Thermal damage of target with separation between part of the target and the pigmented area requires deposition of sufficient heat energy into the absorbing area, and good heat exchange between this area and the targeted external structures. Heat deposition depends on the absorption coefficient of the absorber and the EMR power density. Heat exchange depends in turn on the distance between the heater and the outermost part of the target and on the heat transmission coefficient between the absorber and the intervening tissue. However, at a sufficiently high temperature both the heater absorption coefficient and the heat transmission coefficient from the heater to the other targeted tissues may become lower due to phase transitions and destructive processes such as bleaching, melting, boiling, and bubble formation. This results in inefficient use of EMR energy for phase transition processes within the absorber and the intervening tissue. To prevent these undesirable effects, the heater peak temperature has to be limited to a prescribed value, T1max, called hereafter the temperature of heater absorption loss. The temperature of heater absorption loss T1max of most endogenous chromophores (e. g., melanin, hemoglobin, and water) exceeds 1000C. Simultaneously, to ensure permanent damage of the whole target, the temperature should exceed a second prescribed value, the damage temperature T2, throughout the target area. This temperature is lower than the temperature of heater absorption loss T1max. More precisely, the damage temperature, T2, is the temperature at which irreversible thermal damage of the target occurs. We suggest that the basic damage mechanism in soft tissue is the dena – turation of proteins. As an alternative to the rigorous Arrhenius rate process integral [see Eq. (3.17)] [60], the dynamic denaturation process may be described approximately by using the simpler damage-temperature concept. For human-skin collagen, T2 is about 65-75°C, and for cells T2 it is about 60°C if the exposure duration is several tens of milliseconds [60]. Furthermore, the tissue temperature should not exceed the water boiling point, to prevent formation of vapor bubbles that could insulate the absorbing area from the surrounding tissue. Strictly speaking, vapor bubbles can transfer heat from the absorbing area to the target, but this process is unpredictable because vapor bubbles can move in different directions.
To meet the temperature limitations described earlier, the EMR power must be limited, (but there must be sufficient to heat the target up to the damage temperature) and, therefore,
the EMR pulse has to be made sufficiently long to deliver enough energy. Other important criterion is selection of wavelengths of light. It is necessary to provide relatively uniform heat deposition in pigmented area during EMR pulse and at same time to absorb maximum EMR energy in the pigmented area. To meet this criterion, optical density of the pigmented area has to be in the range 1 < i2dx < 3. We define the thermal damage time (TDT) of the target to be the time required for irreversible target damage with the sparing of the surrounding tissue. For a nonuniformly absorbing target structure, the TDT is the time when the outermost part of the target reaches the target damage temperature T2 through heat diffusion from the heater. Because the heat-diffusion front becomes blurred when propagating into the tissue, part of the heat energy will leave the target. Therefore, the heated area will be larger than the damaged area. However, we demonstrate later here that the target damage can still be selective, even though the TDT is many times as long as the TRT of the whole target. Apparently, the optimum EMRpulsewidth, t0, should be shorter than or equal to the TDT. So, in contrast to the standard theory of selective photothermolysis, nonuniformly pigmented structures have to be treated by long EMR pulses: the pulsewidth must typically be longer than the target TRT. In addition, the EMR power should be limited to prevent reduction of the heater absorption by bleaching, vaporization, etc.
Figure 3.16 shows the general structure of a target that is thermally denatured by heat diffusion from a heater. The heater includes an endogenous or exogenous chromophore (pigment) with a high photon absorption coefficient. The target exhibits weak EMR absorption. The distance between the heater and the target is d. Photons from the EMR source are absorbed by the heater. As discussed in the Section 3.6.1.1, the EMR power density has to be adjusted so that during the time of treatment the heater temperature T1 does not exceed the temperature Tjmax where the absorption coefficient may begin to drop. The heat propagates from the heater to the target due to either thermal diffusion or two other possible mechanisms. These mechanisms are hot ablation products emanating from the heater, or steam. In this chapter, we will concentrate exclusively on the thermal diffusion mechanism. The process of target thermal damage is completed when its temperature reaches T2, while the temperature of the surrounding tissue remains below its damage temperature. In general, it is not possible to damage the target without damaging the tissue between the target and the heater. For this target type, precise selective damage of the target is impossible. But
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Figure 3.16 The general structure of a target that is thermally denatured by heat diffusion from a heater; the heater includes an endogenous or exogenous chromophore (pigment) with a high photon absorption coefficient; The target exhibits weak EMR absorption; the distance between the heater and the target is d. |
if the treated target is a layer or a shell of tissue roughly symmetrical with respect to the heater, the target damage can be made precisely selective. This means that the damage zone covers the whole target without extending beyond it. After the end of the EMR pulse, the target temperature at the outermost point goes on growing until it reaches a maximum. The time delay between the end of the EMR pulse, t = r0, and the moment when the temperature of the outermost point is reached, the maximum temperature T2 is denoted by e and thus TDT = r0 + e. Therefore, the EMR pulsewidth is equal to or shorter than the TDT. This delay e is roughly equal to the propagation time of the heat front from the heater to the target e ~ cFlk, e is therefore close to the target TRT. As we shall see subsequently, TDT is significantly longer than the TRT in most cases. So, for selective treatment the pulsewidth should be approximately equal to the TDT: r0 = TDT. The TDT depends in turn on T1, T2, and the target size. For a better understanding of this dependence we first look more closely at heat diffusion from the heater to the target. Specifically, we will be focused on a target comprising a heavily pigmented long cylinder of diameter d1 and a surrounding treated area of diameter d2 (Fig. 3.17). This simple geometry can be used to model thermal damage of hair follicle by hair-shaft heating or blood vessel destruction. We consider two heating modes. The first mode utilizes a rectangular EMR pulse (Fig. 3.18a) and the second one utilizes a flattop temperature pulse (Fig. 3.18d). In the case of the rectangular EMR pulse, the heater temperature grows during the EMR pulse and reaches T1 at the end of the pulse (Fig. 3.18b). In the case of the flattop temperature pulse, the temperature of the heater is constant during the EMR pulse, which requires a special pulse shape (Fig.3.18c). For both heating modes, the heater temperature is below the temperature of heater absorption loss T1max so the absorption coefficient of the heater does not change.
The sequence of thermal profiles during the heating process is depicted in Fig. 3.17. The input parameters for modeling are d1 = 70 pm, d2 = 210 pm. The temperature of heater absorption loss T1 is 100°C (the boiling point of water). The damage temperature is 65°C,
(a)
Figure 3.17 Temperature distribution in the tissue with cylindrical absorber with diameter 0.07 mm and target with diameter 0.21 mm [59]: (a) shows the temperature distribution for a rectangular EMR pulse at two points in time: bottom curve at t = TRT = 27.5 ms and top curve at t = TDT = 1.6 s; (b) shows the temperature distribution for a flattop temperature pulse at two points in time: bottom curve at t = TRT = 27.5 ms and top curve at t = TDT = 0.36 s. Maximum temperature of the absorber is T1 = 100°C. Damage temperature is T2 = 65°C. Initial temperature is T0 = 37°C. The absorption of the tissue surrounding the heater was neglected.
Figure 3.18 Time dependence of electromagnetic radiation (EMR) power and temperature of the heater (absorber) [59] Two basic cases are shown: (a) rectangular EMR pulse; (b) shows heater temperature as a function of time that is produced by a rectangular EMR pulse; (c) shows EMR power as function of time that produces a flattop temperature pulse at the heater and (d) flattop temperature pulse.
which is the average protein denaturation temperature in the 10-1000 ms pulsewidth range. We assume that the EMR absorption is confined to the heater and that the thermal properties of the heater, the target, and the surrounding tissue are the same. Heat diffusion from the heater takes place simultaneously with the growth of the heater temperature due to light absorption. This process is described well by the heat conduction equation.
Figure 3.17a and b shows the temperature profiles in the cylindrical target and the surrounding tissue at different instants of time for the rectangular EMR pulse and the flattop temperature pulse, respectively. Curve 1 in both figures is the temperature profile at the time equal to the thermal relaxation time of the whole target. The latter time is TRT = d22/16k. In our case the TRT = 27 ms. We can see that at the time instant t = TRT the boundary temperature of the target is still significantly below the damage temperature. Curve 2 in both figures is the temperature profile at the moment when the boundary temperature of the target reaches the damage temperature T2. At this moment, the whole target is damaged but the surrounding tissue is still intact. It is this time that has been defined above as the thermal damage time. In our case TDT = 0.63 s for the rectangular EMR pulse and TDT = 0.16 s for the flattop temperature pulse. Based on this example, we can arrive at two main conclusions. First, the ratio TDT/TRT is about 23 and 6 for the rectangular EMR pulse and the flattop temperature pulse modes, respectively. Therefore, in both modes the pulsewidth t = TDT is significantly longer than the TRT of the entire target. Second, at the time instant when t = TDT, the heated area is significantly larger than the damaged target.
These observations present a striking contrast to the classical case of selective photothermolysis. This distinction is a result of the spatial separation of the heavily pigmented and treated areas. Actually, in contrast to the classical case, the basic damage mechanism is now heat diffusion rather than direct heating by EMR absorption. The heat diffusion front is not sharp and, therefore, heat is spreading outside the damaged area; however, the damage is still rather selective.
We have described the difference in treatment modality between uniformly and nonuniformly pigmented targets. The new extended theory of selective thermal damage of nonuniformly pigmented structures in biological tissue postulates the following:
1. The EMR wavelength should be chosen to provide sufficient contrast between the absorption coefficient of the pigmented area and that of the tissue surrounding the target and provide optical density of pigmented area in the range 1- 3.
2. The EMR power should be limited to prevent absorption loss in the pigmented area, but it must be sufficient to achieve a heater temperature higher than the target damage temperature.
3. The pulsewidth should be made shorter than or equal to the thermal damage time (TDT), which can be significantly longer than the thermal relaxation time of the target.
