vessels in three layers at different depths z = 150, 500, and 1000 μm, (3 vessels with a diameter of 30 μm (on the left), 3 vessels with a diameter of 100 μm (in the middle) and 3 vessels with a diameter of 300 μm (on the right))

Figure 4 shows the calculated temperature levels for 9 vessels (3 vessels with a diameter of 30 μm (on the left), 3 vessels with a diameter of 100 μm (in the middle center) and 3 vessels with a diameter of 300 μm (on the right), exposed to the irradiation generated by different laser systems. The vessels of each diameter were assumed to be located at a depth of 150, 500 and 1000 μm respectively. The laser radiation settings were taken from the Table 1. The deeper vessels received less energy and heated at the lower temperature due to decreasing of absorption of light with depth.

[2456-279y-1-1-4]

Figure 4: The calculated temperature distribution of the tissue and vessel according to the depth and transverse coordinate. Three vessels with a diameter of 30 μm (on the left), three vessels with a diameter of 100 μm (at the center) and three vessels with a diameter of 300 μm (on the right) are located at a depth of 150, 500 and 1000 μm respectively. Fluence value for PDL (F = 2.95J/cm2 ) (a), for CVL (F = 13.7 J/cm 2 ), for diode laser (F = 80J/cm2 ) (c) and for Nd:YAG laser (F = 140J/cm2 ) (d).

According to calculation results, the maximum heating temperature of the vessel and basal layer under CVL laser exposure is lower than under PDL laser irradiation. At the depths of the vessel location in dermis up to 2 mm, CVL and PDL have a distinct advantage in heating the vessels compared with other types of lasers (Nd:YAG and diode). To obtain the same degree of vessel heating (75°C), as for CVL and PDL, diode and Nd:YAG lasers would require an increase in energy by order of magnitude, and employ fluence value more than 100 J/cm2 (see Figure 4).

It is possible to determine the therapeutic range of fluences for selective photodestruction of the increased diameter vessels. The fluences range, where the vessel heating remains selective (i.e., the vessel heating is above 75 0C, and the tissue and basal layer temperature is below 75 0C), corresponds to 6-17.7 J/cm2 for the CVL, 2-6 J/cm2 for the PDL, 40-100 J/cm2 for the diode laser and 80-170J/cm2 for the Nd:YAG laser.

When using the fluence values exceeding this limit, photodestruction becomes nonselective, “hot iron” effect achieved, i.e., coagulation of the vessel, basal layer, and surrounding tissue is taking place(temperature exceeds 750C). The use of such dosages in medical practice could lead to complications and longer postoperative rehabilitation period for patients (see Figure 5).

[2456-279y-1-1-5]

Figure 5: The calculated distribution of the temperature tissue and vessel according to the depth and transverse coordinate. 3 vessels with a diameter of 30 μm (on the left), 3 vessels with a diameter of 100 μm (at the center) and 3 vessels with a diameter of 300 μm (on the right) are located at a depth of 150, 500 and 1000 μm respectively using fluence value for PDL (F = 4J/cm2 ) (a), for CVL (F = 17.7J/cm2 ) for diode laser (F = 100J/cm2 ) (c) and for Nd:YAG laser (F = 175J/cm2 ) (d).

According to the calculation performed, diode and Nd:YAG lasers are characterized by a possibility to selectively heat only the large vessels (over 100 μm in diameter). At the same time, heating small vessels (of 30-100 μm in diameter), appearing in port-wine stains, by these laser systems, fails to be effective.

The decreasing energy deposition during CVL and PDL laser treatment the tissue temperature is lower than (See at Figure 4(a, b)) under diode and Nd:YAG laser irradiation. In the case of overtreatment (blanching appearance of the skin) by diode and Nd:YAG lasers, a doctor can get up to 2 mm overheated and damaged tissue surrounded of a vessel. It could lead to complications like scarring and permanent depigmentation.

[2456-279y-1-1-6]

Figure 6: Spatial distribution of maximum fluencies vs. the vessel diameter and the vessel depth. The region between two surfaces corresponds the conditions of maximum vessel temperature at a range of 75-100 0С, and maximum temperature of the tissue and basal layer do not exceed 75 0С for PDL (a), CVL (b).

As the main result, Figure 6 can be used for calculating the depth and the diameter of dilated vessels which can be selectively heated by a given fluence. The region between two surfaces (transparent and solid) corresponds the conditions of vessel temperature at the range of 75-100 0С , and temperature of the tissue and basal layer do not exceed 75 0C for PDL (Fig. 6a), CVL (Fig. 6b).

The results of our simulations for CVL and PDL were compared with reports of histological studies by Tan et al. [17-18] and histochemical study by Neumann et al. [19] concerning coagulated vessels as deep as 0.7 mm for 577 nm and 1.2 mm for 585 nm laser light. It allows making the conclusion that described model is in excellent agreement with experimental data and predicts the vascular selective heating with slight perivascular collagen damage.

Conclusions

We successfully modeled the main characteristic features of blood vessel heating using various laser systems employed in medical practices. The limiting values of the fluencies to provide selective vessel coagulation were determined.

The use of pulsed yellow light that falls into the oxyhemoglobin and deoxyhemoglobin high absorption band allows achieving the maximum efficiency of heating the dysplastic vessels of the vascular skin lesions. For PDL and CVL the ratio of temperature rise in the blood vessels to temperature rise in the epidermis was maximal.

According to calculations, the 10-times higher fluences, needed for vessel heating by the long pulse Nd:YAG and diode lasers to the coagulation temperature, causes the increased heat dissipation throughout the dermis and produces the risk of scarring, hypo- and hyperpigmentation.

Based on the calculated data, the mode of heating the dysplastic vessels by a series of the CVL micropulses is safer than a short high-energy PDL pulse, since the CVL provides heating vessels different diameters below the blood boiling point, which provides the vessel selective coagulation without the effects of vascular rupture and the development of purpura and the hematomas formation in case of using the PDL.

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© 2018 A.E. Pushkareva et al.; licensee Payam Publishing Pvt. Lt..
This is an Open Access article under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The license is subject to the Advanced Modelling and Simulation terms and conditions: (http://www.jfips.com/saea)

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