3.1.

Evolution of Light Scattering

Cartilage and cornea have very similar absorption spectra. Both of these tissues are comprised of water, collagen, and proteoglycans, but have different secondary and tertiary (organizational) structures. This makes these tissues interesting for comparative examination of laser-induced structural alterations using the light scattering technique. Figure 2 is an example of the time course of the intensity distribution of light passing through a sample during FEL irradiation. Figure 2 shows the intensity of light transmitted, and the loss of light transmitted is due to an increase of light scattering in the tissue sample. From these (and other data of a similar nature), we have analyzed the dynamics of light scattering, in particular the maximal light intensity (I_m), the half width (w), and the 2-D integral on the intensity distribution of the scattered light (A). The 2-D integral was defined on the assumption that there exists a cylindrical symmetry of the intensity distribution of the scattered probe beam, and the photodiode array records the 1-D cross section of this distribution. The results show that the 2-D integral is a more reliable parameter to characterize the tissue denaturation. Some of the time dependencies of A are plotted in Figs. 3 and 4 for different laser wavelengths and radiant exposures. All experiments have been repeated two to three times. The procedure of averaging has been carried out not at the stage of initial processing of the experimental data, but at the stage of determining essential kinetic parameters.

Figure 2

The spatial distribution of a probe beam at the plane of a photodiode array (magnification×2.8) and its alternations by cartilage irradiated by FEL. The numbers refer to the duration of the irradiation (in seconds); FEL wavelength λ=8.5 μm, pulse radiant exposure F=0.23 J/cm ², f=20 Hz. I is the intensity of the visible scattered light in arbitrary units, and Coordinate is the position on the photodiode array in millimeters.

Figure 3

Kinetics of relative intensity of the light scattering in cartilage as a function of FEL pulse radiant exposure (noted at the curves) for λ=5.30 μm: (a) maximal value of scattered light intensity I_m versus the time of irradiation (in seconds); (b) half-width w of the scattered light distribution versus the time of irradiation (in seconds); and (c) 2-D integral of the intensity distribution of scattered light A versus the time of irradiation (in seconds).

Figure 4

Kinetics of the 2-D integral A (normalized to the initial value) versus time of irradiation (in seconds) as a function of wavelengths (noted at the Figure) at F≅0.1 J/cm ², for (a) cartilage at (b) cornea.

Figures 2 3 4 indicate that the light distribution becomes broader and the intensity of light passing through a sample decreases with time and increasing FEL radiant exposure. It represents an increase in the light scattering due to structural alterations in tissue being irradiated. For small F, neither were alterations in light distribution seen during the period of observation, nor were visible changes on the irradiated surface observed using a light microscope. For higher F values, we have observed partial whitening of the irradiated spot and visible alterations in I_m, and A commence with a delay depending on laser radiant exposure and wavelength λ (Figs. 3 and 4). However, we did observe this trend to reverse (at t>t_a) . Results of experiments for F=0.29 J/cm ², and for λ=5.30 μm, and also for F=0.38 J/cm ², λ=8.05 μm are found more specifically. Under these conditions, we observed a hollow and darkening on the tissue surface irradiated. Plausible explanations for the observed reversal include tissue dehydration preceding the onset of carbonization, the onset of ablation resulting in decrease of optical density of the sample, or a change in the length distribution of scattering centers. Since tissue carbonization itself cannot be responsible for decrease in optical density, the carbonization is accompanied by a sharp increase in the absorption coefficient. This accelerates the heating of tissue a number of times and may result in tissue ablation.¹

3.2.

Time Delay of Tissue Denaturation

We defined the denaturation delay time t^* in the first instance as the value when A drops up to 10 of its initial value. Plotting t^* as a function of F (Fig. 5), we have found the value of the denaturation threshold F_th, which is determined as an asymptotic laser radiant exposure when t^* tends to infinity. The curves on Fig. 5 fit to the experimental data with the function

Figure 5

Denaturation delay time t^* (in seconds) versus the pulse radiant exposure F (in J/cm²) for cartilage: (1) λ=8.05 μm, (2) λ=6.00 μm, and (3) λ=2.50 μm. The solid curves are calculated in accordance with the function t^*=t₀+B/(F−F_th)². The denaturation threshold F_th is determined as an asymptotic pulse radiant exposure when denaturation delay tends to infinity.

Assume that t^* is the sum of two values: t_h is the time necessary to heat a tissue surface up to a certain temperature T_d for which the denaturation starts, and t₀ is the minimal time necessary for redistribution of tissue structural elements. According to the model of the diffusion-limited denaturation of biopolymers under laser radiation,¹² t₀≅L²/D, where L is a characteristic size of the structural alterations in a tissue, and D is an effective diffusion coefficient of moving structural elements. Following Ref. 12 and using, for the estimation of denaturation of the cartilage, L≅5 μm, D≅10⁻⁶ cm ²/s, we get t₀≅0.25 s, which is much smaller than a characteristic time of our experiments.

The calculation of t_h has been described in detail elsewhere (Ref. 1, Sec. 1.2). When the inequality α(at_h)^1/2≫1 is true and we are ignoring the thermal effect of water evaporation (see Ref. 12), the simple expression for the superficial temperature can be used¹

Setting the measurement time t_m to t_h, we obtain an expression for F_th:

3.3.

Wavelength Dependencies

For χ=5×10⁻³ W/K⋅cm, a=1.4×10⁻³ cm ²/s, T_d=70 °C ¹² and for experimental conditions used f=20 Hz, t_m=20 s, formula (3) gives F_th≈0.1 J/cm ², which is quite close to the experimental values of the denaturation threshold for FEL wavelengths near the 2.9- and 6.1-μm water absorption bands, where the absorption α is relatively high and the inequality α(at_h)^1/2≫1 is true. For other IR wavelengths, this inequality is not obeyed. The wavelength dependence of F_th and the absorption spectrum of cartilage are shown in Fig. 6(a).

Figure 6

Dependency of denaturation threshold F_th (in J/cm²) as a function of wavelength λ (in μm); the plotted solid curve is the absorption spectrum for cartilage in arbitrary units: (a) F_th versus λ; (□) cartilage, (^*) cornea; and (b) composition αF_th versus λ; (•) cartilage and (○) cornea.

It should be noted that the minimal experimental value of F_th=0.03 J/cm ² has been observed at λ=6.45 μm. It could be due to the heterogeneous absorption of light by different components of cartilage. The specific absorption of collagen for λ=6.45 μm and its effect on laser-tissue interaction was previously established and discussed in Ref. 13.

When the IR light absorption depth is not very small compared to the thickness of a sample, denaturation starts in a layer of 1/α in thickness, and the minimal time for denaturation is t₀. For the onset of the denaturation process and when the relation α(at)^1/2≪1 is true, the depth heated under laser radiation is governed mainly by the absorption depth 1/α, and instead of Eqs. (2) and (3) we should write¹

3.4.

Approximate Description of the Denaturation Dynamics

The Arrhenius formalism is often used for the description of the kinetics of various chemical reactions, including the reaction of denaturation.^{14 15 16} The rough approximation of the activation energy of cartilage denaturation using the data presented in Fig. 7 gives E_a≈180 kJ/mol. This value correlates with the values determined for the denaturation of cornea^{14 15} E_a≈106 kJ/mol, and liver E_a≈260 kJ/mol. ¹⁶ The typical values of activation energy of denaturation lie between 100 and 400 kJ/mol.¹⁶ Generally, tissue denaturation is a multistage, diffusion-limited reaction accompanied by the complex motion of macromolecules and their segments.^{1 12} This reaction cannot be described adequately with the Arrhenius formalism. In particular, the Arrhenius formalism does not allow describing the existence of the threshold of denaturation. It has been noted elsewhere¹⁷ that a single kinetic rate process may not be indicative in the description of the coagulation process. Actually, the Arrhenius formulas, taking into consideration only the single-stage unidirectional reaction, can be used only as a first approximation of the complex, multistage process. We limit ourselves with a simple consideration based on the phenomenological equations of thermoconductivity and phase transformations.¹ A dynamic approach should consider nucleation and growth of the light scattering centers and take into account that denaturation occurs in the heated layer, where the thickness depends both on light absorption depth and on heating kinetics in the tissue, and also that dynamics of denaturation is diffusion dependent.¹ Nonetheless, Eqs. (3) and (4) account for several features of the experimental results, in particular the denaturation threshold.

Figure 7

Dependency of kinetic coefficient k (in inverse seconds) on pulse radiant exposure F (in J/cm²) for cartilage: (□) λ=8.05 μm; (•) λ=6.00 μm; and (○) λ=2.5 μm.

The rate constant or kinetic coefficient k can be found from a standard, approximate model for kinetics:

Figure 8

Kinetic coefficient k (in seconds) as a function of FEL wavelength λ (in μm): (□) cartilage, F≅0.1 J/cm ²; (•) cornea, F≅0.1 J/cm ²; and (^*) cartilage, F≅0.2 J/cm ².

Equation (5) can be derived from the first order phase transformation kinetics¹

This rough description allows us to characterize the denaturation kinetics with only one coefficient k and to investigate the effect of laser fluence and wavelength on k (Figs. 7 and 8). From Eq. (6) we have k=dη/dt at η=0.

Typically, k is a temperature-dependent value interpreted in terms of a molecular mechanism. We do not consider different models for rate constant, but present simple formulas that allow us to understand the wavelength dependence of the denaturation rate. In our experiments the exposure time is much longer than the characteristic diffusion time t₀. As a first approximation, let η=H/H₀, where H₀ is the tissue sample thickness, and H is the thickness of a layer denatured under laser radiation. The exact (but quite complicated) formulas to calculate H are presented elsewhere.^{1 13}

For a high absorption coefficient, the absorption depth is very small, and we can write for the first approximation:¹ H≅νt, where ν≅Ff/Q_d is the moving velocity of the denaturation front, and Q_d is the denaturation heat per tissue volume. For high α, it follows that k=dη/dt≅ν is proportional to F, which is in agreement with the data shown in Fig. 7 (for λ=6 μm) . When the absorption coefficient is not very high, the denaturation cannot be described with such a simple formula, since the kinetics of the process depend both on the initial absorption depth and on laser fluence. This suggests an explanation for the observation that when α is small, k does not depend strongly on the radiant exposure, as is the case for high α (Fig. 7).

It is also seen in Fig. 7 that k goes to zero with decreasing F. This could be another way to determine denaturation thresholds. The values of F_th obtained from the fluence dependencies of k are similar to the values F_th found from the dependencies of t^* on F. [They differ by no more than 30 from those shown in Fig. 6(a).]

The results presented in Fig. 8 indicate that there is a tendency for k to increase with the absorption coefficient, and that the rate of denaturation can be tuned by wavelength. For example, k is higher for 6.45 μm than for 6.0 μm, inversely correlating with the wavelength dependence of the absorption coefficients. As we mentioned before, this may be due to the specific absorption of collagen for 6.45 μm established and discussed elsewhere.¹³ It is interesting to note the relatively high values of k were found for wavelengths near 8 μm, where 7.5 to 8.2 μm is the wavelength range for the amide III band.¹³

3.5.

IR Absorption Spectra

Figure 9 presents the ATR spectra of 2.4-mm-thick cartilage samples measured before and after irradiation at 6.0 and 2.2 μm. At 6.0 μm, where the absorption is relatively high, the spectrum of the irradiated (front) surface shows changes. In comparison, the spectrum of the back surface was identical to that before irradiation. We attribute this difference to pyrolytic denaturation at the front surface due to laser heating in a small absorption depth. At 6.0 μm, we overheated the irradiated surface to produce significant light scattering. As the sample was thick enough to heat the back surface, the spectrum of the back surface was identical to that before irradiation. For 2.2-μm irradiation, where the absorption is relatively small, the spectrum of the front and back surfaces of the irradiated sample were unchanged from before irradiation, although light scattering indicates the onset of denaturation. These observations suggest that the absorption is too small to produce measurable alteration of structure. Furthermore, we conclude that the light scattering technique is more sensitive than the spectroscopic FTIR technique for studying the onset of denaturation, when laser energy is much higher than the threshold of denaturation.

Figure 9

ATR FTIR spectra of cartilage: (1) nonradiated sample, (2) back surface of the irradiated sample, and (3) front surface of the irradiated sample for the FEL wavelengths of (a) 6.00 and (b) 2.2 μm. The ATR spectra are scaled for a coincidence of the top of water peak at 1640 cm⁻¹ and of the base from the right hand of this peak.