Magnetoencephalography (MEG) is by far the most

advanced technique of measuring and evaluating the magnetic fields generated by

brain activities. When brain functions, the interaction among brain cells

generates tiny electrical voltages 1. The resulting flow of the intracellular

electrical current over the brain cortex produces magnetic fields. This amount

of magnetic field is tiny, but still can be detected and evaluated using

extremely sensitive magnetometers. Figure 1 shows the process that synchronized

neuronal currents induce weak magnetic fields over the brain. The magnetic

field generated from brain activity is in range of femtotesla (fT), and the

magnetic noise induced by ambient environment has the order of nanotesla (nT).

Therefore one big challenge with MEG is to detect the weak target signal from

the environmental noise.

The time resolution capabilities of MEG are in range

of 10 milliseconds or even faster. Comparing to a functional MRI, MEG can best

resolve events with a precision of several hundred milliseconds. Though MEG can

provide information of the activities of colonies of neurons of the cerebral

cortex (outmost thin layer that covers the cerebrum), it has a limitation in which

the neuron signals can only recorded from the scalp 2.

One major challenge for MEG system is source

localization since a unique solution to the problem of reconstructing where

exactly the sources of these signals are localized within the brain does not

exist 3. The standard approach to overcome the non-uniqueness of the inverse

problem in MEG is to introduce constraints on the possible solutions to determine

the most suitable solution to interpret the data. Thus, the source localization

of the MEG signals depends to some degree on the models used and on the

corresponding assumptions, and therefore will have some degree of uncertainty.

1.2 Neurons – the origin of MEG

signals

As mentioned earlier, MEG signals are originated from

the interchange of ions among neurons. Neurons and glial cells are the major

building blocks of the brain. Neurons are the information processing unit there

their cell bodies and dendrites are concentrated in the grey matter. Glial

cells are the important unit for supporting the neuron structures and maintaining

the proper concentrations of ions. Glial cells can also transport nutrients and

other substances between blood vessels and brain tissue. Figure 2 is the

schematic drawing a neuron.

Neuron is a nerve cell which designated to transmit

information to other nerve cells and muscles. The process of transmitting

information among cells are referred as intra-cellular signaling and

extra-cellular signaling. Both types of neuronal signaling are essential to

maintain the functionality of the nervous system. When neuronal signaling takes

place, a voltage pulse is generated and travels along the axon. Once the

voltage at the axon reaches the firing threshold (about 40mV), an action

potential will be initiated and then causing a series of cascading events for

neurotransmission.

There are over 10000 types of neurons which can be

categorized in three types: motor type, sensory type and interneurons. The

three types of neurons govern the brain functions such as movement, sensing

(visual, audio, olfactory, tactile) and recognitions. Figure 3 shows a more

illustrated brain functioning map.

1.3 Forward Problem

The forward problem in bio-magnetics studies the

magnetic field and electric potential arise from a known source. For practical

purposes, appropriate physics models must be selected for the source and the biological

object. In this section, the forward problem is discussed, however only fields within

a homogenous media due to electric source currents are considered. We describe

how the magnetic induction (B) and the electric potential (V) are computed

using the approximation of Maxwell’s equations and also by Biot-Savart law.

(1)

Suppose

that the conductor consists of the whole space with constant conductivity U.

Then equation (1) is Poisson’s equation with the solution 5:

(2)

where

the integration is over a region containing the source J’. Using the vector

identity V’. (J'(r’)Ir- r’1-I) = Ir-r’l-‘V’ – Ji(r’)+ Ji(r’) – V'(lr- r’1-I)

with V'(lrr’1-I) = Ir – r'(-3(r – r’) and the Gauss theorem we can transform

equation (1) to the form,

(3)

because

the surface integral jaGJ'(r’)lr – r’1-I * dS = 0 since J’ = 0 on the boundary

aG of G. Equation (2) is a convenient formula for V because it is also valid

for J’ which is not differentiable everywhere. Using the identity V’ x (J(

r’)lr – r’l”) = Ir – r’I-‘V’ x J( r’) +V'( (r – r’1-I) x J( r’) and Stokes’

theorem we obtain:

If the source current is evenly distributed on a

homogeneous line or surface, equations (2) and (3) remain valid if we replace

the volume density J’ by a line or a surface density and the volume integral by

a line or a surface integral, respectively 6.

(4)

To

measure the magnetic source within brain (treated as a homogenous media), we

derive a formula for B outside a spherically symmetric conductor and we assume

that J’ is a current dipole Q at located at distance ro from the

center of the sphere. The total current J outside from conduct is zero, and

thus V x B = 0. The magnetic field outside the conductor can then be expressed

in terms of a magnetic scalar potential U:

(5)

To

find an expression for U, we fix r outside G and consider a line integral of U

along the radius r+ter from 0 to infinity because U vanishes at

infinity, we obtain

(6)

The

last integral is easy to compute and we obtain and we got

(7)

Where

F = a(ra+r2-r0

r) and a = r-r0. Eventually the

magnetic general equation is derived as shown in equation (7)

Where

.

Equations

(6) and (7) show another important property of a spherical conductor: if the

source dipole is radial, then B outside G vanishes.

1.4 Inverse Problem

Inverse problem is much more difficult than forward

problem. For inverse problem, we need to search for the unknown sources by analysis

of the measured field data. The result may contain unlimited number of

solutions. Somethings the transfer of energy between magnetic and electric fields

within the brain media also complicates the inverse problem. To determine the

appropriate solution among all possible solutions, extra special conditions

must be added and we need to apply restrictions of possible source

configurations 7.

1.5 Instrumentation

The most advanced and mature technology to implement

MEG signal measurement is using Superconducting quantum interference device (SQUID)

based imaging system. A SQUID system has gradiometers arranged to cover the

brain area and they have extremely high sensitivity and low noise which can

pick up even fetal brain signals 8. One of the major challenge for SQUID

based MEG signal measurement is environmental noise, which will be elaborated

in later sections. Approaches which have been adapted to solve the

environmental noise issue include noise cancellation, MEG source localization

which depends no noise cancellation and MEG inversion which contributes to

noise cancellation 9.

For noise cancellation, shield is the most straight

forward approach. A thin layer of highly conducted metal is applied to block

noise at low frequency. The noise from far distance and higher frequencies are

taken care by gradiometers. The higher order of the gradiometer more noise can

be attenuated. Usually a maximum of three order gradiometer is used because

higher order requires a large space 10.

MEG inversion contributes to noise cancellation

involves beam former which can be classified as linearly constrained minimum

variance (LCMV), synthetic aperture magnetometry (SAM) and signal space

projection (SSP). Also equivalent current dipole (ECD) which uses iterative

method for optimization of the result is also mostly used to model brain source

activity. But it is very sensitive to noise and correct result removal 11.