Superposition and Integration

Electric and magnetic fields and the associated potential distributions obey the principle of superposition: the field distribution associated with a complex 3D pattern of currents is the integral over the contributions of all of the source currents flowing within the conducting volume. Within a small volume element (voxel), the distribution of cellular and volume currents can be modeled adequately by an equivalent point current with some orientation and magnitude, and the field of the entire volume can be computed as the sum over the contributions of all of the voxel currents.

Although the dendritic tree of a single neuron is often contained within a single voxel of an anatomical magnetic resonance image, each segment of current within the dendritic processes makes a contribution to the observed magnetic field and potential distributions. If the dendritic tree has a radially symmetrical geometry, the contributions may cancel and produce no effect observable at a distance. Cells of this configuration have been termed ''closed field''

Figure 2 Vector summation of neuronal intracellular currents. (a) The regular array of cortical neurons is evident in this classic drawing of Golgi-stained neural tissue. (b) The partial symmetry of an open-field neuron (pyramidal cell) gives rise to a net intracellular current vector aligned normal to the cortical surface. (c) The radial symmetry of a closed-field interneuron produces current cancellation resulting in no net intracellular current vector.

Figure 2 Vector summation of neuronal intracellular currents. (a) The regular array of cortical neurons is evident in this classic drawing of Golgi-stained neural tissue. (b) The partial symmetry of an open-field neuron (pyramidal cell) gives rise to a net intracellular current vector aligned normal to the cortical surface. (c) The radial symmetry of a closed-field interneuron produces current cancellation resulting in no net intracellular current vector.

neurons. Neurons with an asymmetric dendritic arborization have a net current vector and are termed "open field.'' These configurations are illustrated in Fig. 2. The neurons of neocortex have a net asymmetry that is normal (i.e., perpendicular) to the local cortical surface. Experimental validation of this prediction comes from experimental observations from linear arrays of microelectrodes penetrating the cortex. Such measurements find layered distributions of current sources and sinks across the thickness of cortex, whereas tangential potential differences are small within an extended area of activation. This basic prediction also is consistent with NEM measurements of responses from systematically arrayed sources in somatosensory or primary visual cortex.

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