Three component magnetic field data Impact on minimum norm solutions in a biomedical application Luca Di Rienzo Dipartimento di Elettrotecnica, Politecnico di Milano, Milano, Italy Jens Haueisen Biomagnetic Center, Friedrich-Schiller-University, Jena, Germany, and Cesare Mario Arturi Dipartimento di Elettrotecnica, Politecnico di Milano, Milano, Italy Abstract Purpose – To demonstrate the improvement of three-axial magnetic sensors systems for magnetocardiography when using minimum norm solutions (MNS). Design/methodology/approach – The thesis is proved by using figures of merit and by means of repeated numerical simulations, starting from a BEM model for forward calculations. Findings – We found out that both for under-determined and over-determined problems two figures of merit show better performance of a three-axial sensor system when compared with two mono-axial sensor systems. We also showed the positive impact of three component magnetic field data on MNS by means of repeated simulations. Research limitations/implications – The analysis is limited to theoretical sensor systems and can be applied also to realistic measurement set-ups. Noise is considered uncorrelated. The analysis could be carried out with the help of other figures of merit. More refined models for the human body could be adopted. Practical implications – The use of three axial sensor systems is encouraged in the field of magnetocardiography. Originality/value – Numerical analysis of inversion algorithms using three-dimensional magnetic field data in magnetocardiography have been never carried out. Keywords Magnetic devices, Medical equipment, Sensors, Numerical analysis Paper type Research paper 1. Introduction For a variety of medical applications the reconstruction of the electrical activity in the human body with the help of external and non-invasive measurements is of crucial interest. For example, a reconstruction of the altered cardiac electric activation in patients with coronary artery diseases can be obtained with the help of minimum norm solutions (MNS) based on externally measured magnetic fields (Leder et al., 1998). In the past, such multi-channel biomagnetic measurement systems have almost exclusively The Emerald Research Register for this journal is available at The current issue and full text archive of this journal is available at www.emeraldinsight.com/researchregister www.emeraldinsight.com/0332-1649.htm The authors thank Thomas Kno ¨sche for inspiring discussions and comments. This work was in part supported by the German Federal Ministry of Trade (BMWA), the German Academic Exchange Service (DAAD), and the Conferenza dei Rettori delle Universita ` Italiane (CRUI). Magnetic field data 869 COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Vol. 24 No. 3, 2005 pp. 869-881 q Emerald Group Publishing Limited 0332-1649 DOI 10.1108/03321640510598193