名古屋工業大学学術機関リポジトリ Nagoya Institute of Tchnology Repository
Improved heat transfer modeling of the eye for
electromagnetic wave exposures
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Akimasa Hirata
IEEE transactions on biomedical engineering
54
5
959-961
2007-05
http://id.nii.ac.jp/1476/00005333/
doi: 10.1109/TBME.2007.893492(http://dx.doi.org/10.1109/TBME.2007.893492)
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>IEEE Transactions on Biomedical Engineering. (DOUBLE-CLICK HERE TO EDIT) <
1
Improved Heat Transfer Modeling of the Eye for
Electromagnetic Wave Exposures
Akimasa Hirata, Member, IEEE
Abstract— This study proposed an improved heat transfer
model of the eye for exposure to electromagnetic waves.
Particular attention was paid to the difference from the simplified
heat transfer model commonly used in this field. From our
computational results, the temperature elevation in the eye
calculated with the simplified heat transfer model was largely
influenced by the electromagnetic absorption outside the eyeball,
but not when we used our improved model.
Index Terms— heat transfer model, electromagnetic exposures,
temperature elevation, eye safety
I. INTRODUCTION
T
HE eye is said to be one of the organs most sensitive to
electromagnetic (EM) wave radiation. Thus, computational
investigation of the temperature elevation in the eye under
microwave exposure has been conducted extensively (e.g., [1, 2, 3, 4]).
A simplified heat transfer model for the eye was often used till
recently for calculating the temperature elevation due to microwave
exposures. In the simplified heat transfer model [1, 2, 5], the eye was
simplified as an object thermally isolated from the remainder of the
head. Then, the boundary between the eye and head is expressed as a
heat transfer coefficient. In this heat transfer model, the EM power
absorbed outside the eye cannot be taken into account. For microwave
exposures, however, the EM energy is deposited not only inside but
also outside the eye. The amount of EM energy deposited outside the
eyeball would largely depend on the frequency and source. The
purpose of this study is to propose an improved heat transfer model of
the eye which takes into account the whole head model, and then to
clarify the effectiveness and limitation of the simplified heat transfer
modeling used in previous studies.
II. METHOD AND MODEL
The FDTD method [6, 7] was used for investigating the interaction
between the head model and microwaves. Our MRI-based human head
model [4] was used in the present study (See Fig. 1). This model has a
resolution of 2 mm and is comprised of 18 tissues. The electrical
constants of tissues were taken from [8]. For calculating the
temperature elevation in the head, the bioheat equation [9], which
takes into account the heat exchange mechanisms such as heat
conduction, blood perfusion, and EM heating, was used. The thermal
constants of tissues were borrowed from [8] for eye tissues and from
[10] for the remaining head tissues. For microwave exposure, it takes
Manuscript received 17 June, 20xx. A. Hirata is with Department of
Computer Science and Engineering, Nagoya Institute of Technology, Nagoya
466-0855, Japan. (phone: +81-52-735-7916; fax: +81-52-735-7916; e-mail:
[email protected]).
30 minutes till the temperature elevation reaches the steady state. Then,
the duration of exposure was set at 30 minutes in this study.
III. HEAT TRANSFER MODELS FOR EYE
We define a ‘conventional heat transfer model’ as that used in the
temperature elevation calculation according to handset antennas and
medical applications, where the thermal source in the whole body
model is taken into account. Additionally, the heat transfer model in [1,
2, 5] is defined as a ‘simplified heat transfer model’, in which the eye
is considered as an object thermally isolated from the rest of the head.
Figure 2 illustrates a schematic explanation of these heat transfer
models. In this figure, H1 , H 2 , and H 3 denote, respectively, the
heat transfer coefficient between air and eye surface, sclera and body
core, and skin and body core. In the present study, these values were
chosen as follows: H1 = 20 W/m 2 / o C, H 2 = 65 W/m 2 / o C [5]
and H 3 = 10 W/m 2 / o C . In the conventional model, the choroid
and/or high blood perfusion in the choroid was not taken into account.
This is because it is almost impossible to consider such a thin tissue in
the head model with the spatial resolution of a few millimeters. In
addition, only a few data for the blood perfusion in the choroid were
available. In the simplified transfer model, the eye is considered as an
object thermally isolated from the head. This simplification was
considered as valid under the following assumptions [1, 2, 5]: i) the
blood perfusion in the eye is absent, and ii) the heat exchange between
the eye and surrounding tissues is negligible. The latter assumption
was mainly based on the presence of large blood perfusion in the
choroid. Thus, the effect of blood perfusion in the choroid is implicitly
taken into account in the heat transfer coefficient between the eye
surface and body core H 2 . Since H 2 includes the effect of heat
conduction as is evident from the original formula of bioheat equation,
it is considered that the blood perfusion in the choroid and the heat
conduction between the eyeball and body core are substituted for the
heat transfer coefficient H 2 . The weakness of this simplified heat
transfer model is that it cannot consider the SAR (specific absorption
rate) or absorbed EM power outside the eyeball, unlike the
conventional heat transfer modeling. Note that in [5] the thermal
source (water bath heating) was located on the cornea (air-eye surface)
only when the heat transfer coefficient H 2 was derived. Namely, the
SAR and/or heat source did not exist outside the eyeball.
IV. COMPUTATIONAL RESULT AND DISCUSSION
In this section, we attempted to match two heat transfer models by
virtue of the linearity of the bioheat equation in the thermally steady
state [11]. We introduced an equivalent blood perfusion in the
compound retina/choroid/sclera tissue instead of taking into account
the choroid [10, 12]. Then its equivalent blood perfusion is derived in
the following manner.
>IEEE Transactions on Biomedical Engineering. (DOUBLE-CLICK HERE TO EDIT) <
1.
2.
3.
The temperature elevation in the eye is calculated using the
simplified heat transfer model.
The temperature elevation in the eye is calculated by using the
conventional eye model. The SAR outside the eye is assumed as
nonexistent. The equivalent blood perfusion in the
retina/choroid/sclera F ( Bcho ) is considered as a variable.
The blood perfusion in the compound tissue is determined so
that the following function F ( Bcho ) becomes minimal:
F ( Bcho ) =
∑ (δT
simp
−δTconv ).
(1)
M
In procedure 2, the SAR outside the eye was assumed as nonexistent
even for microwave exposures in order to make the total amount of
SAR identical in simplified and conventional models. This fictitious
discussion enables us to connect the simplified and conventional heat
transfer models mathematically due to the linearity of the bioheat
equation in the thermally-steady state. The following six cases were
considered in all: a plane wave and a dipole antenna (distant from the
eye surface at 12 mm) at 900 MHz, 1.5 GHz, and 1.9 GHz [10]. Note
that the SAR distribution is localized around the surface and interior of
the eye for near-field and far-field exposures, respectively [10]. The
dependency of the function F in Eq. (1) on the equivalent blood
perfusion is shown in Fig. 3 for plane wave exposures. As is evident
from Fig. 3, the best-fitted equivalent blood perfusion in the
retina/choroid/sclera is marginally dependent on the frequency. The
function thus becomes minimal in the range between 13400 - 13700
W/m 3 ⋅D C . Note that the differences in voxel temperature elevations
between the simplified and improved models were at most 5% for all
cases. For the dipole antenna, a comparable value was obtained:
13200-13300 W/m 3 ⋅D C . This slight difference in the estimated blood
perfusion would be caused by the anatomy in the surrounding structure.
On the other hand, the heat transfer coefficient in the simplified heat
transfer model was assumed to be uniform over the orbit of the eyeball.
In the following discussion, we use the equivalent blood perfusion in
the retina/choroid/sclera as 13500 W/m 3 ⋅D C . The conventional heat
transfer model with this equivalent blood perfusion is defined as the
‘improved heat transfer model’.
We calculated the maximum temperature elevation in the lens with
the simplified and improved transfer models. Note that the SAR
outside the eyeball is also taken into account, unlike in the
above-mentioned fictitious discussion. As listed in Table 1, the
maximum temperature elevations in the lens with the simplified model
are 15-45 % smaller than those with the improved model, depending
on the source and frequency. It should be noted that these differences
are caused by the SAR outside the eyeball only, since the bioheat
equation is reduced to be a linear equation in the thermally steady state.
It is confirmed that the contribution of SAR outside the eye is larger
for the plane-wave exposure than for the dipole antenna. Note that the
heat can diffuse up to a few centimeters in biological tissues [11], and
thus the SAR outside the eyeball influences the temperature elevation
in the lens. This result suggests that the simplified heat transfer model
is well applicable when the SAR exists in the eyeball only, e.g.,
medical application in [13]. Based on the above finding, it is worth
commenting a heat transfer modeling in [14]. In [14], Flyckt et al.
compared temperature elevation with detailed vascular modeling,
conventional bioheat modeling, and simplified heat transfer modeling.
By changing the heat transfer coefficients in the simplified model,
they evaluated the effectiveness of simplified modeling. As a result,
the suitable heat transfer coefficient depends on the frequency and the
position of the eye. This happened due to the heat diffusion from
outside the eyeball. This study bridged the gap between the
2
conventional bioheat and simplified modelings.
For application of the simplified heat transfer model to localized
exposures to the eye, it is worth deriving a more reliable heat transfer
coefficient between eyeball and body core, since systemic anesthesia
was applied in [5]. Note that the reduction of blood perfusion due to
anesthesia has been reported in [15], e.g. In [12], a heat transfer model
for rabbits was developed by comparing calculated and measured
results with local anesthesia of the eye only. In this discussion, the
thermal constants of tissues for rabbits derived in [12] were used. The
heat transfer coefficient can be derived in a similar manner when
deriving the equivalent blood perfusion in the retina/choroid/sclera. In
this case, the blood perfusion in the retina/choroid/sclera is already
known in [12], and the heat transfer coefficient is treated as a variable.
From our computational results, the heat transfer coefficient was
H 2 = 110 W/m 2 / o C , although including some uncertainty which is
attributed to stair-casing modeling of the eye [16]. In [5], the
experimentally-obtained value of H 2 was 65 W/m 2 / o C , while
theoretical prediction was 110 W/m 2 / o C . Hence, our estimation is
coincident with the prediction in [5]. The reduction rate due to
administration of anesthesia can be estimated as 40 %, which is in
good agreement with our estimation (30-35%) in [12].
V. SUMMARY
In this study, we proposed an improved heat transfer model of the eye.
This heat transfer model used a well-known bioheat equation with an
equivalent blood perfusion in the retina/choroid/sclera. In particular,
we focused on the difference between simplified and improved heat
transfer models where the eye was considered as an object thermally
isolated from the head in the former model. Then, we found that the
simplified model was influenced by the SAR distribution outside the
eyeball. That effect depended on the frequency and source. The heat
transfer coefficient between the eye and the remaining head was
derived as 110 W/m 2 / o C using our thermal model for rabbits [12],
which was larger than 65W/m 2 / o C obtained under anesthesia in [5].
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3
Fig.2: Schematic explanation of (a) the simplified and (b) conventional heat
transfer models.
Fig.3: The dependency of the function F on the term associated blood
perfusion B in the retina/sclera/choroid.
o
Table 1: Maximum temperature elevation [ C ] in lens calculated by (i)
simplified and (ii) improved heat transfer model. In the model (ii), equivalent
blood perfusion in retina/choroid/sclera is taken into account: (A) due to dipole
antenna at 1.2 cm from eye surface with 1W and (B) due to plane wave
exposure of power density of 1.0 mW/cm2.
(A)
Fig.1:Top view of the head model across the center of the eye.
(B)
900 MHz
1.5 GHz
1.9 GHz
900 MHz
1.5 GHz
1.9 GHz
(i)
1.00
1.76
2.60
0.035
0.030
0.032
(ii)
1.39
2.27
3.12
0.058
0.050
0.055