Magnetic source imaging (MSI) provided nonredundant information in 33% of patients. In those who have undergone surgery to date, MSI added useful information that changed treatment in 6 (9%), without increasing complications. MSI has benefited 21% who have gone to surgery.
Magnetic source imaging can provide unique localization information that is not available when other noninvasive methods are used. Magnetic source imaging appears most useful for cases of neocortical epilepsy. In particular, when an MS imaging study revealed six or more interictal spikes that were densely clustered in a single anatomical location, the MS image was highly correlated with the zone of seizure origin identified by ECoG. In these cases the MS imaging data may be useful to guide placement of intracranial electrodes.
Localizations were compared for the same human seizure between simultaneously measured MEG and iEEG, which were both co-registered to MRI. The whole-cortex neuromagnetometer localized a dipole in a sphere phantom, co-registered to the MEG sensor array, with an error of 1.4 mm. A focal afterdischarge seizure was induced in a patient with partial epilepsy, by stimulation at a subdural electrocorticography (ECoG) electrode with a known location, which was co-registered to the MRI and to the MEG sensor array. The simultaneous MEG and ECoG during the 30-second seizure was measured and analyzed using the single, moving dipole model, which is the localization model used clinically. The dipole localizations from simultaneous whole cortex 68-channel MEG and 64-channel ECoG were then compared for the repetitive spiking at six different times during the seizure. There were two main regions of MEG and ECoG activity. The locations of these regions were confirmed by determining the location clusters of 8,000 dipoles on ECoG at consecutive time points during the seizure. The mean distances between the stimulated electrode location versus the dipole location of the MEG and versus the dipole location of the ECoG were each about one (1) centimeter. The mean distance between the dipole locations of the MEG versus the dipole locations of the ECoG was about 2 cm. These errors were compared to errors of MEG and ECoG reported previously for phantoms and for somatosensory evoked responses (SER) in patients. Comparing the findings from the present study to those from prior studies, there appeared to be the expected stepwise increase in mean localization error progressing from the phantom, to the SER, to the seizure.
The set of all rational functions with any fixed denominator that simultaneously nullify in the infinite point is parametrized by means of a well-known integrable system: a finite dimensional version of the discrete KP hierarchy. This type of study was originated in Y. Nakamura's works who used others integrable systems. Our work proves that the finite discrete KP hierarchy completely parametrizes the space Rat Λ n of rational functions of the form f x q x /z n , where q x is a polynomial of order n − 1 with nonzero independent coefficent. More exactly, it is proved that there exists a bijection from Rat Λ n to the moduli space of solutions of the finite discrete KP hierarchy and a compatible linear system.
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