Thermal diffusion and chemical kinetics in laminar biomaterial due to heating by a free-electron laser

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Abstract
We have theoretically investigated the role of thermal diffusion and chemical kinetics as a possible dynamic explanation for the preferential ablative properties of infrared radiation from a free-electron laser ~FEL!. The model is based on a laminar system composed of alternating layers of protein and saline. We have compared exposure to 3 mm where water is the main absorber and 6.45 mm where both water and protein absorb. The picosecond pulses of the superpulse are treated as a train of impulses. We find that the heating rates are sufficient to superheat the outer saline layers on the nanosecond time scale, leading to explosive vaporization. We also find that competition between the layer-specific heating rates and thermal diffusion results in a wavelength-dependent separation in layer temperatures. We consider the onset of both chemical bond breaking and the helix-coil transition of protein prior to vaporization in terms of the thermal, chemical, and structural properties of the system as well as laser wavelength and pulse structure. There is no evidence for thermal bond breaking on these time scales. At 6.45 mm, but not 3 mm, there is evidence for a significant helix-coil transition. While the native protein is ductile, the denatured protein exhibits brittle fracture. This model provides a dynamic mechanism to account for the preferential ablative properties observed with FEL radiation tuned near 6.45 mm. Experiments demonstrate that the free-electron laser ~FEL! is a particularly effective tool for etching soft bioma- terials with remarkably little damage surrounding the site when tuned to wavelengths near 6.45 mm @1#. Based on these observations, human neurosurgical @2# and ophthalmic @3# procedures were developed and have been performed successfully. As for the underlying physical mechanism, these results cannot be accounted for with models solely based on average penetration depth. A thermodynamic model has been proposed to account for the wavelength dependence suggesting that the optical, thermal, and mechanical proper- ties of protein as distinct from saline are important @1#. How- ever, the dynamics and how they relate to the superpulse structure of the Mark-III have not been well understood. Here we present a dynamic theory to account for the wavelength and pulse-structure dependence in terms of ther- mal diffusion and chemical kinetics in a laminar system that is highly representative of cornea as exposed to FEL radia- tion. We find that the competition between the layer-specific heating rates and thermal diffusion results in a wavelength- dependent separation in layer temperatures that increases on the nanosecond time scale. As a consequence, significantly more protein denaturation accumulates at 6.45 mm than at 3 mm. Native protein is ductile, whereas denatured protein is brittle. We attribute the preferential ablative properties of the FEL, tuned to wavelengths near 6.45 mm, to the brittle na- ture of denatured collagen. II. THEORETICAL MODEL