Analysis of Trans-Cutaneous

    Implanted medical devices must often communicate with the outside world, either to program the implant or gather data from it. If the implant is relatively close to the surface, then a simple method of communication is by transformer: A coil built into the implant couples to another coil in an external reader or programmer. A clinician brings the external device close to the implant, so that the two coils form a weakly-coupled transformer. This permits communication in either direction at distances of 2 or 3 inches (3 to 7 cm). Basic ideas related to this form of communication are presented here.
    The situation considered is one involving relatively small amounts of data. One device (one coil) transmits while the other receives and the two devices transmit alternately. For example, the external programmer might send a message telling the implant to go to some prescribed state or mode of operation. The implant might then send back an acknowledgement that it has done so. A further assumption is that signaling is relatively simple, such as on-off keying or pulsing in which the presence of the carrier burst or pulse represents a binary one and its absence represents a binary zero.
    The implant will usually be battery-operated. The external programmer may also be battery operated for convenience or safety. Consequently, the communication should require minimal expenditure of energy. Some ideas are presented for minimizing power consumption -- especially in the implant.

The situation is that of figure 1. Two circular coils -- one built into the programmer and the other built into the implant -- are arranged so that they face each other. Each coil consists of several hundred turns of wire, with the coil radius (r1 or r2) being substantially larger than the coil thickness. The initial analysis assumes that the coils are coaxial and parallel as shown. Later, small misalignments (coils not parallel and axes offset) are considered. The coil at the left, with turns N1 and radius r1 is arbitrarily chosen to be the transmitting coil.

In [1] chapters 11 and 12 deal with mutual inductance of coaxial circular coils. The approximate mutual inductance for the arrangement of figure 1 is

where M0 is the mutual inductance between two single-turn current loops. M0 is given by

When there are multiple turns r1 and r2 become the mean radii. If r1 and r2 are in cm, then f is found from a table in [1] and M0 is in m H. A value kx is also involved in determining f. It is given by

where x is the distance between the planes of the coils. Smaller kxproduces a larger mutual inductance, so that best coupling results when r1 = r2. There are also the not too surprising observations that very small x or (r1+r2) much greater than x improve coupling. There will often be other constraints that prevent r1 = r2 and that prevent r1 or r2 from being much larger than x. Typical values might be r1 = x = 1 inch.

Let V1 = V1(t) = voltage applied to transmit coil and V2 = induced receive voltage. Then

where k is a constant that includes M0, I1 = transmit coil current, L1 = transmit coil self-inductance. Here it has been assumed that the transmit coil resistance is negligible compared to its inductance at frequencies of interest. The data presented in [1] suggests that k is largest for flattened coils. That is, other things being equal, a coil should be shaped like a washer instead of a doughnut. Again, however, there may be other constraints that force us toward the doughnut shape.

The equation for V2 is recognized as the ideal transformer formula when k=1. It suggests that N2/N1 should be made large to get a large received signal. However, if coils transmit to each other alternately, this may not be a good strategy. It may help to tap the coils and drive across only a portion of each coil, while receiving across the full coil.

To get an idea of the magnitudes involved, let r1 = 1 inch (2.54 cm), r2 = 0.5 inch (1.27 cm), and let x vary over a range of several inches. Also, to calculate representative values of V2/V1, assume N1 = N2 = 200. From other sources it can be determined that the self inductance of the transmit coil is L1 = 2.8 mH. M0 is calculated from tables in [1]. And (V2/V1) = N1N2M0/L1. M0 and (V2/V1) versus x are plotted in figure 2.

At larger values of x, M0 and the received voltage drop off as approximately the 3rd power of x. At x = 2 inch, M0 is 1.06 nH. A finite element analysis [2] of this situation also yields 1.06 nH, but varies a few percent as boundary conditions are changed. At x = 2 inch, the predicted gain is V2/V1 = 0.0151. This agrees relatively well with experimental coils.

With minimum "gain" on the order of 0.005 to 0.01, and transmit voltages on the order of 50 to 100 volt, the received voltage will be in the range of 0.25 volt to 1 volt. This is easily detected with just a comparator. However, if a coil is driven with logic level voltages of 3 to 5 volt, the output will be as low as 15 mV and some amplification may be required.

Figure 1 represents an ideal alignment of the two coils. Since one coil is typically held near the other by the clinician, some misalignment of the two coils is inevitable. It is possible to get some idea of the effect of misalignment by using a more complete formula for M0 that is also given in reference [1]. The formula applies when the coil axes are offset from each other and at an angle to each other but still intersect. The formula is very ugly and is not repeated here. However, it was implemented using an Excel [3] spreadsheet. The analysis was applied to the example given above, with x = 2 inch (5.08 cm). The maximum angle is assumed to be 10 degrees and maximum offset is assumed to be equal to the smaller of the two coil radii or 0.5 inch (1.27 cm).

With no offset and maximum angle of 10 degree, the spreadsheet analysis shows that M0 (and therefore V2/V1) drops by only about 1%. With maximum offset and maximum angle, M0 drops by about 13%. Although these calculations are done for just this one set of dimensions, we can probably conclude that misalignment is not likely to cause a gross reduction in output. Misalignment is clearly secondary compared to the effect of separation.

Use of iron or ferrite cores to concentrate or focus magnetic flux might seem reasonable to try to increase V2/V1. We might try the arrangement of figure 3, for example.

It can be shown, however, that self-inductance (L1) increases along with mutual inductance (M). The result is hardly any increase in M/L1 = V2/V1.

Although there is little improvement in gain, there may still be other reasons to use cores. A given low-frequency response can be maintained, for example, with fewer turns.

There are several reasons not to use cores: (1) They are heavy, (2) they are possibly fragile (ferrite), and (3) they take up space that may be needed for other functions. Also, if either coil is part of a tuned circuit, then a core may lead to greater inductance variation and greater difficulty in maintaining tuning.

Rectangular coils or coils of other geometry may be required to satisfy packaging or other constraints. These aren't easily analyzed, except possibly with finite element analysis. If the coils aren't too far from being circular, then the methods and results given here are still valid.

A more complete circuit, including transmit and receive impedances, is illustrated in figure 4. Z2 is any impedance that loads the receive coil. Z1 is any impedance in series with the transmit voltage generator and includes the coil resistance. V2' would typically be applied to a receive comparator or amplifier.

Now there is effectively a voltage divider at both transmitter and receiver, so that the transfer function becomes

It is apparent that for light loading (large Z2) and low source and coil impedance (small Z1) the expression reverts back to the previous one for V2/V1.

In some instances, bandpass filtering is desired. This makes it less likely that stray magnetic fields will influence the receiver. And since the two coils are already present, only the addition of tuning capacitors is required to complete the passive filters. At the transmitter side a series capacitor C1 is added. Then Z1 = R1+1/sC1. Then sL1/(sL1+Z1) becomes sL1/R1. If a capacitor C2 is also used at the receive side to tune out L2, the circuit is as in figure 5.

The expression for Z2 becomes Z2 = R2/(sC2R2+1) and the steady-state gain becomes

If R1 is strictly winding resistance, then R1 is also proportional to N1 and the expression reduces further to

where k1 is a new constant that includes k. This suggests that the steady state gain can be made arbitrarily large, just by increasing R2 or by decreasing N2. However, an additional consideration may be the length of time to build up the received signal. The time constant of, for example, the receive circuit alone is 2C2R2. Since low N2 implies high C2, the higher the value of R2 or the lower the value of N2, the longer the build-up will take. If coils are used alternately to receive and transmit, or if the data communication uses on-off keying of the carrier, then the time for carrier to build up and decay may limit the turn-around time or data rate.

A variation on the tuned circuit approach is to tune the receive coil but not the transmit coil. The transmit coil is just driven by a square-wave burst. Assuming that Z1 is almost zero compared to sL1, the steady-state gain becomes

where k2 = a constant that includes k and use has been made of the fact that L2 is proportional to the square of N2.

The center frequency of the bandpass filter will be approximately

. L can probably be held to within 2%, while capacitors are now commonly available to a tolerance of 1%. This implies a frequency variation of about 1.5% and a frequency mismatch between devices of 3%. This can be excessive for high Q, so that a trimmer capacitor may be needed to accurately set the center frequency. It may also happen that the two coils are dimensionally different; and that there are no off-the-shelf C1 and C2 values that will provide L1C1 = L2C2.

A trimmer capacitor may be a nuisance, especially in the implant. It may be preferred to sacrifice some of the circuit Q (and gain) in favor of looser tuning requirements. For the circuit of figure 5, the circuit Qs are reduced by increasing R1 or decreasing R2.

Note that either coil will have some self-capacitance. Therefore, either coil will have an associated resonant frequency. This is sometimes the motivation for adding more capacitance and making use of the resonance. (That is, if you can't beat 'em, join 'em.) But if you need the highest possible frequency response, it becomes necessary to get rid of C2. This is done with a transimpedance receiver.

The original expression (marked ***) for V2prime/V1prime applies to circuits in which a parasitic capacitance C2 may limit frequency response unless R2 is made very small. In this case it may be best to make R2 almost zero by using a transimpedance connection at the receive coil output, as shown in figure 6. That is, the coil looks into the virtual ground of an opamp.

In this case R2 becomes primarily the resistance of the receive coil. Assuming that sL1 is much larger than Z1, we get

where Iout is the output current, k3 = a constant that includes k, and use has been made of R2 proportional to N2 and L2 proportional to the square of N2.

One method of achieving a pulse of transmit voltage much higher than the supply voltage is to operate L1 like an ignition coil. That is, let current build up in the coil and then interrupt it. If there is no breakdown or clamping of V1 by other components, it is limited only by the parasitic or added capacitance across L1. The transmit voltage will ring at the frequency determined by L1 and C1, and will decay exponentially. A coil and drive circuit are illustrated in figure 7.

The diode is needed to prevent the N-channel MOSFET drain-source diode from clamping the inductor voltage when it swings below ground. It is still needed if an NPN bipolar transistor is used for the drive, since the base-collector junction would otherwise become forward-biased.

Let Ip be the current in L1 before interruption and let C1 be the capacitance across L1. Then, neglecting the exponential decay, the coil voltage will rise to

upon interruption. The coil resistance and supply voltage limit Ip. Assume that the time between pulses is long enough to fully charge the coil and let the supply voltage be Vs. Then the largest that V1 can be (this neglects RDS(ON) of the MOSFET and the diode drop) is

Assuming that Z2 (defined earlier) is much larger than sL2 (defined earlier), the approximate peak pulse at the receiver is

Here, k4 includes k and use is made of R1 proportional to N1 and L1 proportional to the square of N1.

Is there any advantage to tapping the coil and letting current build up in only a portion of it? It turns out that this will not increase V2prime. The current prior to interruption will increase. But because of the corresponding decrease in inductance (for the tapped portion), the stored energy prior to interruption remains the same. There may still be a reason to tap the coil and drive only part of it. For example, the switch that performs the interruption may have easier voltage or current requirements. Suppose that the overall coil is expected to produce 100 volt p-p and that it is tapped to have a 1:2 ratio. Suppose also that the MOSFET switch drives only the tapped portion of the coil. Then, neglecting the supply voltage, the MOSFET will need only a 25 volt rating.

Another possible advantage to tapping the coil and letting current build up in only part of it is decreased charging time. Since coil L decreases as the square of the number of turns and coil R decreases directly as the number of turns, the time constant L/R is reduced.

A potential problem with this method is insufficient damping. It may be necessary to increase damping if the ringing lasts into the next pulse. This can be done by putting a resistor in parallel with the full coil.

Another possible problem with this form of drive is parasitic inductance. That is, there will be some small amount of inductance, including wiring inductance, that is outside of the tank circuit as shown in figure 8.

This will subject the MOSFET to a huge voltage spike when it is turned OFF. This extra inductance is the same as leakage inductance in a transformer and is dealt with by methods explained in various MOSFET application notes.

Note that this method can be particularly wasteful of power. It not only dissipates the stored coil energy. It also heats the coil prior to interruption. To maximize pulse output it is necessary to let the coil charge almost completely (time constant is L1/R1) so that nearly the full supply voltage is across the coil resistance. The power drawn from the supply Vs is derived as follows. The coil current (assuming current build-up in the full coil) is

where R1 includes the winding and switch resistance, tau = time constant = L1/R1, t = time. The instantaneous power drawn from the supply is

Let T = time between pulses. Then assume continuous pulsing and that the inductor charging time is Z time constants. Then average power consumption is

A typical length of time to charge the inductor is 4 time constants. Then Z = 4 and average power is approximately

The tone burst drive is somewhat the opposite of the ignition coil drive discussed previously. Instead of the coil starting out with a large energy and ringing down to zero, it starts out at zero and the ringing gradually builds. A capacitor C1 is placed in series with L1 and the combination is driven with a small periodic voltage at the resonant frequency. As with the ignition coil method, coil voltage can easily be built up to many times the supply voltage. When the receive coil is also resonated at the same frequency, then the ratio of steady-state output to input is as found previously in equation (****). Note that, if both coils are resonated, the build-up must occur in both the transmitting and receiving tank circuits. In some cases the burst may end before the receive voltage reaches steady state. The transient receive voltage for these more complicated situations may be analyzed or simulated using SPICE.

In steady state the energy lost per cycle in the transmit coil just equals the amount being supplied. Reducing the amount of energy lost per cycle increases the steady-state voltage. But it also increases the time to reach the steady-state voltage.

Both the ignition coil and tone burst drive methods intentionally consume power. Next, we consider methods that don't.

An important consideration in battery-powered devices is minimization of power consumption. We see that if the winding resistance of L1 (transmit coil) is zero, then the coil itself dissipates no power. Signaling methods that build up current in the transmit coil can recover this current, so that energy consumption is ideally very low. The circuit of figure 9, for example, draws current out of the supply when switches are as shown (position A) and then puts it back when switches are thrown to the opposite position (position C). The switches are set at position B between pulses. A bipolar voltage pulse is generated, as shown.

The circuit of figure 9 is a simplification. There is usually no way to operate the switches in a precise enough manner that the current integrates to zero. Consequently, some energy is invariably lost. Some form of clamp (such as a zener diode) is placed across the coil to absorb this left-over energy. The coil and switches will also have resistance that contributes additional loss.

When resistance is added to the coil model, then it becomes important to switch the applied voltage quickly compared to the L1/R1 time constant of the coil.

Using this form of drive, it is more difficult to get to the same coil voltages (hundreds of volts) that are possible with the ignition coil or tone-burst methods. Generally, we have to start with a high supply voltage. In battery-operated equipment this implies the use of a DC-DC converter, which may mean additional expense and inefficiency.

The same coil should serve both transmission and reception. Usually the receiver output is just ignored or the receiver is shut OFF during transmission. If the coil is driven with voltages outside of the receive circuit supply rails, then the receive circuit should be appropriately protected. An example of the combined coil, driver, receiver, and protective components (diodes and resistor) is given in figure 10. The switch is closed for transmit and open during receive.

If possible the protocol should be arranged so that the implant talks as little as possible, thus conserving its battery. A "husband-and-wife-speak" approach is desired. We call it this because it is reminiscent of the conversation when a wife wants detailed knowledge of something while the husband is otherwise absorbed. The husband's answers tend to be "yes" and "no" until the totality of information is extracted. (Obviously, to avoid sounding sexist, we hasten to add that the terms wife and husband can be interchanged here.)

When dissipative pulsing is used, each pulse represents a loss of battery energy. If some reduction in data rate is tolerable, then coding can be used to reduce the number of pulses that must be used. That is, the preponderance of data transmitted are zeros or the absence of a pulse. An example is given in the following table.

Original Trio of Bits	Coded Bits
000	000000
001	000001
010	00001
011	0001
100	001
101	01
110	10
111	11

On average this requires 3.75 bits to represent 3 bits; and reduces the number of "1" bits from 12 to 8. If the data isn't entirely random to start with, this may not help. Or else there may be better schemes that make use of the known characteristics of the data. There are limits to the number of consecutive zeros that can be transmitted, because of the need to synchronize. This topic is covered in books on data communication.

A common approach for the overall data comm architecture (programmer and implant) is to move complexity into the programmer where possible. Thus, the implant responses should be terse, as explained above. The implant circuitry should also be simple. It should be designed to transmit a small coil voltage and expect a relatively large receive voltage. The programmer complements this by transmitting a large voltage and expecting a small one.

Any wire near the transmitting coil will develop a small induced voltage. It isn't likely that enough power could ever be induced to cause damage. However, if the susceptible wire happens to be part of a sensor/signal conditioner circuit, this circuit may produce erroneous readings. It is usually not too difficult to simply put distance between the transmit coil and the susceptible wire. Using the example above, the ratio of V2'/V1' for a distance of 10 inch (25 cm) and single-turn receive coil is 1.08 microvolt per volt.

The driven coil will radiate to some extent. The principal frequency involved is the resonant frequency formed between L1 and C1, where C1 is either the coil self-capacitance or an added capacitance. The question is whether the EMI produced and radiated from L1 could be large enough to violate existing emission standards. The most prevalent document governing EMC of medical devices is EN60101-1-2 [4]. This refers to CISPR 11 [5], which specifies emissions beginning at 30 MHz. Since our focus is on much lower frequencies, this probably isn't applicable. The FCC Part 15 [6] defines either the programmer or the implant as an "intentional radiator" and specifies a field strength for frequencies down to 9 kHz. In the range of 9 kHz to 1.705 MHz, at 300 meter the maximum acceptable field strength is 2400/f microvolt/meter, where f is the frequency in kHz.

In [7] an equation for the field strength at a distance from a circular conductor is given. This is a coil of just one turn. Presumably, for a coil of N turns, the field strength is N times as great. The equation for field strength magnitude, suitably modified, is

where N = number turns, I = current, A = coil area in square meter, omega = radian frequency, c = speed of light = 3e8 meter/second, e0 = permittivity of free space = 8.8e-12 farad/meter, d = distance at which field is measured in meter. Using as an example the larger of the two coils described in the example above (radius = 1 inch = 0.0254 meter, N = 200), at d = 300 meter and I = 0.25 amp (typical value), the above equation reduces to

where f is in Hz and E is in microvolt/meter. The acceptable field strength and calculated field strength (by the above equation) are plotted in figure 11. This suggests that the EMI could start to be a problem at around 1 MHz.

Above 1.705 MHz the FCC Part 15 acceptable field strength jumps up to a constant 30 microvolt/meter. But the measurement distance drops to 30 meter. The calculated field strength is already above 10 microvolt/meter at 2 MHz and d = 300 meter. At d = 30 meter it would jump to more than 100 microvolt/meter. So, if nothing in the example coil is changed, the calculated field strength above 1.705 MHz would be much too high.

From the above analysis, the things that can be done to keep emissions in check are:

Unfortunately, the last two choices generally reduce the received signal. If emissions are a concern, then the net effect of operation at higher frequencies is that overall signal levels must be reduced.

Note that, although the FCC Part 15 specifies the electric field component of radiation, the more effective (i.e., worse) component at these frequencies and distances (near-field) is probably the magnetic field component. The magnetic field component can also be calculated by equations given in [7].

Other higher-frequency EMI sources, such as the microcomputer clock oscillator or switching circuits, may need to be suppressed. A convenient way to do this is often a metal enclosure. But, at frequencies of interest, a conductive enclosure can suppress the desired magnetic field [8]. If the enclosure is necessary, a possible compromise is to keep the coil outside and connect to it using EMI-suppressing feedthroughs. Another is to score or break up the shielding so that it is not very effective for the desired magnetic fields, but still suppresses higher-frequency EMI. This may require some experiment.

It is important that there be no conductive loops of radius comparable to r1 or r2 and located near the coils. Such a loop acts as a shorted turn and can greatly reduce the received signal. Another no-no is to use ferrous or other highly permeable materials near the coil. Materials to be avoided are iron, cobalt, and nickel.

The battery is often one of the largest items in the device. To keep the device small, the battery cells inevitably end up close to the coil. Some care must be taken in battery selection and placement because the batteries, themselves, can contain ferromagnetic materials. NICAD batteries, for example, may have a nickel-plated steel case [9].

It may not be entirely possible to avoid ferrous material or a conductive loop near the coil. Some experiments may be necessary to determine their effects. For example, check to see that the output remains about the same, whether the coil is hanging in a free space or placed in the proposed package.

The tissue that surrounds the implant is conductive and will cause some attenuation of signal. The amount of attenuation increases with frequency. It is probably small enough, however, to be insignificant compared to the effects of separation of the two coils.

Although this discussion has been concerned primarily with signaling in only one direction at a time, this is not a fundamental limitation. Many schemes for simultaneous signaling can be envisioned. One that uses separate carrier frequencies is shown in figure 12.

Interference Coupling From Other Inductors

Either the implant or programmer circuit may contain other inductors that could couple interference to the receiving coil. Inductors are frequently used, for example, in DC-DC converters and may normally have currents on the order of an amp or more. There are several steps that can be taken to prevent interference:

1. Design the converter to run at a frequency that is far away from signaling frequencies.

2. Orient the offending inductor so that its axis is at right angles to the receiving coil axis.

3. If possible use an inductor that is made with a ferrite core to constrain its field.

It is possible to build a coil into the printed circuit pattern of a multi-layer printed circuit board. The coil spirals outward, for example, in layer Q. It then spirals back inward in layer Q+1. And so on. Make sure, of course, that the direction of current flow (clockwise, for example) is always the same in each layer. This will probably increase the coil resistance above what can be achieved with copper wire, which will influence the type of drive. It saves the cost of a custom coil, the need to inventory the coil, and the mechanical assembly related to the coil. It may also make the whole device smaller and lighter. If, however, the number of board layers must increase just to do the coil, then you may not save anything.

A frequent problem, at least in the programmer, stems from the fact that most of the time it is not in use. Its circuits are in a SLEEP mode and draw very little current. But when called upon to do some work, it may have to draw an enormous supply current for a short time. Batteries and voltage regulators and other circuit parts tend to be un-cooperative about this. Batteries have internal resistance: A battery that's perfect for the SLEEP mode won't be big enough during communication. And voltage regulators that can supply a lot of current tend to draw a lot even when they aren't supplying it. Components choices are always a compromise between these two situations.

A way around it is to use an ON-OFF switch instead of a SLEEP mode. But marketing considerations may preclude this. (What if your VCR remote control had its own ON-OFF switch?)

An alternative, at least for the battery problem, may be to use an energy caching device. Developed within the past couple of years, these are low-voltage, high-capacitance (typically several farads) capacitors . Representative examples are the PowerCache Ultracapacitor line from Maxwell Technologies [10]. The devices have very low internal resistance and are therefore better suited than a battery to providing a large, short burst of energy. In effect, the battery that is used with one of these caching capacitors can be sized to supply energy rather than power. You have to decide whether the combination of a battery and a caching capacitor is an improvement in terms of size and cost over just a larger battery.

It could be argued that the two coils are actually two antennae and that the information presented here is actually a subset of a larger arena of investigation: that of bio-telemetry using near-field radio communication. This subject is treated in detail in [11]. Our purpose here was to look only at the situation where the two coils are close enough that they can be analyzed as a transformer.

1. Grover, F.W., Inductance Calculations, Working Formulas and Tables", Instrument Society of America, 1946.

4. "Medical Electrical Equipment, Part 1: General Requirements for Safety. Part 2: Collateral Standard: Electromagnetic Compatibility -- Requirements and Tests," EN60601-1-2, Brussels, CEN/CENELEC, 1995.

5. "Limits and Methods of Measurement of Electromagnetic Disturbance Characteristics of Industrial, Scientific, and Medical (ISM) Radio Frequency Equipment," CISPR 11, Geneva, International Special Committee on Radiation Interference, 1990, 1996.

6. Code of Federal Regulations, Title 47, Volume 1, Part 15 --RADIO FREQUENCY DEVICES, 47CFR15, U.S. Government Printing Office. (Federal Communications Commission, 445 12th St. S.W., Washington DC 20554.)

7. White, R.J., and Mardiguian, M., EMI Control Methodology and Procedures, Interference Control Technologies, 1985, Virginia.

8. Ott, H.W., Noise Reduction Techniques in Electronic Systems, 1976, Wiley, chapter 6.

9. Nickel-Cadmium Battery Application Engineering Handbook, 2nd edition, General Electric, 1975.

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