Fujiwara, Osamu; Shiozawa, Toshiyuk. Citation Bioelectromagnetics, 27(8): Rightsavailable at www3.interscience.wile

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1 Computational verification of anest Titlevariations in rabbit eyes exposed t energy Hirata, Akimasa; Watanabe, Soichi; Author(s) Ikuho; Wake, Kanako; Taki, Masao; S Fujiwara, Osamu; Shiozawa, Toshiyuk Citation Bioelectromagnetics, 27(8): Issue Date URL Copyright c 2006 Wiley-Liss, Inc. T Rightsavailable at www3.interscience.wile Type Journal Article Textversion author 名古屋工業大学学術機関リポジトリは 名古屋工業大学内で生産された学術情報を電子的に収集 保存 発信するシステムです 論文の著作権は 著者または出版社が保持しています 著作権法で定める権利制限規定を超える利用については 著作権者に許諾を得てください Textversion に Author と記載された論文は 著者原稿となります 実際の出版社版とは レイアウト 字句校正レベルの異同がある場合もあります Nagoya Institute of Technology Repository Sytem i offer electronically the academic information pr Technology. The copyright and related rights of the article a The copyright owners' consents must be required copyrights. Textversion "Author " means the article is author Author version may have some difference in layou version.

2 Computational Verification of Anesthesia Effect on Temperature Variations in Rabbit Eyes Exposed to 2.45-GHz Microwave Energy Akimasa Hirata 1, Soichi Watanabe 2, Masami Kojima 3, Ikuho Hata 3, Kanako Wake 2, Masao Taki 4, Kazuyuki Sasaki 3, Osamu Fujiwara 1 and Toshiyuki Shiozawa 5 1: Department of Computer Science and Engineering, Nagoya Institute of Technology, Japan 2: National Institute of Communication Technology, Tokyo, Japan 3: Department of Ophthalmology, Kanazawa Medical University, Kanazawa, Japan 4: Department of Electrical Engineering, Tokyo Metropolitan University, Tokyo, Japan 5: Institute of Science and Technology Research, Chubu University, Aichi, Japan Correspondence to Akimasa Hirata ( ahirata@nitech.ac.jp) 1

3 Abstract This paper computationally verifies the effect of anesthesia on temperature variations in the rabbit eye due to microwave energy. The main reason for this investigation is that our previous paper suggested a reduction in blood flow due to the administration of anesthesia, resulting in an overestimated temperature increase. However, no quantitative investigation has yet been conducted. The finite-difference time-domain (FDTD) method is used for calculating power absorption and temperature variation in rabbits. For this purpose, we used a computational rabbit phantom, which is comprised of 12 tissues (including 6 eye tissues) with a resolution of 1 mm. Thermal constants of the rabbit were derived by comparing measured and calculated temperatures. For intense microwave exposure to the rabbit eye, time courses of calculated and measured temperatures were in good agreement both for cases with and without the administration of anesthesia. The point to be stressed is that under anesthesia the thermoregulatory response was inactivated and the basal metabolism was reduced. Keywords: computational dosimetry; eye; anesthesia; active blood flow model 2

4 1 Introduction There has been increasing concern about adverse health effects from exposure to electromagnetic waves. Various public organizations have established safety guidelines for such exposure (e.g., [1, 2, 3]). For RF near-field exposures, the guidelines limit the peak spatial-average specific absorption rate (SAR). In the ICNIRP guideline, the average mass is 10 g and the limit is 2.0 W/kg. The rationale for this regulation is that thermal damage could occur in sensitive tissues during partial-body exposure. Substantial attention has been paid to eye tissues, since it has been reported that RF energy causes a variety of ocular abnormalities, including cataracts, due to high-intensity exposure (reviewed in [4, 5]). Guy et al. [1975] investigated the effects of microwave (MW) exposure on the lens of albino rabbits under systemic anesthesia. The threshold power density for inducing cataract formation was 150 mw/cm 2 for a duration of 100 min [6]. The same group has discussed cataractogenic mechanisms using hypothermic rabbits [7]. In their investigation, the rabbits were anesthetized. They then concluded that temperature elevation is essential to produce microwave-induced cataractogenic effect. Saito et al. [1998] discussed ocular effects due to MW exposure for white rabbits under non-anesthetic conditions [8]. The eye SAR was 26.5 W/kg for an exposure of min. In that study, no cataractous change was observed. Kamimura et al. [1994] reported in a similar study that no abnormality was found on corneal endothelial cells without anesthesia [9]. These reports suggested that, although different exposure conditions and types of subject were used, the influence of anesthesia on ocular effects and temperature increases would not be negligible. Our group then measured temperature increases in rabbit eyes with and without anesthesia for near-field microwave exposure [10]. A major result was that much higher temperatures were observed in the eyes 3

5 of anesthetized than in those of unanesthetized rabbits. In this paper, a computational model of a rabbit was developed for quantitatively verifying the effect of anesthesia on temperature variations in the eye. An eye was assumed to be an object thermally isolated from the head [11, 12], and that simplified model has been used until recently [13, 14, 15]. However, the model developed in our present study was based on a conventional bioheat equation [16], while taking into account the whole rabbit body. 2 Experimental System A detailed description of our experimental system is found in our previous paper [10]. Thus, only brief outline of this setup is given here. In order to ensure localized exposure of the eye, a dielectric-filled waveguide antenna was developed [17]. The aperture dimension of the waveguide was 43.2 mm 86.4 mm. The ratio of the eye averaged SAR to the wholebody averaged SAR is 70. Each young adult male pigmented rabbit was immobilized in a polycarbonate rabbit holder while exposed to MWs. During MW exposure, temperatures of the eye segments were measured with a Fluoroptic thermometer (Luxtron 790, Luxtron, Santa Clara, CA) according to the following procedures: each rabbit eye was anesthetized with a 0.4% oxybuprocaine hydrochloride ophthalmic solution applied as eye drops; thermometer probes (0.5 mm in diameter) were then inserted into the anterior chamber, vitreous cavity, and retrobulbar cavity of the orbit. The tip of thermal probes for the anterior chamber and vitreous cavity were set at the center of the pupil. Body (rectal) temperature was measured by a Fluoroptic thermometer (FL-2000, Anritsu, Tokyo, Japan). A flexible thermal probe (1.6 mm in diameter) was inserted 15 cm into the rectum. The Fluoroptic thermometer was calibrated using a standard thermometer. Room temperature 4

6 and humidity were also measured with a psychrometer. This paper considers two cases, i.e., with and without systemic anesthesia. In anesthetized cases, a solution of ketamine hydrochloride (5 mg/kg) and xylazine (0.23 mg/kg) was injected intramuscularly. 3 Rabbit Phantom and Computational Method Most previous studies [13, 14, 15] that investigated temperature elevations in the eye simplified it as an object thermally isolated from the head [11, 12]. This concept was first proposed by Emery [1975] [11], and then improved upon by Lagendijk [1982]. In this simplification, the thermal flow at the boundary between the eyeball and body core was represented as a heat transfer coefficient. It should be noted that the convection coefficient could be considered as a combination of blood flow in the choroid and heat conduction between the eyeball and body core [18]. In addition, the isolated eye model could not take into account the SAR outside the eyeball in the temperature calculation, leading to an underestimated temperature increase. In most studies that investigated the temperature increase in the human head due to handset antennas (e.g., [19, 20]), the effect of blood flow in the choroid was not taken into account since no reliable blood flow data in the choroid have been reported and because the temperature increase in the eye due to a handset was small. On the other hand, the DIVA (discrete vasculature) thermal model, which allows for the effect of individual vessels was proposed by Kotte et al. [1996]. This model can accommodate a whole body model quite easily. However, a complicated process is required to develop vascular distributions. This section describes a thermal model of a rabbit, which takes into account the animal s whole body, while remaining simple compared with the DIVA. 5

7 3.1 Rabbit Phantom We have developed an anatomically-based rabbit phantom with a resolution of 1 mm. This was constructed on the basis of X-ray CT images taken at Kanazawa Medical University, Japan [17]. It is noteworthy that the thicknesses of most eye tissues, such as retina, choroid, and so forth are smaller than the spatial resolution of the phantom. Thus, the retina, choroid, and sclera were considered as a compound tissue, and their average electrical and thermal constants were used in our calculation. Similarly, the iris and ciliary body were treated as a compound tissue. The developed model is comprised of 12 tissues: skin, muscle, bone, fat, brain, CSF, anterior chamber, vitreous cavity, retina/choroid/sclera, iris/cilaiary body, lens, and cornea. The mass of the left eye, on which MW was irradiated, is 3.1 g. 3.2 SAR Calculation The FDTD method [22] is used for investigating MW power absorbed in the rabbit phantom. For a truncation of the computational region, we adopted perfectly matched layers as the absorbing boundary. To incorporate the rabbit model into the FDTD scheme, the dielectric properties of tissues were required. They are determined with the aid of the 4-Cole-Cole extrapolation [23]. For harmonically varying fields, the SAR is defined as SAR = σ 2ρ Ê 2 = σ 2ρ ( Êx 2 + Êy 2 + Êz 2 ), (1) where Êx, Ê y, and Êz are the peak values of the electric field components, σ and ρ, denoting the conductivity and mass density of the tissue, respectively. 6

8 3.3 Temperature Calculation Our formula for the temperature calculation was mainly based on the studies by Spiegel [1984], Hoque et al. [1988], and Bernardi et al. [1998]. Note that these papers have paid attention to the thermoregulatory response of humans. It is important to develop an activated blood flow model for rabbits, in order to monitor temperature variations in the eyes of unanesthetized rabbit. We were attentive to the temperature increase in the eye tissues, whose thicknesses are at most a few millimeters. Such resolutions made it impossible to monitor blood flow around the eye. Therefore, it became essential to derive the parameters of an active blood flow model by comparing measured and calculated temperatures. In this study, we attempted to apply the human blood flow model to rabbits, to then conduct a parametric study for an active bloodflow model. Note also that the sweat glands in rabbits are virtually nonfunctional, allowing us to neglect this mechanism in our modeling. During heat stress, rabbits try to sustain homeothermy using internal physiological measures [27], such as changes in breathing rates and peripheral (ear) temperatures. Since these mechanisms are not fully taken into account in our modeling, their effect on the calculated results will be discussed in Computational Results Bioheat Equation For calculating temperature increases in the rabbit model, the bioheat equation was used [16]: T (r, t) C(r)ρ(r) t = (K(r) T (r, t)) + ρ(r)(sar(r)) + A(r) B(r, t)(t (r, t) T B (t)) (2) where T (r, t) and T B (t) denote the respective temperatures of tissue and blood, C the specific heat of tissue, K the thermal conductivity of tissue, A the basal metabolism per unit volume, and B the term associated with blood flow. The boundary condition between air and tissue 7

9 for Eq. (2) is given by the following equation: T (r, t) K(r) n = h (T s (r, t) T e (t)) (3) where H, T s, and T e denote, respectively, the heat transfer coefficient, surface temperature, and air temperature. The heat transfer coefficient h is given by the summation of radiative heat loss h rad, convective heat loss h conv, and evaporative heat loss h e, and is represented by the following equations [20]: h = h rad (T e (t)) + h conv (T e (t)) + h e (4) h rad (T e (t)) = ε δa eff ((T skin (r, t) + 273) 4 (T e (t) + 273) 4 ) (5) h conv (T e (t)) = h c A eff (T skin (r, t) T e (t)) (6) h e = k evap A N (P w,skin P w,air ) (7) where ε, δ, A eff, h c, k evap, A N denote, respectively, the emissivity of the body, the Stefan- Boltzmann constant (= W/(m 2 K 4 ) ), the effective area coefficient, the convective heat transfer coefficient (=2.7 W/m 2 / C), the evaporative coefficient (0.35 W/(m 2 mmhg)), and the area of the voxel exposed to air. ε is close to unity, and is thus assumed to be 1. Note that Eq. (7) is neglected at the air-skin surface, as mentioned above. Room temperature fluctuated by 1 o C or more during our measurements, although it was kept constant as much as possible by an air conditioner. In order to compensate for this difference, the measured temperature was incorporated into our thermal calculation Thermoregulatory response For a temperature elevation above a certain level, the blood flow was activated in order to carry away the excess heat produced. As to blood perfusion for all tissues except the skin, the 8

10 regulation mechanism was governed by the local tissue temperature. When that temperature remained below a certain level, blood perfusion was equal to its basal value B 0. Once the local temperature exceeded a threshold, the blood flow increased almost linearly with the temperature in order to carry away the heat produced. For humans, these mechanisms are expressed by the following equations [25]: B(r, T (r)) = B 0 (r), T (r) T A (8) B(r, T (r)) = ( B 0 (r) 1 + (α 1) T (r) T ) A, T B T A T A < T (r) T B (9) B(r, T (r)) = αb 0 (r), T (r) > T B (10) where T A [ C] and T B [ C] denote the threshold temperatures at which the blood perfusion activates and saturates, respectively. The coefficient α must be larger than 1. The variations in blood flow in the skin through vasodilatation are expressed in terms of the temperature increase in the hypothalamus (T H T H0 ) and the average temperature increase in the skin T S : B(r, T (r, t)) = (B 0 (r) + F HB (T H (t) T H0 ) + F SB T S (t)) 2 (T (r,t) T 0(r))/6 (11) where T S (t) = S (T (r, t) T 0(r))dS. (12) S where T 0, F HB, and F SB are the steady-state temperature without heat load and the weighting coefficients of signal from the hypothalamus and skin, respectively. The temperature of blood is changed according to the following equation in order to satisfy the thermodynamic laws. Q BT OT (t) = T B (t) = T B0 + V t Q BT OT (t) C B ρ B V B dt (13) B(t)(T B (t) T (r, t))dv. (14) 9

11 where Q BT OT is the net rate of heat acquisition of blood from body tissues. C B (=4000 J/kg C), ρ B (=1050 kg/m 3 ), and V B denote the specific heat, mass density, and total volume of blood, respectively. Note that the blood volume per unit of rabbit body mass is ml/kg (the average value is 56 ml/kg). The blood volume is ml, since the weight of our rabbits averaged around 2.5 kg. Due to this uncertainty, the measured rectal temperature was used as the blood temperature in Eq. (2), and was measured every 30 seconds, a time period during which the variation in rectal temperature is sufficiently small. Thus, in our computation, the blood temperature changed every 30 seconds using the measured data. The difference between the computationally-predicted and measured values will be discussed in Computational Results. 3.4 Thermal Constants of Tissues Table 1 lists specific heat, thermal conductivity, basal metabolic rate, and the term associated with blood flow for rabbit tissues. The specific heat and thermal conductivity of tissues are extrapolated on the basis of their water content [28]. Note that the water content of tissues can be roughly estimated from electrical constants at microwave frequencies. The blood flow except for eye tissues are extrapolated from the data for sheep, rats, etc (e.g., [29, 30]), together with the correlation between the body mass and the basal metabolic rate [31]. The latter was estimated by assuming that it was proportional to the blood flow [32]. The blood flow in the vitreous cavity, aqueous chamber, lens, and cornea can be safely disregarded so that this value is also assumed as zero. Note that the blood flow in the retina and choroid are comparable to and times larger than that in the brain [33, 34]. The blood flows in the fat and vitreous humor, which exist close to the retina/choroid/sclera, are 10

12 negligible. Since the thicknesses of the retina, choroid, and iris are , , and 0.6 mm, respectively, the term associated with the blood flow in the compound tissue is roughly estimated as W/m 3 with a resolution of 1 mm. Note that the thicknesses of the retina and choroid are dependent on their position. Specifically, their thicknesses become largest around the optic nerve head. In our model, the retina/choroid/sclera are further classified into two parts on the basis of the amount of blood flow, as shown in Fig. 1. First, we discussed the heat transfer coefficient between the skin and air. When we considered h in the skin, h e is negligible at normal room temperature. Temperature of the scalp was then measured and compared with the calculated value for deriving the heat transfer rate in rabbit skin. The remaining thermal parameters are assumed as the constant in this process. For two rabbits, the value was 2-3 W/m 2 / C. Note that a small variation in temperature (±0.3 C) is observed even at a thermally steady state. From this result and Eqs.(4)-(7), A eff is estimated at around 0.25, which is much smaller than that of humans ( 1), since rabbit skin is covered by fur. This coefficient was obtained at a room temperature of 25 C. Then, the heat transfer coefficient between the skin and air could be given at any room temperature by substituting this coefficient in Eqs. (5) and (6). In our calculation, the heat transfer coefficient at the air-skin boundary varies with the passage of time. Next, the heat transfer coefficient between the cornea and air was determined. This value should include the following effects: i) evaporation of the tear film, ii) convective exchange with the air, and iii) radiative exchange with surrounding objects. It is worth noting that, in our measurements, the rate of evaporation would be affected by at least two factors: tears due to the insertion of probes, and the application of saline solution at room temperature to prevent the eye surface from drying out. Also note that the eye was kept open during our 11

13 measurements. In our experiment, the range of this value was W/m 2 / C for five rabbits, depending on the individual rabbit eye (It was 20 W/m 2 / C in the measurement by Lagendijk [1982]). Furthermore, the heat transfer coefficient between tissue and internal air was set at 55 W/m 2 / C [35]. Due to major uncertainties, the heat transfer coefficient at the cornea-air boundary was simplified to be constant in our calculation. The basic procedure for deriving the thermal constants of tissues was summarized. These constants are related to each other: e.g., the value of blood flow in the choroid affects the convection coefficient between the eye and air. The values presented in this section were determined iteratively. 4 Computational Results 4.1 Temperature Variations in Unanesthetized Rabbits The effectiveness of the coefficients in Eqs. (8)-(11) should be discussed for proper thermoregulatory modeling. The threshold temperatures for activating blood flow in the inner tissues T A was 39 C for humans [25], whose normal temperature is 37 C. Since the normal rectal temperature of rabbits is C [36], their threshold temperature can be expected to be 39 C or higher. Additionally, the blood perfusion was modeled to be proportional to the temperature increase and to reach saturation at a temperature increase of 5 C, at which point the blood flow was increased by a factor of 5 compared to the norm [25]. Furthermore, the coefficients of F HB and F SB in Eq. (7) were W/(m 3 oc2 ) and 110 W/(m 3 oc2 ) for humans [26, 37]. The temperature variation in an unanesthetized rabbit was monitored for exposure to

14 GHz localized MW exposure. The antenna was positioned 4.0 cm from the eye surface. The incident power density of the microwave was 300 mw/cm 2, and the probes were located at the center of the lens and vitreous. The rectal temperature of the rabbit was 38.7 C at the initial state. Note that the humidity during this period ranged from 68% to 74%, while the room temperature was about 25 C. In this condition, rabbits were considered to be free of heat stress except for MW heating [27]. The heat transfer coefficient between the cornea and air was determined as 20 W/m 2 / C by comparing measured and calculated temperatures in the lens without MW exposure. In Fig. 2, the measured temperature is compared with calculated temperature for (a) different threshold temperatures of T A and T B, (b) different values of T B T A, and (c) different coefficients of α. In these discussion, the other parameters are assumed to be identical to those of humans. It should be also noted that the initial values of calculated temperatures in the vitreous and lens are not identical to those obtained by the measurements. The differences at the center of the lens and vitreous were 0.35 and 0.32 C and would be caused by computational modeling; e.g., the discretization in constructing the rabbit phantom and the convection coefficients between air and body are time-dependent. To evaluate the temperature increase properly, the computed temperature was shifted to the measured one so that they coincide at the initial state. As seen from Fig. 2 (a), the time course of temperature is obviously affected by T A and T B. When T A and T B are increased by 1 C, the saturated temperature also rises by 0.4 C. For three rabbits, the value of T A was C. Some abrupt changes were observed in measured temperatures due to the rabbit moving slightly in the holder, which also altered the probe position. In Fig. 2 (b), the difference in the threshold temperatures varied from 2 13

15 to 5 C. From this computational example, it is found that this parameter does not play an important role. This coefficient would be more important for a lower input power density (e.g., 150 mw/cm 2 ). Since our focus was on the localized and intense exposure for an assessment of possible cataract formation, further discussion of this parameter is omitted in this paper. In Fig. 2 (c), T A and T B are set to 39 and 44 C, and then α is varied. As seen from this figure, the effect of α on the temperature is obvious for small values, but diminishes for α > 5. For the three rabbits, this value was in the range of 5 7. Additionally, we investigated the effect of uncertainties of F HB and F SB on the temperature variation. When altering these values by a factor of 3, the resultant temperature time course in the eye changed by only 0.1 C or less, suggesting that the parameters for humans are applicable to those of rabbits. In the following discussion, the following parameters were used in cases without the anesthesia [25]: T A =39 C, T B =44 C, α=5. The heat transfer coefficient between tissues and internal air should be varied by the change in breathing rate due to heat stress. Additionally, the rabbit erect the ear lobe for lowering the temperature during heat stress [27]. In most rabbits, these behaviors are observed simultaneously 1 after 20 minutes or so. The temperature increase at the center of the brain, corresponding to the hypothalamus, was 1 o C or more. It has been reported that a small temperature increase at the hypothalamus alters thermoregulatory behavior [38]. Thus, this could be one of the causes of such altered thermoregulatory behavior, even under localized MW exposure. When the heat transfer coefficient between internal air and tissues and that between air and the ear lobe varied by a factor of 3 or more, the temperature in the eye changed at most 0.1 o C at most. Thus, these values are assumed as the constants. These two coefficients, 1 We have conducted measurement for 20 rabbits in each condition, although all of them are shown in this paper. 14

16 together with uncertainty of active blood flow model for the skin, would affect the temperature variation of blood defined in Eq. (13). The measured temperature increase in the blood at 60 minutes for the case without anesthesia was 1.2 C, while the corresponding calculated value was 1.5 C. This is due both to such simplified treatment and to the uncertainty in the amount of blood. Figure 3 shows the time course of temperatures in the vitreous cavity and lens of the same rabbit for the first five minutes. The motivation for further investigation was to confirm the effectiveness of the heat capacity and thermal conductivity of tissues, two parameters closely related to each other. Any variation in the heat capacity of tissues affects the transient temperature behavior or the time constant of the temperature increase, though this effect is marginal when paying attention to the the saturation of temperature increases, as can be seen from Fig. 2. In that figure, calculated temperatures and their shifted temperatures are plotted for comparison. Namely, the temporal evolution of the temperature in the lens has also been shifted so that the initial temperatures coincide with each other, as has already been applied to the vitreous body in the above discussion. As can be seen from this figure, the differences between the calculated and measured temperature increases are less than 10%. Figure 4 shows the calculated SAR and temperature distribution at 40 minutes on the horizontal cross section of the exposed eye. From Fig. 4 (a), significant SAR values are observed in the aqueous and vitreous, which have high conductivities. A comparison between Figs. 4 (a) and (b) shows a clear difference in the distributions between SAR and temperature. There are two main reasons for this difference: one is heat diffusion, and the other is the initial temperature distribution. Namely, the temperature in the cornea is lower than that in the remaining part of the eye due to air cooling. Then, the maximum temperature is observed 15

17 in the posterior of the lens; it is interesting to note that this position coincides with the computationally predicted one in [6]. 4.2 Temperature Variations in Anesthetized Rabbits Fifteen minutes after administration of systemic anesthesia, a rabbit was exposed to 300 mw/cm 2 for 20 minutes. The rectal temperature at the initial state was 41.1 C, a value only slightly larger than those of the normal temperature. This would be caused by an altered heat transfer condition and by tension as the rabbit is immobilized in the holder. Measured temperature variations in the rabbit eye are illustrated in Fig. 5, together with calculated ones. The blood flow and basal metabolic rate for all tissues decreased uniformly so that calculated and measured temperatures at the lens and vitreous are best fitted in the initial state. The rationale for this modification is that the reduction in blood flow has been reported as due to the administration of anesthesia [30]. Following this procedure, the blood flow and metabolic rate were found to be reduced by 30%, though it was 35% in another rabbit. Additionally, the α in Eqs. (5) and (6) was almost 1 in the anesthetized rabbit. Some discrepancy was observed in temperature variations in the vitreous body. The reason for this would be that the effect of anesthesia on blood flow and metabolic rate is not uniform over the whole body, while they were assumed to be uniform in our calculation. Although not shown in this paper, these discrepancies were largely due to individual differences in the rabbits, suggesting that the administration of anesthesia reduced the blood flow and basal metabolic rate, together with inactivating thermoregulatory response. 16

18 4.3 Temperature Variation in Same Rabbit Eye for Cases with and without Anesthesia In the above two subsections, different rabbits were used to investigate the temperature increase with and without anesthesia, respectively. The aim of this subsection is to confirm the reproducibility using the same rabbit. Measured data from our previous paper [2004] have been used in this discussion. First, fifteen minutes after the temperature probes were inserted into the eye (after the anesthesia had worn off), the eyes were exposed to 300 mw/cm 2 for 1 h, followed by a cooling time of 1 h. During that time, the temperature reached a thermally steady state. Fifteen minutes after the administration of systemic anesthesia, the rabbit was again exposed to 300 mw/cm 2 for 1 h. Calculated temperature variations in the rabbit eye are illustrated in Fig. 6 for cases without and with anesthesia, respectively. The respective rectal temperatures at the initial state were 39.3 and 41.8 C for these cases. The higher rectal temperature in the case with anesthesia would be due to the combined effect of i) inflammation due to the first exposure, ii) above-mentioned change in heat-transfer conditions due to the holder, and iii) the administration of anesthesia, with the first and second factors causing the temperature increase while the last factor caused it to decrease because of the reduced blood flow [30]. In Fig.6 (a), temperatures are shown for cases with and without the thermoregulatory response. Note that we define the calculation using a non-active blood flow model (α=1) as the case without thermoregulatory response. In addition, the basal metabolism and blood flow were assumed to be those of an unanesthetized rabbit. The temperatures with a thermoregulatory response were in good agreement with the measured data without anesthesia. The calculation results without thermoregulatory response are overestimated compared with 17

19 the measurements. As sen in Fig. 6 (b), the measurement and calculation without the effect of thermoregulatory response were in good agreement. In this calculation, the basal blood flow and basal metabolic rate were reduced by 20%. Thus, the thermoregulation is equated with inactivation. As mentioned above, such a reduction rate would be caused not only by the anesthesia, but also by the inflammation due to the first exposure. The point to be stressed here is the fact that the blood flow was reduced by the administration of anesthesia and the inactivation of thermoregulation, rather than by a reduction rate of blood flow, namely, qualitatively confirming the result in Fig. 5. The temperature increased steeply after the death of the rabbit (at 26 minutes). This death itself was caused by heart shock once the anesthesia had partially worn off. Insignificant behavior was then observed when the rabbit struggled to escape from restraint and exposure. In this calculation, the blood flow over the whole body was set at zero after 26 minutes. This result confirms that the blood flow and temperature increase were closely related to each other (see also [39]). 5 Summary This study developed a computational model for calculating the temperature increase in a rabbit eye under localized MW exposures. Particular attention was paid to the effect of anesthesia on the temperature increases in the eye, since our previous work had suggested a reduction in blood flow due to the administration of anesthesia. For this purpose, the thermal constants of rabbit tissues and the convection coefficients were derived by comparing measured and calculated temperatures. The parameters of an active blood-flow model were 18

20 also determined using a similar approach. During intense MW exposure to the rabbit eye without anesthesia, the time courses of calculated and measured temperatures were in good agreement. The active blood flow model for humans was found applicable to rabbits. In those case with anesthesia, our computational results suggested that the thermoregulatory response of the rabbit would be inactivated, together with reductions in blood flow and basal metabolism. Those findings could be helpful for reviewing previous works and future work in this field. 19

21 Figure 1: Top view of rabbit model across the center of left eye. Nose located above eye in this figure. Figure 2: Measured and computed temperature increases in vitreous body for exposure to 2.45-GHz microwave at power density of 300 mw/cm 2 : (a) Effect of threshold temperatures T A and T B for T B T A =5 C and α=5, (b) Effect of differences in threshold temperatures T B T A for T A =39 C and α=5, and (c) Effect of increasing rate of blood flow with temperature increase α for T B T A =5 C and T A =39 C. Figure 3: Temperature increase in lens and vitreous for first 5 minutes of 2.45-GHz microwave exposure with power density of 300 mw/cm 2. Figure 4: (a) SAR and (b) temperature distributions (at 40 minutes) on horizontal cross section of rabbit eye under 2.45-GHz microwave exposure at power density of 300 mw/cm 2. Figure 5: Measured and computed temperature increases in lens and vitreous of anesthetized rabbit under exposure to 2.45-GHz microwave energy at the input power of 300 mw/cm 2. Figure 6: Measured and computed temperature increases in same rabbit eye (a) without and (b) with anesthesia (300 mw/cm 2 ). Rabbit eye was first irradiated to 2.45-GHz microwave for 60 minutes without anesthesia, followed by a 60-minutes intervals. Eye was then irradiated under same intense microwave for 45 minutes. In (a), temperature increase for case of disregarding thermoregulatory response is also drawn for comparison. 20

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27 Table 1: Thermal properties of tissues in the rabbit model. C: the specific heat of the tissue [J/kg C], K: the thermal conductivity of the tissue [W/m C], B: the term associated with blood flow [W/m 3 C], A: the basal metabolic rate [W/m 3 ]. Tissues C K B A Skin Muscle Bone Fat Brain C.S.F Vitreous Cavity Anterior Chamber Lens Cornea Retina/Choroid/Sclera (1) (2) Iris/Ciliary Body

28 Retina/Choroid/Sclera (1) Retina/Choroid/Sclera (2) Lens Cornea Vitreous Anterior Chamber Iris/Ciliary Body : probe positions Figure1. (A. Hirata et al.)

29 43 TA=41 C, TB=46 C Temperature [ C] TA=39 C, TB=44 C TA=40 C, TB=45 C Time [min.] Figure2(a). (A. Hirata et al.)

30 43 42 TB - TA=5 C Temperature [ C] TB - TA=3 C TB - TA=2 C Time [min.] Figure2(b). (A. Hirata et al.)

31 43 42 α=1 α=5 Temperature [ C] α= Time [min.] Figure2(c). (A. Hirata et al.)

32 41 40 Temperature [ C] Vitreous Lens Calculated Shifted Measured Time [min.] Figure 3. (A. Hirata et al.)

33 Figure 4(a). (A. Hirata et al.) [W/kg]

34 Figure 4(b). (A. Hirata et al.)

35 46 Temperature [ C] Vitreous Lens Time [min.] Figure 5. (Hirata et al.)

36 Temperature [ C] w/ thermoregulatory response w/o thermoregulatory response measured Vitreous Anterior Chamber Retrobulbar Time [min.] Figure 6(a). (A. Hirata et al.)

37 Temperature [ C] Anterior Chamber Vitreous Retrobulbar w/o thermoregulatory response measured Time [min.] Figure 6(b). (A. Hirata et al.)