In 1976 Cohen et al. introduced in a sequence of publications a method to construct so-called pseudo current density- or arrow-maps from multichannel biomagnetic signals obtained by magnetocardiography (MCG) [1
]. The purpose was to transform the measured magnetic field values in a way that the resulting maps could be more easily related to the underlying current density distribution. Later this method was frequently referred to as the Hosaka-Cohen (HC) transformation and its performance was analyzed in some detail [5
]. However, it did not find widespread application until recent years, when a kind of renaissance of this method occurred. Recently, the HC-transformation is used in MCG [7
], fetal MCG [22
], magnetoencephalography (MEG) [25
] and magnetoneurography (MNG) [28
A reason for this new development may be the advance of computing power and visualization tools. In addition, in former times system designers preferred to display magnetic field maps (MFM), since they were interested in the measured physical quantity. However, for the end-user -the physicians- MFMs are not very instructive, as the MFM maximum values do not occur above those positions where the generating currents are flowing.
Figs. , , illustrate this point: it shows two instants of the atrial excitation marked by the cursors in the MCG-butterfly-plot in Fig. (a butterfly-plot is obtained by superpositioning the MCG-Signals of all channels in one display). The respective pseudo current density (PCD-) plots show very clearly and intuitively the preceding activation over the right atrium (Fig. , right) followed by that over the left atrium (Fig. , right), whereas the MFMs in Fig. (left) and in Fig. (left) require expert knowledge to interpret them in the same way.
Butterfly plot of a multichannel magnetocardiogramm. The two cursors mark the time instants related to the visualizations shown in Fig. 2 and 3 respectively.
Figure 2 Visualization of the atrial activation for the first time instant marked by a cursor in Fig.1. Left: Bz-map drawn as isocontour maps with a magnetic flux density difference of 0.5pT between adjacent contour lines (red: positive, i.e. directed towards (more ...)
Visualization of the atrial activation for the second time instant marked by the respective cursor in Fig.1.
Other features of modern pseudo current density maps helped to spur interest:
i) while Hosaka and Cohen coded the information of the pseudo current density amplitude into the size of the arrows the recent display techniques added an underlying false-colour scaling to the maps.
ii) visually attractive results are achieved, if a sequence of maps is presented as an animated clip. Then the spatio-temporal dynamics of the electrophysiological function are more easily perceptible.
The question that remains open is: what do pseudo current density maps really show? Already the term "pseudo" indicates that the real current density distribution is different and may deviate considerably. This is already evident when considering the fact that the PCD-maps are only 2D-projections of a 3D reality. The initial papers of Hosaka and Cohen just gave an empirical explanation, why their maps produce an approximate image of the underlying current density distribution. Later explanations e.g. by other authors [7
] relating the curl of the measured magnetic induction curl
with the current density
were incorrect and misleading. Therefore in the following chapters an analytically based calculation is presented that illustrates the physical justification and the limitations of this visualization method.
This paper will not deal with minimum norm estimates or other inverse methods calculating the current density from field maps. Rather, the Hosaka-Cohen transformation provides just another representation of the measured magnetic field by a postprocessing of the magnetic field data. The underlying current distribution does not enter in the calculation of the HC-transformation. We intend to clarify in which way certain features of the PCD-maps can nevertheless be related to the underlying current distribution. Some common fallacies in the interpretation of PCD maps are elucidated.
Finally we would like to stress the utility of PCD maps to provide a visualization of measurement results obtained by biomagnetic systems with very different sensor configurations. Whether magnetometers, planar gradiometers or vector magnetometers are used always similar PCD maps may be computed and will thus allow a simple cross-platform, i.e. multicentre comparability of biomagnetic investigations.