Damage integral and other predictive formulas for nonisothermal heating during laser exposure

Significance: Physics-based models supply simulated temperature rises to photothermal damage rate models and provide comprehensive risk assessments for laser-induced damage. As the physics-based models continue to be refined, the damage rate models have not advanced. This peculiar lack of improvement is counterintuitive considering the damage integral (Ω), originally derived for isothermal heating events, and fails to accurately represent the nonisothermal heating from short laser exposures.

Aim: Derive a nonisothermal form of the damage integral and predict more accurately the damage induced by short laser exposures, as well as identify the role of heating rate in laser damage.

Approach: From first principles, we derived a version of the damage integral specific to the shape of thermal profiles rather than the square function provided by Arrhenius plots. We used previously published threshold thermal profiles, where all nonisothermal frequency factors (Anon) solved all Ωnon values to unity. Nonisothermal correction factors correct isothermal Aiso values.

Results: The Ea values were identical for both the isothermal and nonisothermal conventions. Correction factor values for Ωiso ranged from 0.0 (20-s exposures at thermal steady state) to -0.93 (0.05-s exposures). Based on empirical results, we have derived a two-dimensional empirical formula that predicts the heating rate as a function of exposure duration and ambient temperature. Threshold peak temperatures (Tpthr) and threshold critical temperatures are mathematically determined without thermal profiles when appropriate Ea and Anon values are established.

Conclusions: We have identified a modified damage integral that does not rely on the Arrhenius plot and provides a value for the frequency factor (A) that accounts for the nonisothermal nature of short laser exposures. The method, validated in our in vitro retinal model, requires thermal profiles recorded under threshold conditions, such as at minimum visible lesions or the boundary of cell death. The method is a new option for laser damage modelers.