Discrete Ordinates Method for Transient Radiation Transfer in Cylindrical Enclosures

The Discrete Ordinates Method (DOM) for solving transient radiation transfer equation in cylindrical coordinates is developed for radiation heat transfer in participating turbid media in pico-scale time domain. The application problems addressed here are laser tissue welding and soldering. The novelty of this study lies with the use of ultrashort laser pulses as the irradiation source. The characteristics of transient radiation heat transfer in ultrafast laser tissue welding and soldering are studied with the DOM developed. The temporal distribution of radiative energy inside the tissue cylinder as well as the radiative heat flux on the tissue surface is obtained. Comparisons are performed between laser welding without use of solder and laser soldering with use of solder. The use of solder is found to have highly concentrated radiation energy deposition in the solder-stained region and reduce the surface radiative heat flux accordingly. Comparisons of transient radiation heat transfer between the spatially square-variance and Gaussian-variance laser inputs and between the temporally Gaussian and skewed input profiles are also conducted. INTRODUCTION The study of short-pulsed laser radiation interaction and propagation in turbid media is of great significance in a wide spectrum of emerging technologies such as in optical tomography [1-3], laser medical treatment [4], laser ablation [5,6], and laser material processing of microstructures [7-9], to name a few. Many new phenomena occurred with the use of short laser pulses are attributed to the short time duration. For example, our previous studies [10-13] have shown that the wave propagation of transient radiation with the speed of light is a unique feature in ultrashort-pulsed laser radiation transport. Recently the study of transient radiation transfer has attracted considerable interest in heat transfer community. Here we will apply ultrashort laser pulses with pulse duration from picoseconds down to femtoseconds to laser tissue welding and soldering. Laser welding of tissues is a surgical technique for bonding of tissues by using a laser beam to activate photothermal bonds and/or photochemical bonds. This method is potentially more advantageous than the conventional suturing technique because it is a non-contact method, which does not introduce foreign materials, and it is capable of forming an immediate watertight seal. For over 25 years, laser tissue welding has been studied as an alternative tool of tissue closure [14]. Typical tissue enclosure methods include sutures, clips, or staples. Sutures create a scar during passage of the needle and tying the knot. This tissue scar and foreign body reaction can result in inflammation, stenosis, and granuloma formation [15]. Unlike handcrafted sutures, clips and staples have limited range of adaptability in the face of different conditions such as tissue friability and thickness. Furthermore, these traditional methods are hardly applicable to tissue closure in microsurgery like vascular anastomosis, closure of nerve and uterine horn. Laser tissue welding can be augmented with solders. The solders serve two roles. First, the solders can include chromophores that are used to control the laser penetration such that it is concentrated at the fusion site. Since extrinsic chromophores are not limited to the absorption characteristics of native tissue or body fluids, solders may be tailored to selectively absorb energy that passes through normal tissue. Second, solders can include other biochemical constituents to improve the weld strength and/or weld leakage characteristics. Typical additives include native collagen, gelatinous collagen, fibrin, elastin and albumin. In addition to solders, many researchers are using feedback control to optimize and improve laser welding consistency. Temperature, radiation scattering and birefringence, optical properties are among the parameter candidates. Suitable lasers deliver wavelengths that are highly absorbed either by water or the tissue’s natural chromophores [16]. For example, argon lasers (488 and 514 nm) and KTP lasers (532 nm) are used with hemoglobin [17], Nd:YAG (1.064 and 1.320 μm) and CO2 (10.6 μm) lasers are used with water [18]. Endogenous and exogenous materials such as