Nevzat Gencer

International Summer School and Workshop on Brain Dynamics, July 23 - 28 , 2012
ELECTRO-MAGNETIC SOURCE
IMAGING OF THE HUMAN BRAIN
Nevzat G. Gençer
Department of Electrical and Electronics Engineering,
Middle East Technical University, 06800, Balgat, Ankara, Turkey
Institute of Theoretical and Applied Physics (ITAP), Marmaris, TURKEY
1
Outline
• METU Brain Research Laboratory
• Electro-Magnetic Source Imaging (EMSI)
–
–
–
–
Signal properties
Realistic Head Modeling using MRI data
Forward/Inverse Problem Solutions
Instrumentation
• Electrical Impedance Imaging
– Forward/Inverse Problem Solutions
– Instrumentation
– Experimental Results
2
METU MAP
3
Brain Research Laboratory
Department of Electrical and Electronics Engineering
Middle East Technical University, TURKEY
Research interests :
Numerical Methods
applied to EEG and MEG research
Mathematical and
Computational aspects of Medical Imaging
Medical Instrumentation
Multi-channel EEG system design
Novel imaging systems
Medical Image Processing
Image segmentation from MRI data
Parallel Processing
Numerical solution of electromagnetic
field problems using Beawolf Clusters
Visulalization
Facilities:
2 Laboratories,
Programming resources,
2 Computer Clusters,
256-channel EEG device,
Electronic measurement devices,
Prototype novel imaging systems
Education Support:
Analog Electronics, Semiconductor Devices
and Modeling, Medical Imaging,
Bioelectricity and Biomagnetism,
Physiological Control Systems
Prof. Dr. Nevzat G. Gençer
Tel : +90-312-2102314
Fax: +90-312-2102304
Web: http://www.eee.metu.edu.tr/~biomed/brl
4
Brain Research Laboratory
Department of Electrical and Electronics Engineering
Middle East Technical University, TURKEY
Research Projects :
Faculty:
Electro-magnetic source imaging of the human brain
Prof. Dr. Nevzat G. Gençer
Extraction of Evoked Responses
Segmentation using MR images
Finite Element/Boundary Element Method Modeling
Inverse Problem algorithms
Multi-channel EEG devices
Graduate students :
Electrical impedance imaging
Electrical Impedance Imaging via contactless measurements
Applied/Induced Current Electrical Impedance Imaging
Conductivity imaging via evoked potentials
Brain Computer Interfaces (BCIs)
P300 based BCI systems
Cue based Motor imagery BCI systems
Balkar Erdoğan,
Berna Akıncı
Reyhan Tutuk,
Feza Carlak,
C. Barış Top
Koray Özkan
Software support:
Didem Menekşe
Prof. Dr. Nevzat G. Gençer
Tel : +90-312-2102314
Fax: +90-312-2102304
Web: http://www.eee.metu.edu.tr/~biomed/brl
E-mail: [email protected]
5
ELECTO-MAGNETIC SOURCE IMAGING
6
Role of Electro-magnetic Source Imaging
• Magnetoencephalography (MEG)
and electroencephalography (EEG)
devices respectively measure the
magnetic fields near the head and
the electric potentials on the scalp
surface due to the electrical
activities inside the human brain.
• Localization of the brain activities
using EEG and MEG measurements
is called electromagnetic source
imaging (EMSI).
EEG sensors
MEG sensors (Vectorview from
Elekta Neuromag)
7
Applications
• Localizing centers (audial, visual, language,
motor) of the human brain prior to brain
surgery,
• Improved understanding and treatment of
serious neurological and neuropsychological
disorders such as intractable epilepsy,
schizophrenia, depression, and Parkinson’s
and Alzheimer’s diseases.
8
Basic properties compared to other
functional brain imaging modalities
• Direct measurement of electrical brain activity and
offer the potential for superior temporal resolution
(ms) when compared to PET and fMRI (1 s).
• The spatial resolving power of MEG and EEG does not,
in general, match that of PET and fMRI (1-3 mm).
Resolution is limited by:
– the relatively small number of measurements,
– The inherent ambiquity of the underlying static
electromagnetic inverse problem (ill-posedness).
9
Forward and Inverse problems
• The electrical activities in the brain are usually modeled using
current dipoles.
• The purpose of EMSI is to obtain information about the
spatio-temporal behavior of these dipoles.
• The solution of the scalp potentials and magnetic fields for a
specific dipole configuration is the forward problem of EMSI.
• Complementarily, the inverse problem is the localization of the
sources based on the measurements and the calculations.
10
Head Models
• Accurate modeling of the human head is necessary to
increase the accuracy of EMSI solutions.
• Realistic head models are usually obtained via MRI data. This
requires image processing, more specifically, application of
segmentation algorithms.
• When the realistic head models are used, a numerical method
must be adopted to solve the forward problems.
• The most widely used numerical methods are the boundary
element method (BEM), the finite element method (FEM)
and the finite difference method (FDM).
• To increase the numerical accuracy in the solutions either the
numerical formulation is improved or the quality of the
meshes used in the calculations is increased.
11
Electro-Magnetic Source Imaging
Imaging/Image
processing
Forward
problem
Computing
Data Acquisition
(EEG/MEG)
Inverse
Problem
MRI
Segmentation
Head Modeling
Source Localization
12
Critical Steps for succesful localization
Inverse
Problem
Algorithm
Reference
Electrode
Selection
Appropriate
Data Period
Registration
Forward
Problem
Approach
Electrode/sensor
Locations
Data
Acquisition
System
Mesh
Generation
Segmentation
Source
Localization
Apriori
assumption
about the
source
13
Milestones in elecrophysiology literature
Sheerington
introduced the
concept of
synapse, in 1897
The term neuron
was applied to
neural cell by
Weldeyer in 1891
The first high
quality ECG
recorder was
developed by
Eindhoven
(1908)
The first
magnetocardiogram
(MCG) was recorded by
Baule and McFee (1963)
Young shows the
applicabiity of the
squid axon for
electrophysiology
studies in 1936.
In 1902 Bernstein
developed the "membrane
theory" of electrical
potential in biological cells
and tissues.
1900
Hodgkin and Huxley
developed an accurate
mathematical model of the
activation process in 1952
MEG devices
with multiple
sensors are
developed
(1980s)
Cohen and Zimmermann recorded
the first magnetoencephalogram
(MEG) using SQUIDs (1972)
2000
1950
Neher and Sakmann
invented the patch
clamp technique
(1976)
Gasser and Erlanger record
the time courses of nerve
impulses in 1922.
Basic research into the
study of neurons was
undertaken by August
Forell, Wilhelm His and
Santiago Cajal
Adrian formulated all-ornothing law of the neural
cell, 1912.
Granit developed a
microelectrode that permits the
measurement of electric
potentials inside a cell (1939).
Berger made the first
recording of the
electroencephalography
(EEG) on a human (1924)
MEG devices
that contain
about 300
sensors are
developed.
The RF squid was invented by
Jaklevic, Lambe, Silver and
Zimmerman (1965)
Eccless
investigated
synaptic
transmission
in 1950s.
EEG devices
that acquire
data from 256
electrodes are
developed.
Cohen measured the magnetic
alpha rhythm with an induction
coil magnetometer (1968)
14
Origin of EEG/MEG signals
cortical surface
Structure of cortex
Structure of Neuron
3 mm
dentrites
soma
(Wikipeida.org)
1010 neurons
1014 connections
50000 neurons/cm3
70 % of neurons are
pyramidal cells
white matter
axon
15
Basic properties
• Nerve cells (neurons) are
excitable.
• Cell membranes generate
electrochemical impulses (action
potentials APs) as a consequence
of excitation.
• Membranes conduct APs without
attenuation.
Action
potential
Amplitude
(Wikipedia.org)
Action
potential
Postsynaptic
potential
100 mV
10 mV
Postsynaptic
potential
16
Period
1 ms
10 ms
Resting-Graded-Action potentials
Silverthorn, Human Physiology, Prentice Hall,1996
(http://cwx.prenhall.com/bookbind/pubbooks/silverthorn2/)
17
Obserbing a propagating AP

e (r )
observation
point
-
Vm
+

1  i Vm 
e (r )  
a z  (1 / R) dV 

4  e V z '
Vm  i  e
 
R  r  r'
z’
e :extracellular potential
i :intracellular potential
Vm :transmembrane voltage
18
Q: How do we model the source of APs?
ELECTRICAL POTENTIAL OF DIFFERENT SOURCE TYPES
SOURCE TYPE
Monopole
Volume distribution
of monopolar sources
Surface layer of
of monopolar sources
SYMBOL
Io
UNIT
A
POTENTIAL EXPRESSION

 (r ) 
I0
 
4 r  r 
1


I sv (r )
  dV 
r  r


I s (r )
  dS 
r  r
Isv
A/m3

1
 (r ) 
4
Is
A/m2

1
 (r ) 
4
Am

 

p (r  r )
 (r ) 

4 r  r 3
Dipole

p
Volume distribution
of dipolar sources

pv
A/m2
 (r ) 
Surface distribution
of monopolar sources
ps
A/m
 (r ) 


V
S
1
 
1

pv (r )  (1 / R) dV 
4 V

ps (r )(1 / R)  n dS 
4 S
19
For a volume distribution of current dipole sources
pv(r), expressed in A/m2 , in an unbounded medium of
conductivity , we have

1
e ( r ) 
4
 
 pv (r ' )  (1 / R) dV 
V
It is evident that, an AP propagating in a single fiber
posesses an equivalent volume dipole density:
 

pv (r )   i (Vm / z)a z
20
Source model of propagating AP is a quadrupole.
field point
e (z )
i (z ' )
fiber
21
z’
Q: How do we model for the source of postsynaptic
potentials?
intracellular
current
Postsynaptic
cell
z
Excitatory
-Io
Presynaptic
cell
Depolarization
AP
d
Io
dendrite
Hyperpolarization
soma


p  I0 d
axon
Presynaptic
cell
Inhibitory
AP
‘’The primary source of the evoked field
is the intracellular current from dendrite
to soma and can be represented by a
current dipole as a first approximation
(Okada, 1983).‘’
22
Source model of postsynaptic potentials is a current
dipole.
Postsynaptic
cell
Depolarization
dendrite


p  I0 d
Hyperpolarization
soma
axon
23
Q: Which model is more appropriate for EEG and MEG
signals? Quadrupole or dipole model?
• The fields of a quadrupole decreases
much faster compared to the fields of a
current dipole.
• The frequency content of the evoked
fields (0.5-50 Hz) is much lower than the
frequency content of an action potential.
Whereas it is in the range of the post
synaptic potentials.
• Consequently, one may assume 1) the
scalp potentials as the cumulative effect
of the postsnaptic potentials, 2) the
source model of EEG/MEG is a current
dipole.
• Note that, EEG/MEG measurements are
due to a large number of (1015-1016)
synchronously fired pyramidal cells.
Action
potential
Postsynaptic
potential
Amplitude
100 mV
10 mV
Period
1 ms
10 ms
Model
quadrupole
dipole
24
Fields of a shallow dipole
Potential field
25
Magnetic field
INSTRUMENTATION AND
MEASUREMENT SENSITIVITY
26
EEG Measurements
• The amplitude of background
EEG is on the order of few  V
– 75  V.
• The frequency band is divided
into 4 intervals:
Delta ()
0.5 Hz - 4.0 Hz
Theta ()
4.0 Hz - 8.0 Hz
Alpha ()
8.0 Hz - 13 Hz
Beta ()
13.0 Hz - 50 Hz
• The amplitude of the evoked
potentials are on the order of 1
V and one should apply special
techniques to extract it.
The international 10-20 system
27
Properties of the research/commercial EEG devices
(Usakli and Gencer, 2007)
28
Multi-channel EEG device design
A multichannel EEG device for ESI should satisfy a number of requirements based on
signal dependent, environmental, medical, and economical reasons (Usakli and Gencer,
2007).
•
•
•
•
•
•
•
•
•
•
•
•
The system must accurately measure signals with an amplitude less than 300 mV in the
frequency range of 0–30 Hz. The recordings should preserve the original waveform.
To obtain a high spatial resolution, more than one hundred electrodes should be placed on the
scalp surface.
Considering possible contact impedance, the input impedance of the circuit should be sufficiently
large (for example, >1 G).
To reduce power line interference, the CMRR of the instrumentation amplifiers (IA) should be
high (>100 dB) and the system should be battery powered.
The noise (referred to input) should be less than 2 V (rms).
To reduce electronic noise, the analog and digital grounds should be properly isolated.
To follow the signal details, the digital resolution of ADCs should be high (number of effective bits
>12).
The cross talk rejection figure between the channels should be high.
There should be no delay in the sampling instants of different channels.
The system should be transportable and a PC interface must be provided with no additional I/O
card installed in PC.
The communication means should handle the transfer rate of a multichannel high resolution
digital data.
The above-given requirements should be satisfied by using available and less expensive
components.
29
Sensitivity of surface electrodes to the electrical activities in the brain.
(Puikkonen
and Malmivuo,
1987)
30
MEG Measurements
• Information about the brain activity
can also be obtained from the
recorfing of magnetic fields outside
the skull. These recordings are
called Magnetoencephalogram
(MEG).
• Baule and McFee’s coil arrangement
was used by Cohen (1968) to detect
the magnetic field of the alpha
rhythm of the brain.
• Introduction of the SQUID
(Superconducting Quantum
Interference Device) into
biomagnetic studies (James Edward
Zimmerman) improved the
sensitivity of magnetic field
measurements by several orders of
magnitude, thus enabling the realtime monitoring of spontaneous
brain activity.
Early MEG studies
(Williamson, Romani,Kaufman
and Modena, 1983)
31
MEG Measurements
Coil configurations
MEG sensors (Vectorview from
Elekta Neuromag)
32
Magnetic signals produced by various sources
Magnetic shielding
(Malmivuo and Plonsey 1995)
(Wikipedia.org)
33
Sensitivity of a circular coil to the electrical activities in the brain.
Isosensitivity lines in MEG
measurement in a spherical head
model with a single coil magnetometer
having a radius 10 mm . The sensitivity
is everywhere oriented tangential to
the symmetry axis which is the line of
zero sensitivity. Within the brain area
the maximum sensitivity is located at
the surface of the brain and it is
indicated with shading (Malmivuo and
Plonsey, 1995).
34
REALISTIC HEAD MODELING
35
Image segmentation
• To create a realistic head model, one must first classify the main tissues of
the head from high resolution volume images. Segmentation is the
process of classifying image elements that have the same properties.
• There are three major segmentation methods in the literature:
(1) the deterministic methods that use classical image
processing tools like thresholding, region growing and
morphological operations,
2) the statistical methods based on probabilistic methods that
may also estimate the inhomogeneity in the MR images ; and
(3) methods that use a deformable atlas
• To use realistic head models, in general, only the main tissues in the head,
such as scalp, skull and brain layers, are included.
• To classify these tissues, usually, T1-weighted MR images are employed,
since it provides high soft tissue contrast.
• If cerebrospinal fluid (CSF) is to be included in the model, T1-weighted
images are not sufficient since CSF cannot be distinguished from the skull.
36
• In the METU BRL, the scalp, skull, CSF, eyes,
GM and WM are segmented from the threedimensional multimodal MR images of the
head.
• A hybrid algorithm is developed that applies
the snakes algorithm, region growing,
thresholding and morphological operations
(Akalın and Gencer 2000).
37
Segmentation
The background is
segmented using the
PD images
38
Segmentation
The skull is segmented
using the PD images
39
Segmentation
The eye tissue is
obtained from T1
images using
a template
40
Segmentation
The segmented images
are discarded from the
head images. The scalp
is segmented from the
remaining T1 images
41
Segmentation
The scalp is removed from the
head images.
Using the raw image of the
cortex, the CSF, the cortex and
the WM are segmented
42
Segmentation
The remaining voxels are
labeled according to their
neighboring.
43
Segmentation Results
Scalp
White matter
Skull
Cortex
44
FORWARD PROBLEM
45
Quasi-static approximation
for biological systems
• The capacitive component of tissue impedance is
negligible in the frequency band of internal
bioelectric events (Schwan and Kay,1957).
• The volume conductor currents were essentially
conduction currents and only tissue resistivity
must be specified.
• The electromagnetic propagation effect can also
be neglected (Geselowitz, 1963).
46
• Thus the time-varying bioelectric currents and
voltages in the human body can be examined
in the conventional quasistatic limit (Plonsey
and Heppner, 1967).
• All currents and fields behave, at any instant,
as if they are stationary.
• The description of the fields resulting from the
applied current sources is based on the
understanding that the medium is resistive
only.
• The phase of the time variation can be ignored
(i.e., all fields vary synchronously).
47
 / ratio for various tissues
at different frequencies
10 Hz
100 Hz
1000 Hz 10000Hz
Lung
0.15
0.025
0.05
0.14
Fatty
tissue
-
0.01
0.03
0.15
Liver
0.2
0.035
0.06
0.20
Heart
muscle
0.1
0.04
0.15
0.32
48
Poisson’s Equations
As a consequence of the above conditions

E  
 
 
J  J s   E  J s   
Starting from the continuity equation we obtain


  J    ( J s    )  0

  ( )    J s   I sv
49
Forward problem of electrical source imaging
To calculate the scalar potential outside the head due to a
given primary current distribution.
       J


0
n
s
inside V

B

S
on S
p   J dV
s
50
Integral equation
We obtain the well known formula in the literature of the EEG
forward problem formulation:
2
1
( P) 
Vo (P) 
( k   k )
2

j 1 S j

( j   j )

(1 / R)  dS j
( k   k )
This integral equation is the basis of the Boundary Element
Method (BEM) formulation for the numerical calculation of the
potential function.
1
V0 ( P ) 
4
s
J
 (1/ R) dV
V
V0 represents the potential
at P due to Js in an infinite
homogeneous medium with
unit conductivity.
51
Forward problem of neuromagnetism
• To calculate the magnetic field B outside the head or
thorax from a given primary current distribution.
• The starting point is the Maxwell’s equation using the
quasi-static approximation.


  B  o J
• A solution to B that obeys Maxwell’s third equation
(divergence of B is zero), and the condition that B
vanishes at infinity is given by the Ampere-Laplace
law.
52
Ampere-Laplace Law
 o
B
4

 
J R
dV
R3

R
 (1 / R)  (1 / R)
3
R

 R 


J  3  J  (1 / R)  (  J ) / R    ( J / R)
R
 o


o
B
(  J ) / R dV  
  ( J / R)dV 
4
4


53
Applying the Stoke’s theorem



 
  A dV  A  dS



  ( J / R) dV   ( J / R)  dS 


This term is equal to zero when there are no sources on the object
surface.
 o

B
(  J ) / R dV 
4

54
Components of the measured field
 
 
J  J i   E  J i   

 o   J i
o   ( )
B
dV 
dV
4 V R
4 V
R

 o   J i
 o   
B
dV 
dV
4 V R
4 V
R
 






direct effect of the
primary current
contribution of the
volume currents
55
Another form of the B field expression
 
 o J  R
B
dV
3
4 R
 o 
B
J  (1 / R)dV
4
 o 
o
B
J i  (1 / R)dV 
  (1 / R)dV
4
4




56
NUMERICAL MODELING
• An essential part of this methodology is the solution of the
forward problem, i.e. solving the potentials and magnetic
fields knowing the source distribution and physical properties
of the head.
• A homogeneous sphere has been widely used in literature to
model the head (Barnard 1967, Brody et al 1973, Cuffin 1978,
Budiman and Buchanan 1993). This simple model provides a
quick way of calculating the associated field patterns
approximately.
• In a realistic head model, complicated numerical methods
have to be employed to solve these fields accurately.
57
NUMERICAL MODELING
Boundary
Element
Method (BEM)
• Formulated using integral equations.
• More efficient than other methods in terms of
computational resources for problems with
small surface/volume ratio.
• Results in dense coefficient matrix.
Finite Element
Method (FEM)
• Finds approximate solutions to the partial
differential equations.
• Handles complicated geometries with relative
ease.
• Results in sparse coefficient matrices.
Finite
Difference
Method (FDM)
• FDM in its basic form is restricted to
rectangular shapes
• Very easy to implement.
• Results in sparse coefficient matrices.
58
Head models and solution methods
3-4 surface spherical models
(analytical solutions)
Realistic models
Boundary Element Method (BEM)
(Akalın ve Gencer, 2004)
Realistic Models
Finite Element Method (FEM)
(Gencer ve Acar, 2004)
59
BEM Formulation
Integral equation for the Potential Field:
1
 (r )  2 g (r ) 
2
 

1 pR
g (r ) 
4 0 R 3
  k   k 
' R
'

(
r
)

dS
(
r
)
 k 1        
k
3
R
i  Sk
 i
n
Integral equation for the Magnetic Field:

 '
 
  0 n
' R


B(r )  B0 (r ) 
( k   k )   (r ) 3  dS k (r )

k 1
4
R
S
 
 
0 p  R
B0 (r ) 
4 R 3
k
60
Spherical Meshes
61
BEM Formulation
Each surface
S k is discretized into N area elements.


N
 R  
 R i 
 (r ) 3  dS k (r )
S  (r ) R3  dSk (r )  

R
i 1 S i
k
k
Shape functions
m
m
x   N i ( , , ) x
i 1
e
i
m
y   N i ( , , ) y
i 1
z   N i ( , , ) zie
i 1
m
e
i
   N i ( , , )ie
i 1
62
BEM Formulation
Element surface integrations can be expressed in terms of the
local coordinates (,).


1
1
N
 R  
 R 
 (r ) 3  nGdd
S  (r ) R3  dS (r )  


R
i 1 0 0
k
G can be expressed as:


r  r 
G

 
The integral on the local coordinates can be approximated by
Gauss-Legendre quadrature
1 1

0 0
1 gp
f ( , )dd   f ( j , j ) w j
2 j 1
63
BEM Formulation
Thus the surface integrals can be expressed as:


gp
N
R( j , j ) 
 R  
1
 ( j , j ) w j
 n ( j , j )G ( j , j )

3
S  (r ) R3  dS (r )  
R( j , j )
i 1 2 j 1
k
The potential at any local coordinate can be expressed in terms
of the node potentials

Mk
 R  
c j j
S  (r ) R3  dS (r )  
j 1
k
In matrix notation we obtain
 M 1  CM M   g M 1
  [ I  C ]1 g
M: number of nodes
64
FEM Elements and Source Models
• Linear or quadratic isoparametric
hexahedral volume elements with
constant conductivity
• Two Source models:
– Element volume current (Gencer, et. al.)
– Dipole inside element (Yan, et. al.)
Linear element:
8 nodes
• Sparse, symmetric, positivedefinite matrix equation: A=b
Quadratic element: 20 nodes
65
Sample Volume meshes: Realistic-Grid
Skull
CSF
Eyes
Grid-based mesh obtained from segmented MR images
66
FEM Formulation
       J


0
n
P

B
inside V

S
on S
Using Galerkin’s weighted residuals method:
p
 Ni  (σ e ) dV   Ni  J dV
Ve
Ni : ith shape function
e : conductivity of the element
i  1 ... 20
Ve
Jp : Current density inside
the element (source)
67
FEM Formulation
After applying appropriate vector identities and Gauss’s theorem:

 σ eNi   dVe   Ni σ e  dSe i  1... 20
Ve
Se
p 
 e  n  J  n
p 
 σ Ni   dVe   Ni J  n dSe
Ve
i  1 ... 20
Se
68
FEM Formulation
20
Since
 

N i ie
i 1

 e
p 


σ

N


Ν
dV
i  1 ... 20

e
i
j
e  j   N i J  n dS e



j 1  Ve
Se

20
In matrix form:
Global matrix equation:
A Φ b
e
e
AΦ = b
e
A : M M Matrix - geometry
and conductivity information.
 : M 1 Unknown potentials
b : M 1 Source vector
69
FEM & BEM Comparison
•
•
•
•
FEM
Volume Elements
Can model arbitrary
conductivity distributions
including anisotropy
High number of nodes
(200,000 – 2,000,000)
Sparse Matrix
•
•
•
•
BEM
Surface Elements
Conductivity is assumed
to be homogeneous in
compartments
Low number of nodes
(1,000 – 10,000)
Dense matrix
70
FEM Computational Problems
• Realistic Mesh = Large Matrix
Edge length
5 mm
2 mm
Elements
37 600
588 000
Nodes (linear)
38 000
560 000
Nodes (quadratic)
150 000
2 240 000
71
Parallel implementation of the accelerated BEM
approach for EMSI of the human brain
• Computational complexity is a limiting factor that prevents the use of
detailed BEM models. In order to avoid long processing times and to
prevent running out of memory, even the recent studies use coarse
meshes for realistic models.
• Recent work by Akalın-Acar and Gencer (2004), introduced the
accelerated BEM formulation for EEG and MEG in order to speed-up the FP
solutions.
• Accelerated BEM formulation computes transfer matrices from the BEM
system matrix (coefficient matrix) and electrode/sensor positions. Once
these matrices are computed, the FP solutions are reduced to simple
matrix-vector multiplications.
• Unfortunately, even with accelerated BEM approach, the pre-computation
phase takes a long time for detailed meshes, and the transfer matrices
require additional memory.
72
METU Marvin cluster
The four Nodelin workstations are
connected to each other over a 100 Mb/s
Ethernet switch and the Athlin nodes are
connected to each other over a Gigabit
Ethernet switch.
All cluster nodes are running under the
Linux operating system. The controlling
workstation is running FreeBSD and provides
access to the cluster nodes.
The computation nodes have the following
libraries for parallel processing and
numerical operations: message passing
interface (MPI), automatically tuned linear
algebra subroutines (ATLAS) version of basic
linear algebra subprograms (BLAS), linear
algebra package (LAPACK), and PETSc .
These libraries are organized in a
layered structure, in which the PETSc
is the top most layer.
73
Contributions
Our main contributions are
summarized as follows:
(1) A feasible and scalable
parallelization scheme is
presented for the accelerated
BEM approach.
(2) The performance of the
proposed parallelization scheme
is tested. It was observed that
our scheme provides memory
scaling as well as faster
operation with a considerable
speed-up in the matrix filling,
transfer matrix calculation and
solution phases.
74
Sensitivity of EEG and MEG measurements to
tissue conductivity
75
Main motivation
• To identify the region(s) where a particular
measurement is more sensitive
• To reveal the tissue type that is more effective in the
measurements
• To compare the sensitivity of electrical and magnetic
measurements to conductivity perturbations
• To provide a means for updating the assigned
conductivity values.
76
Relating the change in the potential measurements
to change in conductivity perturbations
Expression for :   ( )    J p
Insert   0   and    0  
   00   0( )  0  ( )    J p
  ( 0( ))    (0 )
( )
0
n
77
Special cases:
1)
Perturbation confined on a
specific tissue:
2)
Uniform initial conductivity
distribution
 

 2 ( )    
0 
 0

   
0
n
 0 2 ( )    0 
  
0
n
3)
Uniform perturbation in an
initially uniform
conducting body
 0 ( )  
2
 
0
n

0

0
(  J p )
(  J p )
77
Field Profiles
 0
( )
79
Interpretation of the sensitivity equations
• The resulting fields are due to secondary
dipole sources located at the position of
conductivity perturbations.
• These dipoles are in the direction of the
initial electric field at the perturbation
point
80
Relating the change in the magnetic
measurements to changes in the conductivity
perturbations
0
R

Secondary B field: B s ( ) 




dV
3
4 
R
0
B s ( 0   ) 
4
R
  0   0    R3 dV 
0
0
R
R
B 
 0  3 dV  
0  3 dV


4
R
4
R
81
Sensitivity: Numerical Implementation
From:  ( 0( ))   (0 )
Using:      0
  ( 0( ))    (0 )    ( 00 )
A( 0 )  (A( ) 0  A( 0 ) 0 )
For s sensors:  s  S
1 
A( ) 0  
 s  SA( 0 )

 
 s  S 
0
82
Sensitivity: Numerical Implementation
0
0
R
R
B 
 0  3 dV  
0  3 dV


4
R
4
R
B 
0
0
R








d
V

0
4 
R3
4
R










 0 0 0 3 dV
R
B  C( 0 )  C( )0  C( 0 ) 0 
 

1 
C( ) 0   C( 0 )A( 0 )
A( ) 0   
B  

 
  0
  0 

B  SB 
83
Mapping Sensitivity Distributions
• The sensitivity matrix reveals the sensitivity of
measurements at the selected sensors to element
conductivity for each dipole.
• It presents a 3D data for each sensor/dipole
combination.
• Total Sensitivity concept visualizes the sum of the
sensitivity matrix rows.
84
Sensitivity Distributions
Spherical Head - EEG Electrode Pair Sensitivity
85
Sensitivity Distributions
Spherical Head - MEG Single Lead Sensitivity
86
Total lead sensitivity:
Spherical Head
Problem Geometry
87
EEG Total Lead Sensitivity
88
MEG Total Lead Sensitivity
89
Total lead sensitivity:
Realistic Head
Problem geometry
90
EEG Total Lead Sensitivity
Realistic Head - EEG Total Sensitivity
91
MEG Total Lead Sensitivity
Realistic Head - MEG Total Sensitivity
92
Contributions
• Two equations are derived that relate change
in measurements to conductivity
perturbations.
• A numerical formulation is obtained to find
the sensitivity using a realistic head model.
• Total lead sensitivity concept is used to
analyze the sensitivity maps.
93
Summary
• EEG measurements are more sensitive to
conductivity perturbations on the skull and the
brain tissue in the vicinity of the dipole.
• The sensitivity values for perturbations in the skull
and brain conductivity were found comparable and
strong function of dipole orientation.
• The sensitivity to scalp conductivity is important
only when the perturbation is very close to the
measurement electrodes and it is less dependent on
the dipole orientation.
94
• The effects of the perturbations on the skull are more pronounced for
shallow dipoles.
• For deep dipoles, the measurements are more sensitive to the
conductivity of the brain tissue near the dipole.
• MEG measurements are more sensitive to perturbations near the
dipole location.
• Sensitivity to other tissues (CSF, scalp, and skull) between the dipole
and sensor is comparable but smaller than the sensitivity to the brain
tissue near the dipole.
• The sensitivity to perturbations in the brain tissue is much greater
when the primary source is tangential and it decreases as the dipole
depth increases.
• The derived equations can be used to update the initially assumed
tissue conductivities. They can also be used to reconstruct the
conductivity distribution from a known source distribution.
95
Critical Steps for succesful localization
Inverse
Problem
Algorithm
Reference
Electrode
Selection
Appropriate
Data Period
Registration
Forward
Problem
Approach
Electrode/sensor
Locations
Data
Acquisition
System
Mesh
Generation
Segmentation
Source
Localization
Apriori
assumption
about the
source
96
INVERSE PROBLEM
97
A priori assumptions
• Inverse problem solutions should
not be mathematical solutions
that solely satisfy the equations.
• Realistic a priori assumptions are
necessary to solve the actual
biological sources.
• The chosen a priori assumption
determines the characteristics of
the solution.
• As we obtain more information
about the sources these
assumptions will change and new
approaches will be developed.
98
Overdetermined (dipolar) models
A priori assumption:
The electrical potentials can be
determined by small number of
electrical dipoles.
• To obtain a unique solution the
number of unknowns should be
less than the number of
measurements.
• Non-linear optimization methods
are employed.
• The solutions may converge to a
local minimum.
99
• As the number of dipoles
increases the probability to
converge a local minimum
increases.
Single dipole localization performance (Mosher et al. 1993)
• 4-shell sphere
model,
• 127 electrodes,
• Single tangential
dipole ,
• S/N =10
• Referans electrode is
at infinity.
• To avoid local
minimum, initial
point is 1 cm close to
the actual solution
• Result of Monte
Carlo simulations
with 100 repetitions.
100
Genetic Algorithm
• Global iterative optimization
algorithm
• Starts with a population of
estimates (chromozomes).
• New estimates (generations) are
obtained via genetic operations
like Selection/crossover
and mutation
• The relative difference between
the calculated and measured data
decreases for each generation.
101
• Uses the cost function itself,
does not require its derivative.
• Use more computational
resources compared to other
methods.
How many dipoles do wee need?
•
Investigated in a number of experimental and numerical studies (Achim et
al., 1991; Cabrera Fernandez et al., 1995; Miltner et al., 1994; Zhang and
Jewett, 1993, 1994; Scherg et al., 1999)
•
In the earlier studies, evoked responses and epileptic activities were
modeled using small number of dipoles. Recent studies sho that this is not
always valid (Michel et al., 2004; Scherg et al., 1999).
•
To find optimum number of dipoles mathematical techniques like MUSIC
can be used (Mosher et al., 1992). However, there are difficulties in
implemetation when realistic head models are used. To ovecome these
difficulties a new algorith called RAP-MUSIC was proposed (Mosher and
Leahy, 1998).
•
fMRI could be used to estimate the number of dipoles. Some studies report
independent analysis is better (Ahlfors et al., 1999; Liu et al., 1998). There
are also studies that use fMRI and EEG together (tough MR compatiple
electrodes are requried).
102
Underdetermined (distributed) source
models
• Do not require the number of
activities
• Electrical activity is reconstructed
on a known surface in the 3D
space.
• The number of unknowns is much
larger than measurements.
• The goal is to find a solution as a
linear combination of the known
activities.
103
Underdetermined (distributed) source
models
• Infinitely many solutions satisfy
the measurements.
• Unique solution can be obtained
if additional a priori assumptions
are used.
• There are a number of studies
that employ different
assumptions.
104
• A priori assumptions:
– Mathematical,
– Physiological,
– Structural and functional
ingformation obtained from
other imaging modalities.
• The resultant solutions are valid
as long as the assumptions are
realistic.
• Ölçümlerdeki gürültünün etkisini
azaltmak için regularizasyon
gereklidir.
Minimum norm (MN)
• Assumes a solution with
minimum norm (Hamalainen
and Ilmonemi, 1984, 1994).
• Generates a unique solution.
• There is no physiological basis
for the validity of this
assumption.
• MN solutions are usually found
shifted from the actual location
to the scalp surface.
105
Weighted Minimum Norm
(WMN)
• Used to avoid shifts in the
reconstructions.
– Normalization with respect to
the column (lead field matrix)
norms (Lawson and Hanson,
1974)
– Weighting using the
covariance data matrix
(Greenlatt, 1993)
Laplacian Weighted Minimum
Norm (LORETA)
• More constraints are added to
the depth weighting (PascalMarqui et al., 1994).
• Selects the solution with a
smooth spatial distribution by
minimizing the Laplacian of the
weighted sources.
Local autoregressive average
(LAURA)
•
Incorporates biophysical laws as
constraints in the minimum norm
algorithm
(Grave de Peralta and Gonzales,
2002, Grave de Peralta et al., 2001,
2004)
• The strength of the source falls off
with
– inverse of the cubic distance for
vector fields,
– inverse of the squared distance for
potential fields.
•
106
The method thus assumes that the
activity will fall off according to
these physical laws when moved
away from the source.
Beamformer
• Originates from radar and
sonar signal processing.
• Spatial filtering of the data to
discriminate signals from a
region of interest and those
originating from other regions.
• Beamformer approaches aim to
estimate the activity at one
brain site by minimizing the
interference of other possible
simultaneous active sources.
Evaluation and
comparison
Which source localization
method should be
chosen?
There is no direct answer.
• There is no clear established
gold standard that would allow
judging the goodness of the
result of the inverse solutions.
• Other functional imaging
methods such as fMRI cannot
be used as a gold standard as
long as the spatial and
temporal relation between
electrical and heamodynamic
responses are not known.
• Most commonly, source
localization algorithms are
evaluated and compared
through simulations with
artifical data.
• These studies are usually
based on a single dipole
source.
• It has been used to
evaluate
– The variabilty in localization
precision between different
regions of the brain (Cuffin,
2001; Cuffin et al., 2003;
Kobayashi et al., 2003)
– The dependency of
equivalent dipoles
• on source depth (Yvert
et al., 1996),
• on the noise level
(Achim et al., 1991;
Vanrumste et al., 2002;
Whittingstall et al.,
2003),
• on the number of
recording electrodes
(Krings et al., 1999;
Yvert et al., 1996),
• on the head model
(Cuffin et al., 2001;
Fuchs et al., 2002)
Comparison of different algorithms
PascualMarqui
(1999)
Leahy et
al. (1999)
MN
WMN
RWMN







Bayesian


Bayesian
TrujilloBarreto et
al. (2004)
Grave de
Peralta
and
Gonzales
(2002)
Philips et.
al. (2002)



LORETA


LAURA
Bayesian
EPI
FOCUS
Other


WINNER
LORETA
EPIFOCUS
followed by
LAURA

WMN with
constraints
WMN with
constraints
DETEMINING THE SOURCES OF AUDITORY EVOKED
FIELDS: AN EXPERIMENTAL STUDY
111
Electrode montage
Suha
Yağcıoğlu
Zeynep
Akalın
Hacettepe University Medical School
Dept. Biophysics, Ankara
112
Concluding Comments
• Electro-magnetic source imaging is the only technique
that offer millisecond responses to brain events.
• EMSIs are obtained using a coordinated action of
different fields: signal processing, image processing,
numerical electromagnetics, parallel processing,
inverse problems, and instrumentation. Each part can
be improved to improve the localization performance.
• Due to recent advances in technology, EMSI systems
can be put in daily clinical practice, either alone or
complementary to other functional imaging systems.
113