The optimal dimensions of thin coil systems of three and four square coils for producing uniform magnetic fields are calculated. We find that for three square coils, of side d and separation s between the outer coils, the most uniform field distribution occurs with s/ d = 0.821 116 and with l' /1 = 0.512 797. 1'/1 is the ratio of the currents in the center coil to that of the outer coils. With four square coils, the best uniformity is obtained when a/ d = 0.128 106 and b / d = 0.505 492, where a is the distance from the center to the inner coils and b is the distance from the center to the outer coils. The ratio of the current in the inner pair of coils to that in the outer pair must be 1'/ 1 = 0.423514. We compare the uniformity of the field produced by these coil systems with each other and with Rubens' five-coil system, both on and offaxis. It is shown that the optimal four-coil design is superior to the three-and five-coil systems. The sensitivity of the uniformity to the precision of construction is discussed. Dimensions of regions around the center of the coil systems, uniform to 1 part in 10 6 to 1 part in 10 2 , are given.
It is believed that the magnetoencephalogram (MEG) localizes an electrical source in the brain to within several millimeters and is therefore more accurate than electroencephalogram (EEG) localization, reported as 20 mm. To test this belief, the localization accuracy of the MEG and EEG were directly compared. The signal source was a dipole at a known location in the brain; this was made by passing a weak current pulse simulating a neural signal through depth electrodes already implanted in patients for seizure monitoring. First, MEGs and EEGs from this dipole were measured at 16 places on the head. Then, computations were performed on the MEG and EEG data separately to determine the apparent MEG and EEG source locations. Finally, these were compared with the actual source location to determine the MEG and EEG localization errors. Measurements were made of four dipoles in each of three patients. After MEGs with weak signals were discounted, the MEG average error of localization was found to be 8 mm, which was worse than expected. The average EEG error was 10 mm, which was better than expected. These results suggest that the MEG offers no significant advantage over the EEG in localizing a focal source. However, this does not diminish other uses of the MEG.
We describe a fast and numerically effective biomagnetic inverse solution using a moving dipole in a realistic homogeneous torso. We applied the localization model and high-resolution magnetocardiographic mapping to localize noninvasively the ventricular preexcitation site in ten patients suffering from Wolff-Parkinson-White syndrome. In all cases, the computed localization results were compared to the results obtained by invasive catheter technique. Using a standard-size torso model in all cases, the average 3-D distance between the computed noninvasive locations and the invasively obtained results was 2.8 +/- 1.4 cm. When the torso was rescaled to better match the true shape of the subject in five cases, the 3-D average was improved to 2.2 +/- 1.0 cm. This accuracy is very satisfactory, suggesting that the method would be clinically useful.
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