Photoepilation. Photoepilation utilizes light to cause thermal or mechanical damage of hair follicles. To achieve hair growth delay, it is sufficient to either damage matrix cells of anagen hair follicles or coagulate blood vessels of the papilla, or possibly destroy part of the outer root sheath [56]. For permanent hair-follicle damage, in accordance with current knowledge, it is necessary to damage stem cells that are located in the bulge area at the interface of the outer root sheath and the connective tissue sheath [61]. One can also irreversibly damage a hair follicle at the level of the dermis by replacing it with connective tissue.
The matrix cells produce the hair shaft. The matrix cells contain melanosomes that produce hair melanin. The concentration of melanin in the matrix cells is significantly higher than in the hair shaft. Melanin is distributed uniformly and densely in the matrix cells. So for a pulsewidth longer than the TRT of individual melanosomes (1 ps), the matrix cells act as a uniformly pigmented target. This is a typical example of a target where standard selective photothermolysis theory is applicable. For selective and effective treatment, the energy and pulsewidth have to be significantly shorter than the TRT of the matrix cells. The matrix cells form a dome-shaped structure with the smallest cells close to half of the hair shaft diameter dh. So the TRT of the hair matrix can be estimated as the TRT of a layer with thickness dh/2, that is, dh2/32k. The pulsewidth values for effective treatment are presented in Table 3.3 .
Another method of halting hair shaft growth is to coagulate blood vessels in the papilla. The loop of blood vessels in the papilla is located in the center of the matrix cell dome. Blood absorption is significantly lower than melanin absorption in the neighboring matrix cells because of the small vessel size. So, the most effective method of papilla blood vessel coagulation is to utilize heat diffusion from the matrix cells that absorb light. This is a typical case where the extended theory of selective photothermolysis can be applied. The highly pigmented heater (the matrix cells) and the lightly pigmented target (the blood vessels) are separated by a distance of about dh/2. We calculated the TDT of the hair papilla blood vessels using our thermal diffusion model, assuming the maximum heater temperature to be T1 = 100°C and the blood vessel coagulation temperature to be T2 = 65°C. The TDT value for different hair sizes and heating modes are presented in Table 3.3. We can see a significant difference in optimum treatment pulsewidth for: (1) the matrix cells by direct light absorption and (2) the papilla blood vessel loop by heat diffusion.
Let us now consider damage of hair stem cells. They are located in the basal cell layer of the outer root sheath of the lower isthmus. The stem cells do not have any pigment that can effectively absorb light in the therapeutic window (600-1200 nm), which is also the best wavelength range for photoepilation [56]. However, the stem cells can be damaged by heat diffusion from the melanin-rich hair shaft or an artificial chromophore inside the inner root sheath. This case is very well-described by the cylindrical model that we considered in some detail previously. The optimum treatment pulsewidth of the stem cells is close to the TDT of the follicle structure. If we assume that the maximum hair-shaft temperature is
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Table 3.3 Optimum Pulsewidth for Hair-Follicle Treatment [59]
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T1 = 100°С and the damage temperature of the stem cells is T1 = 65°C, we can calculate the TDT as shown in Table 3.A2 (approximate formulas give us slightly lower values than the exact modeling we presented in Fig. 3.20). Calculation results for a follicle with a ratio of follicle diameter to hair-shaft diameter of x = 3 are presented in Table 3.3.
To estimate power density P and fluence F for the rectangular light pulse case, we can use formulas from Table 3.A2 (see Appendix) that we can simplify for the follicle case as:
F = P • TDT [J/cm2],
where pa (cm-1) is the hair-shaft absorption coefficient, and q is the ratio of the radiance at the target location to the input power density (attenuation factor). For our calculation, we use typical treatment conditions: wavelength is 800 nm, dark hair with pa = 100 cm-1, x = 3, q = 1 (low isthmus level of follicle), T1 = 100°C, T2 = 65°C, and T0 = 36°C. Using the formulas shown here, we calculate the following values: power density is 560 W/cm2 for 30 pm fine hair, 100 W/cm2 for 70 pm terminal hair and 35 W/cm2 for 120 pm coarse hair. For these hair with equal melanin concentration and different diameters, the fluence necessary to damage the stem cells is the same. The fluence value is 40 J/cm2. The pulsewidth value appears in Table 3.3 as the TDT for a rectangular light pulse. We can see from Table 3.3 that selective and complete hair-follicle damage can be achieved over a very broad range of pulsewidths. For example, for a hair shaft diameter of approximately d1 = 70 pm and a hair follicle diameter of d2 = 210 pm, this range is 170-610 ms, which is significantly longer than the TRT (27 ms). If the energy of the ablation products is not too high, most of them release their energy inside the hair follicle and heat up the follicle structure. So, all the absorbed energy was utilized to heat the follicle structure (including IRS and ORS). For a pulsewidth significantly shorter than 30 ms with the same fluence, we can expect more hair-shaft ablation and escape of the hair-shaft ablation products from the hair follicle. In this case, the damaged volume of the hair follicle should decrease with decreasing pulsewidth and, for very short pulses, it should be limited to the hair shaft.
Photosclerotherapy. Photosclerotherapy produces thermal or mechanical damage of the vessel structure due to light absorption by blood [62]. The blood hemoglobin exhibits selective light absorption over a wide wavelength range. Optimum vessel closure can be achieved by denaturation of the endothelium that is in direct contact with blood. This case is well – described by the standard theory of selective photothermolysis [55]. Other authors have suggested that permanent vessel closure requires denaturation of the vessel wall structure [57,58]. These structures do not contain any strongly absorbing chromophores and can be damaged by heat diffusion from blood. Therefore, we will apply the extended theory of selective photothermolysis to estimate treatment parameters for different vein sizes. As a first approximation, the vein can be modeled as a cylinder. However, this is true just for limited constrained cases depending on the light wavelength and vein size. The cylindrical model is valid if the light penetration depth in the blood exceeds the vessel internal diameter D. In this case, the blood is heated uniformly. If scattering of the blood is lower than absorption, the light penetration depth is roughly equal to the inverse blood absorption
coefficient 1/pa. Thus the cylindrical model can be used when D < 1/pa. In this case, the heater diameter is d1 = D and the target diameter is d2 = D + 2w, where w is the vessel-wall thickness. If D >>; 1/pa, the heated zone is a cylindrical blood layer, in contact with the vessel wall. The heated-zone thickness is approximately equal to the penetration depth 1/pa. This case can be roughly described by the planar model with heater thickness d1 = 1/pa and target thickness d2 = 1/pa + 2w. Analytic evaluation of the TDT using the expressions of Table 3.A2 is possible in the rectangular light-pulse case, when the whole blood volume is uniformly irradiated. If this is the case, then the cylindrical target model is applicable. In the opposite limiting case of very strong blood absorption, a thin layer of blood adjacent to the vessel wall is only irradiated. In the latter case one may apply the planar model. Here, the analytic and numeric results show rather good agreement. In other cases both the TDT and the input flux were evaluated numerically. The maximal heater temperature is T1 = 100°C (limited by blood coagulation and vaporization), vessel wall denaturation temperature is T2 = 65°C, and the initial body temperature is T0 = 37°C. The calculations were performed for two wavelengths l: l = 577 nm (maximum hemoglobin absorption), where 1/pa = 43 pm; and moderate hemoglobin absorption pi = 1060 nm, where 1/pa = 1400 pm [63,64]. To estimate the power density and fluence for a rectangular light pulse, we can use formulas from Table 3.A2 and direct modeling for a flattop temperature pulse. Calculation results for different types of spider veins are presented in Table 3.4.
As we see from Table 3.4 , the TDT of the entire vein wall structure is shorter for the 577 nm wavelength that coincides with the strong hemoglobin absorption peak. The TDT can be very long, typically for large veins. The perfusion factor can also be important, but is not discussed in the present study. Blocking of the blood flow can be important for optimum treatment with such a super long pulse. The large veins need significantly lower flu – ence, power density, and longer pulsewidth than small veins. This dependence is even stronger for light with low absorption in hemoglobin. The water absorption of surrounding tissue can be important for long treatment wavelengths (l > 750 nm) due to parallel nonselective heating by water absorption that can increase the tissue temperature T0. As we showed earlier, the TDT will be shorter in this case, and the fluence will be lower.
The parameters for spider-vein treatment suggested by the new theory are very different compared to typical clinical parameters used for photosclerotherapy, and should be clinically proven.
Following from Tables 3.3 and 3.4, the treatment time (pulsewidth) for hair follicles and spider veins is on the order of several hundreds of milliseconds. As was shown in ref. [65], parallel cooling of the epidermis (simultaneous heating by light absorption and heat removal by heat diffusion into the skin and cooling agent) is very effective in this pulsewidth range. This cooling mode is important for epidermal protection and makes the procedure more effective, because high fluence can be delivered through the epidermis.