Fractional Beer-Lambert law in laser heating of biological tissue

Abstract

In this article we propose an alternative formulation to model a thermal-optical coupled problem involving laser heating. We show that by using the Fractional Beer-Lambert Law (FBLL) instead of the Beer-Lambert Law (BLL) as the governing equation of the optical problem, the formulation of the laser heat source changes, along with consequently, the distribution of temperatures. Our theoretical findings apply to laser thermal keratoplasty (LTK), used to reduce diopters of hyperopia. We show that the FBLL offers a new approach for heat conduction modeling of laser heating, which is more flexible and could better fit the data in cases where the BLL approach does not fit the data well. Our results can be extended to laser heating of other biological tissues and in other general applications. Our findings imply a new insight to improve the accuracy of thermal models, since they involve a new formulation of the external heat source rather than the heat equation itself.

Keywords

• partial differential equations
• fractional beer-lambert law
• laplace transform
• thermal therapies
• heat equation
• corneal laser irradiation