A mathematical model for calculating the vector magnetic field of a single muscle fiber

A model of the magnetic fields created by single motor unit compound action potentials in skeletal muscle

We have developed a computationally simple model for calculating the magnetic-field strength at a point due to a single motor unit compound action potential (SMUCAP). The motor unit is defined only in terms of its anatomical features, and the SMUCAP is approximated using the tripole model. The distributed current density J is calculated within the volume defined by the motor unit. The law of Biot and Savart can then be cast in a form necessitating that J be integrated only over the region containing current sources or conductivity boundaries. The magnetic-field strength is defined as the summation of the contributions to the field made by every muscle fiber in the motor unit. Applying this model to SMUCAP measurements obtained using a high-resolution SUper Conducting Quantum Interference Device (SQUID) magnetometer may yield information regarding the distribution of action currents (AC's) and the anatomical properties of single motor units within a muscle bundle.