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

To determine the significance of the effect of each factor and interaction in Table 7.6, we compute the control limit Fα,v1,v2, where α, ν1, and ν2 are the significance level, the numerator DOF, and the denominator DOF, respectively. The values of ν1 and ν2 are given as 1 and 21, respectively. For a significance level, α of 1%, the value of Fα,v1,v2 = F0.01,1,21 obtained from the F distribution chart is found to be 8.017. Since the values of Fo for all factors and interactions shown in Table 7.6 are greater than 8.017, we may conclude that these factors and interactions have significant effects on the corneal surface temperature.

7.7.2. Taguchi Method

From the results of ANOVA carried out in Sec. 7.7.1, the ambient convection coefficient, the blood convection coefficient, the tear evaporation rate, the tumor size, and the tumor metabolic heat generation have all been found to contribute significantly to the temperature changes at the superior of the corneal surface. Since our objective is to detect the eye tumor based on a warmer corneal surface temperature, it is essential that the IR camera captures only the signal originating from the eye tumor and is not affected by the other factors that are classified as noise.

In this section, we carry out an optimization procedure based on the Taguchi method to determine the optimal setting of factors that maximizes the signal from the factor of interest while minimizing effects from noise factors.23 The Taguchi method is a statistical tool developed by Taguchi.23 It is used primarily in the manufacturing sector but has recently been applied to various other fields, such as in biomedical engineering.15 The Taguchi method discriminates between signal and noise and estimates the positive or negative effect of each factor in each alternative level.

An analysis based on the Taguchi method is carried out for all five factors, A, B, C, D, and E, which we have shown to be significant factors in ANOVA. Each factor is again assumed to have two levels, low and high, where their respective values are presented in Table 7.2. The signal of interest is defined by the effects from the factors pertaining to the eye tumor, including the size (D) and the metabolic heat generation (E), while effects from the ambient convection coefficient (A), blood convection coefficient (B), and tear evaporation rate (C) are categorized as noise.

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Temperature Distribution Inside the Human Eye with Tumor Growth

One of the important variables in the Taguchi method is the signal to noise ratio (SNR), which reflects the variability in the response of a system caused by noise factors.22 Three types of SNR are available, “larger is better,” “nominal is best,” and “smaller is better.”22 Since the signal of interest is defined by the increase in corneal surface temperature, it is decided that the “larger is better” SNR shall be used here. The “larger is better” SNR is mathematically given as:

i=1

where n is the number of occurrences and yi is the ith response of the system defined by the temperature at the superior of the corneal surface.

Table 7.7 summarizes the results obtained from the Taguchi analysis. The values of Tave represent the mean response of a particular factor at a given level. As shown in Table 7.7, the response of the system is found to increase with the size and metabolic heat generation of the eye tumor. The values of SNR in Table 7.7 suggest that the signal from the eye tumor is maximized when the size of the tumor becomes larger or when the metabolic heat generation of the tumor increases. This conclusion is, however, not definite as the combination of factors A, B, and C that causes the effects from the eye tumor to be insignificant has not been considered.

Table 7.7. Results of the Taguchi analysis.

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

Table 7.8. Effects and average SNR of various factors.

For a more conclusive analysis, we calculate the effects and the average values of SNR (SNR) of the various factors at both the low and high levels. These are presented in Table 7.8. The values of SNR of a particular factor are obtained by calculating the mean of the SNR values in Table 7.7 at the desired level. Similarly, the values of effects in Table 7.8 are obtained by averaging the values of Tave in Table 7.7 for a particular factor at a given

level. For instance, the value of SNR and the effect of factor A at low level are calculated from

SNRA,low = 31.14 + 31.02 + 31.20 + 31.12 4

and

= 36.06 + 35.55 + 36.30 + 35.97 , respectively. 4

From Table 7.8, it is found that the combination of factors A, B, and C atlow, high, and low temperature produces effects that are stronger than the effects of factors D and E. This combination is undesirable since the signal that is captured comes primarily from factors A, B, and C, which have been classified as noise. The opposite combination is thus preferred where factors A, B, and C are at high, low, and high temperatures, respectively. At this combination, the effects are found to be smaller than the effects of factors D and E (see bold numbers). As a result, the contributions of the noise factors on the signal are minimized. A similar conclusion may also be derived from the values of SNR in Table 7.7.

258

Temperature Distribution Inside the Human Eye with Tumor Growth

7.7.3. Discussion

Based on the results from the ANOVA and the Taguchi method, the best setting to capture the signal from the eye tumor is at the high rate for the ambient convection coefficient and the tear evaporation and at the low rate for the blood convection coefficient. To increase the value of the ambient convection coefficient simply means to increase the convective heat loss from the corneal surface. This ideal level can be realized by keeping the ambient temperature low. To increase the evaporation rate of the tears, the eyelids of the patient can be kept open for a substantial period before measurement is taken. This allows a continuous evaporation of tears and prevents blinking that refreshes the layer of tears on the corneal surface. However, steps should be taken to ensure that the eyelids are not refrained from blinking for too long, as this would induce tearing that would cause severe changes in the temperature of the corneal surface. It is also possible to increase the tear evaporation rate by reducing the humidity of the surroundings.53

The blood convection coefficient depends on the blood flow inside the choroid.38 In the human body, physically inactivity helps to maintain the blood flow at its basal level, which prevents any major fluctuations in the blood flow rate. Blood flow inside the human eye, however, has been shown to be auto-regulated,54 meaning that the human eye is able to maintain an almost constant level of blood flow despite changes in the perfusion pressure which are usually associated with physical activities. According to Lovasik et al.55 the choroidal blood flow increases by only 10% when an individual undergoes physical activity such as cycling. Kiss et al.56 discovered that significant changes in the choroidal blood flow are only possible during heavy physical activity that increases the ocular perfusion pressure by nearly 70%. Although it may seem that the autoregulation of the ocular blood flow helps to maintain the blood convection coefficient at an almost constant level regardless of whether the patient is physically active or otherwise, it should be noted that the blood convection coefficient is the second most dominant factor that affects the corneal surface temperature (see Table 7.6). This factor should, therefore, be kept at its lowest (basal) level possible so that the interference on the signal is minimal.

It is also found that the signal from the eye tumor becomes stronger when the size of the eye tumor increases. Likewise, a larger metabolic

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