Temperature Distribution Inside the Human Eye with Tumor Growth

7.6. Results

7.6.1. Numerical Model

Three categories of eye tumor, T1, T2, and T3, are examined in the present study. T4 is not considered, since the tumor has grown beyond the region defined by the model of the human eye (see Table 7.1). Based on the range of values given in Table 7.1, values of 10 and 15 mm are selected to be the diameter of the sphere used for generating the model of the eye tumor for categories T1 and T2, respectively. A value of 17 mm is assumed for category T3 since the largest value of LBD is not explicitly defined.

For each category of eye tumor examined, investigations are carried out for two locations of tumor growth. In the first location, the tumor is assumed to grow in the positive y region of the human eye. Specifically, the center of the sphere used to generate the eye tumor is placed at coordinates (0.013, 0.0105, 0). This example is defined as Case 1. In the second location, which we define as Case 2, the tumor is assumed to grow at the back of the human eye so that it is symmetrically aligned around the pupillary axis. In this case, the center of the sphere is placed at coordinates (0.0244, 0, 0). Locations of the eye tumors inside the human eye in Cases 1 and 2, as viewed in the mid-sagittal plane, are illustrated in Fig. 7.4.

In carrying out the numerical scheme outlined in Sec. 7.5, the boundaries of each region of the human eye are discretized into small triangular elements. In Case 1, 2,212; 2,362; and 2,306 elements are generated in the human eye model with categories T1, T2, and T3 eye tumors, respectively,

Fig. 7.4. Locations of eye tumor in Cases 1 and 2.

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Fig. 7.5. The discretized structure of the cornea, anterior chamber, lens, posterior chamber, vitreous, sclera, and eye tumor (figures are not to scale).

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while in Case 2, 2,388; 2,316; and 2,332 elements are generated, respectively. Boundary discretization is implemented using the built-in mesh generator of the partial differential equation calculator, COMSOL Multiphysics. To implement the dual reciprocity method, 100 interior points are selected inside the region occupied by the eye tumor for Cases 1 and 2 and for each category of eye tumor investigated. The meshed structures of each region of the human eye and a category T2 eye tumor in Case 1 are illustrated in Fig. 7.5.

Fig. 7.6. Temperature variations along the pupillary axis of an eye with a category T1 eye tumor in Case 1.

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7.6.2. Case 1

The effects of eye tumors in categories T1, T2, and T3 on the temperature distribution along the pupillary axis are plotted in Figs. 7.6, 7.7, and 7.8, respectively. Values of the temperature difference shown in Figs. 7.6, 7.7, and 7.8 represent the increases in temperature from the case in which no tumor grows inside the eye.

An increase in the temperature along the pupillary axis is apparent when a tumor grows inside the human eye. The “bell-shaped” curves seen in

Fig. 7.7. Temperature variations along the pupillary axis of an eye with a category T2 eye tumor in Case 1.

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Temperature Distribution Inside the Human Eye with Tumor Growth

Fig. 7.8. Temperature variations along the pupillary axis of an eye with a category T3 eye tumor in Case 1.

Figs. 7.6, 7.7, and 7.8 imply that the thermal effects of the eye tumor are greater at the vicinity of the tumor region. Similar thermal characteristics have been reported by other researchers who carried out investigations on the human breast and skin.18−20 The temperature plots in Figs. 7.6, 7.7, and 7.8 show that a category T3 eye tumor produces the largest increase in temperature, and categories T2 and T1 follow. This implies that a larger tumor produces greater warming effects than a smaller tumor, which may be caused by the larger amount of metabolic heat generated by the larger-sized tumor.

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In each category of eye tumor examined, changes in metabolic heat generation produce the largest variation in the temperature along the pupillary axis. The effects of the thermal conductivity and blood perfusion rate are roughly the same and in both cases, they are found to be smaller than the effects of metabolic heat generation.

Increases in eye tumor thermal conductivity and metabolic heat generation are found to increase the temperature along the pupillary axis. The opposite is observed for the blood perfusion rate, where a decrease in temperature is predicted. These are true for all categories of eye tumor investigated. A larger thermal conductivity generally encourages more heat transfer between the eye tumor and the surrounding ocular regions.

Similarly, a larger metabolic heat generation suggests that more heat is produced by the eye tumor, so that it causes the temperature of the surrounding ocular regions to increase. The opposite effects of the blood perfusion rate may be explained using Eq. (7.2). The first term on the right-hand side of Eq. (7.2) corresponds to the heat transfer due to blood perfusion, which serves as a medium for transferring excessive heat from the human eye. Therefore, a stronger blood flow will lead to heat loss, thus reducing the temperature inside the human eye.

In the eye with a category T1 eye tumor (Fig. 7.6), variations in the tumor thermal conductivity and blood perfusion rate appear to have minimal effects on the temperature distribution inside the human eye when compared to the metabolic heat generation. The largest increase in temperature is found to be approximately 0.16◦C, which occurs when the value of the tumor metabolic heat generation is the highest (75,000 Wm−3). Similar results are observed in eyes with category T2 and T3 eye tumors (see Figs. 7.7 and 7.8). In these cases, however, the effects of the blood perfusion rate are much stronger than the category T1 eye tumor, which is a further indication of the importance of size in governing the temperature increase inside the human eye. The largest increase in temperature caused by the category T2 and T3 eye tumors are found to be approximately 0.5 and 0.7◦C, respectively. These numbers are within the range of temperature rise predicted by the models of the human breast and skin.18−20

Table 7.3 summarizes the increase in the temperature at the corneal surface caused by the growth of a tumor inside the human eye. The location of the central, superior, inferior, nasal, and temporal points are defined by

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Table 7.3. Increase in temperature on the corneal surface in Case 1.

points A, B, C, D, and E, as shown in Fig. 7.2. The coordinates of these points are given as (0, 0, 0), (0.0025, 0.0064, 0), (0.0025, −0.0064, 0), (0.0025, 0, −0.0064) and (0.0025, 0, 0.0064), respectively. Points B, C, D, and E generally describe the periphery of the cornea. Values in the second column of Table 7.3 represent temperatures at points A, B, C, D, and E of a normal human eye. Results presented in Table 7.3 are obtained for values of eye tumor thermal conductivity, blood perfusion rate, and metabolic heat generation at the control.

Out of the five points analyzed, the increase in temperature at the superior point is found to be the largest for all three categories of eye tumor examined. This increased temperature may be because the superior point is closest to the eye tumor. Consequently, the warming effects from the metabolic heat generated by the eye tumor are greater here than the other points on the corneal surface. At the inferior, the point on the corneal surface farthest from the eye tumor, the increase in temperature is the smallest, further supporting the argument given above. As expected, a larger tumor produces a larger increase in the corneal surface temperature.

In the second column of Table 7.3, points at the periphery of the corneal surface of a normal eye are found to have temperatures that are not significantly different from one another. The temperature at the center, meanwhile, is approximately 0.2◦C lower than at the periphery. This implies a

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symmetrical thermal profile on the corneal surface of a normal human eye. When a tumor grows inside the human eye, the temperature at the superior is approximately 50% and 60% higher than the central and the inferior, respectively. This heat indicates a thermal asymmetry along the vertical geometrical center of the cornea. An average increase of 0.066, 0.198, and 0.273◦C are found on the corneal surface of eyes with categories T1, T2, and T3 eye tumor, respectively.

Fig. 7.9. Temperature variations along the pupillary axis of an eye with a category T1 eye tumor in Case 2.

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