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Neurology and Clinical Neurophysiology 2004:94 (November 30, 2004)
Calibration of a Vector-MEG Helmet System
Pasquarelli, A, De Melis, M, Marzetti, L, Müller, H-P, Erné, SN
Division for Biosignals and Imaging Technologies, ZIBMT, University of Ulm, Germany
Corresponding Author: Hans-Peter Müller, Division for Biosignals and Imaging Technologies,
ZIBMT, University of Ulm, Ulm, Germany
Phone: +49-731-5025325; Email: hans-peter.mueller@zibmt.uni-ulm.de
ABSTRACT
The MEG system Argos 500, recently installed at the University of Ulm, is designed for clinical
application and routine use, to allow investigation of a large number of patients per day. To reach this
goal, the system design meets the requirements of reliability, high field sensitivity, minimal set-up
overhead before each measurement and an easy-to-handle user interface.The sensor system consists of a
163 vector-magnetometer array oriented and located in a suitable way to cover the whole head of the
patient. Four additional triplets are available as references to build software gradiometers. To use this
system at a high performance level, it must be properly calibrated, with these goals: to determine the
actual geometry of the sensors array, which can deviate from the design specifications, and to determine
the actual sensitivity of each sensor. The calibrating source consists of 31 coils placed at the corners of a
head-size dodecahedron. Various details of the calibration system and process are presented here.
KEY WORDS
Magnetoencephalography, Calibration, Vector magnetometer, Whole-head system, Helmet system
INTRODUCTION
The goals of the calibration of our Argus 500 MEG system are the estimation of the sensors locations,
the orientation of the normal vectors to the surface, and the deviation of the sensors sensitivity from the
nominal values given as system specifications. To achieve these goals, a dedicated magnetic source has
been developed and constructed. The processing algorithm consists of three main steps: 1) estimating the
position and orientation of the calibration device; 2) estimating the sensors geometrical parameters; and 3)
calculating the magnetometer sensitivities. Simplex conjugate minimization techniques are used for steps
1 and 2. Step 3 is achieved by minimizing the difference between measured and predicted fields, in the
least squares sense. The large number of sources and their different orientations allow for a precise and
redundant characterization of all the sensors present in the Argos500 helmet system [Pasquarelli, 2004],
including the reference triplets used for the noise suppression, by forming vector gradiometers with the
main sensors.
METHODS
A dedicated magnetic source has been developed and constructed. It consists of 31 coils (diameter 5
mm) regularly distributed on a sphere (diameter 10 cm), at points equivalent to the corners of a
dodecahedron and its reciprocal icosahedron (Fig. 1). Both solids are inscribed in the sphere. The 32nd
point of this assembly, the “south pole”, is used for the mounting fixture. The coils axes are radial and
therefore the magnetic dipoles are orthogonal to the surface of the sphere. A dedicated circuit activates
sequentially the coils with a low-frequency sinusoidal signal for a time length which can be programmed
through the acquisition script (typically 15 seconds). The signals generated in this way are measured by
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Neurology and Clinical Neurophysiology 2004:94 (November 30, 2004)
the 500-channel helmet system and are used
in a best-fit procedure to get a robust
estimation of the system parameters.
To increase the signal-to-noise ratio of
both magnetic signals and electrical
reference, the excitation frequency is
estimated and a resonant band-pass filtering
centred at that frequency is applied to the
signals.
General Overview of the Algorithm
The first part of the calibration algorithm
consists of the estimation of the geometrical
parameters of the calibration sphere. The six
parameters to be fitted are the position and
the orientation { }sphsphsphsphr ψϕθ ,,,ρ of the
reference system positioned at the centre of
the sphere, with respect to the helmet
reference system (HRS). A first rough fit,
based on the minimization of the distances
of coil to sensor, delivers a first set of
values. Using these values as first guess, refinements of these values are found through the iteration of a
new best fit criterion between the predicted field generated by the whole of all the magnetic dipoles and
the measured field over the whole sensors array, i.e. the maximization of the correlation coefficient
between the predicted and the measured fields.
Figure 1. The calibration device: the 31 coils are
placed at the corners of a dodecahedron and its
reciprocal icosahedron, both inscribed in the sphere.
We assumed that the diameter of the circular lo f
wavelength. This hypothesis is satisfied in our cas e
MEG fields [Sarvas, 1987]. The relevant content in
signals is, in fact, below 1 kHz, and generall c
approximation, the equations for H
ρ
are simplified e
solution is implemented for non-negligible dimensio
The fitting procedure is a simplex conjugate al s
the number of parameters to be estimated, as possib g
iteration. Each parameter of the set for a test point r
limit which reflects the geometry of the system inte
For each of the test points, the predicted field is r,
and the match with the measured field matrix M is ).
Demeaned and normalized quantities are used for b
ˆ
g
not the correlation values influenced by the signals e
best set of parameters for the calibration device has o
the solution. The cartesian positions of the coils in e
pointing outwards from the sphere are finally cal l
structure of the calibration device, once the centre o
op carrying electric current is very small in terms o
e due to the quasi-static approximation valid for th
the temporal frequency spectrum for MEG and EEG
y in the range 0.1 – 100 Hz. In the quasi-stati
by the assumption 0=β [Hämäläinen, 1993]. Th
ns of the coils.
gorithm, which uses pn×3 test points, where 6=pn i
le new centre of the sphere for each trial of the fittin
is randomly distributed between an upper and a lowe
raction between calibration sphere and sensor array.
calculated for each coil at the location of each senso
evaluated in terms of correlation coefficients (Fig. 2
oth the M matrix and the predicted field sˆ nH
ρρ ⋅ , bein
amplitude, but for the non zero mean value. Once th
been found, the fit is repeated to assure robustness t
the HRS and the vectors normal to the coils surfac
culated, exploiting the knowledge of the geometrica
f the sphere has been localized. 2
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Neurology and Clinical Neurophysiology 2004:94 (November 30, 2004)
Estimation of the corrections for the coils geometrical parameters.
a b
Figure 2. (a) Measured field distribution of the helmet generated by the coil 30. (b) Calculated field
distribution of the helmet generated by the coil 30.
The actual coils orientations may differ from the nominal values, because the coils turns may not be
perfectly coaxial. This can be corrected by estimating the actual values of the orientations for each coil.
Also the actual intensity of the dipoles can be different from the design values. This can be caused by
machining tolerances. By means of a minimization algorithm, these errors can be calculated and the
corrected values are substituted to the ideal ones in the calibration process to eliminate the contribution of
the imperfections of the construction.
Fit of the sensors geometrical parameters.
The locations and the orientation of the vectors normal to the sensors surface, pointing towards the
sphere, for each sensor, are the objectives of a new fitting routine which processes the sensors one by one.
The fitting algorithm is again a simplex conjugate one with randomly distributed starting points. Now the
predicted field used to calculate the correlation values is given by the contribution of all coils to the
sensor under estimation. Correspondingly, the information about one sensor and all the coils is extracted
from the matrix. This means that the number of observations for the fit of the six sensor parameters
drastically reduces to . A new set of positions and normal vectors for the sensors is found and is
substituted to the construction values in the following steps of the algorithm.
Mˆ
311×
Calculation of the physical parameters of the sensors.
In the previous step, the sensors sensibilities have been supposed equal for all sensors. Actual values of
these parameters are calculated as follows: the fit of the geometrical parameters of the calibration object
and of the sensor array are iteratively repeated using the new values, until an equilibrium solution for the
geometrical parameters, as well as for the sensors sensitivities is achieved. The relative sensitivity of the
sensors array is calculated in analogy with the calculation of the magnetic dipoles intensities.
RESULTS
To check the consistency and the precision of the estimated results, four data sets have been acquired
at different positions of the sphere, starting at the innermost of the helmet and then at nominal 40, 60 and
80 mm displacement, along the z axis of the HRS. The algorithm is able to reproduce these positions with
a tolerance of approximately 1 mm, which is also the precision achievable in the manual positioning of
the calibration device.
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During normal operation of Argos systems the data acquisition system performs real time noise
cancellation using a compensation matrix to generate what is normally called "software gradiometers".
This is necessary because the standard MSR does not have a sufficient shielding factor at very low
frequencies, and this makes it necessary to compensate for the 1/f environmental noise.
The real time noise cancellation algorithm works by using, in the acquisition phase, the compensation
coefficients providing the linear combination of magnetic and/or reference channels, as in
Κ+++= 2211 iiiiii raramy
where i is the i-th magnetometer, and ik is the k-th reference channel for the i-th magnetometer. The
k coefficients are, in general, obtained through the minimization of the environmental noise
contribution in a given frequency band.
m r
ia
The last set of system parameters to be determined during calibration is the so called compensation
matrix. Different from other construction schemes where the basic sensors are already gradiometers, here
the basic sensors are magnetometers. To compensate low frequency environmental noise, artificial,
software gradiometers are generated, subtracting from each sensor a suitable linear combination of
reference signals, i.e signals measured from special sensors located at some distance from the sensing
array (7 to 10 cm).
Once these coefficients have been appropriately estimated, they are saved in the configuration template
for the data acquisition and then stored in the header of the data file in the section 'Compensation Map'.
This matrix, is used in the correction of the predicted field generated by a given source in the off line
signal analysis. This procedure is implemented in the OMEGA software [Müller, 2005].
The estimation of the compensation matrix for the Argos 500 is related to the geometry of the sensors
array for this system. For the helmet system Argos 500, the different spatial orientations of the
magnetometers, makes the choice of the references channels not so straightforward. Therefore, the
optimal choice of the reference triplets for each pyramid is the object of our current work.
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Pasquarelli A, Rossi R, DeMelis M, Marzetti L, Trebeschi A, and Erné SN. Argos 500: Operation of a
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