Active compensation of magnetic field distortions based on vector spherical harmonics field description

Wyszyński, G.; Bodek, K.; Afach, S.; Bison, G.; Chowdhuri, Z.; Daum, M.; Franke, B.; Komposch, S.; Lauss, B.; Ries, D.; Zsigmond, G.; Perkowski, M.; Rozpędzik, D.; Zejma, J.; Fertl, M.; Koss, P.; Severijns, N.; Wursten, E.; Kirch, K.; Kozela, A.; Qúeḿener, G.; Schnabel, A.

doi:10.1063/1.4978394

Cited by 10 publications

(15 citation statements)

References 13 publications

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“…We also assume that the MSR can be approximated as a static, source-free space. The magnetic field can then be described by

as shown by [ 29 ]–[ 31 ]. l = 0 has not been included here since the derivative of Y 00 is 0 and so this term has no impact on the observed magnetic field.…”

Section: Methodsmentioning

confidence: 99%

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Magnetic Field Mapping and Correction for Moving OP-MEG

Mellor

Tierney

O'Neill

et al. 2022

IEEE Trans. Biomed. Eng.

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Background: Optically pumped magnetometers (OPMs) have made moving, wearable magnetoencephalography (MEG) possible. The OPMs typically used for MEG require a low background magnetic field to operate, which is achieved using both passive and active magnetic shielding. However, the background magnetic field is never truly zero Tesla, and so the field at each of the OPMs changes as the participant moves. This leads to position and orientation dependent changes in the measurements, which manifest as low frequency artefacts in MEG data. Objective: We modelled the spatial variation in the magnetic field and used the model to predict the movement artefact found in a dataset. Methods: We demonstrate a method for modelling this field with a triaxial magnetometer, then showed that we can use the same technique to predict the movement artefact in a real OPM-based MEG (OP-MEG) dataset. Results: Using an 86channel OP-MEG system, we found that this modelling method maximally reduced the power spectral density of the data by 27.8 ± 0.6 dB at 0 Hz, when applied over 5 s non-overlapping windows. Conclusion:The magnetic field inside our state-of-the art magnetically shielded room can be well described by low-order spherical harmonic functions. We achieved a large reduction in movement noise when we applied this model to OP-MEG data. Significance: Real-time implementation of this method could reduce passive shielding requirements for OP-MEG recording and allow the measurement of low-frequency brain activity during natural participant movement.

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“…We also assume that the MSR can be approximated as a static, source-free space. The magnetic field can then be described by

as shown by [ 29 ]–[ 31 ]. l = 0 has not been included here since the derivative of Y 00 is 0 and so this term has no impact on the observed magnetic field.…”

Section: Methodsmentioning

confidence: 99%

“…as shown by [29]- [31]. = 0 has not been included here since the derivative of 00 is 0 and so this term has no impact on the observed magnetic field.…”

Section: A Theorymentioning

confidence: 99%

Magnetic Field Mapping and Correction for Moving OP-MEG

Mellor

Tierney

O'Neill

et al. 2022

IEEE Trans. Biomed. Eng.

View full text Add to dashboard Cite

show abstract

“…We also assume that the MSR can be approximated as a static, source-free space. The magnetic field can then be described by as shown by [29]–[31]. ( r,θ, ϕ ) are spherical coordinates, such that x = r sin θ cos ϕ, y = r sin θ sin ϕ, z = r cos θ , where x, y and z are the Cartesian coordinates.…”

Section: Methodsmentioning

confidence: 99%

“…as shown by [29]- [31]. ( , , ) are spherical coordinates, such that = sin cos , = sin sin , = cos , where , and are the Cartesian coordinates.…”

Section: A Theorymentioning

confidence: 99%

Magnetic Field Mapping and Correction for Moving OP-MEG

Mellor

Tierney

O'Neill

et al. 2021

Preprint

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Background: Optically pumped magnetometers (OPMs) have made moving, wearable magnetoencephalography (MEG) possible. The OPMs typically used for MEG require a low background magnetic field to operate, which is achieved using both passive and active magnetic shielding. However, the background magnetic field is never truly zero Tesla, and so the field at each of the OPMs changes as the participant moves. This leads to position and orientation dependent changes in the measurements, which manifest as low frequency artefacts in MEG data. Objective: We modelled the spatial variation in the magnetic field and used the model to predict the movement artefact found in a dataset. Methods: We demonstrate a method for modelling this field with a triaxial magnetometer, then showed that we can use the same technique to predict the movement artefact in a real OPM-based MEG (OP-MEG) dataset. Results: Using an 86-channel OP-MEG system, we found that this modelling method maximally reduced the power spectral density of the data by 26.2 ± 0.6 dB at 0 Hz, when applied over 5 s non-overlapping windows. Conclusion: The magnetic field inside our state-of-the art magnetically shielded room can be well described by low-order spherical harmonic functions. We achieved a large reduction in movement noise when we applied this model to OP-MEG data. Significance: Real-time implementation of this method could reduce passive shielding requirements for OP-MEG recording and allow the measurement of low-frequency brain activity during natural participant movement.

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“…Such designs are made in plasma physics [1][2][3] magnetic resonance imaging (MRI), [4][5][6][7][8][9] transcranial magnetic stimulation (TMS), 10,11 magnetic particle imaging (MPI), 12 and in zero-field magnetometry. 13 Further applications of surface-coil design include, .e.g., field control in physics experiments 14,15 and pickup coils of magnetic sensors. 16,17 The methods used in coil design are also involved in modeling eddy current patterns induced in thin conductive sheets 5,18,19 and field fluctuations due to thermal noise currents.…”

Section: Introductionmentioning

confidence: 99%

Magnetic-field modeling with surface currents: Physical and computational principles of bfieldtools

Mäkinen,

Zetter,

Iivanainen

et al. 2020

Preprint

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Surface currents provide a general way to model magnetic fields in source-free volumes. To facilitate the use of surface currents in magneto-quasistatic problems, we have implemented a set of computational tools in a Python package named bfieldtools. In this work, we describe the physical and computational principles of this toolset. To be able to work with surface currents of arbitrary shape, we discretize the currents on triangle meshes using piecewise-linear stream functions. We apply analytical discretizations of integral equations to obtain the magnetic field and potentials associated with the discrete stream function. In addition, we describe the computation of the spherical multipole expansion and a novel surface-harmonic expansion for surface currents, both of which are useful for representing the magnetic field in source-free volumes with a small number of parameters. Last, we share examples related to magnetic shielding and surface-coil design using the presented tools.

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Active compensation of magnetic field distortions based on vector spherical harmonics field description

Cited by 10 publications

References 13 publications

Magnetic Field Mapping and Correction for Moving OP-MEG

Magnetic Field Mapping and Correction for Moving OP-MEG

Magnetic Field Mapping and Correction for Moving OP-MEG

Magnetic-field modeling with surface currents: Physical and computational principles of bfieldtools

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