NONLINEAR MODELLING IN BIOMEDICAL APPLICATIONS

USING ANNS

Vančo Litovski and Miona Andrejević Stošović

Faculty of Electronic Engineering, University of Niš, A. Medvedeva 14, 18000 Niš, Serbia

Keywords: Nonlinear modelling, hearing aid, transducer, artificial neural network.

Abstract: During the design of many biomedical prostheses based on electrical and electronic fundamental actions,

simulation is indispensable. It comprises, however, necessity for adequate models to be used. Main

difficulties related to the modelling of such devices is their nonlinearity and dynamic behavior. Here we

report application of recurrent artificial neural network for modelling of a nonlinear two-terminal circuit

equivalent to a specific implantable hearing device. The method is general in the sense that any nonlinear

dynamic two-terminal device or circuit may be modelled in the same way. The model generated was

successfully used for simulation and optimization of a driver (operational amplifier) - transducer ensemble.

That confirms our claim that optimization in the electrical domain should take place in order to achieve best

performance of the hearing aid. It is to be contrasted to the optical methods based on surgery frequently

used.

1 INTRODUCTION

Most of the prostheses that are used nowadays are

based on electrical and/or electronic transducers per-

forming appropriate conversion of electrical signals

into movement or vice-versa. Among these are the

implantable hearing aids (IHA) that are mounted in

the middle ear (Hakansson, 1994) so bypassing the

tympanic membrane. As for example that will de-

monstrate the concepts we intend to implement, Fig.

1a represents a cross section of a part of the ear and

the way how the IHA is mounted. This structure is

known as floating mass transducer (FMT) (Dietz,

T.G., 1997), (Ball G., 1996), (Dazert, S., 2000) as

depicted in Fig. 1b. It consists of a solenoid (coil)

that produces magnetic field forcing the iron core to

move forth-and-back. The movement is limited by

rubber balls that become compressed and produce

repulsive force to limit the amplitude of the displa-

cement. Note that the chamber is in vacuum to avoid

acoustic effects due to air compression and decom-

pression that would arise at the ends of the core. As

an alternative to the FMT one may find TICA

(totally integrated cochlear amplifier) as described in

(Heinrich, B. M., 2005). The proceedings that follow

are not restricted to any specific IHA.

The system may be characterized as two-termi-

nal, electro-magneto-mechanical, dynamic, and non-

linear. The dynamic behaviour comes mainly from

the coil while much of the nonlinearity comes from

the balls (or springs) that are distorted under the

pressure force. One can see from Fig. 1a that this de-

vice is excited by an electronic circuit - driver - that

we here consider is an operational amplifier (OA) si-

tuated at the output of the complex electronic system

that controls the intensity and the frequency charac-

teristic of the signal coming from the microphone.

When designing such a system we may accept

two approaches. One is to consider the electronic

circuit as fixed and to optimize the FMT to get the

desired performance. In the opposite approach, that

will be considered here, we suppose that the FMT

has fixed characteristics while the driver is subject to

optimization.

To perform this we need electrical model, i.e.

voltage-current dependence, of the FMT that will be

used in conjunction with the transistor model exis-

ting in usual electronic simulator. That will allow for

repetitive simulations with output-transistor's featu-

res optimized until optimum is reached.

In this paper we propose a new modelling proce-

dure that results in a closed form model of nonlinear

dynamic two port devices suitable for simulation

application. It is based on implementation of so cal-

led recurrent artificial neural networks (ANN). We

will also present the results obtained after one step

115

Litovski V. and Andrejevi

´

c Stošovi

´

c M. (2008).

NONLINEAR MODELLING IN BIOMEDICAL APPLICATIONS USING ANNS.

In Proceedings of the First International Conference on Biomedical Electronics and Devices, pages 115-118

DOI: 10.5220/0001055801150118

Copyright

c

SciTePress

of driver optimization that represent a serious impro-

vement in the system's high-frequency characteristic.

The paper is organized in the following way. We

first discuss the problem of electronic modelling.

After that we introduce the ANN for implementation

of the black-box modelling concept. Follows the

implementation and the results obtained.

a)

b)

Figure 1: a) Cross section of the ear showing the implant

mounted on the incus, and b) the inner structure of the

implant. (Photographs taken from Symphonix Devices

marketing material).

2 ELECTRONIC DEVICE

MODELLING

As mentioned above, we are looking for the current-

voltage characteristic of the device under conside-

ration expressed by a set of mathematical expressi-

ons. The following difficulties are encountered when

generating a model of nonlinear dynamic devices:

choice of approximation function

choice of the excitation signal

To achieve this, two approaches are implemen-

ted (Chua, L., 1975).

a. Physical approach

To implement this approach one needs to understand

physical processes in the component or system.

Advantages of this approach are: the procedure is

understandable, and there exists the correspondence

between the physical and technological quantities

and model parameters.

There are no disadvantages of the physical ap-

proach, but there is a problem when we do not

understand the whole physics of the component, or

when we are not aware of all the effects influencing

the component including parasitics.

b. Black box approach

When using this concept, the characteristics of the

modelling object have to be measured first, and

then approximated using functions that fulfill the re-

quirements imposed by the method for equation

formulation implemented within the simulator.

Advantage of the black-box approach is getting a

perfect model obtained with no need to fully know

and understand the mechanisms behind the compo-

nent’s operation. This method is specially conve-

nient for sensors and actuators modelling, because

the price of modelling is very low.

Disadvantages related to this approach are:

Difficult choice of approximation function (which

function is the most convenient?)

The model application is limited only to the con-

ditions under which the measurement was done,

referring to the signals (amplitudes, frequencies,

wave forms) and ambient (temperature, brightness

and so on).

A special problem is the choice of the test signals

needed for establishing the device properties by

measurements.

There is no correspondence between physical and

technological process parameters and model para-

meters.

Having in mind that the ambient and signal con-

ditions for operation of the transducer under consi-

deration are well established, in order to apply this

method, we will need to find appropriate approxi-

mants. That will be ANNs.

3 ANNS AND NETWORK

MODELLING

Artificial neural network is (Hecht-Nielsen, R.,

1989.):

A set of mutually coupled computational opera-

tors with specific topology and computational po-

tential, and

algorithm for determining the operator coeffici-

ents (i.e. learning).

ANNs are considered to be universal approxima-

tors, meaning that ANN can interpolate any function

BIODEVICES 2008 - International Conference on Biomedical Electronics and Devices

116

(Scarselli, F., 1998). It is the motive for using ANNs

in modelling in black-box approach. They solve one

of the basic problems: choice of approximation func-

tion. To shorten the explanations we refer to (Hecht-

Nielsen, R., 1989) for detailed explanation of the

ANN’s structure and the properties of the processing

elements.

Feed-forward ANNs were successfully used for

many modelling applications the first being the mo-

delling of the MOS transistor (Litovski, V., 1992).

In (Litovski, V., 1997) a magnet with moving

armature was modelled for the first time by ANNs.

That, however, having no memory properties, is not

convenient for modelling of dynamic circuits and

systems. In order to introduce the memory property

a structure depicted in Fig. 2 has to be used. It is

time a delayed recurrent ANN.

Dt

ANN

y

n

y

n-

1

y

n-

2

x

n-

2

x

n-

1

x

n

x

n

Dt

Dt

Dt

Figure 2: A time delayed recurrent ANN.

The learning procedures for such a network in-

cluding choice of its complexity may be found in

(Bernieri, A., 1994.).

Figure 3: The exciting signal used for modelling.

To capture the dynamic properties of the system

to be modelled and its nonlinearities by measure-

ment, we propose the chirp signal depicted in Fig. 3.

It is a constant amplitude linearly frequency modu-

lated signal. The frequency interval is to be chosen

so that to cover the complete frequency characteris-

tic of the device while the amplitude is supposed to

be large enough to capture all relevant nonlineari-

ties.

To create the neural model of the device under

consideration, after measurement, samples from the

time domain response of the devices are used to train

the ANN, as described in (Andrejević, M., 2002)

and

(Andrejević, M., 2003). After training the ANN is

supposed to capture all electrical properties of the

device seen from its terminals.

4 IMPLEMENTATION EXAMPLE

In order to demonstrate the method, instead of using

a specific device, we propose a nonlinear dynamic

electronic circuit (NDEC) as depicted in Fig. 4.

1

1

1

3

2

2

2

Figure 4: Nonlinear dynamic two terminal circuit.

Figure 5: The static characteristic of the NDEC.

Its static characteristic is depicted in Fig. 5, while

Fig. 6 represents its response to a chirp signal. After

extracting the envelope one obtains the frequency

response of the circuit as depicted in Fig. 7.

Figure 6: Time domain response of the test circuit.

Samples of the response from Fig. 6 were used to

train the ANN in the time domain. Its response after

training is exactly the same as the response of the

original NDEC and is drawn in Fig. 7 overlapped

with the frequency response of the original circuit.

NONLINEAR MODELLING IN BIOMEDICAL APPLICATIONS USING ANNS

117

That was used to load an OA supposed to drive

the NDEC. The overall response of the driver-trans-

ducer ensemble is depicted in Fig. 8. This result is

by itself an important one because it shows the abi-

lity of simulation of the NDEC in every envi-

ronment.

To go further we redesigned (only one iteration)

the output part of the OA in order to improve the

frequency response of the ensemble. The result of

the new design is depicted in Fig. 9. representing a

full success.

Figure 7: Frequency characteristic of the element being

modelled (envelope of the time response), and Frequency

characteristic of the model.

Figure 8: Frequency characteristic of the response of the

OA loaded by the NDEC.

5 CONCLUSIONS

Figure 9: Frequency characteristic of the improved OA

loaded by the NDEC.

A procedure for modelling nonlinear dynamic

two-terminal circuits equivalent to IHAs is

described. It enables complete characterization of

the device and, in the same time, simulation and

optimization of the driving circuitry. That, we

consider, is more effective way for characterization

of the device in comparison with optical methods,

not to mention the optimization possibilities.

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