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.

Modeling Skin Injury from Hot Rice Porridge Spills

The present work analyzes skin burns from spills of hot rice and milk products. The traditional Norwegian rice porridge serves as an example. By testing spills on objects emulating an arm, it was concluded that spills were seldom thinner than 3 mm, and stayed in place due to the viscosity of the porridge for more than one minute. The Pennes bioheat equation was solved numerically for such spills, including heat conduction to the skin and convective heat losses from the porridge surface. Temperatures were analyzed in the porridge and skin layers, and the resulting skin injury was calculated based on the basal layer temperature. Parameters influencing burn severity, such as porridge layer thickness, porridge temperature, removal of the porridge and thermal effects of post scald tempered (15 °C) water cooling were analyzed. The spilled porridge resulted in a prolonged heat supply to the skin, and the skin injury developed significantly with time. The porridge temperature turned out to be the most important injury parameter. A 70 °C porridge temperature could develop superficial partial-thickness burns. Porridge temperatures at processing temperatures nearly instantly developed severe burns. It was demonstrated that prompt removal of the hot porridge significantly reduced the injury development. The general advice is to avoid serving porridge and similar products at temperatures above 65 °C and, if spilled on the skin, to remove it quickly. After such scald incidents, it is advised to cool the injured area by tempered water for a prolonged period to stimulate healing.

Modeling Skin Injury from Hot Spills on Clothing

The present work analyzes scald burns from hot beverages, such as coffee and tea, spilled on the lap, i.e., an incident that may occur in daily life. The Pennes bioheat equation is solved numerically for small spills wetting the clothing, i.e., the fabric prevents the spilled liquid from draining away. Temperatures are analyzed in the wetted fabric and the skin layers and the resulting skin injury is calculated based on the basal layer temperature. Parameters influencing burn severity, such as clothing thickness, liquid temperature, removal of fabric and thermal effects of post scald water cooling are analyzed. The fabric cools the water some but represents a threat since the entrapped water results in a prolonged heat supply. The liquid temperature turned out to be the most important injury parameter, where liquid temperature of about 80–85 °C seems to be a limit for developing superficial partial-thickness burns in the present minimum case, i.e., where the liquid just wets the fabric. Spilling water in excess of just wetting the fabric, more severe burns will develop at lower liquid temperatures due to the prolonged heat supply. Higher liquid temperatures will nearly instantly develop more severe burns. It is demonstrated that removal of the clothing within the first seconds after the spill may significantly reduce the scalding severity. The general advice is therefore to avoid excessive heating of beverages and, if the beverage is spilled, to quickly remove the wetted clothing. Prolonged tempered water cooling is advised to improve the healing processes.