When photons traveling in a tissue are absorbed, heat is generated. Generated heat induces several effects in tissue which can be presented in the order of amount of heat deposition: temperature increase and reversible and irreversible alterations in tissue. The following types of irreversible tissue damage are expected as tissue temperature rises past Tcrit: coagulation (denaturation of cellular and tissue proteins) is the basis for tissue welding, vaporization [tissue dehydration and vapor bubbles formation (vacuolization), T > 100°C)] is the basis for tissue mechanical destruction; pyrolysis (T~ 350-450°C). For short light pulse, all these processes develop as explosion or thermal ablation. All these phenomena are named as photothermal mechanism. During ablation, high pressure is developing in tissue, which can be a reason for shock wave formation and mechanical damage of tissue. This phenomenon is named photomechanical mechanism.
The generated heat, described by the heat source term S at a point r is proportional to the fluence rate of light f(r) (mW/cm2) and absorption coefficient yUa(r) at this point [48-52]:
S(r) = ma(r)f(r). (3.15)
The traditional bioheat equation originated from the energy balance describes the change in tissue temperature over time at point r in the tissue
rc^IM = V[kmVT(r, t)] + S(r) + rCw(T – Tv) (3.16)
dt
where r is the tissue density (g/cm3), Cis the tissue specific heat (mJ/g°C), T(r, t) is the tissue temperature (°C) at time t, km is the thermal conductivity (mW/cm°C), S(r) is the heat source term (mW/cm3), wis the tissue perfusion rate (g/cm3s), Ta is the inlet arterial temperature (°C), and Tv is the outlet veinual temperature (°C), all at point r in the tissue. In this equation convection, radiation, vaporization, and metabolic heat effects are not accounted
for, because of their negligible effect in many practical cases. The source term is assumed to be stationary over the time interval of heating. The first term to the right of the equal sign describes any heat conduction (typically away from point r), and the source term accounts for heat generation due to photon absorption. In most cases of light (laser) tissue interaction, the heat transfer caused by perfusion (last term) is negligible.
To solve this equation, initial and boundary conditions must be accounted for. The initial condition is the tissue temperature at t = 0 and the boundary conditions depend on tissue structure and geometry of light heating. Methods of solving of the bioheat equation can be found in refs. [48-50].
Damage to a tissue results when it is exposed to a high temperature for a long time [48-52]. The damage function is expressed in terms of an Arrhenius integral:
where t is the total heating time (s); C(0) is the original concentration of undamaged tissue; C(t) is the remaining concentration of undamaged tissue after time t ; A is an empirical determined constant (s-1); Ea is an empirically determined activation energy barrier (J/mole); R is the universal gas constant (8.32 J/mole-K); and T is the absolute temperature (K).
At noninvasive optical diagnostic and some photochemical applications of light, one has to keep tissue below the damaging temperature so-called the critical temperature Tcrit. This temperature is defined as the temperature where the damage accumulation rate, dQ/dt, is equal to 1.0 [51]:
E
T =
crit = R ln( A)
The constants A and Ea can be calculated on the basis of experimental data when tissue is exposed to a constant temperature [49]. For example, for pig skin, A = 3.1 x 1098 and Ea = 6.28 x 105, that gives Tcrit = 59.7°C.
With CW light sources due to the increase of the temperature difference between the irradiation and the surrounding tissue, conduction of heat away from the light absorption point and into surrounding tissue increases. In dependence of light energy, large tissue volumes may be damaged, or losing of heat at the target tissue component may be expected. For pulsed light, a little heat is usually lost during the pulse duration since light absorption is a fast process while heat conduction is relatively slow; therefore, more precise tissue damage is possible.
The disadvantage of thermal ablation with CW light sources is undesirable damage to surrounding tissue via its coagulation. Pulsed light can deliver sufficient energy to ablate tissue in each pulse, but in a short enough time, that tissue is removed before any heat is transferred to the surrounding tissue. To achieve a precise tissue ablation, lasers with a very short penetration depth, like excimer ArF laser or Er:YAG, are used (Fig. 3.2).
For skin as a turbid medium irradiated with wide laser beams (>0.1mm), the effect of backscattering causes a higher subsurface fluence rate compared with the incident laser fluence [Eq. (3.7)]. Therefore, the z-axial light distribution in tissue and the corresponding
stress distribution have a complex profile, with a maximum at a subsurface layer. The stress amplitude adjacent to the irradiated surface dp(0) and the stress exponential tail into the depth (Z) of the tissue sample are proportional to tissue absorption coefficient pa and the incident laser pulse energy E0 [53,54]:
dp(0) = GmaE(0), at surface (z = 0), (3.19)
dp(Z) = GmabsE0exp(- meffz), for z > i/meff, (3.20)
where Г = bva2/cT, cT is the specific heat of the tissue, bs is the factor that accounts for the effect of backscattered irradiance that increases the effective energy absorbed in the subsurface layer, peff is defined early, E(0) is the subsurface irradiance, and E0 is the incident laser pulse energy at the sample surface (J/cm2). For optically thick samples [53, 54]:
E(0) – (1 + 7.1RE (3.21)
where Rd is the total diffuse reflection.
The Gruneisen parameter Г is a dimensionless, temperature-dependent factor proportional to the fraction of thermal energy converted into mechanical stress. For water it can be expressed with an empirical formula as [53]:
Г = 0.0043 + 0.00537] (3.22)
where temperature Tis measured in degrees Celsius; for T = 37°C, Г – 0.2.
Equations (3.19) and (3.20) are strictly valid only when the heating process is much faster than expansion of the medium. The stress is temporarily confined during laser-heat deposition when the duration of the laser pulse is much shorter than the time of stress propagation across the depth of light penetration in the tissue sample. Such conditions of temporal pressure confinement in a volume of irradiated tissue allow for the most efficient pressure generation [53,54].