II. BACKGROUND
2.7: Thermomechanical Response of Tissue to Pulsed Irradiation
The spatial distribution of volumetric energy density resulting from pulsed laser irradiation of tissue generates significant thermal and mechanical transients. These thermomechanical transients are the driving force for all laser ablation processes that are not photochemically mediated.
2.7.1 Thermal Confinement
In the absence of photochemical or phase transition processes, the energy absorbed by the tissue in response to pulsed laser irradiation is entirely converted to heat.
Once the energy is absorbed, it is subject to spatial redistribution by thermal diffusion.
Spatially confined microsurgical effects can be achieved by the use of laser exposures that are shorter than the characteristic thermal diffusion time of the heated volume [6].
For laser ablation, the heated volume is typically a layer of tissue of thickness 1/µa, and
the characteristic thermal diffusion time, τth [s], is given as td = 1/(4αµa2), where α is the thermal diffusivity [m2/s]. Thermal confinement is attained when the ratio of the laser pulse duration to the thermal diffusion time is somewhat less than 1. Water is most often the main chromophore for pulsed IR ablation. When using a wavelength that is absorbed by water, one must consider whether the concept of thermal confinement applies not only to the heated volume as a whole but also to the individual microscopic tissue structures that absorb the radiation. If the laser radiation is thermally confined in a small volume of the tissue, the possibility exists that ablation can occur before it would be expected in the same volume of water. Thus one must be cognizant of the microscopic tissue effects of tissue when trying to understand the ablation mechanism with respect to a given laser source.
2.7.2 Stress Confinement
Rapid heating of tissue by pulsed laser radiation also leads to the generation and propagation of thermoelastic stresses as the heated tissue volume reconfigures to its new equilibrium state. The longitudinal speed of sound in the medium, σ [m/s], the laser pulse duration, τp [s], the depth of the heated volume, 1/µa [m], and an intrinsic thermophysical property known as the (dimensionless) Grüneisen coefficient, Γ, govern the magnitude and temporal structure of the thermoelastic stresses. The Grüneisen coefficient is simply the internal stress per unit energy density generated upon depositing energy into a target under constant volume conditions.
Thermoelastic stresses are most prominent when the laser pulse duration tp is smaller than, or on the order of, the characteristic time for a stress wave to propagate across the heated volume. Stress confinement is achieved when the ratio of the laser pulse duration to the stress propagation time, τstr., is less than 1. In this case, heating of the laser-affected volume is achieved under isochoric conditions, and the internal stresses generated do not propagate outside the heated volume during the laser irradiation, causing pressure buildup and propagation of strong transients after the laser pulse.
While thermal expansion of a heated volume generates compressive thermoelastic stresses, subsequent propagation of these thermoelastic stresses result in transients that contain both compressive and tensile components [6]. Tensile stresses arise from the reflection of the compressive stress waves at a boundary to a medium with lower acoustic impedance (tissue-air, tissue-water) or from the three-dimensional characteristics of acoustic wave propagation. The magnitude of these stress transients is most prominent when irradiation takes place under conditions of stress confinement and when the laser beam diameter is comparable to the optical penetration depth of the incident radiation.
The tensile stresses can significantly affect the ablation process by catalyzing the phase transition processes or by causing direct tissue fracture and mechanical failure (known as spallation).
Depending on the temperature rise in a given target, negative thermoelastic stresses can lead to the accelerated growth of preexisting nucleation centers or initiate the nucleation and growth of vapor bubbles. The presence of tensile stresses can cause explosive boiling processes at temperatures much less than 300 °C [6]. Thermoelastic tensile stresses can reduce both the ablation threshold and the ablation enthalpy. This
reduction is likely achieved by direct fracture of the tissue matrix or by its catalytic effect on nucleation and explosive boiling.
Figure 2.2 The conditions for stress confinement, thermal confinement, and no confinement are shown with respect to pulse duration and penetration depth. The dotted line is the penetration depth at 6.45 µm. Inscribed on this line are the pulse durations for the FEL macropulse (5 µs), which is not confined, the strontium vapor pulse (50 ns), which is thermally confined, and the OPO pulse (100 ns), which is thermally confined.
The micropulse duration for the native FEL and the stretched pulse are not shown because they are to the far left of the given line and are both stress and thermally confined. From Uhlhorn, 2002 [21].
Figure 2.2 shows the effect of pulse length and penetration depth on the mechanisms of stress confinement and thermal confinement. The relevant pulse structures of the laser sources discussed in this proposal have been placed along the 6.45 µm penetration depth line. It is clearly seen that the FEL macropulse is not confined,
native and stretched FEL micropulses are off the diagram to the left, thus they are both stress and thermally confined.