Optical-Thermal Response of Laser-Irradiated Tissue

The development of a unified theory for the optical and thermal response of tissue to laser radiation is in its infancy. This book describes our current understanding of the physical events that can occur when light interacts with tissue. We present a sequence of formulations that estimate the optical and thermal responses of tissue to laser radiation. Part I considers basic tissue optics. Tissue is treated as an absorbing and scattering medium and methods are presented for calculating and measuring light propagation. Also, methods for estimating tissue optical properties from measurements of reflection and transmission are discussed. Part II concerns the thermal response of tissue owing to absorbed light, and rate reactions are presented for predicting the extent of laser-induced thermal damage. Methods for measuring temperature, thermal properties, and rate constants are detailed. Part III is devoted to examples that use the theory presented in Parts I and II to analyze various medical applications of lasers.

Optics for laser irradiation of tissue is best described by examining the response of a target within tissue to light. Suppose tissue (e.g., skin) has a chromophore (e.g., a melanocyte) somewhere inside the tissue at coordinate r with respect to some frame of reference (Fig. 2.1). What is the rate of heat that is generated in the chromophore when the tissue is irradiated at some wavelength with constant power P over the laser beam radius W _L ? The key question that needs to be answered is: how many photons per second will reach the chromophore and be absorbed? Tissue optics should provide the answer to this question.

Light propagation in scattering and absorbing materials like tissue is usually described by the integro-differential equation of radiative transfer. There are two problems associated with the use of this equation.

Monte Carlo simulations of photon propagation offer a flexible yet rigorous approach toward photon transport in turbid tissues. This method simulates the “random walk” of photons in a medium that contains absorption and scattering. The method is based on a set of rules that govern the movement of a photon in tissue. The two key decisions are (1) the mean free path for a scattering or absorption event, and (2) the scattering angle. Figure 4.1 illustrates a scattering event. At boundaries, a photon is reflected or moves across the boundary. The rules of photon propagation are expressed as probability distributions for the incremental steps of photon movement between sites of photon—tissue interaction, for the angles of deflection in a photon’s trajectory when a scattering event occurs, and for the probability of transmittance or reflectance at boundaries. Monte Carlo light propagation is rigorous yet very descriptive. However, this method is basically statistical in nature and requires a computer to calculate the propagation of a large number of photons. To illustrate how photons propagate inside tissues, a few photon paths are shown in Fig. 4.2.

This chapter describes the adding-doubling method for solving the radiative transport equation. The advantages and disadvantages of the method are presented, followed by sections describing its theory and computer implementation. A detailed example is given with intermediate numerical results. Accurate tables with values of reflection and transmission for slabs of varying thicknesses with mismatched boundaries are given.

In this chapter light is principally described by particles with energy hv and velocity c. These particles are scattered or absorbed by structures in turbid media such as biological tissues and are reflected at boundaries according to the laws of Fresnel. In this chapter we will consider only monochromatic light, which covers most practical situations in medical laser applications. The formulations are easily extended by polychromatic light as long as scattering events are elastic. The theory becomes more complicated for inelastic scattering, such as the occurrence of fluorescence. However, even the diffusion theory for those cases is a straightforward extension of the discussions given in the following sections. Finally, we neglect polarization and interference. To include polarization one would need four diffusion equations instead of one.¹ Polarization of incident light is usually lost in highly scattering media within a millimeter from the surface.² Therefore, the effort required to extend the diffusion approximation to include polarization is probably not worthwhile, given the limited validity of that approximation, in particular near surfaces and sources of collimated light.

The diffusion approximation of the radiative transport equation is used extensively because closed-form analytical solutions can be obtained. The previous chapter gave closed-form solutions to the one-dimensional diffusion equation. In this chapter, the classic searchlight problem of a finite beam of light normally incident on a slab or semi-infinite medium will be solved in the timeindependent diffusion approximation. The solution follows naturally once the Green’s function for the problem is known, and so the Green’s function subject to homogeneous Robin boundary conditions will be given for semi-infinite and slab geometries. The diffuse radiant fluence rates are then found for impulse, flat (constant), and Gaussian shaped finite beam irradiances.

In this chapter, the various experimental techniques which have been developed to measure the optical scattering and absorption properties of tissues are discussed, together with the theory underlying these methods. The fundamental optical properties of interest are the absorption coefficient, µ _a , scattering coefficient, µ _s , total attenuation coefficient, µ _t = µ _a + µ _s , scattering phase function, p(cosθ), or scattering anisotropy, g reduced scattering coefficient, µ′ _s = µ _s (1 − g) and the tissue refractive index, n. These optical properties are parameters in the radiation transport equation which describes the propagation of light in tissue (see Chapters 2, 3, and 6). Another parameter often measured is the effective attenuation coefficient, µ _eff , which describes the exponential attenuation of scattered light with depth in tissue.

Photon movement in a turbid medium such as biological tissue has posed challenging problems due to the strong influence of light scattering at ultraviolet, visible, and near-infrared wavelengths. Photons which escape from a tissue as either reflectance or transmittance may have propagated along many different paths within the tissue. Therefore, it is difficult to interpret the magnitude of photon escape in terms of either tissue absorption or the presence of an internal heterogeneity. The use of measurement techniques which allow time-resolved measurements of photons has offered a new approach toward understanding photon propagation.

In the previous chapter the propagation and measurement of short light pulses in turbid media such as tissue was described. In this chapter we will discuss the propagation of light produced by sinusoidally modulated sources. The relationship between the two is illustrated in Fig. 10.1. If an infinitesimally short pulse is applied to a scattering medium, this pulse is broadened in time as it propagates due to the many possible photon paths between source and detector. The observed quantity in the time domain is h(t) the number of photons reaching the detector per unit time at a given time, t. If instead we have a sinusoidally modulated light source, the photon flux at the detector will also be sinusoidal in time but the oscillation will be delayed in time relative to the source and reduced in amplitude relative to the average flux. The observed quantities in this case are the phase angle between the detected and source (or some reference) signals and the amplitude of the oscillation relative to the DC level. This latter quantity, defined as A/B in Fig. 10.1, is referred to as the modulation.

Medical use of lasers began soon after the first ruby laser was invented in 1960.¹ Laser radiation is now used routinely in surgery to incise, coagulate, or vaporize tissues. The use of lasers in surgery introduces some desirable features such as increased precision, improved hemostasis, and less tissue manipulation.² The biological effects of laser energy depend on the laser wavelength, the irradiance, the duration of irradiation, and optical as well as thermal properties of the tissue involved. The laser-tissue interaction mechanisms may be thermal, photochemical, or mechanical in nature. Surgical procedures that involve coagulation or ablation of tissue are thermal.

During laser irradiation of biological tissue several steps have to be considered: (a) propagation of light in tissue including reflection and scattering, (b) transformation of laser light into photochemical, acoustic, or thermal energy, depending primarily on the absorber, pulse energy, and pulse duration, (c) propagation of the spatial temperature profile for the fraction of light energy that was transformed into thermal energy, and propagation of acoustic transients for the fraction of light energy that was converted into mechanical energy, and (d) the dependency between temperature elevation and tissue damage, which can be described by the Arrhenius law.

Several exact solutions for the heat conduction equation are presented in Chapter 12. As shown in Chapter 12, the solution for an instantaneous point source can be integrated over space and time to obtain the temperature response due to laser radiation. If the geometry and boundary conditions of a problem preclude the use of analytical methods, then a number of numerical methods, such as finite difference or finite element, can be employed.

The transport of thermal energy in living tissue is a complex process involving multiple phenomenological mechanisms including conduction, convection, radiation, metabolism, evaporation, and phase change. The equilibrium thermal properties presented in this chapter were measured after temperature stability had been achieved. The notation used in this chapter is listed in Appendix 14.7.3.

The objective of this chapter is to present the fundamental mechanisms, instrumentation techniques, and error analyses for temperature measurements in laser-irradiated biologic media. Because temperature is a significant biological parameter, it is important to understand and minimize potential measurement errors.^1–8 Temperature measurements in a radiative field are particularly difficult because:

The phenomenon of thermal radiative emission is the basis of a materials evaluation technique known as photothermal radiometry. This technique involves irradiation of the sample with monochromatic light which is absorbed, causing a temperature rise. The increase in the blackbody radiative emission due to this rise is recorded with an infrared detector that views the sample surface. The detected signal contains information about the optical and thermal properties of the sample. Previous studies have used either modulated or pulsed light excitation methods; in this chapter, we will examine the applicability of the latter approach, known as pulsed photothermal radiometry (PPTR), to the study of optical properties of tissue.

The first two parts of this book describe various theories associated with light propagation in tissue and the resulting thermal response. We assume that the transport equation governs the optical interaction of light with tissue and the heat conduction equation provides the basis for estimating the thermal response of tissue to laser radiation. In Part III of this book, the theory for optical and thermal interactions of laser light with tissue are used to analyze medical applications. In particular, the concepts of Parts I and II

In laser medicine, light has to be transported from the laser to the location of treatment or, for tissue diagnostics, from the site of tissue fluorescence to the sensing equipment. The most effective and practical way of transportation for most laser wavelengths and most applications is the use of fiber optics.¹ As illustrated in Fig. 19.1, the components of a fiber-based delivery system are (a) the laser, emitting the laser beam; (b) the fiber coupler, launching the beam into a fiber positioned in an XYZ translating platform; (c) the fiber, transporting the laser light; and (d) the (modified) fiber tip or probe, emitting the laser light coming out of the fiber.

The diagnosis of disease is becoming more and more a technologic task. The clinician’s goal is to assess the structural and functional changes in diseased tissue, infer the identity and stage of the disease, and predict the ultimate consequences to the organism as a whole, intervening with the proper treatment whenever possible.¹ The diagnostic ordnance varies, both for the suspected disease and with the specialty of the clinician. Radiologists, for example, assess gross structural abnormalities utilizing variations in tissue or contrast agent absorption of X-rays. This structural information, although useful diagnostically, provides limited insight into the molecular etiology and pathogenesis of the disease, factors now appreciated to be important prognostically and in selecting appropriate therapy.¹ Pathology provides the most widely used clinical method of elucidating chemical information from diseased tissues.^1.2 Traditional techniques of histology probe the microscopic structural alterations of diseased tissue. Using histochemical stains, many of the corresponding chemical alterations can be mapped out on a microscopic scale. The chief disadvantage of histologic techniques is that they can only be applied in vitro, necessitating the removal of tissue.² The requirement of biopsy limits the utility of this approach; it implies that only small areas of tissue, accessible to either biopsy forceps or needles, can be sampled.

The motivation for the material presented in this chapter came initially from the development of a new generation of pulsed lasers for laser angioplasty, in which laser light delivered through a fiberoptic is used to ablate intravascular plaque. In the eighties continuous wave (cw) lasers were used for the ablation task in conjunction with a variety of modified fiber tips. More recently there has been a shift from cw to pulsed lasers for laser angioplasty. In general, pulsed laser ablation seems to be a trade off between thermal and mechanical damage to tissue adjacent to the ablation crater. Currently, pulsed lasers are being used for tissue ablation in many medical applications. Two main groups of pulsed lasers are particularly attractive for photo-ablation of tissue. These operate either in the mid-infrared (IR) or the ultraviolet (UV) region of the spectrum. Even though both types of lasers are employed clinically, the mechanisms of ablation are not fully understood.

The rationale for the use of a new modality such as laser-induced hyperthermia in the treatment of human neoplasm is based on a broad spectrum of research. The general research on hyperthermia has been conducted over a centennial, whereas the work on laser-induced hyperthermia has been carried out over the last decade.

Port wine stains (PWS) are vascular malformations that are present at birth. Historically, vascular birthmarks have been described in prominent individuals such as Marcus Tullius Cicero (106–43 B.C.), the famous Roman orator, James II of Scotland (1430–1460), and in the twentieth century, Mikhail Gorbachev, the past leader of the Russian Communist party. Cicero was described by George Hieronymous Velsch in 1672 as having a vascular birthmark, the size of a pea below his left eye. Evidence from woodcut portraits of James II of Scotland suggests that he did indeed have a port wine stain on the left side of his face. Mikhail Gorbachev with his PWS birthmark on his forehead, amounting almost to a trademark, was the target for laser treatment by many therapists across the world.

Laser balloon angioplasty (LBA) is presented as an example of a potential therapy based on thermal alterations of tissue by laser. Its future acceptance as a full clinical modality depends significantly on how its efficacy, advantages, and limitations compare with the current alternative angioplasty techniques described in Section 24.2. To guide its evaluation, discussions have been included which cover the LBA concept (Section 24.3), thermal welding of tissue (Section 24.4), catheter development and usage (Section 24.5), treatment goals (Section 24.6), laser dosimetry using simulation models (Section 24.7), and both acute and long-term tissue responses (Section 24.8). The LBA story reminds us that an engineered device and its implementation may be superb, but its intended application can be limited because of unfavorable biological reactions. In the case of LBA, the deterrent is the long-term restenosis following excellent acute enlargement of the vessel lumen.

It had been theorized that the high rate of restenosis seen following balloon angioplasty could be decreased if the obstruction could be removed rather than simply pushed aside. It was proposed that pulsed lasers could be used to remove arterial obstructions. The purpose of this chapter is to present the theory and practice of pulsed laser ablation of tissue in light of the important and interesting therapeutic goal: removal of arterial obstructions.

Throughout this book, authors have described the optical and thermal response of tissue to laser irradiation. Much of it has been based upon linear analysis; that is, if the irradiance is increased by a factor of k, then fluence rate, rate of heat generation, and temperature rise increase by the same factor of k. Obviously, many medical applications of lasers involve nonlinear processes and hence parameters that do not remain constant during a diagnostic or treatment procedure.