Transcript Document

Using Physics to Image Brain Function
Vladislav Toronov, Ph. D.
outline
Functional MRI: lack of physiological
specificity
Principles of Near Infrared Spectro-Imaging
NIR study of the physiological basis of fMRI
signal
NIR imaging of brain function
Quantities used in MRI

Longitudinal relaxation
time T1

Transverse relaxation
time T2 (T2*)

Proton density
Why MRI provides nice
structural images?
Due to the large differences in T1 or T2 between tissues
Can MRI be used for metabolic
measurements?

Answer: it is very difficult to do because T1
and T2 can depend on many parameters

Example:
Changes in the blood content during
functional activity
Oxygen Transport to Tissue

Oxygen is transported in hemoglobin
molecules of red blood cells:
Deoxy-hemoglobin HHb
Oxy-hemoglobin: HbO2

Metabolic measurement: Can MRI be used to
measure [HHb] and [HbO2]?
Blood Oxygen Level Dependent effect:
Oxygen in the blood modifies T2*
Functional brain mapping
Quantitative physiological
model of the BOLD signal:
R. Buxton, 1998
DS  1Dq  2D v
where
Dq=D[HHb]/[HHb]0
Dv=D[tHb]/[tHb]0
Conclusion: MRI does not allow simple separation of
oxygenation effects from blood volume effects
Near-Infrared
Spectro-Imaging
(NIRSI)
Optical Spectroscopy
Beer’s law:
a    i ci

i
NIRSI
Light Propagation in Tissues
Absorption
a ~0.1 cm-1
Scattering
’s ~ 10 cm-1
NIRSI
Boltzmann Transport
Equation
ˆ , t)
1 L(r , 
ˆ , t )
ˆ  (    ) L( r , 
ˆ , t) 
 L ( r , 
a
s
v
t
ˆ , t ) f (
ˆ ,
ˆ )d
ˆ   S (r , 
ˆ , t)
 s  L( r , 
Where
 , t ) - radiance [W cm-2 steradian-1]
L(r , 
a
s
- absorption coefficient [cm-1]
- scattering coefficient [cm-1]
 , t ) - source term [W cm-3 steradian-1 s-1]
S (r , 
Diffusion Approximation
 a     s (1  cos )
'
s
Diffusion Equation:
Diffusion coefficient
(scattering)
1  D 2

   a  r     r , t   q0  r , t 

 c t c

Absorption
Photon
Density
Source
Type of the source
modulation:

Continuous Wave

Time Domain (pulse)

Frequency-Domain
Frequency-domain approach
Light Source:
 Modulation frequency: >=100 MHz
 AC, DC and phase
NIRSI
Absolute measurements with
frequency-domain spectroscopy
Frequency-domain multi-distance
solution for
Semi-infinite medium
method
80
AC*r2
phase
-2
70
-4
50
AC
60
-5
Log
-3
-6
S
Sac
-7
40
30
20
-8
10
-9
0
10
20
r (mm)
30
0
40
phase ()
-1
a: absorption coefficient
s’: reduced scattering
coefficient
w:
angular modulation
frequency
v:
speed of light in tissue
S: phase slope
Sac: ln(r2ac) slope
Method of quantitative FD
measurements: Multi-distance
Detector fiber
bundle
Source fibers
Flexible
pad
Direct light block
Estimation of physiological
parameters
Beer’s law:



 a   HbO [ HbO2 ]   HHb [ HHb ]
2
Total HB
[tHB]  [ HbO2 ]  [ HHb ],
2
~CBV
[ HbO 2 ]
Oxygenation Ox 
 100(%),
[ HbO 2 ]  [ HHb ]
NIRSI
Near-infrared tissue oximeter
RF
electronics
pmt b
pmt a
detector
bundles
laser driver 2
laser driver 1
multiplexing
circuit
NIRSI Instrumentation
source fibers
laser
diodes
NIR Imaging System
Advantages of NIRSI

Non-invasive

Fast (~ 1 ms)

Highly specific (spectroscopy)

Relatively inexpensive (~$100 K)

Can be easily combined with MRI
NIRSI in Functional Magnetic Resonance Imaging
Study of the physiology
of the BOLD effect
BOLD= Blood Oxygen Level
Dependent
fMRI Mapping of the Motor Cortex
BOLD signal model
DS  1Dq  2D v
where
Dq=D[HHb]/[HHb]0
Dv=D[tHb]/[tHb]0
Study of the BOLD effect
Multi-distance optical probe
Detector fiber
Laser
diodes
690 nm
&
830 nm
Study of the BOLD effect
Collocation of fMRI signal
and optical sensor
Optical probe
Motor Cortex
Study of the BOLD effect
Activation paradigm
Motor activation
Relaxation
Stimulation
Вlock Design - 10s/17s
Time
Study of the BOLD effect
Data analysis:
Folding (time-locked) average
Raw data
Folded data
Study of the BOLD effect
Time course of hemodynamic
and BOLD signals
stimulation
Study of the BOLD effect
BOLD signal model
DS  1Dq  2D v
where
Dq=D[HHb]/[HHb]0
Dv=D[tHb]/[tHb]0
Study of the BOLD effect
Biophysical Modeling of
Functional Cerebral
Hemodynamics
O2 Diffusion Between Blood and
Tissue Cells
fout
fin
Modeling
“Balloon” Model
dq 1  E (t )
q( t ) 
  f in
 f out
dt  
E0
v (t ) 
q- normalized Deoxy Hb
v- normalized Total Hb
=V0/F0 – mean transit
time
E  f in 
Oxygen Extraction Fraction
Modeling
OEF as function of CBF
(Buxton and Frank, 1997)
E  f in   1  (1  E0 )1/ fin
Modeling
Modeling
“Balloon” Model
dq 1  E (t )
q (t ) 
  f in
 f out

dt  
E0
v(t ) 
dv 1
  f in  f out 
dt 
E  f in   1  (1  E0 )1/ f in
q- normalized Deoxy Hb
v- normalized
Total Hb
Oxygen Extraction Fraction
Functional Changes in Cerebral
Blood Flow from Balloon Model
Stimulation
110
fin
fout
108
fin ,fout(%)
106
104
102
100
98
0
5
10
15
Time (s)
20
25
30
Modeling
Why oxygenation increases?

The increase in cerebral blood oxygenation
during functional activation is mostly due to an
increase in the rCBF velocity, and occurs
without a significant swelling of the blood
vessels.
Washout Effect
Modeling
Outcomes
The time course of the BOLD fMRI signal
corresponds to the changes in the deoxyhemoglobin concentration
BOLD fMRI provides no information about
the functional changes in the blood volume
This information can be obtained using
NIRSI
Optical Mapping of
Brain Activity
in real time
Locations of the sources and detectors of
light on the human head
3
4
2
B
5
1
A
6
3 cm
8
7
detectors
light sources
Motor Cortex
Brain mapping
Backprojection Scheme
C34=.5*S3 + .5*S4
3
C34=.75*S3+.25*S4
1
2
3&4 3
3
3
2
2
2
2
2 1&2 1
1
1
1 1&8
3&4 3
3
3 2&3 2
2
2
2
2
2
2
2 1&2 1
1
1 1&8
3
3 2&3 2
2
2 2&2 2&2 2
2
2 1&2 1
1
8
8
2 1&2 1&8 8
8
8
6 6&7 7&8 8
8
8
8
4
4
4
4
4
4
4
4
4
4
3 2&3 2
3&
2&3 2
4
4&
5&6 6
5
B
2&
2 2&6 2&6 2&6
2
6
6&
6 6&2 2&6 2&6
6
2
A
4
5
5 5&6 6
6
6 6&6 6&6 6
6
6 6&7 7
7
8
4&5 5
5
5 5&6 6
6
6
6
6
6
6
6 6&7 7
7
7 7&8
4&5 5
5
5
5 5&6 6
6
6
6
6
6 6&7 7
7
7 1&8
5
6
7
7
8
detectors
light sources
(758 and 830 nm)
Brain mapping
Real time video of brain activation
D [Hb] (M)
-1.0
-0.5
0.0
3
0.5
1
2
A
B
4
5
6
8
7
Brain mapping
3D NIR imaging of brain
function using structural
MRI
S
D
A small change in absorption
S
U sd
D
dU sd
da
U sd
 d Ln
n
a
n
Ln –the mean
time photon
spends in voxel
n relative to the
total travel time
Solve an equation:
dU sd
U sd
 d L
n
a n
n
Number of measurements<< number of voxels
Underdetermined Problem
3D imaging
Sensitivity is high near the surface
and low in the brain
Source
Detector
3D imaging
Using structural MRI info
Scalp
CerebroSpinal
Fluid
Scull
Brain
CONSTRAINT
3D imaging
How do we find Ln –the relative
voxel time?
dU sd
U sd
 d L
n
a n
n
Monte Carlo Simulation
Structural MR image
is segmented in
four tissue types:
• Scalp
• Skull
• CSF
• Brain
10,000,000 “photons”
Source
Detector
3D imaging
Image Reconstruction
dU sd
U sd
 d L
n
a n
n
Underdetermined Problem
Y=Ax
Solution: Simultaneous Iterative Reconstruction Technique
3D imaging
Activation of Human Visual Cortex
Flashing or reversing
checkerboard
EXPERIMENT
50
mm
40 mm
10 mm
3D imaging
Probe for imaging human visual cortex
in the MRI scanner
Placement of the optical probe on
the head inside the “birdcage”
head coil of the MRI scanner
Magnetic bore of
the MRI scanner
Birdcage
head coil
B
0
To/from the
NIR spectrometer
Optical probe
Optical fibers
Time course of hemodynamic
changes in the activated region
-4
2
Average changes in [HbR] and [HbO] at 2 Hz
x 10
[HbO]
[HbR]
Vis. Stim.
Average hemo changes (mM)
1.5
1
0.5
0
-0.5
-1
0
10
20
30
Time (sec)
40
50
60
Results of the group statistical
analysis of variance
Using AFNI medical
Image processing
software
BOLD
-D[Hb]
D[HbO2]
3D imaging
Outcomes
In combination with structural MRI,NIRSI can
be used for non-invasive 3D imaging of
physiological processes in the human brain
A two-wavelength NIR imaging provides
independent spatially-resolved
measurements of changes in oxy- and
deoxyhemoglobin concentrations.
General Conclusion and
Perspective

Alone or in combination with other imaging
techniques, NIRSI can be used as a quantitative
metabolic imaging tool in a variety of biomedical
applications:
Neuronal activity ~10 ms temporal resolution
Neonatology
~Baby’s head has low size and
absorption
Mammography ~ Non-ionizing, specific
Small animals ~ Neuroimaging, fast
assessment in cancer research