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Ooi, E.H. and Ng, E.Y.K.

12.7.3. Thermal Damage Assessment

One of the major concerns of LTKP, as we have pointed out in Sec. 12.1, is the risk of inducing thermal damage onto the cornea, since the temperature to which the cornea is heated can be very high.9,10,12 The numerical results obtained in the present study have shown this rise in temperature to be as high as 111C during pulsed laser treatment (see Figs. 12.4, 12.5, and 12.6).

Based on the magnitude of the temperature rise inside the cornea alone, the pulsed laser appears to produce a greater amount of thermal damage than the continuous-wave laser. However, the degree of thermal damage inflicted on human tissues is dependent not only on the magnitude of temperature, but also on the duration of heating.14

In this section, we carry out a thermal damage assessment to estimate the degree of thermal damage experienced by the cornea during treatment of LTKP. Investigations are carried out using the thermal damage model of Henriques and Moritz.14

In 1947, Henriques and Moritz14 developed a mathematical model to predict the degree of thermal damage inside the human skin when the skin is burned. Henriques and Moritz assumed the thermal damage of the human skin was a biochemical process defined by the thermal denaturation of proteins, such that the process could be described in terms of an Arrhenius relationship.32 Assuming that the same biochemical process takes place inside the cornea during LTKP, we may then express the degree of thermal damage inside the cornea, at r = 0 using the Arrhenius integral, which is given by14:

(z, t)r=0 = 0

tf

A exp

Ea

dt,

(12.16)

 

 

RT(0, z, t)

 

where Ea is the activation energy, R is the universal gas constant, tf is the time thermal damage is evaluated, and A is an empirically valued coefficient given as:

A =

kb

T(0, z, t)

exp

S

,

(12.17)

 

h

R

where kb is the Boltzmann constant, h is the Planck constant, and S is the entropy of activation. The values of the parameters used for calculating Eqs. (12.16) and (12.17) are obtained from Kampmeier et al.33 and Incropera and DeWitt34 and are summarized in Table 12.5.

370

Temperature Changes Inside the Human Eye During LTKP

Table 12.5. Values of the parameters used in estimating the damage integral.

Parameter

Value

aActivation energy, Ea (Jmol1)

aEntropy of activation, S(Jmol1K1)

bUniversal gas constant, R (Jmol1K1)

bBoltzmann constant, kb (kgm2s1K1)

bPlanck constant, h (kgm2s1)

106 × 103

39

8.314

1.38 × 1023

6.63 × 1034

aValues obtained from Ref. [33]. bValues obtained from Ref. [34].

Fig. 12.13. Thermal damage inside the cornea during pulsed laser radiation.

Using the values tabulated in Table 12.5, the degree of thermal damage at various depths inside the cornea are estimated by evaluating Eq. (12.16) numerically using the trapezoidal rule. Figure 12.13 shows the thermal damage profile of the cornea during pulsed laser radiation. The largest thermal

371

Ooi, E.H. and Ng, E.Y.K.

damage is observed at the surface of the cornea where the increase in temperature is at a maximum. The “step” profile observed in Fig. 12.13 is due to the irregular radiation of the pulsed laser. A large increase in thermal damage occurs only when there is an increase in the corneal temperature, i.e. during the application of each laser pulse.

In order to assess the severity of the damage illustrated in Fig. 12.13, we assume that the thermal damage characterization for skin is applicable in the case of the cornea. Therefore, a value of < 0.53 describes reversible thermal damage; 0.53 < 1 defines the range of irreversible thermal damage, and 1 describes complete tissue necrosis.14 From Fig. 12.13, it is found that pulsed laser radiation produces no irreversible thermal damage, since the largest value of is less than the threshold of 0.53.

The thermal damage induced onto the cornea during continuous-wave laser radiation is illustrated in Figs. 12.14 and 12.15 for the 10-s and minute coagulations, respectively. Both figures show similar profiles. The sharp increase in thermal damage observed in the 10-s and minute coagulations plots are attributed to the continuous heating of the cornea during continuous-wave laser radiation. Once laser radiation is terminated, no major changes in the thermal damage are observed. The thermal damage induced onto the cornea during the 10-s coagulation appears smaller than the

Fig. 12.14. Thermal damage inside the cornea during 10-s coagulation of continuous-wave laser radiation.

372