### Abstract

Although the single equivalent point dipole model has been used to represent well-localised bio-electrical sources, in realistic situations the source is distributed. Consequently, position estimates of point dipoles determined by inverse algorithms suffer from systematic error due to the non-exact applicability of the inverse model. In realistic situations, this systematic error cannot be avoided, a limitation that is independent of the complexity of the torso model used. This study quantitatively investigates the intrinsic limitations in the assignment of a location to the equivalent dipole due to distributed electrical source. To simulate arrhythmic activity in the heart, a model of a wave of depolarisation spreading from a focal source over the surface of a spherical shell is used. The activity is represented by a sequence of concentric belt sources (obtained by slicing the shell with a sequence of parallel plane pairs), with constant dipole moment per unit length (circumferentially) directed parallel to the propagation direction. The distributed source is represented by N dipoles at equal arc lengths along the belt. The sum of the dipole potentials is calculated at predefined electrode locations. The inverse problem involves finding a single equivalent point dipole that best reproduces the electrode potentials due to the distributed source. The inverse problem is implemented by minimising the χ^{2} per degree of freedom. It is found that the trajectory traced by the equivalent dipole is sensitive to the location of the spherical shell relative to the fixed electrodes. It is shown that this trajectory does not coincide with the sequence of geometrical centres of the consecutive belt sources. For distributed sources within a bounded spherical medium, displaced from the sphere's centre by 40% of the sphere's radius, it is found that the error in the equivalent dipole location varies from 3 to 20% for sources with size between 5 and 50% of the sphere's radius. Finally, a method is devised to obtain the size of the distributed source during the cardiac cycle.

Original language | English (US) |
---|---|

Pages (from-to) | 562-570 |

Number of pages | 9 |

Journal | Medical and Biological Engineering and Computing |

Volume | 39 |

Issue number | 5 |

State | Published - 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

- Dipole localisation
- Distributed source
- Single equivalent dipole model

### ASJC Scopus subject areas

- Biomedical Engineering
- Computer Science Applications

### Cite this

*Medical and Biological Engineering and Computing*,

*39*(5), 562-570.

**Applicability of the single equivalent point dipole model to represent a spatially distributed bio-electrical source.** / Armoundas, A. A.; Feldman, A. B.; Sherman, D. A.; Cohen, R. J.

Research output: Contribution to journal › Article

*Medical and Biological Engineering and Computing*, vol. 39, no. 5, pp. 562-570.

}

TY - JOUR

T1 - Applicability of the single equivalent point dipole model to represent a spatially distributed bio-electrical source

AU - Armoundas, A. A.

AU - Feldman, A. B.

AU - Sherman, D. A.

AU - Cohen, R. J.

PY - 2001

Y1 - 2001

N2 - Although the single equivalent point dipole model has been used to represent well-localised bio-electrical sources, in realistic situations the source is distributed. Consequently, position estimates of point dipoles determined by inverse algorithms suffer from systematic error due to the non-exact applicability of the inverse model. In realistic situations, this systematic error cannot be avoided, a limitation that is independent of the complexity of the torso model used. This study quantitatively investigates the intrinsic limitations in the assignment of a location to the equivalent dipole due to distributed electrical source. To simulate arrhythmic activity in the heart, a model of a wave of depolarisation spreading from a focal source over the surface of a spherical shell is used. The activity is represented by a sequence of concentric belt sources (obtained by slicing the shell with a sequence of parallel plane pairs), with constant dipole moment per unit length (circumferentially) directed parallel to the propagation direction. The distributed source is represented by N dipoles at equal arc lengths along the belt. The sum of the dipole potentials is calculated at predefined electrode locations. The inverse problem involves finding a single equivalent point dipole that best reproduces the electrode potentials due to the distributed source. The inverse problem is implemented by minimising the χ2 per degree of freedom. It is found that the trajectory traced by the equivalent dipole is sensitive to the location of the spherical shell relative to the fixed electrodes. It is shown that this trajectory does not coincide with the sequence of geometrical centres of the consecutive belt sources. For distributed sources within a bounded spherical medium, displaced from the sphere's centre by 40% of the sphere's radius, it is found that the error in the equivalent dipole location varies from 3 to 20% for sources with size between 5 and 50% of the sphere's radius. Finally, a method is devised to obtain the size of the distributed source during the cardiac cycle.

AB - Although the single equivalent point dipole model has been used to represent well-localised bio-electrical sources, in realistic situations the source is distributed. Consequently, position estimates of point dipoles determined by inverse algorithms suffer from systematic error due to the non-exact applicability of the inverse model. In realistic situations, this systematic error cannot be avoided, a limitation that is independent of the complexity of the torso model used. This study quantitatively investigates the intrinsic limitations in the assignment of a location to the equivalent dipole due to distributed electrical source. To simulate arrhythmic activity in the heart, a model of a wave of depolarisation spreading from a focal source over the surface of a spherical shell is used. The activity is represented by a sequence of concentric belt sources (obtained by slicing the shell with a sequence of parallel plane pairs), with constant dipole moment per unit length (circumferentially) directed parallel to the propagation direction. The distributed source is represented by N dipoles at equal arc lengths along the belt. The sum of the dipole potentials is calculated at predefined electrode locations. The inverse problem involves finding a single equivalent point dipole that best reproduces the electrode potentials due to the distributed source. The inverse problem is implemented by minimising the χ2 per degree of freedom. It is found that the trajectory traced by the equivalent dipole is sensitive to the location of the spherical shell relative to the fixed electrodes. It is shown that this trajectory does not coincide with the sequence of geometrical centres of the consecutive belt sources. For distributed sources within a bounded spherical medium, displaced from the sphere's centre by 40% of the sphere's radius, it is found that the error in the equivalent dipole location varies from 3 to 20% for sources with size between 5 and 50% of the sphere's radius. Finally, a method is devised to obtain the size of the distributed source during the cardiac cycle.

KW - Dipole localisation

KW - Distributed source

KW - Single equivalent dipole model

UR - http://www.scopus.com/inward/record.url?scp=0034783013&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034783013&partnerID=8YFLogxK

M3 - Article

C2 - 11712653

AN - SCOPUS:0034783013

VL - 39

SP - 562

EP - 570

JO - Medical and biological engineering

JF - Medical and biological engineering

SN - 0140-0118

IS - 5

ER -