Magnetoencephalography (MEG) Flashcards
Why does MEG have a higher spatial resolution than EEG?
Because magnetic fields generated by the brain are not distorted by the scalp or the skull like electric fields are.
What is the main challenge of MEG?
The neuromagnetic signal is small (around 100 fT in strength) so it is hard to detect.
State the MEG forward problem
Given a known current distribution in the brain, can we compute the magnetic field distribution outside the head?
What are the two key approximations made to solve the MEG forward problem
The spherically symmetric conductor approximation: assume that the head/brain is a single sphere with homogeneous conductivity.
The current dipole approximation: when viewed from a distance, the field from a large number of synchronised post-synaptic currents looks like the field of a single current dipole.
What is an alternative to using the spherically symmetric conductor approximation?
Using more complex models from a patient’s MRI scan.
When is the current dipole approximation reasonable?
When the region of the brain activated is small.
Give the equation for the total current that can contribute to an MEG signal
J(r’) = total current
Jp(r’) = primary current
Jv(r’) = volume current
State the Geselowitz formula
B(r) = magnetic field
J^P(r’) = primary current
r’ = location inside the brain
R = r - r’
V = electric scalar potential
n(r’) = vector normal to the surface element
∇A x ∇B = ?
∇ x (A∇B)
State Stokes’ Theorem
How can the Geselowitz formula be derived?
- Define total current.
- Define volume current in terms of conductivity and ∇V (E = - ∇V).
- Use the Biot-Savart law to define the B-field outside of G.
- Substitute the primary and volume current in and separate the terms.
- Redefine the volume current using ∇A x ∇B = ∇ x (A∇B) and Stokes’ theorem.
State the Geselowitz formula after applying the two forward problem approximations
B(r) = magnetic field
Q = dipole magnitude and direction
r_Q = position of the current dipole
e_r = vector normal to the plane of the magnetic field detector
r = position
What does the Geselowitz formula represent after approximations have been applied?
An analytical forward model solution for a single current dipole in a spherically symmetric conductor.
What parts of the brain is MEG most sensitive to? Why?
Shallow sources in the cortex because the field decays with the square of distance.
MEG is only sensitive to dipoles oriented ___________.
Tangentially
State the MEG inverse problem
Can we calculate a current distribution inside the brain given a known magnetic field distribution outside the head?
Why is the MEG inverse problem ill-posed?
There are infinite solutions so an estimate is required using optimisation techniques.
What is a lead field?
An N-dimensional vector containing the magnetic field that would be measured at each end of N sensors in response to a single current-dipole source of unit amplitude at a pre-determined location in the brain.
What does the lead field represent?
The solution to the forward problem for all sensor locations for all possible source locations and orientations.
Describe the matrix system for MEG data
m = sensors
L = lead field at the i-th sensor form a unit of the j-th dipole
q = current dipoles
How does the lead field model help to solve the MEG inverse problem?
It allows the field to be calculated at each channel where each channel scans a section of the brain.
In reality, there are ~______ locations in a ~1mm voxelisation of the brain and only ~___ channels.
20,000
300
Give the matrix equation for MEG data
m = sensors
L = lead field
q = current dipoles
Describe how dipole fitting for MEG data works
- The number of active dipoles at r_Q is assumed to be 1.
- Knowing this, Q and r_Q are iteratively varied to minimise the sum squared difference between the model (m_model) and the data (m).
- Minimising the error reveals the optimum location, orientation, and strength of the dipole in the brain.
