Strategies for Optimal Design of Biomagnetic Sensor Systems

by    S. Lau, R. Eichardt, J. Haueisen, L. Di Rienzo, E.G. Schukat-Talamazzini

Preprint series: 07-05 , Reports on Computer Science

90C31 Sensitivity, stability, parametric optimization
90C56 Derivative-free methods
92C50 Medical applications (general)
92C55 Biomedical imaging and signal processing [See also 44A12, 65R10]

Abstract: Magnetic field imaging (MFI) is a technique to record contact free
the magnetic field distribution and estimate the underlying source
distribution in the heart. Currently, the cardiomagnetic fields
are recorded with superconducting quantum interference devices
(SQUIDs), which are restricted to the inside of a cryostat filled
with liquid helium or nitrogen. New room temperature optical
magnetometers allow less restrictive sensor positioning, which
raises the question of how to optimally place the sensors for
robust field reconstruction.

The objective in this study is to develop a generic object-oriented
framework for optimizing sensor arrangements (sensor positions and
orientations) which supports the necessary constraints of a limited
search volume (only outside the body) and the technical minimum
distance of sensors (e.g. 1~cm). In order to test the framework, a
new quasi-continuous particle swarm optimizer (PSO) component is
developed as well as an exemplary goal function component using
the condition number (CN) of the leadfield matrix. Generic constraint
handling algorithms are designed
and implemented, that decompose complex constraints into basic
ones. The constraint components interface to an operational
exemplary optimization strategy which is validated on the
magnetocardiographic sensor arrangement problem. The simulation setup
includes a three compartment boundary element model of a
torso with a fitted multi-dipole heart model.

The results show that the CN, representing the reconstruction
robustness of the inverse problem, can be reduced
with our optimization by one order of magnitude
within a sensor plane (the cryostat bottom) in front of the torso
compared to a regular sensor grid. Reduction of
another order of magnitude is achieved by
optimizing sensor positions on the entire torso surface. Results also
indicate that the number of sensors may be reduced to 20-30 without
loss of robustness in terms of CN.

The original contributions are the generic reusable framework
and exemplary components, the quasi-continuous PSO algorithm with
constraint support and the composite constraint handling algorithms.

Keywords: Magnetic sensor setup, constraint optimization, swarm intelligence, magnetometer, magnetocardiography

Upload: 2008-01-11

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