# MEG source localization using an MLP with a distributed output representation

**ABSTRACT** We present a system that takes realistic magnetoencephalographic (MEG) signals and localizes a single dipole to reasonable accuracy in real time. At its heart is a multilayer perceptron (MLP) which takes the sensor measurements as inputs, uses one hidden layer, and generates as outputs the amplitudes of receptive fields holding a distributed representation of the dipole location. We trained this Soft-MLP on dipolar sources with real brain noise and converted the network's output into an explicit Cartesian coordinate representation of the dipole location using two different decoding strategies. The proposed Soft-MLPs are much more accurate than previous networks which output source locations in Cartesian coordinates. Hybrid Soft-MLP-start-LM systems, in which the Soft-MLP output initializes Levenberg-Marquardt, retained their accuracy of 0.28 cm with a decrease in computation time from 36 ms to 30 ms. We apply the Soft-MLP localizer to real MEG data separated by a blind source separation algorithm, and compare the Soft-NMP dipole locations to those of a conventional system.

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**ABSTRACT:**Fitting an equivalent current dipole (ECD) to magnetoencephalography (MEG) data is a widely used method for analyzing MEG data, especially in clinical applications. However, as is well known, the iterative fitting algorithms routinely employed can converge on a local minima far from the best fit. While a host of fitting algorithms have been proposed to remedy this problem, the simple exhaustive search optimization algorithm has not been considered in the literature — possibly because it is assumed to be too slow for routine use. Taking advantage of the speed of modern computers, it is demonstrated that using exhaustive search to fit the parameters of a single ECD to 151 MEG channels yields both robust and reproducible fits within reasonable computation times. On a high end personal computer, with a 2 mm grid spacing over the head, exhaustive search can fit 450 ECD's per hour with only an additional 5 min spent on calculating the lead fields. As the algorithm is fully automatic, it is very useful when the goal is to detect ECD's in a large dataset. Also, an interpreter can be provided with parameters from the ECD that fits for all latencies after stimulus, allowing a more informed decision of which latency to use for further analysis.International Congress Series 06/2007; 1300:121-124. - SourceAvailable from: Barak A. Pearlmutter
- SourceAvailable from: Barak A. Pearlmutter[Show abstract] [Hide abstract]

**ABSTRACT:**The match between the physics of MEG and the assumptions of the most well developed blind source separation (BSS) algorithms (unknown instantaneous linear mixing process, many sensors compared to expected recoverable sources, large data limit) have tempted researchers to apply these algorithms to MEG data. We review some of these efforts, with particular emphasis on our own work.Proc SPIE 01/2003; 5102:129-134.

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786IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 6, JUNE 2003

MEG Source Localization Using an MLP With a

Distributed Output Representation

Sung Chan Jun*, Barak A. Pearlmutter, and Guido Nolte

Abstract—We present a system that takes realistic magnetoencephalo-

graphic (MEG) signals and localizes a single dipole to reasonable accuracy

in real time. At its heart is a multilayer perceptron (MLP) which takes

the sensor measurements as inputs, uses one hidden layer, and generates

as outputs the amplitudes of receptive fields holding a distributed rep-

resentation of the dipole location. We trained this Soft-MLP on dipolar

sources with real brain noise and converted the network’s output into an

explicit Cartesian coordinate representation of the dipole location using

two different decoding strategies. The proposed Soft-MLPs are much

more accurate than previous networks which output source locations in

Cartesian coordinates. Hybrid Soft-MLP-start-LM systems, in which

the Soft-MLP output initializes Levenberg–Marquardt, retained their

accuracy of 0.28 cm with a decrease in computation time from 36 ms to

30 ms. We apply the Soft-MLP localizer to real MEG data separated by

a blind source separation algorithm, and compare the Soft-MLP dipole

locations to those of a conventional system.

Index Terms—Distributed representation, magnetoencephalography,

multilayer perceptron, source localization.

I. INTRODUCTION

Source localization using electroencephalography (EEG) and

magnetoencephalography (MEG) identifies brain regions that emit

detectable electromagnetic signals. The multilayer perceptron [1], a

particular sort of universal approximator, has been recently used to

build fast dipole localizers [2], [3, and reference therein]. All this

work used multilayer perceptrons (MLPs) whose outputs represented

source location or dipole moment vectors in Cartesian coordinates—a

representation which might be expected to limit their performance and

robustness.

We propose an MLP with a distributed representation1of the dipole

location. Our Soft-MLP network, which uses that representation, lo-

calizes a dipole to reasonable accuracy in real time from MEG signals

contaminated by considerable noise. Its output consists of the ampli-

tudes of Gaussian receptive fields evenly distributed within a spherical

head model, which taken together represent the dipole location. Like

the Cartesian representation, this does not confine the dipole to a finite

set of grid locations; but unlike the Cartesian representation, it is natu-

rally tolerant to noise far from the region of interest.

ManuscriptreceivedJune3,2002;revisedDecember15,2002.Thisworkwas

supported by the National Science Foundation (NSF) under CAREER award

97-02-311, the MIND Institute, and the NEC Research Institute. Asterisk indi-

cates corresponding author.

*S. C. Jun is with the Biological & Quantum Physics Group, MS-D454,

Los Alamos National Laboratory, Los Alamos, NM 87545 USA (e-mail:

jschan@lanl.gov)

B. A. Pearlmutter is with the Hamilton Institute, NUI Maynooth, Maynooth,

Co. Kildare, Ireland (e-mail: barak@cs.may.ie).

G. Nolte is with the Human Motor Control Section, Medical Neu-

rology Branch, National Institute of Neurological Disorders and Stroke,

National Institutes of Health, Bethesda, MD 20892-1428 USA (e-mail:

NolteG@ninds.nih.gov).

Digital Object Identifier 10.1109/TBME.2003.812154

1The term distributed representation is standard in neural networks [4].

II. METHOD

A. Data

The synthetic data used in our experiments consisted of corre-

sponding pairs of dipole locations and sensor activations, as generated

by a forward model. Given a dipole location and a set of sensor

activations, the minimum error dipole moment can be calculated

analytically [5]. Therefore, although the dipoles used in generating the

data set have both location and moment, we discarded the moment in

all the experiments below.2

We made two datasets, one for training and the other for testing.

Dipoles were drawn uniformly from truncated spherical regions [3,

Fig. 1]. Their moments were drawn uniformly from vectors of strength

? ??? nA ? m. The corresponding sensor activations were calculated

by adding the results of a forward model and a noise model. To make

sure the network does not inappropriately project external sources into

the brain,3and allow the network to interpolate rather than extrapo-

late, thus improving performance, the training set used dipoles from

the larger region, while to better approximate field conditions the test

set contained only dipoles from the smaller inner region. We used the

sensor geometry of a 4-D Neuroimaging Neuromag-122 whole-head

MEG system [7],4and an analytic forward model of quasistatic elec-

tromagnetic propagation in a spherical head [3, Section 2.1].

In order to properly compare the performance of various localizers,

we need a dataset for which we know the ground truth, but which con-

tains the sorts of noise encountered in actual MEG recordings. To this

end, we collected real brain noise from unaveraged MEG recordings

(task involving abrupt visual stimulation and subsequent brief motor

output and audio feedback, two right-handed myopic middle-aged fe-

male subjects, analog bandpass filter 0.03–100 Hz) during periods far

fromthestimulusorresponse.Thisnoisehadasquarerootmeansquare

(RMS) sensor reading of ??? ?? ? ??? fT?cm. We measured the

signal-to-noise ratio (SNR) of a dataset using the ratios of the powers

in the signal and noise, SNR (in decibels) ? ????????????, where

??is the RMS sensor reading from the dipole.

B. Soft-MLP Structure

The Soft-MLP charged with approximating the inverse mapping had

an input layer of 122 units, one for each sensor; one hidden layer with

? units; and an output layer of ? ? ??? units representing the am-

plitudes of three-dimensional Gaussian receptive fields in the training

region of the head model. The target output representation of a dipole

at location ? was the ?-dimensional (?-D) vector ???? defined by

????? ? ??????? ? ?????????where ?? is the center of Gaussian

receptive field ? and ? is the length scale of the receptive fields. The re-

ceptive field centers ??were evenly distributed with a spacing of 3 cm,

and we set ? ? ??? cm. These parameters were determined empiri-

cally.Withthese,? ? ???receptivefieldsservedtocoverthetraining

region.

2We experimented with a dataset containing as targets both the location and

moment of each dipole, and despite the increased generalization expected for

multitask training [6], we found no decrease in localization error. Typically, an

accurate estimate of the location is much more important than of the moment

direction or strength. We also found that networks trained without a moment

target to be more robust.

3This can easily occur in practice, for instance when the head position is in-

correctly measured. This is a condition we would like our system to note, rather

than silently projecting external dipoles into the region it believes to be occu-

pied by the brain.

4This MEG system has 61 pairs of first-order planar gradiometers.

0018-9294/03$17.00 © 2003 IEEE

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 6, JUNE 2003787

TABLE I

DISTRIBUTION OF SNR FOR THE 4500 TESTING PATTERNS

The output units had linear activation functions,5while to accel-

erate training the hidden units had hyperbolic tangent activation func-

tions [8]. Adjacent layers were fully connected, and there were no

cut-through connections. Input data were usually preprocessed to im-

prove the performance [2], and here the 122 MEG sensor activation in-

putswerescaledtoanRMSvalueof0.5.Thenetworkweights,?,were

initialized with uniformly distributed random values between ?0.1.

Backpropagation was used to calculate the gradient of the sum squared

error [1], which in turn was used for online stochastic gradient decent

optimization with an empirically chosen descent rate ?, as in ?? ?

?????.

In determining a reasonable MLP structure, practical considerations

constrained ourexperimentstonetworkswithnomorethan160 hidden

units. We ran experiments with 20, 40, 60, 80, 120, and 160 units in the

hidden layer. Each MLP was trained with noise-free training datasets

ofsize500,1000,2000,4000,8000,16000,and32000.ForeachMLP

the bestgeneralization error6in500 epochs oftraining7wasmeasured,

using a noise-free test set of 5000 patterns. For each MLP size and

training dataset five runs were performed, and the generalization errors

averaged.

The computation time for localization increases linearly with the

number of hidden units, and the training time increases about linearly

with the size of the training dataset and the size of the hidden layer.

When the training dataset is small, generalization error is high. In-

creasing the computation, i.e., increasing the size of the training set

or the number of units in a hidden layer, tends to reduce the generaliza-

tionerror,nearinganasymptoteatabout8000exemplarsand80hidden

units. For this reason we chose to use 80 hidden units.

C. Decoding Strategies

For practical use, and to measure performance, the ?-D distributed

representationofthedipolelocationmustbe convertedtoCartesianco-

ordinates.Weexperimentedwithtwostrategiesfordecodingtheoutput

vector, ? ? ??????????????, under the assumption that ?? ? ?????.

Strategy 1:

• Findtheindexofthereceptivefieldwiththemaximumamplitude,

??? ?????????.

• Linearly interpolate between the centers of the receptive fields

in a ball ?? with center ?? and radius 6 cm (twice the inter-

5In artificial neural networks the activation function computes the output

value of an artificial neuron based on the weighted sum of its inputs. The output

value may be continuous or discrete, and Heavyside, linear, ?????????????,

and hyperbolic tangent activation functions are widely used.

6Because our training sets were large, the performance of the network on the

training dataset and on a new testing dataset would be about the same, were

the testing dataset not taken from a smaller region. The test dataset is used to

verifythesystemperformance,andgeneralizationerrormeanstheaverageerror

obtained on a test dataset.

7In one epoch each exemplar in the training dataset is presented once.

Fig. 1.

Soft-MLP using two sorts of decoding strategies, and their hybrid methods.

Decoding strategy 1 and strategy 2 are denoted by S1 and S2, respectively.

Mean localization error versus SNR for the Cartesian-MLP, the

TABLE II

PERFORMANCE OF CARTESIAN-MLPs, SOFT-MLPs, AND MLP-START-LM

HYBRIDS. EACH NUMBER IS AN AVERAGE OVER 4500 LOCALIZATIONS.

SOFT-MLPs WERE TESTED USING TWO DECODING STRATEGIES (S1/S2)

center distance)8using the activation values as weights, ? ? ?

?????

? ??

??.

Strategy 2:

• For each of the ? receptive field centers place a ball ?? with

center ?? and radius 6 cm (twice the inter-center distance), and

calculate ?? ? ???

• Find ??? ?????????.

• Apply the linear interpolation of Strategy 1 step 2.

? ??

?????? ????????? ???.

III. LOCALIZATION RESULTS

A. Comparison of Soft-MLP and Cartesian-MLP

The training dataset contained 20000 exemplars, contaminated with

real brain noise, and another dataset, of4500 MEG signal patterns con-

taminated by real brain noise, was constructed for testing.9The distri-

bution of SNRs for patterns in the testing dataset are shown in Table I.

Wetrainedforupto500epochs,whichtookabout12honan800-MHz

AMD Athlon for each training dataset.

After each Soft-MLP was trained, its performance in RMS linear

accuracy was measured by converting the outputs to Cartesian

coordinates. Using each of the two decoding strategies led to two

different systems. The Soft-MLP performance, along with that of a

Cartesian-MLP network,10is shown as a function of input SNR in

8When a bigger radius is used, outliers are not filtered out and computation is

more costly. When a smaller radius is used, significant values might be thrown

away. Empirically, twice the inter-center distance balanced these consideration.

9The number of exemplars was constrained in part by the availability of real

brain noise data in which we were confident.

10The structure of Cartesian-MLP was empirically optimized by trading off

computation and accuracy [3].

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788IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 6, JUNE 2003

Fig. 2.

Soft-MLP (S2) for eight actual BSS-separated visual MEG components. (left) Axial view. (middle) Coronal view. (right) Saggital view. The outer surface denotes

the sensor surface, and diamonds on the surface denote sensors. The inner surface denotes the spherical head model.

Dipole source localization results, using real data with sources separated using SOBI. Locations found by standard Neuromag xfit software versus the

Fig. 1. As a whole, the Soft-MLP is more accurate than the Carte-

sian-MLP. The Soft-MLP using Strategy 2 shows a slight performance

advantage over Strategy 1. Each of the Soft-MLP localizers was

used to initialize a Levenberg–Marquardt (LM) optimizer, giving two

variant Soft-MLP-start-LM hybrids. Their performance is shown as

a function of SNR and compared with the hybrid method using the

Cartesian-MLP in Fig. 1. The MLP-start-LMs of the Soft-MLPs show

better localization accuracy at high SNRs than the MLP-start-LM of

the Cartesian-MLP, while they have degraded accuracy at low SNRs.

These results also held for networks trained with other sorts of noise

(not shown).

A grand summary, averaged across various SNR conditions, is

shown in Table II. In comparing the Soft-MLP (S2) and Carte-

sian-MLP localizers, both trained with real brain noise, one sees that

localization error improved from 1.15 to 0.85 cm, while computation

time increased from 0.3 to 1.0 ms. With an increased expense in time,

the distributed output representation yielded much more accurate

(assuming a spherical uncertainty, the zone in which the dipole is

likely located is decreased from 1.5 to 0.6 cm?, a factor of 2.5)

localizations. The MLP-start-LM method using Soft-MLP (S2) has

the same localization error as Cartesian-MLP, 0.28 cm. However, it

is slightly faster! This surprising reduction in total computation time

is due to the Soft-MLP generating a better initial guess, resulting in

fewer iterations of LM.

B. Localization for Actual BSS-Separate MEG Components

We applied the Soft-MLP (S2) trained with real brain noise to lo-

calize dipolar sources from actual BSS-separated MEG signal compo-

nents. The xfit program (standard commercial software bundled with

the 4-D Neuroimaging Neuromag-122 MEG system) is compared with

the methods developed here. We chose eight of the actual BSS-sepa-

ratedMEGsignalcomponentsfromwhichxfitlocalizedasingledipole

source well, and which met other criteria for correct localization laid

out in [9]. (Continuous MEG data were collected, sampled at 300 Hz,

band-pass filtered at 0.03–100 Hz, separated using SOBI, and scanned

for neuronal sources of interest. See [9], [10] for full details.)

Fig. 2 shows the localized dipoles from three viewpoints: axial (?–?

plane), coronal (?–? plane), and saggital (?–? plane). The MLP-es-

timated locations are about 1.18 cm on average from those of xfit.

The trained Soft-MLP is applicable to actual MEG signals, and can

be a good initial guessor for iterative methods with clear advantages in

speed and in the lack of required human interaction.

C. Comparison With the Global Search Algorithm

The global search algorithm uses storage to reduce computation in

dipole localization [11]. Briefly: a number of grid points are selected

in the head model, and the field pattern at the sensors resulting from

orthogonally oriented dipoles at each location are precomputed. This

information allows the orientation and strength of a dipole located at

a particular grid point which best fits a vector of measurements to be

efficiently calculated. When a measured signal is to be localized, the

goodnessoffit(GOF)ofthebestdipoleateachgridpointiscalculated,

and the location of the grid point with the best GOF is used to initialize

a gradient-based optimization routine.

This table-based algorithm is surprisingly efficient at localizing

dipolar sources. For example, it has been used to localize a dipole at

each time point in a large (100000 sample) MEG dataset [11]. The

primary weakness of the global search algorithm is that the gridding

must be fine enough for the problem at hand. In particular, the spacing

of precomputed points must be well above the Nyquist limit of the

highest spatial frequency in the error surface, or the correct optimum

can be skipped over. Therefore, table size, and, therefore, the time

required for a localization, will increase with increasing complexity of

the error surface. The error surface might become more complex under

two circumstances: 1) with a more realistic head model [12]; 2) with

a complex MEG helmet, for instance a helmet with superconducting

magnetic reflectors [13].

In contrast, the Soft-MLP is robust to a complex error surface.

Even with a realistic head model or a highly complex MEG helmet,

Soft-MLP is applicable without modification. Under such circum-

stances, we expect the Soft-MLP to do a single localization much

more quickly than the global search algorithm, even though it may

take longer to train the MLP than to precompute the global search

algorithm’s tables.

Another advantage of the Soft-MLP is that it can be trained using an

arbitrary noise model, characterized only by a set of samples, such as

actualmeasuredbrainnoise.Becausetheglobalsearchalgorithmrelies

on a least-squares fit to determine the GOF at each grid point, its noise

model must be Gaussian.

IV. SUMMARY

We propose the use of distributed representations to encode dipole

locations in the output of MLP-based dipole localizers. Experiments

showedthat suchanetworkwasfastandrobust,and wasabetterdipole

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 6, JUNE 2003789

source localizer (0.85 cm versus 1.15 cm) at slightly greater computa-

tional expense (1.0 ms versus 0.3 ms) than a comparably tuned system

using a Cartesian representation. The hybrid MLP-start-LM method

using the new MLP showed the same accuracy as previous systems

(0.28 cm) but computation time was reduced from 36 ms to 30 ms.

Furthermore, the Soft-MLP was successfully applied to actual MEG

data.

A Cartesian output representation cannot encode the location of

more than a single dipole. Our use of a distributed output representa-

tion was in part motivated by the hope that its greater representational

capabilities might allow Soft-MLP networks to be used for multiple

dipole localization. The improvements in accuracy for a single dipole

were an unexpected benefit, but we will continue our efforts to apply

the Soft-MLP architecture to the multiple dipole case.

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San Mateo, CA: Morgan Kaufmann,

Cambridge,

Independence of Myoelectric Control Signals

Examined Using a Surface EMG Model

Madeleine M. Lowery*, Nikolay S. Stoykov, and Todd A. Kuiken

Abstract—The detection volume of the surface electromyographic

(EMG) signal was explored using a finite-element model, to examine

the feasibility of obtaining independent myoelectric control signals from

regions of reinnervated muscle. The selectivity of the surface EMG signal

was observed to decrease with increasing subcutaneous fat thickness.

The results confirm that reducing the interelectrode distance or using

double-differential electrodes can increase surface EMG selectivity in

an inhomogeneous volume conductor. More focal control signals can be

obtained, at the expense of increased variability, by using the mean square

value, rather than the root mean square or average rectified value.

Index Terms—Detection volume, finite-element model, myoelectric con-

trol, surface EMG.

I. INTRODUCTION

One of the greatest limiting factors in the development of myoelec-

tric prostheses has been the inadequacy of current control strategies.

In response to this problem, many advances have been made in devel-

oping complex signal processing algorithms to increase the amount of

information that can be extracted from each channel of electromyo-

graphic (EMG) activity [1]–[3]. An alternative approach is to increase

the number of independent EMG signals available to the controller.

Preliminary studies on the use of nerve-muscle grafts as a possible

method of achieving this are currently being conducted [4]. For this

technique to work it is important that independent control signals can

be obtained from each nerve-muscle graft and that crosstalk, the detec-

tion of volume conducted signals from muscles other than the muscle

of interest, be kept to a minimum. The relative contributions of motor

units (MUs) located throughout the muscle tissue to the surface EMG

interference pattern, however, are not yet fully known. This issue is

central in determining the feasibility of the proposed technique to suc-

cessfully control multifunctional prostheses and is directly relevant to

many other surface EMG applications.

One method of investigating the pick-up range of the surface EMG

signal is to use model simulation. Anatomical properties and electrode

configuration are both known to affect EMG crosstalk at the skin sur-

face. The effect of interelectrode distance and increased selectivity of

the surface EMG signal with double-differential or higher order spa-

tial filters have been widely studied both experimentally and in model

Manuscript received July 15, 2002; revised December 15, 2002. This work

was supported in part by the Whitaker Foundation under a Biomedical Engi-

neering Research Grant, in part by the National Institute of Child and Human

Developmentunder Grant 1K08HD01224-01A1,and in partby the NationalIn-

stituteofDisabilityandRehabilitationResearchunderGrantH133G990074-00.

Asterisk indicates corresponding author.

*M. M. Lowery is with the Research Department, Rehabilitation Institute of

Chicago, Chicago, IL 60611-4496 USA and also with the Department of Phys-

ical Medicine and Rehabilitation, Northwestern University, Evanston, IL 60201

USA (e-mail: m-lowery@northwestern.edu).

N. S. Stoykov is with the Research Department, Rehabilitation Institute of

Chicago, Chicago, IL 60611-4496 USA and also with the Department of Phys-

ical Medicine and Rehabilitation, Northwestern University, Evanston, IL 60201

USA.

T. A. Kuiken is with the Rehabilitation Institute of Chicago, Chicago, IL

60611-4496 USA and also with the Departments of Physical Medicine and Re-

habilitationandElectricalandComputerEngineering,NorthwesternUniversity,

Evanston, IL 60201 USA.

Digital Object Identifier 10.1109/TBME.2003.812152

0018-9294/03$17.00 © 2003 IEEE