Two methods of modelling electric current systems by analysis of magnetic field data, with particular reference to the quasi-dc magnetic field of the human leg

This thesis deals with two approaches to the problem of obtaining information about electric current distributions by analysing the associated magnetic field. Both methods have been developed within the context of a particular biomagnetic study, the analysis of the quasi dc magnetic field of the human leg. The techniques have been designed to deal with data sensed by a gradiometer in a series of horizontal scans above the current—carrying region and take full account of the gradiometer configuration. Method 1, the line-dipole technique, analyses each scan individually and calculates the dipole term of a multipole expansion which best characterises the current distribution cross-section immediately below the line of scan. Method 2, the line current loop iterative-perturbative algorithm, uses data from all the scans to compute the coordinates of the best fit line current loop for the whole data map. Both methods have been extensively tested with computer simulated data and with real data from current-carrying wire loops and the results show that both methods are capable of producing an accurate replication of the target system provided it satisfies the initial model assumptions. The dc magnetic field of the human leg has been investigated for a number of normal subjects. The line- dipole technique provides a useful method of characterising the data and indicates regions of high current density which allow inferences to be drawn about the physiological nature of the current generators. Analysis of the field from a leg with a fibula fracture shows significant differences from the normal pattern, although a direct, causal connection with the fracture is not necessarily implied. The line current loop technique has been less successful in achieving a high quality fit to the leg data but this lack of success is consistent with a physiologically reasonable model of the source currents. Although both methods have been designed for this rather specialised biomagnetic inverse problem, they are of more general applicability and may be useful in other fields such as geophysics or non-destructive testing