1.1 Short Pulse Laser Imaging
The potential of time-resolved optical tomography as a new diagnostic tool in biomedical imaging of tissues has stimulated considerable interest in the last two decades (Chance and Katzir ). The distinct feature detected is the multiple scattering induced temporal distribution , which persists for a time period greater than the duration of the source pulse and is a function of the source pulse width as well as the optical properties of the medium.
Time-resolved optical imaging of biological tissues has been studied extensively for tissue phantoms simulating the scattering and absorption properties of biological tissues (Liu et al. ).
Small animal imaging systems have received increasing attention over the past decade. Various imaging techniques have been used for tumor detection in small animals, including confocal imaging, fluorescence imaging, and magnetic resonance imaging (MRI) (Lacy et al. ), experimental data from freshly excised rat tissue samples were validated with numerical modeling results for the case of short pulse laser propagation through tissues. Challenges still remain in the numerical validation of experimental measurements for in vivo live animal studies with tumors.
The simulation of the transient radiation transport process necessary to analyze the short-pulse laser propagation through participating media is more complicated than the traditional steady-state analysis. The hyperbolic wave nature of the equation coupled with the in-scattering integral term makes the transient radiative transport equation (RTE) an integro-differential equation and, thus, extremely difficult to solve accurately and time efficiently (Yamada ).
Most past research has suggested that time-resolved optical tomography of tissues can be successfully modeled using the transient radiation transport process, which is capable of providing valuable information about tissue morphology (Kumar et al. ). Although the potential use of an FV DOM based inverse algorithm coupled with fast image reconstruction was demonstrated for optical tomography, there has been very limited study performed involving live animals which is reported in the literature.
1.2 Short Pulse Laser Based Therapy
Pulsed lasers are widely used for therapeutic medical applications. It is critical to perform numerical modeling and analysis prior to treatment in order to optimize the thermal dose delivered to tissues and reduce unwanted damage to surrounding healthy tissue through heat diffusion. Many different models of varying complexity have been developed for such analyses.
Accepted methods for calculating the temperature increase due to heat transfer in biological tissues follow two distinct theoretical foundations. The subset of models including Pennes bioheat transfer equation (PBHT) and other bioheat transfer models (BHTM) assumes instantaneous heat transfer within a finite area of a biological tissue. A generic BHTM has been derived and developed satisfying the conservation of energy for both unheated and heated perfused tissue that couples two separate differential equations for blood and tissue (Shrivastava and Vaughn ). As in any heat transfer model, these BHTM satisfy the requirements of energy conservation while considering the thermodynamic properties of the medium.
Various numerical methods may be employed to solve bioheat transfer problems. Although the most popular numerical methods are finite difference method (FDM), finite element method (FEM), and boundary element method (BEM) , the Monte Carlo method (MC) is also a viable option (Deng and Liu ).
The peak temperatures achieved during laser thermal therapy may be affected by blood flow in living tissues, which convectively cools regions heated above core temperature. Directional blood flow affects tissue temperatures during all types of thermal therapy both by convectively cooling the target tissue and immediately adjacent region (Kou et al. ). Models of laser thermal therapy that include discrete blood vessels with countercurrent blood flow can aid in tailoring treatment regimes to achieve treatment goals while minimizing damage to adjacent healthy tissues.
The two prevailing approaches in modeling the effects of blood flow in computational models of heat transfer in tissue are the continuum model and the vascular model (Staczyk and Telega ). While the continuum model accounts for blood flow as a bulk perfusion term applied to the entirety of a single-phase domain in the heat equation, the vascular model considers a multi-phase domain of discrete vessels containing blood with an assigned velocity field within a solid tissue volume.
Numerical models of laser treatment of tissues yield different results for temperature rises achieved within the target tissues depending on whether a continuum or vascular model is used. Continuum models predicted larger volumes of temperature rise than vascular models did in numerical models of temperature increases in a tissue volume due to a subsurface-focused laser heat source (Ganguly et al. ), strengthening the case for the inclusion of discrete vessels in models of laser thermal therapies.
The laser operating mode must also be taken into consideration in the models considered above. Continuous wave (CW) lasers deliver nearly uniform energy to the target tissue, resulting in a constant treatment of the tissue and steady heat diffusion to tissues surrounding the laser focal point. On the other hand, short pulse lasers provide short pulses of significantly higher power than CW lasers, and the spacing of these pulses in time is shorter than the thermal relaxation time of tissues. Consequently, each pulse of a short pulse laser produces an incremental temperature increase before the energy from the previous pulse can diffuse away from the laser focal point, resulting in a highly localized step-wise temperature rise at the irradiation site (Ganguly et al. ). For a given average power, shorter laser pulses therefore result in greater energy delivered per pulse and more localized rises in temperature.
Ex vivo experiments to determine the thermal dose resulting from laser irradiation may not accurately predict thermal doses achieved by irradiation of living tissues. Thin excised tissues maintained at an ambient temperature of approximately 24 C cannot accurately account for the fact that increasing the temperature of in vivo human tissue with a core temperature of 37 C by 6 C can raise the tissue temperature to the 43 C threshold. Instead, temperature rises of nearly 20 C and unrealistically high average laser powers and/or lasing times are required to heat excised tissue to the 43 C threshold, providing an insufficient model for laser treatment optimization.