Temperature Distribution Inside the Human Eye with Tumor Growth

Table 7.2. Thermal properties for each of the eye component and eye tumor.

See Sec. 7.4.

The variation of temperature and heat flux at the interfaces between two contiguous ocular regions, Iij may be described using the continuity condition such that

where Ti and Tj are temperatures at the interface between regions Ri and Rj , respectively.

The values of the parameters used in Eqs. (7.3) and (7.4) are similar to those in Ooi et al.33 and are summarized in Table 7.2.

7.4. Material Properties

The thermal properties of each component of the human eye shown in Fig. 7.2 are easily obtained from the literature and are listed in Table 7.2. While the thermal properties of each ocular region can be obtained from

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

literature, the same may not be said of the eye tumor. On the other hand, thermal properties of other types of tumors have been measured and reported. To enable simulations in the present study, values of the unknown thermal properties of the eye tumor, specifically, the thermal conductivity, blood perfusion rate, and metabolic heat generation, are chosen to be given over a range of values that are derived based on the experimental data measured from the different types of tumors that grow inside the human body.

Based on the measurements compiled by Jain,40 the thermal conductivities of various tumors (breast, colon, liver, lung, and pancreatic) that grow on different parts of the human body are found to be in the range of 0.35–0.67 Wm−1K−1. No significant differences in the values of thermal conductivity between the same types of normal and metastatic tumors are observed. Values of the tumor blood perfusion rate that were measured by various researchers using different measuring techniques were compiled and published by Fieldman et al.41 Based on the data measured on breast tumors, lymphomas, anaplastic carcinoma, and differentiated tumors, the tumor blood perfusion rate was found to be in the range of 0.0014– 0.0072 m3s−1m−3.

Unlike the thermal conductivity and blood perfusion rate, metabolic heat generation remains an elusive term in the bioheat equation, where experimental data remains scarce.40 One of the more established studies that quantified the values of tumor metabolic heat generation is, perhaps, the work carried out by Gautherie16 on breast tumors. According to Gautherie,16 the metabolic heat generation of breast tumors remains constant during the phase of exponential growth. Experimental data collected from patients diagnosed with breast tumors revealed that the volumetric metabolic heat generated by the tumor is related to the tumor doubling time by

where is a constant that has a value of 3.27 × 106 W · day · m−3 and DT is the tumor doubling time in days, which is defined as the time needed for the tumor to double its volume.42

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