Ultrafast-laser-radiation transfer in heterogeneous tissues with the discrete-ordinates method

Here light propagation and radiation transfer of ultrafast laser pulses in heterogeneous biological tissues are simulated by use of the discrete-ordinates method (DOM). Formulations for solving the time-dependent radiation-transfer equation are deduced for three-dimensional geometries incorporating the Fresnel specularly reflecting boundary condition and characteristics of ultrafast laser pulses. The present method can treat both the incident laser intensity and the scattered radiation intensity from the walls of the targeted tissue as two components, i.e., a diffuse part and a specular part. Reflectivity at the tissue-air interface is calculated by use of Snell's law and the Fresnel equation. The high-order S10 DOM method is found to be adequate for describing the propagation and transfer of ultrafast laser radiation in heterogeneous tissues. The time-dependent radiation field in the tissue as well as the temporal radiation intensity profiles at the boundaries can be obtained simultaneously. The absolute values of the logarithmic slope of the temporal reflectance and transmittance at various detector positions are found to converge to a constant value in a homogeneous tissue model. With the inclusion of a small inhomogeneity, such a value will change in line with the property of the embedded inhomogeneity. The orientation of heterogeneity of the tissues also substantially affects the radiation intensity at the boundaries. The effect of the Fresnel boundary in the modeling is pronounced. The simulated transmitted signals are broadened and amplified under specularly reflecting boundary condition as compared with those under diffusely reflecting boundary conditions.