In biomedical implant field, a transcutanious connection is often used by transferring the radio frequency (RF) power between coupled coils. The DC supply systems without material connection and the data transmitters used in the case of implanted biomedical devices like a cochlear implant, can be well dimensioned by taking into account the power attenuation by both transfer coils misalignment and biological tissue absorption. In this context, we present an optimal study of a DC supply circuit which takes into account these different power attenuation aspects. Practical measurements are done to confirm the theoretical calculations.
Keywords: Biological tissue, misalignment coils, power supply by external field, transmission factor. I. Introduction
In order to communicate with the implanted electronic circuits in the biomedical field, a system of an external transmitter coil coupled with an implanted receiver coil is used. Often, the coil’s system is also used to give directly the power supply for miniaturized implant like cochlear implant, from rectifying the electromagnetic wave, without using accumulators [1], [2], [3], [4], [5]. So, in data communication with implant or in DC current supply of this one by external field, an effective transfer of RF energy is required. This ensures to the implant a sufficient supply power and a better signal on noise or small error rate of the received data.
The analysis of RF power transfer between a pair of coupled coils enables us to evaluate the really received power. The RF power transmission factors under both cases of biological tissue absorption [6] and transfer coils misalignment [7], are considered. An optimal transfer coils system design for a cochlear implant is presented. II. Principle and constraints
The power supply system by external field of the cochlear implant uses two RF energy transfer coils as in figure 1. RF energy is amplified before applying it to the tuned primary coil. The implanted secondary, also tuned, is followed by a fast rectifier D, a filtering capacity C0 with minimum losses, and a Zener diode limiting the DC voltage V0 obtained.
Figure 1: Principle of transcutanious power supply by radio waves
The choice of the coils L1 and L2 is limited by [8]: - The implantation site: temporal bone (behind the ear), - Anatomical constraints:
Typical radius of the implanted coil : 12.5 mm,
Maximum distance of separation between transfer coils: 10 mm.
An electromagnetic field frequency between 1 and 3 MHz, presents a minimum of RF absorption by biological tissues [4], with ensuring a miniaturization of implanted electronic circuits.
III. Optimal Mutual Inductance and Misalignment Tolerance
Figure 2: Coupled coils with combined misalignment.
The C1 and C2 circular coils have respectively N1 spires with radius a, and N2 spires with radius b. The coils are separated with a longitudinal distance d. The analyse uses the spherical and cartesian coordinates.
The mutual inductance is used to evaluate the induced voltage in the receiving coil, and consequently the available power for the implant. The mutual inductance coefficient is [7]:
2 0 2 / 3 2 10
cos
b
cos
d
b
)
k
(
S
a
b
N
N
2
M
(1) Where
is the angle which forms any point of C2 coil relatively to his center P. The function S(k) is given by :
E
,
k
k
2
k
,
F
k
k
2
k
S
2 2 (2)where
F
2,
k
andE
2,
k
are called elliptic integral of 1st and 2nd kind [9], with parameter k :
2
2cos
sin
b
d
b
a
b
a
4
k
(3)and bφ, the quantity :
2
2sin
b
cos
cos
b
b
(4)In case without misalignment
(
0
)
, we have bφ = b, and k becomes also a constant: k=k0. The resolving of M is given, as in [10], by:
M
0
0N
1N
2a
b
S
(
k
0)
(5) The power transmission factor FM of RF signal under the misalignment coils state, is the ratio of received powers by the implant in the cases of aligned and not aligned coils. So, we obtain [7]:
2 2 0 2 / 3 0 2 2 2 0M
cos
b
cos
d
b
)
k
(
S
k
S
4
b
M
M
F
(6) This formula gives the power transmission factor due to a combined misalignment in translation and rotation of the radio frequency transfer coils.Figure 3: Normalised mutual induction versus primary coil radius a
Expression (1) also enables us to deduce the misalignment tolerance of the two coils, for a relative reduction of 10 % in mutual inductance M from its maximum value M0. The obtained curves in figure 4 (a) and (b), give the alignment range until M=9.6 nH :
- Axial range: = 0.37 a = 6.6 mm, - Angular range: = 3/16 = 33.75°.
Figure 4: Normalised mutual induction versus angular (a) and axial (b) misalignment
But for previous misalignments combined together, resulting mutual inductance is related to their directions, as in figure 5 (a) and (b):
- and of same signs: M = 11.7 nH, there is an increase of 9.3 % due to a partial compensation of the two misalignment effects.
Figure 5: Mutual M versus lateral misalignment with Psi > 0 (a), and Psi < 0 (b)
For these two cases, the average value of M remains approximately equal to 9.6 nH, and the power transmission factor is then FM = 45 %.
IV. Loss due to biological tissue and total transmission factor
In the case of the cochlear implant, the biological tissue separating the two transfer coils is made in generally of skin, fatness, blood, and muscle, in a heterogeneous way. We suppose that the tissue is made of these four tissue layers in equal thicknesses d0, along a maximum distance of d = 4d0 = 1cm, as in figure 6.
Figure 6: Separation of the transfer coils by biological tissue
The biological tissue is defined by its parameters of permittivity , conductivity and permeability of vacuum 0.
The relative permittivities 0
and0
, with absolute permittivity 0 =8,8·10 -12F/m, are often indirectly measured by using RF impedance bridges and are provided into tables as function of the frequency ω [11], [12], [13].
In addition, the electromagnetic wave propagates in the biological tissue under attenuation constant , and phase constant [6]:
1
tg
1
2
2 0
(7)
1
tg
1
2
2 0
(8)
The losses of the medium are represented by the tangent of loss [14].
Blood `(f) = 10 .f – 0,1.f + 83,83 ``(f) = 0,0025.f – 1,9.f + 381,5 Muscle `(f) = 18.10-4
.f2 – 0,57.f + 115,26 ``(f) = 0,2.f2 – 30.f + 1380
Propagation wave constants adopted in the biological tissue model, are calculated in table 2.
Table 2: Propagation wave constants in biological tissue
(Np/m) (rad/m)
0- air 0 0,06
1- skin 0,59 0,81
2- fatness 0,16 0,28
3- blood 0,77 0,96
4- muscle 1,53 1,67
The transmission factor of the electromagnetic wave power, is FT = 8 %, after propagating through one centimetre of biological tissue separating the two transfer coils. For an input power pi, and taking in account the transmission factor FM = 45 %, calculated under a simultaneous misalignment of the coils (approximately =7mm and =30°, estimated to be maximum in the case of cochlear implant), the power reaching the implant is Po = FMFT Pi, with FMFT =3.6 %.
V. Optimal calculation of the tuned circuits
The simplified equivalent circuit of figure 1 is given in figure 7, where R represents the parallel load of the secondary coil.
Figure 7: Equivalent circuit of power supply by field
In a test circuit, copper wire of diameter 0.2mm is used to realize the transfer coils. Tables give the resistance of the wire versus its length, its diameter, and the frequency of use [15]. So, the serial resistance at 2 MHz, of a coil with n spires of diameter d, is: r = 1,035.πd.n.
A self induction is proportional to the square of the spires number, L = α n2. Coils are realised with found dimensions: - External coil L1 with radius a =18mm
- Internal coil L2 with radius b = 12.5mm.
It is more convenient to use the serial representation for both tuned circuits on ω0, as illustrated by figure 8. The resistance of load in serial mode becomes equal to RL = R / QS
2
, where QS = R / L2ω0 is the quality coefficient of the secondary loaded by R.
Figure 8: Serial representation of the tuned circuits
So:
R
L
R
2 0 2 L
(11) By using effective voltages and currents, the power developed at secondary coil is:22 0 2 L 2 2 2 2
i
jC
1
R
r
i
.
v
P
(12) Thepower delivered to the load, is:
2 0 2 L 2 L 2 2 L
0
.
P
jC
1
R
r
R
i
.
R
P
(13) Theequation system of voltages at coils is:
2 0 1
0 1
1
jL
.
i
jM
.
i
v
(14)
2 L 2 0
2 2 0 2 L 2 1 0 2 0 22
.
i
r
R
jL
.
i
jC
1
R
r
i
.
jM
i
.
jL
v
(15)The relation between currents is then:
1
L 2
0
2
.
i
R
r
jM
i
(16) So:
1L 2 2 0 0 1
1
.
i
R
r
M
jL
v
(17) The loadof the secondary coil, taken back in series with the primary coil, is:
L 2 2 0 pR
r
M
R
(18)The quality coefficient of the loaded primary coil becomes:
Qp = L1ω0 / (Rp + r1) (19) The load taken back in parallel with the primary coil is then:
Rc = Qp 2
(Rp+r1) = L1 2ω
0 2
L 2 0 2 L 2 0 p 0 2 1 2 2 p 2 1 2
R
r
jC
R
r
M
R
jC
i
i
i
R
v
P
P
(23)The ratio between source power and the power arriving to the load, expresses the power efficiency of the DC supply by external field:
p 1 L 2 p L i 1 1 2 2 0 i 0R
r
.
R
r
R
.
R
P
P
P
P
P
P
P
P
(24) By introducingthe quality coefficients of the two no loaded coils, Q1=L1ω0 / r1, and Q2=L2ω0 / r2, as well as expression (11), we obtain:
2 0 2 2 2 2 2 1 2 2 2 2 2 2 2 0 2M
.
R
r
.
Q
R
r
r
.
r
.
Q
R
r
.
Q
.
M
.
R
(25)The power efficiency of the transfer coils is a multivariable function which can be optimized by annulling its total differential: d = 0, or annulling all its partial derivatives. By writing M = N.M0, where N = N1.N2, we
note that:
0
N
; and
0
r
1
.
So we annul the derivatives relatively to the other variables which remain r2 and Q2. These two variables are attached together, and will be optimized relatively to one of them, so:
2 2 2 2 2 2
Q
1
.
r
R
Q
0
)
Q
(
(26) With coefficient:
2 1 0
r
r
M
Q
(27) So the optimal power efficiency is:2 2 opt
Q
1
1
Q
(28) By takingaccount the transmission factor of the channel, the final efficiency becomes:
η = P0 / Pi = ηopt. FMFT (29) For a necessary power Po at the implant, the required input power is:
2
2 2 T M 0 i
Q
Q
1
1
F
F
P
P
(30)
21 2 0 0 2 2
r
a
5
.
6
n
M
n
Q
in form of k0 n1 (31) In addition, if Vc indicates the amplitude of the amplified wave and available at the primary coil, figure 7, the resistance Rc of load taken back to the primary coil can be written :
21 0 1 0
2 c T D 0 i 2 c c
n
k
1
1
n
P
2
V
F
F
k
P
2
V
R
in form of
21 0 1 1
n
k
1
1
n
k
(32) Howeverthe expression (20), can be written :
2 L
1 2 0 0 2
3 1 2 0 1 c
r
R
n
M
n
a
5
.
6
n
R
in form of1 4 3
3 1 2
n
k
k
n
k
(33) Theequality between the two expressions of Rc, gives an equation of the sixth degree in n1: k12k32+ 2k12k3k4 n1 + (k12k42 – 4k1k2k3) n12 –2k1k2(k0k3 + 2k4)n13 –2k0k1k2k4 n14 + k02k22n16= 0
A realised program, allows the choice and calculation of the various quantities, versus the output power at the secondary coil. For example, by limiting the input power Pi available at the primary coil to 0.44 W, this allows an output power Po at the secondary of 11mW (so 2.2mA under 5V limited by zener diode). The amplified peak voltage of RF wave at the primary, is fixed at Vc = 10V.
Figure 9: Power at the primary coil versus power at the secondary coil
Figure 11: Supply voltage of the implant versus angular misalignment (a) and axial misalignment (b)
In the case of a combined misalignment, for example: = 5 mm, = 10°, we had confirmation of an increase in the output voltage (towards 6V) when misalignments were done in the same direction, and of a reduction (to 5.4V) when these same misalignments were done in opposite directions.
VII. Conclusion
In order to stabilize the efficiency of RF connection in presence of biological tissue absorption and possibly misalignment coils, it is necessary to satisfy a good tolerance in coils misalignment and take into account the nature and thickness of the biological tissue. This was considered in our calculation of a DC supply of the cochlear implant by external field. An optimal calculation gives the number of spires and their diameter for the transmitter coil, according to imposed dimensions of the implanted receiver coil. Our previsions are confirmed by practical measurements done on the tuned circuits of the power supply system, when realised. With absence of equivalent gel to replace the biological tissue, the maximum calculated in misalignment tolerance of the transfer coils, caused a fall in voltage from 6 to 5 V at the loaded secondary coil. It is practically acceptable, because not able to deteriorate the implanted receptor work.
For a combined misalignments, = 5 mm, = 10°, the misalignment directions cause a relative variation of 10% in continuous voltage obtained at the secondary coil.
REFERENCES
[1] M. SOMA, D.C. GALBRAITH, and R.L. WHITE. Radio-frequency coils in implantable devices: misalignment analysis and design procedure, IEEE trans. on biomedical eng., 4, 34 (1987).
[2] W.H. KO, S.P. LIANG, and C.D.F. FUNG. Design of radio-frequency powered coils for implant instruments, med. & biol. eng. & computing, 15:634-640 (1977).
[3] F.C. FLACK, E.D. JAMES, and D.M. SCHLAPP. Mutual inductance of air-cored coils: effect on design of radio-frequency coupled implants, Pergamon press, med. & biol. eng. & computing, 9:79-85 (1971).
[4] D. JEUTTER. Telemetry of biomedical signals, medical & life sciences eng., 13: 131-145 (1994).
[5] M. MEHENNI, M. ABIGNOLI, E. YVROUD, and C. MARCHAL. Feeding by external electromagnetic field for telemetering: design of an experimental bank, Ed. RBM (France), 2, vol.14 (1992).
[6] N. BATEL, M. MEHENNI, S. KOUADIK. Attenuation in transferred RF power to a biomedical implant due to the absorption of biological tissue, Proceedings of world academy of science, engineering and technology, 10:165-168 (2005).
[7] N. BATEL, M. MEHENNI, L. DEKAR. Attenuation in transferred RF power to a biomedical implant due to the misalignment coils, Proceedings of world academy of science, engineering and technology, 10: 160-164 (2005).
[9] M. CHOSSAT. Memorandum of mathematics, 1977, Ed. Dunod. [10] F.E. TERMAN. Radio engineers handbook, 1943, Mac Graw-Hill.
[11] M.A. STUCHLY, S.S. STUCHLY. Dielectric properties of biological substances― tabulated, newspaper of microwave power,
1(15):19-26 (1980).
[12] H.P. SCHWAN. Electrical and acoustic properties of biological materials and biomedical applications, IEEE trans. biomedical eng., 12(31):872-878 (1984).
[13] H.P. SCHWAN, K.R. FOSTER. RF-field interactions with biological systems: electrical properties and biophysical mechanisms, proceedings of the IEEE, 1, vol. 68, pp. 104-113 (1980).
