Equivalent isotropic scattering formulation for transient short-pulse radiative transfer in anisotropic scattering planar media

Spectral Monte Carlo simulation of collimated solar irradiation transfer in a water-filled prismatic louver

The Monte Carlo model was developed to simulate the collimated solar irradiation transfer and energy harvest in a hollow louver made of silica glass and filled with water. The full solar spectrum from the air mass 1.5 database was adopted and divided into various discrete bands for spectral calculations. The band-averaged spectral properties for the silica glass and water were obtained. Ray tracing was employed to find the solar energy harvested by the louver. Computational efficiency and accuracy were examined through intensive comparisons of different band partition approaches, various photon numbers, and element divisions. The influence of irradiation direction on the solar energy harvest efficiency was scrutinized. It was found that within a 15° polar angle of incidence, the harvested solar energy in the louver was high, and the total absorption efficiency reached 61.2% under normal incidence for the current louver geometry.

Transient/time-dependent radiative transfer in a two-dimensional scattering medium considering the polarization effect

Transient/time-dependent radiative transfer in a two-dimensional scattering medium is numerically solved by the discontinuous finite element method (DFEM). The time-dependent term of the transient vector radiative transfer equation is discretized by the second-order central difference scheme and the space domain is discretized into non-overlapping quadrilateral elements by using the discontinuous finite element approach. The accuracy of the transient DFEM model for the radiative transfer equation considering the polarization effect is verified by comparing the time-resolved Stokes vector component distributions against the steady solutions for a polarized radiative transfer problem in a two-dimensional rectangular enclosure filled with a scattering medium. The transient polarized radiative transfer problems in a scattering medium exposed to an external beam and in an irregular emitting medium are solved. The distributions of the time-resolved Stokes vector components are presented and discussed.

Phase-function normalization for accurate analysis of ultrafast collimated radiative transfer

The scattering of radiation from collimated irradiation is accurately treated via normalization of phase function. This approach is applicable to any numerical method with directional discretization. In this study it is applied to the transient discrete-ordinates method for ultrafast collimated radiative transfer analysis in turbid media. A technique recently developed by the authors, which conserves a phase-function asymmetry factor as well as scattered energy for the Henyey-Greenstein phase function in steady-state diffuse radiative transfer analysis, is applied to the general Legendre scattering phase function in ultrafast collimated radiative transfer. Heat flux profiles in a model tissue cylinder are generated for various phase functions and compared to those generated when normalization of the collimated phase function is neglected. Energy deposition in the medium is also investigated. Lack of conservation of scattered energy and the asymmetry factor for the collimated scattering phase function causes overpredictions in both heat flux and energy deposition for highly anisotropic scattering media. In addition, a discussion is presented to clarify the time-dependent formulation of divergence of radiative heat flux.

Study of short-pulse laser propagation in biological tissue by means of the boundary element method

Propagation of short pulses of light through biological tissues can be studied by numerically solving the diffusion equation. The boundary integral method was used to convert the differential equation to integral form and the result was solved using the boundary element method. The effects of different optical parameters of the tissue, i.e. scattering, absorption coefficients and anisotropic factor, on temporal evolution of the diffusely reflected pulse were studied. The results were compared with those obtained using the finite difference time domain method and the boundary integral method was found to be more precise and faster than the last method. The method can be used to investigate reflected pulses in the study of cell morphology and tumours in different types of tissue.

Boundary integral method for simulating laser short-pulse penetration into biological tissues

The study of short-pulse propagation through biological tissues is important due to the medical applications of short-pulse lasers. Techniques used for numerical study of short pulses through human tissues include the Monte Carlo (MC) method, the finite-element method, and the finite-difference time-domain (FDTD), but these are often time consuming. Recently, the boundary integral method (BIM) was applied to overcome this problem. The literature shows that the BIM is faster than the other mentioned methods. We first investigate the precision of results obtained by the BIM by comparison with those results obtained by the MC and FDTD methods. Then we use the BIM to investigate the short-pulse penetration into biological tissues. We also study the effects of optical properties of tissues such as scattering, the absorption coefficient, the anisotropic factor on the penetrating pulse. We also, consider the propagation of pulses emitted from extended sources with different temporal evolutions.

Thermal interaction of short-pulsed laser focused beams with skin tissues

Time-dependent thermal interaction is developed in a skin tissue cylinder subjected to the irradiation of a train of short laser pulses. The skin embedded with a small tumor is stratified as three layers: epidermis, dermis and subcutaneous fat with different optical, thermal and physiological properties. The laser beam is focused to the tumor site by an objective lens for thermal therapy. The ultrafast radiation heat transfer of the focused beam is simulated by the transient discrete ordinates method. The transient Pennes bio-heat equation is solved numerically by the finite volume method with alternating direction implicit scheme. Emphasis is placed on the characterization of the focused beam propagation and absorption and the temperature rise in the focal spot. The effects of the focal spot size and location, the laser power, and the bio-heat equation are investigated. Comparisons with collimated irradiation are conducted. The focused beam can penetrate a greater depth and produce higher temperature rise at the target area, and thus reduce the possibility of thermal damage to the surrounding healthy tissue. It is ideal for killing cancerous cells and small tumors.

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.

Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media

The discrete-ordinates method is formulated to solve transient radiative transfer with the incorporation of a transient term in the transfer equation in two-dimensional rectangular enclosures containing absorbing, emitting, and anisotropically scattering media subject to diffuse and/or collimated laser irradiation. The governing equations resulting from the discrete-ordinates discretization of the angular directions are further discretized in the spatial and the temporal domains by the finite-volume approach. The current formulation is suitable for solving transient laser transport in turbid media as well as for steady-state radiative transfer in many engineering problems. The method is applied to several example problems and compared with existing steady-state solutions and Monte Carlo transient solutions. Good agreement is found in all cases. Short-pulsed laser interaction and propagation in a turbid medium with high scattering albedo are studied. The imaging of an inhomogeneous zone inside a turbid medium is demonstrated.