Biomedical Engineering Reference
In-Depth Information
A.1.4
Neuronal Populations
Neuronal activity gives rise to extracellular electric and magnetic fields, which are
detected inMEGandEEG. The fields generated by a single neuron aremuch too small
to be detected at the scalp, but the fields generated by synchronously active neurons,
with advantageous geometric alignment, can be detected. Dendrites are more able
than axons to generate fields which are detectable at large distances. Stellate cells
have approximately spherical dendritic trees, so the resulting extracellular fields tend
to add with all possible orientations, and effectively cancel at distance.
Pyramidal cells have similar dendritic trees, but the tree branches are connected
to the cell body (soma) by a long trunk, called the apical dendrite. It is a fortuitous
anatomical feature of the cortex that pyramidal cells have their apical dendrites
aligned systematically along the local normal to the cortical surface. In this way,
the fields of synchronously active pyramidal neurons superimpose geometrically
to be measurable at the scalp. Consider an approximately 1 cm
3
region of cortex,
containing an order of 10
7
aligned pyramidal cells. If only 1 % of these neurons were
synchronously active, th
en th
e relative contribution of synchronous to asynchronous
neurons would be 10
5
√
10
7
/
∼
30. Thus, scalpMEG and EEG are largely dominated
by synchronous neural activity.
A.2
Electromagnetic Fields in Conductive Media
A.2.1
Maxwell's Equations
Outside the scalp, we measure the net fields produced by synchronously active neu-
rons. For calculations at this scale, the brain and other head tissues can be considered
bulk materials, characterized by properties such as electric conductivity
. The chal-
lenge is to compute magnetic fields and scalp potentials as a function of neuronal
source currents in a head-shaped conductive medium. We begin here with the fun-
damentals of electric and magnetic fields in matter, and later specialize to biological
tissue.
The physics of electric and magnetic fields are summarized by Maxwell's equa-
tions. In matter the macroscopic fields obey
˃
=
ˁ
∇·
E
,
(A.2)
∇·
B
=
0
,
(A.3)
=−
∂
B
∂
∇×
E
t
,
(A.4)
+
μ
∂
E
∂
∇×
B
=
μ
J
t
.
(A.5)
