217
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. VOL. 39. NO. 3, MARCH 1992
Design of a UHF Applicator for Rewarming of Cryopreserved Biomaterials S . Evans, Melanie J. Rachman, and D.E. Pegg
Abstract-The dielectric properties of cryopreserved biological tissue are discussed in relation to the problems which arise when EM fields are used for rapid rewarming. The UHF band is favored from two aspects: the avoidance of thermal runaway and the uniformity of heating inhomogeneous material. Various resonant cavity applicators are considered for efficient and uniform rewarming. The square-aspect TE 111 cylindrical applicator is favored principally because it allows variation of the E-field orientation as required during the warming profile. An appropriate kidney phantom organ is described. It is used to obtain measured values of the overall efficiency of a TE 111 applicator. The efficiency values are found to fall steadily with increasing temperature from 85%at -4OOC to 45%at the phase change, mainly due to the decreasing tan 6 value of the phantom material.
the same for perfused tissue as for the pure perfusate alone and their absolute values are within + l o % below the phase change. Above it, the values are about 25% lower for the perfused tissue but attention in this paper is mainly confined to the pure perfusate, sometimes gelled with agar to make phantom organs.
Temperature Coeficient of Permittivity, E , and Conductivity, U Below the phase change, which occurs at about - lO"C, the temperature coefficients of E and U are positive, but to some extent an increase in E with increasing temperature helps compensate for the unwelcome increase in U . Attention is therefore directed to the variation with frequency: it is found that the temperature coefficient d a / d T inI. ELECTRICAL PROPERTIES OF CRYOPRESERVED TISSUE creases with increasing frequency from 50 MHz to 2.6 N earlier paper [ 11 presented dielectric measurements GHz, whereas de / d T decreases. Thus, the lower frequenon various perfusates used by biomedical laborato- cies are favored from this aspect. Note that U as used i ries in experiments on the cryopreservation of rabbit and this paper refers to the total effective electrical conductiv dog kidneys and measurements on the perfused tissue it- ity and includes all dissipation processes both dc and self. The results in that paper, of importance when con- Consequently, E is real and, without subscript, it is sidering the use of controlled electromagnetic fields for absolute value. rapid and uniform rewarming of cryopreserved organs, are summarized as follows for the temperature range from Choice of Perjksate -32" to +12"C and frequencies from 50 MHz to 2.6 At the phase change there is a sharp increase in both 6 GHz . and U , and big differences in this respect between one perfusate and another. This is the principal factor causing us Influence of the Perfusate to restrict our attention in this paper to the perfusate known The dielectric properties of the perfused kidney tissue as "ECl + 3MG" (hereafter abbreviated ECl): it has the are dominated by those of the perfusate chosen. This is smallest increase at the phase change. The composition of not surprising but is nevertheless a favorable circum- the various perfusates which have been examined is given stance because it gives us some measure of control of the by Marsland et al. [l] and the thermal properties of EC1 properties. It is the temperature coefficients of the dielec- are in publication by Bai and Pegg [9]. tric parameters E and U , rather than their absolute values, which can help ensure that the warming is sufficiently uni- Choice of Frequency: Overall Increase in U form in an inhomogeneous workpiece placed in an elecAbove the phase change we find that the perfusate EC 1 tromagnetic applicator. Roughly speaking, if d a / d T is has negative d a / d T at the higher frequencies. By considnegative, hot spots and thermal runaway should be avoid- ering the overall factor increase in U from - 30 " to 0 C , able. The form of the temperature and frequency depen- one finds a broad optimum in the choice of frequency from dent curves for permittivity and effective conductivity are 300 to 600 MHz. The magnitude of the overall increase could be reduced by reducing the dc component of the conductivity of the perfusate, which would usually mean Manuscript received January 15, 1991; revised July 31, 1991. S. Evans and M. J. Rachmani are with the Department of Engineering, reducing the ionic concentration. This would be beneficial University of Cambridge, Cambridge, England CB2 1PZ England. from the electrical point of view and may be feasible from D. E. Pegg is with MRC Medical Cryobiology Group, Department of the biomedical view but its discussion is outside the scope Surgery, University of Cambridge, Cambridge, England CB2 2AH. IEEE Log Number 9105590. of this paper (see [2]). In general, the optimum ban
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0018-9294/92$03.00 0 1992 lEEE
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. 3. MARCH 1992
218
TABLE I DIELECTRIC DATAAT 434 MHz Pure ECI
Perfused tissue
D
X
E,
s/m
tan6
mm
mS/m
20 15 10 +5
74 80 87 92
0.34 0.35 0.37 0.38
0.19 0.18 0.18 0.18
67 68 67 67
0 -5 -8
94 96 98
0.40 0.44 0.46
0.18 0.19 0.19
- 10 - 12 -15
42 34 23
0.25 0.25 0.24
-20 -25 - 30
15 11 9
50 mM saline
79 38 7
Temp. "C
Ethane-diol Butan- 1-01
s/m
tan6
mm
X mS/m
0.51 0.46 0.41 0.38
55 56 58 62
0.27 0.27 0.27 0.27
0.20 0.20 0.19 0.18
73 74 75 77
0.72 0.70 0.65 0.57
64 59 57
0.38 0.40 0.40
64 66 66
0.28 0.30 0.32
0.18 0.19 0.20
76 72 67
0.56 0.57 0.60
0.25 0.30 0.43
69 62 53
1.10 1.6 3.0
67 46 31
0.33 0.26 0.22
0.20 0.23 0.29
66 69 67
0.60 0.97 1.7
0.17 0.12 0.08
0.45 0.45 0.37
60 73 99
4.6 5.6 5.5
19 13 11
0.17 0.11 0.09
0.37 0.35 0.34
68 87 98
3.1 4.0 4.4
0.51 0.29 0.16
0.27 0.32 0.95
46 56 44
0.7 1.6 17.8
13
4.2
U
Fat Physiological
5.6
D
E,
U
0.04 0.12
0.3 0.9
Muscle 150 50
which we have identified above would be lowered in frequency by reducing the dc conductivity. Ruggera and Fahy [lo] have recently published reheating results at 27 MHz .
Choice of Frequency: Penetration Depth Finally we should consider the power penetration depth D in the phantom material. This is defined as the distance over which a plane wave in the medium would be reduced in power by the factor l / e . (In some publications it is defined in terms of half power.) At the highest frequencies considered D is of order 5 mm, too small to allow uniform power dissipation in a kidney-sized workpiece of typical dimension 30 mm for the rabbit, up to 90 mm for the human. At the lowest frequencies, D reaches several meters which implies that inordinately high E-fields would be necessary to get sufficient power absorption. So it is fortunate that the values of D in the optimum band identified above are found to be very well suited to uniform dissipation in a kidney-sized workpiece. The ISM frequency of 434 MHz has been adopted for the time being and values of D for perfusate and perfused tissue are given in the next section. 11. THE KIDNEYPHANTOM In the experiments reported in this paper, the workpiece is a kidney phantom consisting of EC 1, gelled by adding 4 g of agar powder per 100 mL of solution, and contained in a celluloid ping-pong ball 36 mm diameter. Rachman [3] has shown that the agar and the celluloid shell have no significant effect on the electrical properties and it is
6 18
53
1.43
1.0
considered to represent a realistic model of perfused tissue since convection is inhibited by the gel, and the shell resists evaporation and makes the whole relatively easy to handle. The volume is similar to that of the rabbit kidney, but of course it lacks the nonuniformity and internal structure. Dog and human kidneys have five to seven times the volume of this phantom.
Substitute Materials Experiments on applicator design using this phantom organ require temperature control and monitoring, preferably down to -50°C or lower and this introduces some experimental complications if the EM fields within the applicator are not to be affected by the monitoring and control apparatus. We therefore make occasional use of some substitute materials whose dielectric parameters at 434 MHz and at room temperature are an approximation to those of kidney tissue perfused with EC1 at the relevant lower temperatures. Table I gives the measured values of E and U at 434 MHz for EC1 and for perfused tissue through the known temperature range. Three distinct regions can be identified during tissue rewarming: i) pre phase change: U = 0.1 S / m , E , = 10 ii) phase change region: U = 0.3 S/m, E , 5: 50 iii) post phase change: U = 0.4 S / m , E , = 60. The substitute materials which have been found to simulate the three separate regions are i) Butan-1-01, ii) ethanediol, iii) 50 mM saline. Values of E and U for the three materials (after Rachman [3]) are included at the foot of Table I from which the accuracy,
EVANS et al.: DESIGN OF UHF APPLICATOR
219
or otherwise, of the simulation can be assessed. Substitute workpieces for use at room temperature consist of a thin glass sphere 36 mm diameter, filled through a fine hole with one of the chosen liquids. Rachman has verified that the glass sphere, when empty, causes no significant dielectric dissipation. Table I also gives calculated values of tan 6, the power penetration depth D, and a parameter x to be introduced below. For interest, data are added for fat and muscle tissue at physiological temperature from the hyperthermia literature [4].
The heating coeflcient x For field strength El within the workpiece medium, the power dissipated per unit volume is
P
(1) The field El in the workpiece must be related to the field Eo in air, supposed to be uniform before the workpiece is introduced. For a spherical workpiece, Stratton [5, sect. 3.241 gives = U@.
So vector El is parallel to Eo-which will still be the field in air at some distance-and El is uniform throughout the workpiece. We now introduce an EM heating coefficient x defined by
P
=
&.
(3) Thus, x relates power dissipated per unit volume in the workpiece to the external field strength at some distance. To calculate x for the kidney phantom material it is noted that the absolute permittivity required in (2) can be complex, so for a spherical workpiece we have
The heat conduction equation gives
+
~ V ~P = T pcaT/at.
(5)
So for uniform heating, when the product of conductivity and V 'T is negligible, the rate of temperature rise is given by aT/at
=
-xE- ~2 . PC
For preliminary estimates we adopt a value of pC = 3.5 MJ/m3 K, appropriate for muscle tissue [6], and on that basis we calculate from ( 5 ) that 85 W must be dissipated in the kidney phantom 36 mm in diameter for a warming rate of 1 K/s, and pro rata. Using (6) which is independent of phantom volume, the value of Eo required for a warming rate of 1 K/s rises from 25 to 55 kV/m with the change of dielectric parameters over the temperature range from -30" to -10°C.
111. FIELDORIENTATION The use of coefficient x in the previous section is in principle restricted to a spherical body in air where the unperturbed field at some distance away is assumed to be uniform. The same analysis could be aplied to any other spherical surfaces which form boundaries between media with different electrical or thermal properties within the workpiece and this might be a helpful model for the boundary between the cortex and the medulla of the kidney, but not in the vicinity of the ureter which can be expected to be sensitive to overheating (see Fig. 1). Furthermore, closely spaced boundaries will not behave like a single surface isolated in a field which is uniform at distance: the boundaries will react on one another. So to understand the effect of inhomogeneous composition we now consider the tangential and normal E-field components at any small plane area, part of a boundary between two lossy dielectric media within the workpiece. A. Tangential E-jeld component E, Since E,, = Et2, the ratio of the powers dissipated per unit volume is
Thus, the more electrically conductive material is heated more. There is no escaping this conclusion and reference to the data at physiological temperatures in Table I shows why tangential fields at the skin surface are used to heat muscle tissue, in preference to fat, in hyperthermia treat ment; but in our application E, produces a most undesirable effect as follows. Suppose the difference in properties is due to a temperature difference which has arisen by chance within an otherwise uniform medium. The temperature gradient is normal to the isothermal surfaces, which can now be thought of as the boundaries between material of different properties, and E, is the component normal to the temperature gradient. It can be seen in Table I that (below the phase change), the higher temperature region will have the higher conductivity and consequently the higher power dissipation: there is positive feedback causing any initial differences in temperature to be magnified. This was the basic reason for reviewing the properties of various cryoprotectants over the radio and microwave spectrum and, for the present, adopting ECl at 434 MHz as offering the lowest positive temperature coefficient of 0 . Negative values, which would be preferred, have not yet been found below the phase change and consequently tangential fields should be avoided as far as possible. The negative coefficient above the phase change offers some reassurance, but in this temperature range the perfusate could be circulated to improve uniformity.
B. N o m 1 E-Field Component En The boundary condition gives (QI
+ hEI)EnI
= (02
+j ~ d E n 2 .
(8)
,
[81
220
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. 3, MARCH 1992
.., .:
Renal Palvis
Ureter
\
‘\--
J’
I
c
Cross-Section ThFough A Tvpcal Kidney
Fig. 1. Cross section through a typical kidney.
d
Fig. 2. Illustrating approximate relations involving gap width, d , and workpiece dimensions, s.
~~
PERFUsEDTISSUE-pOWER
T/OC Er
E,,
TABLE 11 DEPOSITION RATIOS,f ( T ) / f ( T + 5°C)
-30
-25
-20
-15
Oh7
0.70
0.70 1.60
0.96 2.80
1.06
1.32
-5 0.57
2.90
1.10 1.05
times the phantom dimensions. We can make this assumption without being too restrictive on the meaning of “several,” since any real organ, being irregular in size and shape, will produce dangerously nonuniform fields if parts approach the electrodes too closely. In Fig. 2, the total gap Voltage for an initially Uniform field is ug E Eod; the correct value is somewhat less with a workpiece in place. The total power dissipated in the workpiece is
+5 1.15 1.00
1.0
0.90
E, is the field component normal to the isothermal surface, therefore in the direction of the temperature gradient. E, is tangential to the isothermal surface.
Hence,
w,= XZV,
5 - I a2 + Ja~2I2 p2 u21 a, + jaEl 1 2 ‘
(9)
For perfused tissue and for a difference of properties due solely to local differences in temperature, this ratio will generally be dominated by the value of I e2 / E I 2 , and since E increases with temperature below the phase change the situation is much more stable and is the reverse of that for tangential fields. For normal fields, or fields directed along an existing temperature gradient, more power is delivered to the lower permittivity or lower temperature region. The ratios Of P(T”C)’P(T -k 50c) for perfused tissue, taking account of both U and E values, are given in Table 11, where ratios greater than unity imply more heat to the lower temperature region. There is a strong suggestion from these figures that if the two field components were equal in magnitude in the time average, the situation would be stable, or nearly so, and this can be realised in practice for random orientation of boundary or isothermal surfaces in one plane, by rotation of the E-field in that plane. Rapid reorientation of the E-field to produce equal time-average components on three coordinate axes would be more difficult, but possible. I v . CHOICE OF APPLICATOR The estimate given at the end of Section I1 for the Eo required for a given power dissipation and warming rate can be generalized to show that a large transformation will be required from the source impedance (likely to be 50 fl) to the load impedance which appears across some space where the kidney phantom is placed in the applicator and which can be regarded as a gap between two electrodes setting up the Eo field. Suppose the gap width is several
(10)
where VI is the workpiece volume. The effective load conductance appearing across the gap, due,to dissipation in the workpiece, is therefore GI
*
xVl/d2.
(1 1)
as near the lower limit Taking a value of d = 72 for a phantom 36 mm in diameter, V~ = 25 mL, and using the X-value just below the phase change in Table I, we find GI < - 5 pS or, (200 k 9 - I . Accurate values can be found for a defined applicator geOmetry but the point to be made is that the impedance is high. To transform to impedances of this order from a source supplied via a coaxial feed with a characteristic impedance of 50 fl, a resonant system with its associated stored energy is unavoidable. It is a disadvantage that this implies tuning and a restricted frequency range; on the other hand, the total enclosure of the fields offered by a cavity resonator is very cavity Resonators: Calculated Parameters To the value GI, the conductance due to the workpiece, should be added a value Go, effective at the same gap and representing loss of power WOdue to the surface resistivity of the cavity walls. It is always advantageous to choose cavity materials and geometry to minimise Go, at least to make it much less than GI, after which there should be means to tune the cavity, or vary the frequency of the source, to make the input admittance real, and means to adjust the transformer action so that GI + Go matches the source conductance. The definitions and relationships associated with @values, efficiency, bandwidth, and the
~
22 I
EVANS er a l . : DESIGN OF UHF APPLICATOR
TABLE I11 CALCULATED PARAMETERS FOR 434 MHz RESONANT CAVITYAPPLICATORS
Reentrant Fig 3(b)
Type Dimensions [mm1
h = 150, b = 169 a = 260 d = 60, a = 75 h = 72 See Fig. 3
Mode
e,!lo3
Cylindrical Square Aspect Fig 4.
Cylindrical Pill Box Fig. 4. a = 260
TM 010
h = 520
Spherical Fig 5. r = 300
TE 111
TM 010
11
12
36
36
[M?/mz] Working space [mm]
210
116
51
58 104
60 x 120 diam
72 x 128 diam 520
Q,/ 10' W W O + WI [MQ/m2] Efficiency, y
2.1
3.6
18
39
35
0.81
0.70
fr/Qi[kHz1
210
-AfO,o[kHz]
1770
TM 101 45
( E ; / WO) X
128 diam
X
180 106 high
X
67 110 diam x 106 high
17
19
25
27
28
0.50
0.53
0.58
120
24
26
23
898
131
150
138
Q, calculated for surface resistivity R, = 8.0 mQ per square (duralumin). Q, calculated for 36 mm diam phantom with x = 0.8 mS/m. Working space: region of the empty cavity for fields within 5 % of maximum. f r / Q , : bandwidth as defined in the appendix, with kidney phantom in place. -Af!30: decrease in resonant frequency with rise in phantom temperature from -30" to 0".
tuning range required as the workpiece material changes properties with temperature, can be found in the Appendix. Calculated cavity parameters, and some other factors which might be considered, are now introduced for four simple cavity shapes, resonant near 434 MHz. The basis of the calculations is given in the following paragraphs and numerical results are in Table 111. The Qo for the empty cavity is based on the field equations for the stated mode and a surface resistivity of 8 X Q,appropriate for duralumin (bulk conductivity 2.8 X IO7 S/m). The ratio ( z / W o ) , which gives the field strength in the working volume in the absence of the workpiece, is derived on the same basis. The value of Qo could, in principle, be increased by the factor 1.5 if the walls were silver plated to a depth of more than 3 pm. However, the calculated Q values take no account of losses due to imperfectly conducting joints or other features which interrupt the ideal current flow in practice. The importance of these will be apparent when the measured Q values are given and it is not likely that silver plating would produce any improvement in losses of this kind. The working volume quoted in Table I11 is the region within which the field strength is within 5 % of its maximum value, in the empty cavity. The Q factor with a workpiece in place, Q , , and the ratio E / ( W o W , ) , are based on a spherical workpiece 36 mm in diameter with a value of x = 0.8 mS/m, appropriate for perfused tissue approaching the phase change
+
(see Table I). The efficiency y follows from the two Q values; note that it refers to just below the phase change only. The bandwidthf,/Q, is without reference to the source loading. If the coupling is such that the source is matched at resonance, the half-power points would be at twice this frequency interval. The frequency change -Af!30 is the decrease in resonant frequency estimated as the workpiece rises in temperature from -30" to 0°C. This is no more than an estimate since it is made on the basis of the perturbation theory in Appendix 11, substituting the properties of ECl from Table I. I) Coaxial or Reentrant Cavity: Two different aspect ratios for this geometry are illustrated in Fig. 3. Moreno [7] has given a series of curves relating dimensions and resonant frequencies, and an approximate expression for Q,. Dimensions a and d provide a starting point and values of 75 and 60 mm have been chosen to provide a uniform field sufficient to accommodate a rabbit kidney. For the minimum loss conductance, Go,Moreno favors an aspect such that (h - d ) = (b - a ) , which leads to the other dimensions given in Table 111. The great drawback of this otherwise very attractive design is that the field cannot be reoriented as recommended in Section 111. 2) Cylindrical Cavity: Two modes are sketched in Fig. 4 and the field equations are in standard texts (e.g., [8, sect. 10.61). The TM 010 mode with h considerably less than a is popular as an applicator for the high field on the
222
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. 3. MARCH 1992
+'
4=
Spherical TM101
(a) (b) Fig. 3. (a) Coaxial and (b) reentrant applicator geometries showing E-field lines. I
TMOIO
TElll
631
iI
0800000
Fig. 5. Spherical cavity TM 101 field.
sect. 10.81. It has not been followed up in practice because of the difficulty of construction with ready access to the interior.
V. EXPERIMENTAL EVALUATION OF TE 1 1 1 CYLINDRICAL CAVITYAPPLICATOR Construction tz On the basis of factors discussed in the previous section we have constructed a resonant cylindrical applicator of welded duralumin to the dimensions shown in Fig. 6 . The top and bottom end plates are attached with pull-down toggles which compress an RFI shielding gasket, with round elastomer core, into a square section channel. The radius i T l pipes, 47 mm i.d. in the center of each end plate, have flanges allowing them to be fitted either intemally or ex(a) ternally. They allow access for temperature sensors, both Fig. 4. (a) Square-aspect cylindrical cavity showing TE 1 1 1 field. (b) Pillbox aspect ratio showing TM 010 field. optic fiber and sighting for passive infrared, and (mainly due to that fitted intemally) they shift the resonant frequency of the TM 010 mode far enough from the TE 11 1 z-axis. As a simple case we have included it in Table I11 resonance, so that it is not excited accidentally. The pipes for comparative purposes but it suffers from the same themselves are far below cutoff frequency at 434 MHz: drawback as the reentrant cavity: the field orientation is evanescent fields are estimated to be 50 dB down at the fixed. outside ends and no effect on the resonance has been obHowever, when the height is greater than half the free- served due to objects outside. space wavelength, the TE 1 1 1 mode is especially appealA single feed probe, as shown, was found in practice ing for our application since the field can be rotated in the to excite two resonances close together in frequency: they xy plane. When h = 2a, TE 1 1 1 is degenerate with TM were found to be in two polarizations associated with 010 and this is the cavity design which we have followed slight ellipticity of the cylinder section. To fix the polarup though it is not to be expected in practice that the TM ization, an adjustable tuning rod is fitted diametrically op010 resonance will be exactly coincident with TE 1 1 1 . posite the feed probe. Another set of probe and rod is The empty cavity Q is higher than for the reentrant case, fitted at right angles in the same plane to excite the orbut the light loading imposed by the workpiece (which is thogonal polarization; the coupling between the two has effectively in too large a gap) means that the efficiency is been measured to be below -25 dB. dissapointingly low. The length of the probe is adjusted to match the load There is no significant difference in considering a rect- imposed by the workpiece and the cavity at resonance, to angular or cubical cavity in the equivalent modes, except a coaxial 50 Q source. It is convenient for empirical adquestions of mechanical rigidity and access to the interior. justment with a network analyser to use a standard loading 3) Spherical Cavity: The spherical cavity parameters and the substitute workpiece filled with ethanediol at room are included in Table I11 for academic reasons, as some- temperature has lead us to adopt 50 mm for the probe thing of a limiting case. The TM 101 mode is sketched in length. The tuning rod is of similar length which helps Fig. 5 and the necessary field equations are given in [8, ensure symmetry of the field at the center. Use of an ex-
I
223
EVANS et al.: DESIGN OF UHF APPLICATOR
c
n
TABLE IV MEASURED APPLICATOR PERFORMANCE VERSUS KIDNEY PHANTOM TEMPERATURE gasket m channel
524
i262 mm r a q Cylindrical 434 MHz applicator (not to scale) Fig. 6. Cylindrical 434 MHz applicator used for the measurements reported in Section v.
far been successful.
Basic Parameters Resonant frequencies, input reflection coefficient, and Q values, have been measured on this cavity under a wide variety of intemal loading conditions using an HP 8753B network analyzer and HP 85044A test set, which system allows microprocessor correction of measurements made at the test port against a standard short circuit, an open circuit, and a matched termination. Hard copy output has commonly been as Smith charts in admittance coordinates on an HP7440A plotter. The relationships used to derive Q values, and W ) values are given in the Appendix, and results are in Table IV. The first conclusion is that the measured Qo value for the real cavity falls far short of the calculated value of 36 X lo3 for the ideal cavity. The highest measured value is 20 x lo3, and we can attribute the degradation to the pipes in the end plates, the tuning rod, and the feed probe, which increase the effective wall area and interrupt the ideal current flow. Probably more serious is the gasket joint for the top and bottom end plates since loosening of the fixing toggles with use very soon causes Qo to fall into the range 12 to 15 X lo3. This joint therefore merits further attention: for the time being we have based all efficiency values on Qo = 15 x lo3. The parameter WO)which gives the field strength in the working space, has been measured with an alumina sphere as a perturbing body (E,. = 9.0, radius 9.5 mm, Af = 67 kHz) and using the method outlined in the Appendix, equation (A8). The measured value is 24 MQ/m2 which falls short of the calculated value of 58 MQ/m2 by exactly the same factor as is found for the Qo values, as should be expected. One interpretation of this would be that the feed probe and tuning rod do not significantly affect the central field strength.
(E/
-A f/kHz
em3
P
Y
(reference 438.5 MHz)
15
+0.45
-
493 620
2.3 6.2
-0.46
-0.05
0.85 0.59
765 760 756 753 742 727 707 667 605 538 493 462
8.2 8.2 8.1 8.0 7.0 5.0 3.6 2.5 2.1 2.3 2.8 3.6
+0.08 +0.08 +0.08 +0.07 0.0 -0.15 -0.32 -0.46 -0.52 -0.50 -0.42 -0.30
0.45 0.45 0.46 0.46 0.53 0.67 0.76 0.83 0.86 0.85 0.81 0.76
Butan- 1-01 Ethanediol
z
(E/
T/"C Empty cavity
+5 0 -5 - 10 - 15 -20 -25 -30 -35 -40 -45 -50
y is the fraction of the power supplied which is delivered to the phantom.
Loading Versus Workpiece Temperature In Table IV we summarize the results of an experiment in which the kidney phantom specified in Section I1 was cooled to below -50°C and then placed at the cavity center, well insulated with expanded polystyrene, so that the input port behaviour could be recorded by the network analyzer as the temperature rose slowly over a period of several hours. The temperature was monitored with two optic fiber probes (Luxtron type MIW-2) implanted in the phantom. They avoid any disturbance with the cavity fields and are coupled with the Luxtron 755 instrument for recording. Referring to the results in Table IV it is perhaps surprising, in view of the disappointing value of Qo measured earlier, that the measured efficiency with the kidney phantom at -10°C is so close to the calculated value. The calculated efficiency used a value of x = 0.8 mS/m appropriate to the phase change, which occurs between - 12" and - 10°C for perfused tissue, and between - 10" and -8°C for pure EC1. As nearly as we can tell with the measured data at 5 " intervals, the calculated efficiency of 0.53 should be compared with the measured value of 0.46 and thus there is no cause for complacency about the cavity wall losses. Efficiency in some of the the lower temperature range is satisfactory however, basically due to the higher tan 6 value. With the probe length fixed, as in this experiment at the optimum for an ethanediol workpiece, the loss of available power due to mismatch is not too serious: I p l2 is zero at - 15°C and reaches a maximum of 0.27 at -35°C. Rachman [3, Appendix B] has shown that it should pass through zero again at a lower temperature which we have observed to be about -60°C but with insufficient data to complete another line of Table IV.
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224
In a later paper we shall give experimental results for the rewarming of organ phantoms from - 80°C in this TE 111 cylindrical applicator. Future work will be directed to improvements in efficiency in parallel with biomedical experiments to assess the damage when rewarming viable tissue over the widest possible range of warming rates. APPENDIX I. CAVITYBANDWIDTH, EFFICIENCY, AND FIELD STRENGTH The internal Q factor of a resonant cavity at angular frequency w is defined by (All Q = oU/W where U is the total energy stored in the cavity fields and W is the total power dissipated within. Expressions for Q are given in standard texts for simple cavity shapes where the fields are known analytically, so that U is known and W is calculable from the surface resistivity of the cavity walls and surface currents. In those cases the parameter (%/WO) also, is calculable. Assuming that the input admittance is referred to the “detuned-short-circuit” position, x , on the feed line, then values of Q are derived in practice from measurement of the two frequencies, fa andfb either side of resonance, at which the input susceptance B, = +GI, the input conductance. We then use the relation
Q =fr/Ifa -fbl (see, for example, [8 sect. 10.111). No reference is made to source admittance; i.e., it is not assumed to be matched at resonance, so fa and fb are not in general the “halfpower points.” However, we givef,/Q in Table I11 as an indication of the bandwidth and hence the required precision of tuning. Let the power dissipated in the cavity walls be WOand in the workpiece Wl . Then from measurements of Q with and without the workpiece in place we have
If we compare these two under the condition that, when the workpiece is introduced, the total drive power is increased such that the bulk of the fields are unchanged except for a perturbation in the vicinity of the workpiece, then U and WO are the same in the two cases, the two resonant frequencies w1 and wo, are approximately equal, and the efficiency y, in delivering power to the workpiece is given by Wl WI + WO
y=-=-=-
Qo Qo
QI
GI
GI
+ Go‘
(A4)
The relationship to the gap conductances GI and Go also assumes that the cavity gap voltage is unchanged so this is perhaps less accurate than the relationship to the Q’s in cases where the workpiece occupies a large fraction of the
gap. Calculated values of y can be found for simple cavity shapes where the fields are known, so that Wl and WOare calculable. In practice, values of y are obtained for any cavity shape from measurement of the the two Q values. To find the Eo field in relation to the drive power after the workpiece is introduced (the calculated values given in the lower part of Table 111), it is noted that if the drive power is increased to WO + W,, then the Eo field is the same as in the empty cavity and we have
11. APPLICATION OF PERTURBATION THEORY Later developments of Slater’s original perturbation theorem for resonant cavities can be written AU
-
A K - A G
00
(A61
U
where A w is the increase in resonant frequency U, when the time-average energy stored in H-fields is increased by A G , and in E-fields by A C (see, for example, [8, sect. 10.121). The perturbation is assumed to be sufficiently small that the bulk of the fields, and hence the total energy U is not significantly changed. The first application to be considered here is in subsidiary experiments to determine the E-field strength at any point inside a cavity in terms of the power supplied. Stratton [ 5 , sect. 3.251 has shown that the additional stored energy in an electric field of strength Eo, initially uniform in air, when a small dielectric sphere radius rl is introduced is
We define
where C contains properties of the perturber only. We can put A G = 0; the justification is as follows. The dielectric sphere acquires an electric dipole moment and hence, in an oscillatory Eo field there is, in principle, an associated H field. However there is no near-field component of H and we neglect the far fields: not only are they small but the stored energies of the w 2 / r terms for Eo and H6 (the radiation fields) are equal in magnitude and hence their effects cancel in (A6). There is arguably a small component of A G due to the a ’ / . term for E,, not included in Stratton’s static analysis. So by placing a small sphere of lossless dielectric as a perturbing body at a point within the empty cavity applicator, the Eo field at that point can be derived from a measurement of the increase in resonant frequency. -
_ AU -AUE - WO
U
- CO Eo
Qo
(””) WO
(A9)
EVANS el al.: DESIGN OF UHF APPLICATOR
225
This is the relationship used for the measured value of
%/WO at the workpiece position as given in Section V. The Eo field with the workpiece in place is obtained from this measurement and the two Q’s using (A5). The other application of perturbation theory is more approximate: we wish to know the shift in resonant frequency as the workpiece properties change, and how this compares with the the bandwidth (fb - fa) defined earlier. The tuning range required to remain resonant is estimated from (A7), substituting the changing values of C with changing temperature and recognizing that the workpiece volume is likely to be too large for any degree of accuracy from perturbation theory. If Ah is the increase in the resonant frequency, fr, due to an increase in average electric stored energy A U,with change in properties of the workpiece, then comparison with the bandwidth gives
Ah -=---
If, -fbl
AUI
fr
U
If, -fbl
UA U,
-
W O + WJ‘
Absolute values of frequency shift and bandwidth are given for the different cavities in Table IV, but note the elimination of U from the right hand of (AIO); this shows that there is no advantage in minimizing stored energy in order to ease requirements on tuning.
ACKNOWLEDGMENT We are indebted to the Wellcome Trust for an equipment grant covering the cost of this laboratory work. M. J. Rachmann thanks Peterhouse, Cambridge for a research studentship.
REFERENCES [I] T. P. Marsland, S. Evans, and D. E. Pegg, “Dielectric measure[2]
[3] [4] [5]
ments for the design of an electromagnetic rewarming system,” Cryobiol., vol. 24, pp. 311-323, 1987. A. K. Coffey and P. M. Andrews, “Ultrastructure of kidney preservation: varying the amount of effective osmotic agent in hypertonic preservation solutions,” Transplantation, vol. 35, no. 2, pp. 136142, Feb. 1983. M. J. Rachman, “Electromagnetic rewarming of cryopreserved organs,” Ph.D. dissertation, Univ. Cambridge, England, pp. x + 187, Feb. 1990. S. B. Field and C. Franconi, Physics and Technology of Hyperthermia. Dordrecht: Martinus Nijhoff NATO AS1 Series, 1987. J. A. Stratton, EIectromagnetic Theory. New York: McGraw Hill, 1941.
M. Knudsen and J. Overgaard, “Identification of thermal model for human tissue,” IEEE Trans. Biomed. Eng., vol. BME-33, pp. 477485, May 1986. T. Moreno, Microwave Transmission Design Data. New York: Dover, 1958. S. Ramo, J. R. Whinnery, and T. van Duzer, Fields and Waves in Communications Electronics. New York: Wiley, 1984, 2nd ed. X. Bai and D. E. Pegg, “Thermal property measurements on biological materials at subzero temperatures,” ASME Trans. Biomechan. Eng., 1991. P. S. Ruggera and G. M. Fahy, “Rapid and uniform electromagnetic heating of aqueous cryoprotectant solutions from cryogenic temperatures,” Cryobiol., vol. 27, pp. 465-478, 1990.
S. Evans received the B.Sc. degree in physics from the University of Manchester, Manchester, England, in 1951 and the Ph.D. degree in radio astronomy in 1955. He spent two years with Royal Society I.G.Y., expedition to Halley Bay, Antarctica. Following that he spent two years as a lecturer in physics at the University of Manchester. He was an Assistant Director of Research at Scott Polar Research Institute, Cambridge, on radio echo sounding of glaciers and polar ice masses, and dielectric properties of frozen materials. Since 1972, he has been a lecturer in engineering at the University of Cambridge with special interest in microwaves. He has published over 100 papers in various fields.
Melanie J. Rachman was born in Bulawayo, Zimbabwe, in 1962. She received the B.Sc. degree in physics and the M.Sc. degree in electrical engineering from the University of Cape Town, Capetown, South Africa, in 1983 and 1985, respectively, and the Ph.D. degree from the University of Cambridge, cambridge, England, in 1990. She IS now with McDonald Deltwiler Associates, Vancouver, Canada, analyzing satellite images and SLR.
D. E. Pegg received the degrees in medicine from Kings College London and Westminister Medical School in 1956, 1963, and 1967. He joined the Medical Research Council at their Clinical Research Centre and moved to Cambridge as Head of the MRC Medical Cryobiology Group in 1978. He has published over 200 papers on cryobiology.
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. VOL. 39. NO. 3, MARCH 1992
Design of a UHF Applicator for Rewarming of Cryopreserved Biomaterials S . Evans, Melanie J. Rachman, and D.E. Pegg
Abstract-The dielectric properties of cryopreserved biological tissue are discussed in relation to the problems which arise when EM fields are used for rapid rewarming. The UHF band is favored from two aspects: the avoidance of thermal runaway and the uniformity of heating inhomogeneous material. Various resonant cavity applicators are considered for efficient and uniform rewarming. The square-aspect TE 111 cylindrical applicator is favored principally because it allows variation of the E-field orientation as required during the warming profile. An appropriate kidney phantom organ is described. It is used to obtain measured values of the overall efficiency of a TE 111 applicator. The efficiency values are found to fall steadily with increasing temperature from 85%at -4OOC to 45%at the phase change, mainly due to the decreasing tan 6 value of the phantom material.
the same for perfused tissue as for the pure perfusate alone and their absolute values are within + l o % below the phase change. Above it, the values are about 25% lower for the perfused tissue but attention in this paper is mainly confined to the pure perfusate, sometimes gelled with agar to make phantom organs.
Temperature Coeficient of Permittivity, E , and Conductivity, U Below the phase change, which occurs at about - lO"C, the temperature coefficients of E and U are positive, but to some extent an increase in E with increasing temperature helps compensate for the unwelcome increase in U . Attention is therefore directed to the variation with frequency: it is found that the temperature coefficient d a / d T inI. ELECTRICAL PROPERTIES OF CRYOPRESERVED TISSUE creases with increasing frequency from 50 MHz to 2.6 N earlier paper [ 11 presented dielectric measurements GHz, whereas de / d T decreases. Thus, the lower frequenon various perfusates used by biomedical laborato- cies are favored from this aspect. Note that U as used i ries in experiments on the cryopreservation of rabbit and this paper refers to the total effective electrical conductiv dog kidneys and measurements on the perfused tissue it- ity and includes all dissipation processes both dc and self. The results in that paper, of importance when con- Consequently, E is real and, without subscript, it is sidering the use of controlled electromagnetic fields for absolute value. rapid and uniform rewarming of cryopreserved organs, are summarized as follows for the temperature range from Choice of Perjksate -32" to +12"C and frequencies from 50 MHz to 2.6 At the phase change there is a sharp increase in both 6 GHz . and U , and big differences in this respect between one perfusate and another. This is the principal factor causing us Influence of the Perfusate to restrict our attention in this paper to the perfusate known The dielectric properties of the perfused kidney tissue as "ECl + 3MG" (hereafter abbreviated ECl): it has the are dominated by those of the perfusate chosen. This is smallest increase at the phase change. The composition of not surprising but is nevertheless a favorable circum- the various perfusates which have been examined is given stance because it gives us some measure of control of the by Marsland et al. [l] and the thermal properties of EC1 properties. It is the temperature coefficients of the dielec- are in publication by Bai and Pegg [9]. tric parameters E and U , rather than their absolute values, which can help ensure that the warming is sufficiently uni- Choice of Frequency: Overall Increase in U form in an inhomogeneous workpiece placed in an elecAbove the phase change we find that the perfusate EC 1 tromagnetic applicator. Roughly speaking, if d a / d T is has negative d a / d T at the higher frequencies. By considnegative, hot spots and thermal runaway should be avoid- ering the overall factor increase in U from - 30 " to 0 C , able. The form of the temperature and frequency depen- one finds a broad optimum in the choice of frequency from dent curves for permittivity and effective conductivity are 300 to 600 MHz. The magnitude of the overall increase could be reduced by reducing the dc component of the conductivity of the perfusate, which would usually mean Manuscript received January 15, 1991; revised July 31, 1991. S. Evans and M. J. Rachmani are with the Department of Engineering, reducing the ionic concentration. This would be beneficial University of Cambridge, Cambridge, England CB2 1PZ England. from the electrical point of view and may be feasible from D. E. Pegg is with MRC Medical Cryobiology Group, Department of the biomedical view but its discussion is outside the scope Surgery, University of Cambridge, Cambridge, England CB2 2AH. IEEE Log Number 9105590. of this paper (see [2]). In general, the optimum ban
A
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0018-9294/92$03.00 0 1992 lEEE
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. 3. MARCH 1992
218
TABLE I DIELECTRIC DATAAT 434 MHz Pure ECI
Perfused tissue
D
X
E,
s/m
tan6
mm
mS/m
20 15 10 +5
74 80 87 92
0.34 0.35 0.37 0.38
0.19 0.18 0.18 0.18
67 68 67 67
0 -5 -8
94 96 98
0.40 0.44 0.46
0.18 0.19 0.19
- 10 - 12 -15
42 34 23
0.25 0.25 0.24
-20 -25 - 30
15 11 9
50 mM saline
79 38 7
Temp. "C
Ethane-diol Butan- 1-01
s/m
tan6
mm
X mS/m
0.51 0.46 0.41 0.38
55 56 58 62
0.27 0.27 0.27 0.27
0.20 0.20 0.19 0.18
73 74 75 77
0.72 0.70 0.65 0.57
64 59 57
0.38 0.40 0.40
64 66 66
0.28 0.30 0.32
0.18 0.19 0.20
76 72 67
0.56 0.57 0.60
0.25 0.30 0.43
69 62 53
1.10 1.6 3.0
67 46 31
0.33 0.26 0.22
0.20 0.23 0.29
66 69 67
0.60 0.97 1.7
0.17 0.12 0.08
0.45 0.45 0.37
60 73 99
4.6 5.6 5.5
19 13 11
0.17 0.11 0.09
0.37 0.35 0.34
68 87 98
3.1 4.0 4.4
0.51 0.29 0.16
0.27 0.32 0.95
46 56 44
0.7 1.6 17.8
13
4.2
U
Fat Physiological
5.6
D
E,
U
0.04 0.12
0.3 0.9
Muscle 150 50
which we have identified above would be lowered in frequency by reducing the dc conductivity. Ruggera and Fahy [lo] have recently published reheating results at 27 MHz .
Choice of Frequency: Penetration Depth Finally we should consider the power penetration depth D in the phantom material. This is defined as the distance over which a plane wave in the medium would be reduced in power by the factor l / e . (In some publications it is defined in terms of half power.) At the highest frequencies considered D is of order 5 mm, too small to allow uniform power dissipation in a kidney-sized workpiece of typical dimension 30 mm for the rabbit, up to 90 mm for the human. At the lowest frequencies, D reaches several meters which implies that inordinately high E-fields would be necessary to get sufficient power absorption. So it is fortunate that the values of D in the optimum band identified above are found to be very well suited to uniform dissipation in a kidney-sized workpiece. The ISM frequency of 434 MHz has been adopted for the time being and values of D for perfusate and perfused tissue are given in the next section. 11. THE KIDNEYPHANTOM In the experiments reported in this paper, the workpiece is a kidney phantom consisting of EC 1, gelled by adding 4 g of agar powder per 100 mL of solution, and contained in a celluloid ping-pong ball 36 mm diameter. Rachman [3] has shown that the agar and the celluloid shell have no significant effect on the electrical properties and it is
6 18
53
1.43
1.0
considered to represent a realistic model of perfused tissue since convection is inhibited by the gel, and the shell resists evaporation and makes the whole relatively easy to handle. The volume is similar to that of the rabbit kidney, but of course it lacks the nonuniformity and internal structure. Dog and human kidneys have five to seven times the volume of this phantom.
Substitute Materials Experiments on applicator design using this phantom organ require temperature control and monitoring, preferably down to -50°C or lower and this introduces some experimental complications if the EM fields within the applicator are not to be affected by the monitoring and control apparatus. We therefore make occasional use of some substitute materials whose dielectric parameters at 434 MHz and at room temperature are an approximation to those of kidney tissue perfused with EC1 at the relevant lower temperatures. Table I gives the measured values of E and U at 434 MHz for EC1 and for perfused tissue through the known temperature range. Three distinct regions can be identified during tissue rewarming: i) pre phase change: U = 0.1 S / m , E , = 10 ii) phase change region: U = 0.3 S/m, E , 5: 50 iii) post phase change: U = 0.4 S / m , E , = 60. The substitute materials which have been found to simulate the three separate regions are i) Butan-1-01, ii) ethanediol, iii) 50 mM saline. Values of E and U for the three materials (after Rachman [3]) are included at the foot of Table I from which the accuracy,
EVANS et al.: DESIGN OF UHF APPLICATOR
219
or otherwise, of the simulation can be assessed. Substitute workpieces for use at room temperature consist of a thin glass sphere 36 mm diameter, filled through a fine hole with one of the chosen liquids. Rachman has verified that the glass sphere, when empty, causes no significant dielectric dissipation. Table I also gives calculated values of tan 6, the power penetration depth D, and a parameter x to be introduced below. For interest, data are added for fat and muscle tissue at physiological temperature from the hyperthermia literature [4].
The heating coeflcient x For field strength El within the workpiece medium, the power dissipated per unit volume is
P
(1) The field El in the workpiece must be related to the field Eo in air, supposed to be uniform before the workpiece is introduced. For a spherical workpiece, Stratton [5, sect. 3.241 gives = U@.
So vector El is parallel to Eo-which will still be the field in air at some distance-and El is uniform throughout the workpiece. We now introduce an EM heating coefficient x defined by
P
=
&.
(3) Thus, x relates power dissipated per unit volume in the workpiece to the external field strength at some distance. To calculate x for the kidney phantom material it is noted that the absolute permittivity required in (2) can be complex, so for a spherical workpiece we have
The heat conduction equation gives
+
~ V ~P = T pcaT/at.
(5)
So for uniform heating, when the product of conductivity and V 'T is negligible, the rate of temperature rise is given by aT/at
=
-xE- ~2 . PC
For preliminary estimates we adopt a value of pC = 3.5 MJ/m3 K, appropriate for muscle tissue [6], and on that basis we calculate from ( 5 ) that 85 W must be dissipated in the kidney phantom 36 mm in diameter for a warming rate of 1 K/s, and pro rata. Using (6) which is independent of phantom volume, the value of Eo required for a warming rate of 1 K/s rises from 25 to 55 kV/m with the change of dielectric parameters over the temperature range from -30" to -10°C.
111. FIELDORIENTATION The use of coefficient x in the previous section is in principle restricted to a spherical body in air where the unperturbed field at some distance away is assumed to be uniform. The same analysis could be aplied to any other spherical surfaces which form boundaries between media with different electrical or thermal properties within the workpiece and this might be a helpful model for the boundary between the cortex and the medulla of the kidney, but not in the vicinity of the ureter which can be expected to be sensitive to overheating (see Fig. 1). Furthermore, closely spaced boundaries will not behave like a single surface isolated in a field which is uniform at distance: the boundaries will react on one another. So to understand the effect of inhomogeneous composition we now consider the tangential and normal E-field components at any small plane area, part of a boundary between two lossy dielectric media within the workpiece. A. Tangential E-jeld component E, Since E,, = Et2, the ratio of the powers dissipated per unit volume is
Thus, the more electrically conductive material is heated more. There is no escaping this conclusion and reference to the data at physiological temperatures in Table I shows why tangential fields at the skin surface are used to heat muscle tissue, in preference to fat, in hyperthermia treat ment; but in our application E, produces a most undesirable effect as follows. Suppose the difference in properties is due to a temperature difference which has arisen by chance within an otherwise uniform medium. The temperature gradient is normal to the isothermal surfaces, which can now be thought of as the boundaries between material of different properties, and E, is the component normal to the temperature gradient. It can be seen in Table I that (below the phase change), the higher temperature region will have the higher conductivity and consequently the higher power dissipation: there is positive feedback causing any initial differences in temperature to be magnified. This was the basic reason for reviewing the properties of various cryoprotectants over the radio and microwave spectrum and, for the present, adopting ECl at 434 MHz as offering the lowest positive temperature coefficient of 0 . Negative values, which would be preferred, have not yet been found below the phase change and consequently tangential fields should be avoided as far as possible. The negative coefficient above the phase change offers some reassurance, but in this temperature range the perfusate could be circulated to improve uniformity.
B. N o m 1 E-Field Component En The boundary condition gives (QI
+ hEI)EnI
= (02
+j ~ d E n 2 .
(8)
,
[81
220
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. 3, MARCH 1992
.., .:
Renal Palvis
Ureter
\
‘\--
J’
I
c
Cross-Section ThFough A Tvpcal Kidney
Fig. 1. Cross section through a typical kidney.
d
Fig. 2. Illustrating approximate relations involving gap width, d , and workpiece dimensions, s.
~~
PERFUsEDTISSUE-pOWER
T/OC Er
E,,
TABLE 11 DEPOSITION RATIOS,f ( T ) / f ( T + 5°C)
-30
-25
-20
-15
Oh7
0.70
0.70 1.60
0.96 2.80
1.06
1.32
-5 0.57
2.90
1.10 1.05
times the phantom dimensions. We can make this assumption without being too restrictive on the meaning of “several,” since any real organ, being irregular in size and shape, will produce dangerously nonuniform fields if parts approach the electrodes too closely. In Fig. 2, the total gap Voltage for an initially Uniform field is ug E Eod; the correct value is somewhat less with a workpiece in place. The total power dissipated in the workpiece is
+5 1.15 1.00
1.0
0.90
E, is the field component normal to the isothermal surface, therefore in the direction of the temperature gradient. E, is tangential to the isothermal surface.
Hence,
w,= XZV,
5 - I a2 + Ja~2I2 p2 u21 a, + jaEl 1 2 ‘
(9)
For perfused tissue and for a difference of properties due solely to local differences in temperature, this ratio will generally be dominated by the value of I e2 / E I 2 , and since E increases with temperature below the phase change the situation is much more stable and is the reverse of that for tangential fields. For normal fields, or fields directed along an existing temperature gradient, more power is delivered to the lower permittivity or lower temperature region. The ratios Of P(T”C)’P(T -k 50c) for perfused tissue, taking account of both U and E values, are given in Table 11, where ratios greater than unity imply more heat to the lower temperature region. There is a strong suggestion from these figures that if the two field components were equal in magnitude in the time average, the situation would be stable, or nearly so, and this can be realised in practice for random orientation of boundary or isothermal surfaces in one plane, by rotation of the E-field in that plane. Rapid reorientation of the E-field to produce equal time-average components on three coordinate axes would be more difficult, but possible. I v . CHOICE OF APPLICATOR The estimate given at the end of Section I1 for the Eo required for a given power dissipation and warming rate can be generalized to show that a large transformation will be required from the source impedance (likely to be 50 fl) to the load impedance which appears across some space where the kidney phantom is placed in the applicator and which can be regarded as a gap between two electrodes setting up the Eo field. Suppose the gap width is several
(10)
where VI is the workpiece volume. The effective load conductance appearing across the gap, due,to dissipation in the workpiece, is therefore GI
*
xVl/d2.
(1 1)
as near the lower limit Taking a value of d = 72 for a phantom 36 mm in diameter, V~ = 25 mL, and using the X-value just below the phase change in Table I, we find GI < - 5 pS or, (200 k 9 - I . Accurate values can be found for a defined applicator geOmetry but the point to be made is that the impedance is high. To transform to impedances of this order from a source supplied via a coaxial feed with a characteristic impedance of 50 fl, a resonant system with its associated stored energy is unavoidable. It is a disadvantage that this implies tuning and a restricted frequency range; on the other hand, the total enclosure of the fields offered by a cavity resonator is very cavity Resonators: Calculated Parameters To the value GI, the conductance due to the workpiece, should be added a value Go, effective at the same gap and representing loss of power WOdue to the surface resistivity of the cavity walls. It is always advantageous to choose cavity materials and geometry to minimise Go, at least to make it much less than GI, after which there should be means to tune the cavity, or vary the frequency of the source, to make the input admittance real, and means to adjust the transformer action so that GI + Go matches the source conductance. The definitions and relationships associated with @values, efficiency, bandwidth, and the
~
22 I
EVANS er a l . : DESIGN OF UHF APPLICATOR
TABLE I11 CALCULATED PARAMETERS FOR 434 MHz RESONANT CAVITYAPPLICATORS
Reentrant Fig 3(b)
Type Dimensions [mm1
h = 150, b = 169 a = 260 d = 60, a = 75 h = 72 See Fig. 3
Mode
e,!lo3
Cylindrical Square Aspect Fig 4.
Cylindrical Pill Box Fig. 4. a = 260
TM 010
h = 520
Spherical Fig 5. r = 300
TE 111
TM 010
11
12
36
36
[M?/mz] Working space [mm]
210
116
51
58 104
60 x 120 diam
72 x 128 diam 520
Q,/ 10' W W O + WI [MQ/m2] Efficiency, y
2.1
3.6
18
39
35
0.81
0.70
fr/Qi[kHz1
210
-AfO,o[kHz]
1770
TM 101 45
( E ; / WO) X
128 diam
X
180 106 high
X
67 110 diam x 106 high
17
19
25
27
28
0.50
0.53
0.58
120
24
26
23
898
131
150
138
Q, calculated for surface resistivity R, = 8.0 mQ per square (duralumin). Q, calculated for 36 mm diam phantom with x = 0.8 mS/m. Working space: region of the empty cavity for fields within 5 % of maximum. f r / Q , : bandwidth as defined in the appendix, with kidney phantom in place. -Af!30: decrease in resonant frequency with rise in phantom temperature from -30" to 0".
tuning range required as the workpiece material changes properties with temperature, can be found in the Appendix. Calculated cavity parameters, and some other factors which might be considered, are now introduced for four simple cavity shapes, resonant near 434 MHz. The basis of the calculations is given in the following paragraphs and numerical results are in Table 111. The Qo for the empty cavity is based on the field equations for the stated mode and a surface resistivity of 8 X Q,appropriate for duralumin (bulk conductivity 2.8 X IO7 S/m). The ratio ( z / W o ) , which gives the field strength in the working volume in the absence of the workpiece, is derived on the same basis. The value of Qo could, in principle, be increased by the factor 1.5 if the walls were silver plated to a depth of more than 3 pm. However, the calculated Q values take no account of losses due to imperfectly conducting joints or other features which interrupt the ideal current flow in practice. The importance of these will be apparent when the measured Q values are given and it is not likely that silver plating would produce any improvement in losses of this kind. The working volume quoted in Table I11 is the region within which the field strength is within 5 % of its maximum value, in the empty cavity. The Q factor with a workpiece in place, Q , , and the ratio E / ( W o W , ) , are based on a spherical workpiece 36 mm in diameter with a value of x = 0.8 mS/m, appropriate for perfused tissue approaching the phase change
+
(see Table I). The efficiency y follows from the two Q values; note that it refers to just below the phase change only. The bandwidthf,/Q, is without reference to the source loading. If the coupling is such that the source is matched at resonance, the half-power points would be at twice this frequency interval. The frequency change -Af!30 is the decrease in resonant frequency estimated as the workpiece rises in temperature from -30" to 0°C. This is no more than an estimate since it is made on the basis of the perturbation theory in Appendix 11, substituting the properties of ECl from Table I. I) Coaxial or Reentrant Cavity: Two different aspect ratios for this geometry are illustrated in Fig. 3. Moreno [7] has given a series of curves relating dimensions and resonant frequencies, and an approximate expression for Q,. Dimensions a and d provide a starting point and values of 75 and 60 mm have been chosen to provide a uniform field sufficient to accommodate a rabbit kidney. For the minimum loss conductance, Go,Moreno favors an aspect such that (h - d ) = (b - a ) , which leads to the other dimensions given in Table 111. The great drawback of this otherwise very attractive design is that the field cannot be reoriented as recommended in Section 111. 2) Cylindrical Cavity: Two modes are sketched in Fig. 4 and the field equations are in standard texts (e.g., [8, sect. 10.61). The TM 010 mode with h considerably less than a is popular as an applicator for the high field on the
222
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. 3. MARCH 1992
+'
4=
Spherical TM101
(a) (b) Fig. 3. (a) Coaxial and (b) reentrant applicator geometries showing E-field lines. I
TMOIO
TElll
631
iI
0800000
Fig. 5. Spherical cavity TM 101 field.
sect. 10.81. It has not been followed up in practice because of the difficulty of construction with ready access to the interior.
V. EXPERIMENTAL EVALUATION OF TE 1 1 1 CYLINDRICAL CAVITYAPPLICATOR Construction tz On the basis of factors discussed in the previous section we have constructed a resonant cylindrical applicator of welded duralumin to the dimensions shown in Fig. 6 . The top and bottom end plates are attached with pull-down toggles which compress an RFI shielding gasket, with round elastomer core, into a square section channel. The radius i T l pipes, 47 mm i.d. in the center of each end plate, have flanges allowing them to be fitted either intemally or ex(a) ternally. They allow access for temperature sensors, both Fig. 4. (a) Square-aspect cylindrical cavity showing TE 1 1 1 field. (b) Pillbox aspect ratio showing TM 010 field. optic fiber and sighting for passive infrared, and (mainly due to that fitted intemally) they shift the resonant frequency of the TM 010 mode far enough from the TE 11 1 z-axis. As a simple case we have included it in Table I11 resonance, so that it is not excited accidentally. The pipes for comparative purposes but it suffers from the same themselves are far below cutoff frequency at 434 MHz: drawback as the reentrant cavity: the field orientation is evanescent fields are estimated to be 50 dB down at the fixed. outside ends and no effect on the resonance has been obHowever, when the height is greater than half the free- served due to objects outside. space wavelength, the TE 1 1 1 mode is especially appealA single feed probe, as shown, was found in practice ing for our application since the field can be rotated in the to excite two resonances close together in frequency: they xy plane. When h = 2a, TE 1 1 1 is degenerate with TM were found to be in two polarizations associated with 010 and this is the cavity design which we have followed slight ellipticity of the cylinder section. To fix the polarup though it is not to be expected in practice that the TM ization, an adjustable tuning rod is fitted diametrically op010 resonance will be exactly coincident with TE 1 1 1 . posite the feed probe. Another set of probe and rod is The empty cavity Q is higher than for the reentrant case, fitted at right angles in the same plane to excite the orbut the light loading imposed by the workpiece (which is thogonal polarization; the coupling between the two has effectively in too large a gap) means that the efficiency is been measured to be below -25 dB. dissapointingly low. The length of the probe is adjusted to match the load There is no significant difference in considering a rect- imposed by the workpiece and the cavity at resonance, to angular or cubical cavity in the equivalent modes, except a coaxial 50 Q source. It is convenient for empirical adquestions of mechanical rigidity and access to the interior. justment with a network analyser to use a standard loading 3) Spherical Cavity: The spherical cavity parameters and the substitute workpiece filled with ethanediol at room are included in Table I11 for academic reasons, as some- temperature has lead us to adopt 50 mm for the probe thing of a limiting case. The TM 101 mode is sketched in length. The tuning rod is of similar length which helps Fig. 5 and the necessary field equations are given in [8, ensure symmetry of the field at the center. Use of an ex-
I
223
EVANS et al.: DESIGN OF UHF APPLICATOR
c
n
TABLE IV MEASURED APPLICATOR PERFORMANCE VERSUS KIDNEY PHANTOM TEMPERATURE gasket m channel
524
i262 mm r a q Cylindrical 434 MHz applicator (not to scale) Fig. 6. Cylindrical 434 MHz applicator used for the measurements reported in Section v.
far been successful.
Basic Parameters Resonant frequencies, input reflection coefficient, and Q values, have been measured on this cavity under a wide variety of intemal loading conditions using an HP 8753B network analyzer and HP 85044A test set, which system allows microprocessor correction of measurements made at the test port against a standard short circuit, an open circuit, and a matched termination. Hard copy output has commonly been as Smith charts in admittance coordinates on an HP7440A plotter. The relationships used to derive Q values, and W ) values are given in the Appendix, and results are in Table IV. The first conclusion is that the measured Qo value for the real cavity falls far short of the calculated value of 36 X lo3 for the ideal cavity. The highest measured value is 20 x lo3, and we can attribute the degradation to the pipes in the end plates, the tuning rod, and the feed probe, which increase the effective wall area and interrupt the ideal current flow. Probably more serious is the gasket joint for the top and bottom end plates since loosening of the fixing toggles with use very soon causes Qo to fall into the range 12 to 15 X lo3. This joint therefore merits further attention: for the time being we have based all efficiency values on Qo = 15 x lo3. The parameter WO)which gives the field strength in the working space, has been measured with an alumina sphere as a perturbing body (E,. = 9.0, radius 9.5 mm, Af = 67 kHz) and using the method outlined in the Appendix, equation (A8). The measured value is 24 MQ/m2 which falls short of the calculated value of 58 MQ/m2 by exactly the same factor as is found for the Qo values, as should be expected. One interpretation of this would be that the feed probe and tuning rod do not significantly affect the central field strength.
(E/
-A f/kHz
em3
P
Y
(reference 438.5 MHz)
15
+0.45
-
493 620
2.3 6.2
-0.46
-0.05
0.85 0.59
765 760 756 753 742 727 707 667 605 538 493 462
8.2 8.2 8.1 8.0 7.0 5.0 3.6 2.5 2.1 2.3 2.8 3.6
+0.08 +0.08 +0.08 +0.07 0.0 -0.15 -0.32 -0.46 -0.52 -0.50 -0.42 -0.30
0.45 0.45 0.46 0.46 0.53 0.67 0.76 0.83 0.86 0.85 0.81 0.76
Butan- 1-01 Ethanediol
z
(E/
T/"C Empty cavity
+5 0 -5 - 10 - 15 -20 -25 -30 -35 -40 -45 -50
y is the fraction of the power supplied which is delivered to the phantom.
Loading Versus Workpiece Temperature In Table IV we summarize the results of an experiment in which the kidney phantom specified in Section I1 was cooled to below -50°C and then placed at the cavity center, well insulated with expanded polystyrene, so that the input port behaviour could be recorded by the network analyzer as the temperature rose slowly over a period of several hours. The temperature was monitored with two optic fiber probes (Luxtron type MIW-2) implanted in the phantom. They avoid any disturbance with the cavity fields and are coupled with the Luxtron 755 instrument for recording. Referring to the results in Table IV it is perhaps surprising, in view of the disappointing value of Qo measured earlier, that the measured efficiency with the kidney phantom at -10°C is so close to the calculated value. The calculated efficiency used a value of x = 0.8 mS/m appropriate to the phase change, which occurs between - 12" and - 10°C for perfused tissue, and between - 10" and -8°C for pure EC1. As nearly as we can tell with the measured data at 5 " intervals, the calculated efficiency of 0.53 should be compared with the measured value of 0.46 and thus there is no cause for complacency about the cavity wall losses. Efficiency in some of the the lower temperature range is satisfactory however, basically due to the higher tan 6 value. With the probe length fixed, as in this experiment at the optimum for an ethanediol workpiece, the loss of available power due to mismatch is not too serious: I p l2 is zero at - 15°C and reaches a maximum of 0.27 at -35°C. Rachman [3, Appendix B] has shown that it should pass through zero again at a lower temperature which we have observed to be about -60°C but with insufficient data to complete another line of Table IV.
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. VOL. 39, NO. 3, MARCH 1992
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In a later paper we shall give experimental results for the rewarming of organ phantoms from - 80°C in this TE 111 cylindrical applicator. Future work will be directed to improvements in efficiency in parallel with biomedical experiments to assess the damage when rewarming viable tissue over the widest possible range of warming rates. APPENDIX I. CAVITYBANDWIDTH, EFFICIENCY, AND FIELD STRENGTH The internal Q factor of a resonant cavity at angular frequency w is defined by (All Q = oU/W where U is the total energy stored in the cavity fields and W is the total power dissipated within. Expressions for Q are given in standard texts for simple cavity shapes where the fields are known analytically, so that U is known and W is calculable from the surface resistivity of the cavity walls and surface currents. In those cases the parameter (%/WO) also, is calculable. Assuming that the input admittance is referred to the “detuned-short-circuit” position, x , on the feed line, then values of Q are derived in practice from measurement of the two frequencies, fa andfb either side of resonance, at which the input susceptance B, = +GI, the input conductance. We then use the relation
Q =fr/Ifa -fbl (see, for example, [8 sect. 10.111). No reference is made to source admittance; i.e., it is not assumed to be matched at resonance, so fa and fb are not in general the “halfpower points.” However, we givef,/Q in Table I11 as an indication of the bandwidth and hence the required precision of tuning. Let the power dissipated in the cavity walls be WOand in the workpiece Wl . Then from measurements of Q with and without the workpiece in place we have
If we compare these two under the condition that, when the workpiece is introduced, the total drive power is increased such that the bulk of the fields are unchanged except for a perturbation in the vicinity of the workpiece, then U and WO are the same in the two cases, the two resonant frequencies w1 and wo, are approximately equal, and the efficiency y, in delivering power to the workpiece is given by Wl WI + WO
y=-=-=-
Qo Qo
QI
GI
GI
+ Go‘
(A4)
The relationship to the gap conductances GI and Go also assumes that the cavity gap voltage is unchanged so this is perhaps less accurate than the relationship to the Q’s in cases where the workpiece occupies a large fraction of the
gap. Calculated values of y can be found for simple cavity shapes where the fields are known, so that Wl and WOare calculable. In practice, values of y are obtained for any cavity shape from measurement of the the two Q values. To find the Eo field in relation to the drive power after the workpiece is introduced (the calculated values given in the lower part of Table 111), it is noted that if the drive power is increased to WO + W,, then the Eo field is the same as in the empty cavity and we have
11. APPLICATION OF PERTURBATION THEORY Later developments of Slater’s original perturbation theorem for resonant cavities can be written AU
-
A K - A G
00
(A61
U
where A w is the increase in resonant frequency U, when the time-average energy stored in H-fields is increased by A G , and in E-fields by A C (see, for example, [8, sect. 10.121). The perturbation is assumed to be sufficiently small that the bulk of the fields, and hence the total energy U is not significantly changed. The first application to be considered here is in subsidiary experiments to determine the E-field strength at any point inside a cavity in terms of the power supplied. Stratton [ 5 , sect. 3.251 has shown that the additional stored energy in an electric field of strength Eo, initially uniform in air, when a small dielectric sphere radius rl is introduced is
We define
where C contains properties of the perturber only. We can put A G = 0; the justification is as follows. The dielectric sphere acquires an electric dipole moment and hence, in an oscillatory Eo field there is, in principle, an associated H field. However there is no near-field component of H and we neglect the far fields: not only are they small but the stored energies of the w 2 / r terms for Eo and H6 (the radiation fields) are equal in magnitude and hence their effects cancel in (A6). There is arguably a small component of A G due to the a ’ / . term for E,, not included in Stratton’s static analysis. So by placing a small sphere of lossless dielectric as a perturbing body at a point within the empty cavity applicator, the Eo field at that point can be derived from a measurement of the increase in resonant frequency. -
_ AU -AUE - WO
U
- CO Eo
Qo
(””) WO
(A9)
EVANS el al.: DESIGN OF UHF APPLICATOR
225
This is the relationship used for the measured value of
%/WO at the workpiece position as given in Section V. The Eo field with the workpiece in place is obtained from this measurement and the two Q’s using (A5). The other application of perturbation theory is more approximate: we wish to know the shift in resonant frequency as the workpiece properties change, and how this compares with the the bandwidth (fb - fa) defined earlier. The tuning range required to remain resonant is estimated from (A7), substituting the changing values of C with changing temperature and recognizing that the workpiece volume is likely to be too large for any degree of accuracy from perturbation theory. If Ah is the increase in the resonant frequency, fr, due to an increase in average electric stored energy A U,with change in properties of the workpiece, then comparison with the bandwidth gives
Ah -=---
If, -fbl
AUI
fr
U
If, -fbl
UA U,
-
W O + WJ‘
Absolute values of frequency shift and bandwidth are given for the different cavities in Table IV, but note the elimination of U from the right hand of (AIO); this shows that there is no advantage in minimizing stored energy in order to ease requirements on tuning.
ACKNOWLEDGMENT We are indebted to the Wellcome Trust for an equipment grant covering the cost of this laboratory work. M. J. Rachmann thanks Peterhouse, Cambridge for a research studentship.
REFERENCES [I] T. P. Marsland, S. Evans, and D. E. Pegg, “Dielectric measure[2]
[3] [4] [5]
ments for the design of an electromagnetic rewarming system,” Cryobiol., vol. 24, pp. 311-323, 1987. A. K. Coffey and P. M. Andrews, “Ultrastructure of kidney preservation: varying the amount of effective osmotic agent in hypertonic preservation solutions,” Transplantation, vol. 35, no. 2, pp. 136142, Feb. 1983. M. J. Rachman, “Electromagnetic rewarming of cryopreserved organs,” Ph.D. dissertation, Univ. Cambridge, England, pp. x + 187, Feb. 1990. S. B. Field and C. Franconi, Physics and Technology of Hyperthermia. Dordrecht: Martinus Nijhoff NATO AS1 Series, 1987. J. A. Stratton, EIectromagnetic Theory. New York: McGraw Hill, 1941.
M. Knudsen and J. Overgaard, “Identification of thermal model for human tissue,” IEEE Trans. Biomed. Eng., vol. BME-33, pp. 477485, May 1986. T. Moreno, Microwave Transmission Design Data. New York: Dover, 1958. S. Ramo, J. R. Whinnery, and T. van Duzer, Fields and Waves in Communications Electronics. New York: Wiley, 1984, 2nd ed. X. Bai and D. E. Pegg, “Thermal property measurements on biological materials at subzero temperatures,” ASME Trans. Biomechan. Eng., 1991. P. S. Ruggera and G. M. Fahy, “Rapid and uniform electromagnetic heating of aqueous cryoprotectant solutions from cryogenic temperatures,” Cryobiol., vol. 27, pp. 465-478, 1990.
S. Evans received the B.Sc. degree in physics from the University of Manchester, Manchester, England, in 1951 and the Ph.D. degree in radio astronomy in 1955. He spent two years with Royal Society I.G.Y., expedition to Halley Bay, Antarctica. Following that he spent two years as a lecturer in physics at the University of Manchester. He was an Assistant Director of Research at Scott Polar Research Institute, Cambridge, on radio echo sounding of glaciers and polar ice masses, and dielectric properties of frozen materials. Since 1972, he has been a lecturer in engineering at the University of Cambridge with special interest in microwaves. He has published over 100 papers in various fields.
Melanie J. Rachman was born in Bulawayo, Zimbabwe, in 1962. She received the B.Sc. degree in physics and the M.Sc. degree in electrical engineering from the University of Cape Town, Capetown, South Africa, in 1983 and 1985, respectively, and the Ph.D. degree from the University of Cambridge, cambridge, England, in 1990. She IS now with McDonald Deltwiler Associates, Vancouver, Canada, analyzing satellite images and SLR.
D. E. Pegg received the degrees in medicine from Kings College London and Westminister Medical School in 1956, 1963, and 1967. He joined the Medical Research Council at their Clinical Research Centre and moved to Cambridge as Head of the MRC Medical Cryobiology Group in 1978. He has published over 200 papers on cryobiology.
