Nuclear magnetic imaging of the lungs can be performed using hyperpolarized noble gases. This technique uses resonance of polarized noble gas atoms in an external magnetic field to study the structure of the lungs, which can be used for diagnosing lung diseases. NMR and optical pumping techniques are used to polarize the noble gases for medical imaging applications. Specifically, optical pumping is used to hyperpolarize gases like helium-3 and xenon-129 outside of the MRI scanner, followed by injection into the patient and scanning to generate images of lung structure and function with improved sensitivity over conventional proton imaging.

1. Nuclear magnetic imaging ofNuclear magnetic imaging of
the lungs usingthe lungs using
hyperpolarized noble gashyperpolarized noble gas
5s
1 2
5 p
1 2
5 p
3 2
B
0
0 B
0
0
m1/2
1/2
m1/2
1/2
m
1/2
1/2
m1/2
1/2
σ Î ”m
j
=+1

2. NMR and Optical Pumping used in medicalNMR and Optical Pumping used in medical
imaging.imaging.
• Proton NMR is used in medical imaging to study theProton NMR is used in medical imaging to study the
structure of tissues containing water.structure of tissues containing water.
• This technique uses resonance of polarized waterThis technique uses resonance of polarized water
molecules in an external magnetic field.molecules in an external magnetic field.
• A more recent method uses resonance in polarizedA more recent method uses resonance in polarized
noble gas, to study the structure of the lungs.noble gas, to study the structure of the lungs.
• This can be used for diagnostics of lung diseases.This can be used for diagnostics of lung diseases.

3. In this presentation ...
Diffusion weighted imaging
MRI: Basic principles
Hyperpolarized gas MRI

4. Timeline of NMR imagingTimeline of NMR imaging
1920 1930 1940 1950 1960 1970 1980 1990 2000
1924 - Pauli suggests that
nuclear particles may have
angular momentum (spin).
1937 – Rabi measures
magnetic moment of
nucleus. Coins
“magnetic resonance”.
1946 – Purcell shows
that matter absorbs
energy at a resonant
frequency.
1946 – Bloch demonstrates
that nuclear precession can be
measured in detector coils.
1972 – Damadian
patents idea for large
NMR scanner to
detect malignant
tissue.
1959 – Singer
measures blood flow
using NMR (in mice).
1973 – Lauterbur
publishes method for
generating images
using NMR gradients.
1973 – Mansfield
independently
publishes gradient
approach to MR.
1975 – Ernst
develops 2D-Fourier
transform for MR.
NMR renamed MRI
MRI scanners
become clinically
prevalent.
1990 – Ogawa and
colleagues create
functional images using
endogenous, blood-
oxygenation contrast.
1985 – Insurance
reimbursements for
MRI exams begin.
Kurt Wüthrich
Felix Bloch
Edward Purcell
Richard R. Ernst
Paul Lauterbur
Peter Mansfield
1980- NMR
protein structure by
WuthrichIsadore Rabi

5. Below:
image of
a brain tumor
On the left:
Rabi’s paper
Bloch’s brief
publication
Above: Lindstrom’s observation
Right: Damadian’s patent
Below: Lauterbur’s first published MR images
Left bottom:
Mansfield’s
gradient slice
sequence

6. I.I. Rabi
1938
E. Purcell
1946
F. Bloch
1946
Superconducting
coil (magnet)
Radiofrequency
coil
Gradient coil
The use of MRI: basic principle
The advantage of magnetic resonance imaging (MRI)
is the absence of any ionizing irradiation to acquire an image.
To make an MRI image use is made of a static magnetic field,
radiofrequency waves (electromagnetic waves similar to the
ones received by a transistor radio) and switched magnetic
fields (gradients).
No adverse health effects are found with the use of MRI
scanners.
Unlike any other medical imaging modality, it are the (nuclei
of atoms within) molecules themselves that are the signal
carriers.
The molecular interactions of water molecules with
macromolecular structures (proteins, cell membranes, etc.) are
responsible for the image contrast.
The superior soft tissue contrast originates from the large amount of water molecules that ‘probe’ the
cellular microstructure. The water molecules interact with cellular components through diffusion,
adhesion, absorption, collision, chemical exchange and magnetization transfer. All these interactions
cause changes in the behavior of the received MR signal.

7. The use of MRI: basic principle
Conventional magnetic resonance imaging (MRI) is based on the radiofrequency signal
that is transmitted from the atomic nucleus of hydrogen atoms placed in a magnetic field and
after they have been excited by a radiofrequency electromagnetic pulse.
Cross-section of an NMR scanner
Water molecule
Radiofrequency coil sweeps
through a range of frequencies
until resonant frequency is reached
external
magnetic field
Cryogenic magnet
Radiofrequency coil
Gradient coil
Hydrogen proton transmits
a radiofrequent electromagnetic
wave (yellow) after excitation
by an RF pulse (red)
The electromagnetic signal transmitted
by the hydrogen protons is received by
the scanner and processed...
The precession takes place with frequency f=γB0 (Larmor
frequency, γ is gyromagnetic ratio)
If the proton is placed in RF magnetic field Brf which has the same
frequency as proton precession frequency, the proton will absorb energy
at this resonance.

8. Larmor frequencyLarmor frequency
.
d
d
BM
M
×= γ
t
.)1( += IIL
B0, z
µ
y
x
ω L
Larmor equation
f = γB0
γ = 42.58 MHz/T
At 1.5T, f = 63.87 MHz
At 4T, f = 170.3 MHz
Field Strength (Tesla)
Resonance
Frequency for
1H
170.3
63.8
1.5 4.0
Lz = Iz  ≡ m  = ± ½  for I = 1/2.
The gyromagnetic ratio g is defined by
µ = γ L.
The z component of the nuclear magnetic moment is
µz = γ Lz = γ Iz  ≡ γ m .
The energy for I = 1/2 is split into 2 Zeeman levels
Em = - µz B0 = - γ mB0 =  γ B0/2 = LL /2.
B0, z
µ
y
x
ω L
Nuclear spin quantum number I
Larmor frequency of hydrogen nucleiLarmor frequency of hydrogen nuclei
(protons) in a 1.5 Tesla field(protons) in a 1.5 Tesla field
 == γ BoBo
 = (42.58 MHz / Tesla)(1.5 Tesla)= (42.58 MHz / Tesla)(1.5 Tesla)
 = 63.87 MHz= 63.87 MHz

9. RFExcitationRFExcitation
Excite Radio Frequency (RF) field
transmission coil: apply magnetic field
along B1 (perpendicular to B0) for ~3 ms
oscillating field at Larmor frequency
frequencies in range of radio transmissions
B1 is small: ~1/10,000 T
tips M to transverse plane – spirals down
final angle between B0 and B1 is the flip
angle
The T1-weighted image (usually used for anatomical
images) measures the rate at which the object placed in
B0 goes from a non-magnetized to a magnetized state –
the longitudinal relaxation
1H nuclei in water (H2O) and1H nuclei in water (H2O) and
fat (~CH2) are in different molecules andfat (~CH2) are in different molecules and
experience a slightly different local magneticexperience a slightly different local magnetic
field which results in slightly differentfield which results in slightly different
resonant frequencies. Theseresonant frequencies. These
local magnetic field variations contribute tolocal magnetic field variations contribute to
the eventual contrast between various tissuesthe eventual contrast between various tissues
in an MRI image.in an MRI image.
““... T1 is a measure of the time required to re-establish thermal equilibrium between the spins and their surroundings (lattice)…”... T1 is a measure of the time required to re-establish thermal equilibrium between the spins and their surroundings (lattice)…”

10. Lorentzian lineshapeLorentzian lineshape
The Fourier Transforms of an exponentially decaying sine wave (left) is
a peak with a Lorentzian shape (right) (a) Atoms with NMR signals that
slowly decay (large T 2 values) create skinny Lorentzian peaks. (b) In
contrast, atoms with NMR signals that rapidly decay (small T 2 values)
create fat or broad Lorentzian peaks

11. Weighting is
achieved by
manipulating TE
(time to echo) and TR
(time to repetition of
the pulse sequence)
1 weighted Density weighted T2 weighted
T1 = recovery of longitudinal (B0) magnetization after the
RF pulse
used in anatomical images
~500-1000 msec (longer with bigger B0)
TR (repetition time) = time to wait after excitation before
sampling T1
T2 = decay of transverse magnetization after RF pulse
TE (time to echo) = time to wait to measure T2 or T2* (after
re-focusing with spin echo)
T1 and TR
Effectively, T1 and T2 images are the inverse of one
another, with T1 typically used to form
anatomical images and T2* used in fMRI

decay
T
TE
eryre
T
TR
XY eeMM 















−=
−−
2
cov
1
0 1
““... T2 is a measure of the time of disappearance of the transverse component of magnetization.”... T2 is a measure of the time of disappearance of the transverse component of magnetization.”

12. Echoes – refocusing of signal
Spin echo: when “fast” regions get ahead in phase, make them go to
the back and catch up
-measure T2
-ideally TE = average T2
Gradient echo: make “fast” regions become “slow” and vice-versa
-measure T2*
-ideally TE ~ average T2*

13. The contrast in NMR is based on
the molecular physics of water molecules
(e.g. spin-spin relaxation)
INTERMEDIATE
LAYER
FREE
WATER
Hydrogen bridges
C
C
O
O
C N BOUND
LAYER
δ+
δ+ δ+
δ+
δ-
δ-
δ-
δ+
δ+
δ- δ-
δ+
δ-
δ-
δ+
δ+δ+
δ+
Protein, polymer, cell membrane
M
M
M
t
t
tLow mobility
High mobility
Malignant tissue often
have higher values
of T1 than normal tissue
of same type

14. k.T
E
1/2
1/2
e
N
N
∆
−
+
−
=
0BE ... γν hh ==∆
B0
-1/2
+1/2
2kTNN
NN
P
1/21/2
1/21/2 νh
=
+
−
=
−+
−+
5 1
P 10
100,000
−
= ≈
( at 3T )
Boltzmann
statistics
MOLECULAR IMAGING WITH MRI
Low sensitivity of conventional 1
H MRI
The sensitivity of conventional MRI is governed by
Boltzman statistics. In a magnetic field of 3T, only an
excess of one of 100,000 atoms is magnetized in the
direction of the applied magnetic field.

15. Bloch equation and stationary solutionsBloch equation and stationary solutions
( )
1
0
2
eff
d
d
T
MM
T
MM
t
zx zyyx eee
BM
M −
−
+
−×= γ ,1 1
0 







−=
−
T
t
enn
T1 is the longitudinal or spin-lattice relaxation time and n0
denotes the difference in the occupation numbers in the
thermal equilibrium. Longitudinal relaxation time because the
magnetization orients itself parallel to the external magnetic
field.
T1 depends upon the transition probability P as
1/T1 = 2P = 2B-½,+½ wL.
where B refers to the Einstein coefficients for induced
transitions and wL is the spectral radiation density at
the Larmor frequency.
( )
( )
( )
( )
( )
.
1
1
,2
1
,2
1
0
21
2
rf
22
2
2
L
2
2
2
L
rf0rf
21
2
rf
22
2
2
L
2
rf0rf
21
2
rf
22
2
2
L
2
2L
M
TTBT
T
M
HMB
TTBT
T
M
HMB
TTBT
T
M
z
y
x
γωω
ωω
χγ
γωω
χγ
γωω
ωω
+−+
−+
=
′′=
+−+
=
′=
+−+
−
=
Stationary solutions to the Bloch equations are
attained for dM/dt = 0:
T2 decay times (in 1.5 T magnet)
white matter 70 msec
grey matter 90 msec
CSF 400 msec
• T1 measures the longitudinal relaxation (along B0) – or the rate at which the
subject (and the various different constituents of that subject) reaches magnetic
equilibrium
• T2 measures the transverse relaxation (along B1) – or the rate of decay of the
signal after an RF pulse is delivered
• T1 – recovery to state of magnetic equilibrium
• T2 – rate of decay after excitation
CSF cerebrospinal fluid
1 Tesla
Fat T1=240ms T2=80ms
heart muscle T1= 570 ms T2=57
ms

16. MR contrast agent
Blood circulation (MRA)
NON SPECIFIC
CONTRAST AGENTS
Perfusion
SPECIFIC
CONTRAST AGENTS
Reporter
Ligand
Vector Receptor
(Target)
• Cell receptor
• Gene sequence
• Enzyme
MOLECULAR IMAGING WITH MRI
Exogeneous contrast agents
Approximate T1 and T2 Values for Human Tissue
(37 o
C)
Tissue
T1 at 1.5 T
(msec)
T1 at 0.5 T
(msec)
T2
(msec)
Skeletal Muscle 870 600 47
Liver 490 323 43
Kidney 650 449 58
Spleen 780 554 62
Fat 260 215 84
Gray Matter 920 656 101
White Matter 790 539 92
Cerebrospinal Fluid >4,000 >4,000 >2,000

17. X-ray
PET
1 μm 10 μm 100 μm 1 mm 1 cm 1 dm
1 mM
1 μM
1 nM
1 pM
MRI
Spatial resolution
Sensitivity
In vivo
molecular
targets
SPECT
MRS
MRI (‘pushing the limits’)
MOLECULAR IMAGING
Increasing the sensitivity of MRI

18. HYPERPOLARISATION
OUTSIDE THE SCANNER
%50P ≈
INJECTION OF
HYPERPOLARIZED
AGENT
SCANNING
THE PATIENT
MOLECULAR IMAGING WITH MRI
HYPERPOLARIZATION:
A possible alternative for boosting NMR sensitivity

19. Parahydrogen
13
C
B0
‘Brute Force’
cooling
room
temperature
(P = 10-5
)
Dynamic
Nuclear
Polarization
94 GHz
13
C
Optical pumping
σ
How to obtain HYPERPOLARIZATION ?

20. Hyperpolarized gas NMR by optical pumping
Philips G.C., Perry R.R., Windham P.M.,
“Demonstration of a Polarized He3
Target
for Nuclear Reactions”
Physical Review Letters, 9, 502-504, 1962.
Bouchiat M.A., Carver T.R. And Varnum C.M.
“Nuclear Polarization in He3
Gas Induced by
Optical Pumping and Dipolar Exchange”
Physical Review Letters, 5, 373-375, 1960.
Walters G.K., Colegrove F.D. and Schearer L.D.
“Nuclear Polarization of He3
Gas by Metastability
Exchange with Optically Pumped Metastable He3
Atoms”, Physical Review Letters, 9, 502-504, 1962.

21. Hyperpolarized gas NMR by optical pumping
Principle: Electron energy states of Rubidium
Bohr model
1.56 eV
0l =
5s
1l =
5p
Fine structure
-3
10 eV
2
1 25 /s
2
1 25 /p
2
3 25 /p
1
2
j =
1
2
j =
3
2
j =
Hyperfine
structure
-6
10 eV
1F =
2F =
1F =
2F =
Zeeman
splittingB
@ 1mT
-8
10 eV
1
0
1−
1
0
1−
2
2−
1
0
1−
1
0
1−
2
2−
Fm
I

e-
J

F J I= +
  
n
e-
Hyperfine interaction
(nucleus – angular momentum)
e-
e-
e-
L

S

J L S= +
 
Fine interaction
(spin – orbital momentum coupling)

22. 1
0
1−
1
0
1−
2
1 25 /s
2
1 25 /p
1( )Fmσ+ ∆ = +
Hyperpolarized gas NMR by optical pumping
Principle: Optical pumping of Rubidium
photon
(S = 1)
794 8. nmλ =
e-
e-
electron = trapped
Fm
1.56 eV
0 0
I
s B z zA g S B I B
I
µ
µΗ = × × + −

I S
2−
2−
2
2e-
•Transitions between the ground and the first excited state are only possible if ΔmF=0 or ΔmF=±1

23. m
1/2
1/2
m
1/2
1/2
m1/2
1/2
m
1/2
1/2
Hyperfine structure
Hyperpolarized gas NMR by optical pumping
Principle
Rb
5s1 2
5 p1 2
5 p
3 2
=+1+ jσ (Δm )
794.7 nm
Fine splitting
Population inversion can be detected by the
resulting increased transmission of the
pumping light.

24. Hyperpolarized gases:
Spin exchange
Rb
Laser-
beam
He3
+σ
OPTICAL
PUMPING
SPIN
EXCHANGE
H = a(r).I.S
temperatures between
80°C and 130°C
plate−
4
λ

25. +σ
Rb He R R Aγ α−Η = + +
    
N.S K.S I.S( ). ( ). .
2
Rb F
e
e
g F
m
µ =

Hyperpolarized gas NMR by optical pumping
Rubidium-Helium Spin-Exchange
L

S

I

F

N

K

Rb He
Spin rotation
Hyperfine coupling
(Rb electron – He nucleus)
Hyperfine coupling
(Rb)
Rb He Rb He↑ + ↓ → ↓ + ↑( ) ( ) ( ) ( )

26. Based on a concept of the University of Virginia Health System
Laser
OPTICS
λ
4
plate
cell
Oven (130 °C)
OPTICAL
SPECTROMETER
Rb
GAS HYPERPOLARIZER
~ 100 W
795 nm ± 1 nm
Helmholtz
coil pair
~ 3 mT
Diode
power supply
Laser diode
stacked bar
Glass cell with Helmholtz coil pair
Heat
exchanger
Circ.
pump
Filter
Laser cooling
RF coil
NMR
ACQUISITION
Preamp and
PIN switch
Control logic
and measurements
DAQ
He3

27. Hyperpolarized gases:
Spin exchange
T1
P
P).(P
dt
dP
RbSE −−= γ
• Rb density
• collision rate
∝SEγ
C)157(T/ml101.47[Rb] 14
°==
1
SE h0.125 −
=γ
Example:
t [h]
Polarization
0
0.2
0.4
0.6
0.8
2.5 h
5 h
10 h
33 h
∞
5 h 10 h
T1
15 h0 h
From: Leawoods et al, Concepts in Magnetic Resonance, 13(5): 277-293, (2001).

28. Magneticspinpolarization
T1
T1-decay
t60 s
Injection
T1 relaxation decay is determined by
the Intra-molecular environment
the solvent
the temperature
the degree of acidity (pH)
20 s – 40 s30 s – 60 sIn vivo
20 min2 h – 30 hin Pyrex test tube
21 daysmonthspure gas
129
Xe3
HeT1
HYPERPOLARISED GAS
Decay time

29. Hyperpolarized gases: Sequences and Applications
In H1
-imaging: T1 is needed for recovery of signal
In He3 , Xe129
-imaging: All imaging has to be performed within a time T1
Small flip angles should be used (FLASH, FISP)
• Static He3
density images (during breath-hold)
• Diffusion images (Optimized Interleaved-Spiral):
Restricted diffusion by alveolar walls (emphysema)
• Xe129
transport into tissue (Compartimental analysis)
• He3
and Xe129
Spectroscopy
• Tagging for monitoring lung ventilation
• Dynamic studies with EPI sequences

30. Dynamic MRI
of the lung
SOURCE: University of Virginia Health Systems
MR ventilation images of the lung
asthma studies with He-3 Hyperpolarized
Xe-129 imaging
3D rendered MRI
of the lung
HYPERPOLARISED GAS NMR:
Some immediate applications

31. HYPERPOLARISED GAS NMR:
Lung imaging
20-year old
non-smoker
62-year old
smoker
Diffusion imaging reveals lung microstructure
Inhalation Exhalation Displacement
vectors
Cai et al, Int. J. Radiation Oncology Biol. Phys. 68, 650-3, 2007Fain et al, J. Magn. Reson. Imaging. 25, 910-23, 2007
Tagging reveals lung motion

32. DiffusionDiffusion
• In 3 dimensions, average diffusion distance <Δr> in aIn 3 dimensions, average diffusion distance <Δr> in a
period of time Δt is:period of time Δt is:
<Δr> = √(6D Δt)<Δr> = √(6D Δt)
where D is the diffusion coefficientwhere D is the diffusion coefficient
• In 1 dimension:In 1 dimension:
<x> = √(2D Δt)<x> = √(2D Δt)
• If we make a plot of <x> vs. √Δt, or <Δr> vs. √Δt,If we make a plot of <x> vs. √Δt, or <Δr> vs. √Δt,
we see a line of constant slope, proportional to √Dwe see a line of constant slope, proportional to √D

33. • We simulate diffusion as a random walk in 3 dimensions:
xn+1 = xn + rsinθcosφ
yn+1 = yn + rsinθsinφ
zn+1 = zn + rcosθ
where θ is a random variable on [-π,π] and
φ is a random variable on [0, 2π], and r is a
Gaussian random variable with mean 0 and width
1 multiplied by √(2D τ), τ being the time between
steps, or time between collisions of He3 atoms
during the diffusion.

34. Diffusion as a Random Walk
Random Walk in 1 and 3 dimensions, starting at initial pointRandom Walk in 1 and 3 dimensions, starting at initial point
(x(xii,y,yii,z,zii), covering N steps), covering N steps

35. • We find the time in which particle diffusion
is observed as Δt=N τ, for N steps taken by
the particle.
<Δr> = √((x-x0)²+(y-y0)²+(z-z0)²)
The plot of <Δr> vs. √Δt plot is proportional to
√D, and this is largest for diffusion in free
space, whereas if there are boundaries in the
space in which diffusion occurs, and the
dimensions of the boundaries are comparable to
the diffusion step, the slope of the graph will be
smaller. Diffusion coefficient is thus a good
measure of local structure of the volume in which
diffusion occurs.

36. • If we plot distribution of diffusion distances
P(Δr) vs. Δr for 3 dimensions, or P(x) vs. x for 1
dimension, the diffusion coefficient is proportional
to the width of the distribution, and it becomes
smaller when the local structure of the geometry
in which diffusion occurs becomes more restricted.
• D=μ2 (the second moment of the distribution).
• For more complicated geometries, like the structure of lung
airway tree, diffusion coefficient is a good measure of
structure in each branch of the tree.
• Diffusion coefficient is larger in the areas where diffusion is
less restricted, for example, where alveolar volume is
increased.

37. HYPERPOLARISED GAS NMR:
Lung imaging
20-year old
non-smoker
62-year old
smoker
Diffusion imaging reveals lung microstructure
Fain et al, J. Magn. Reson. Imaging. 25, 910-23, 2007

38. StructureStructure
• Lung airway tree contains 24 generations of cylindricalLung airway tree contains 24 generations of cylindrical
bronchioles, last 14 of which are acinar, or covered with sphericalbronchioles, last 14 of which are acinar, or covered with spherical
alveoli.alveoli.
• The structure of airway tree is fractal, with lengths and radii relatedThe structure of airway tree is fractal, with lengths and radii related
by:by:
Where LWhere L00 and Rand R00 are length and radius of the aorta.are length and radius of the aorta.
1
3 3
1 02 2
n
n nL L L− −
−= =
1
3 3
1 02 2
n
n nR R R− −
−= =

39. Graphs showing total cross-sectional area as a function of distance fromGraphs showing total cross-sectional area as a function of distance from
entrance of multi-branch-point model (generation number) on the left; andentrance of multi-branch-point model (generation number) on the left; and
distribution of gas inspired per unit volume for a 0.5-liter breath at constant flowdistribution of gas inspired per unit volume for a 0.5-liter breath at constant flow
of 0.25 l/s (dashed line) and 2-liter breath at constant flow of 2 l/s (solid line) onof 0.25 l/s (dashed line) and 2-liter breath at constant flow of 2 l/s (solid line) on
the right.the right.

40. Bronchioles in each generation branch off into two bronchioles of the next generation, at opening angle
of 60˚ and each generation plane is rotated by 90˚ to the plane of the previous generation.

41. Diagrams illustrating lung structure as based onDiagrams illustrating lung structure as based on
biological and medical studies of the lungs.biological and medical studies of the lungs.

42. Computer Simulation ModelComputer Simulation Model
• Using the experimentally found values for sizes of the bronchioles and aciniUsing the experimentally found values for sizes of the bronchioles and acini
• Build airway tree with alveoli at terminal bronchiolesBuild airway tree with alveoli at terminal bronchioles
• Use cylinders to approximate structure of the bronchiolesUse cylinders to approximate structure of the bronchioles
• Use spheres to approximate structure of alveoliUse spheres to approximate structure of alveoli

43. • Diffusion coefficient and Kurtosis measurements can be used to detect diseases of the lung
airways.
• We plot the histogram distribution of the diffusion distances of He3 molecules for N steps in
the diffusion of the molecules inside the structure of the lungs.
• D=μ2 (the second moment of the distribution).
• K = μ4/μ2² - 3 (μ4 is the fourth moment of distribution)

44. Diffusion SimulationDiffusion Simulation
• Using random walk to model diffusion of He3 molecules with random step size notUsing random walk to model diffusion of He3 molecules with random step size not
exceeding the cross-sectional radius of the bronchioles and alveoliexceeding the cross-sectional radius of the bronchioles and alveoli
• Simulate diffusion for N steps with τ being experimentally determined time betweenSimulate diffusion for N steps with τ being experimentally determined time between
collisions of He3 molecules.collisions of He3 molecules.
• Diffusion time is then Δt = N τDiffusion time is then Δt = N τ
xn+1 = xn + rsinθcosφ
yn+1 = yn + rsinθsinφ
zn+1 = zn + rcosθ
where θ is a random variable on [-π,π] and
φ is a random variable on [0, 2π], and r is a
Gaussian random variable with mean 0 and width
1 multiplied by √(2D τ), τ being the time between
steps, or time between collisions of He3 atoms
during the diffusion.

45. • In order to look at the global structure of the geometry, it’s best to look at
the kurtosis, which measures the degree of deviation of the distribution from
the Gaussian distribution:
K = μ4/μ2² - 3 (μ4 is the fourth moment of distribution)
• This quantity is 0 for a Gaussian distribution, it’s negative for a broader
distribution, and positive for narrower distribution. Thus, higher kurtosis reflects
a higher degree of structure of the geometry of the system in which diffusion occurs.

46. • Using MRI scanning techniques, we can only look at areas in the lungs with dimensions of
few millimeters, so we observe signal only locally.
• If we look in the area of the acini, where most diffusion occurs, and where the geometry is
dominated by the alveolar structure, and if we calculate the diffusion coefficient for distribution
in this volume, we will have a good measure of the degree of structure of alveoli.

47. • Measured ADCs (~0.2 cm^2 /s) correspond to mean diffusion distances of about 0.4mm confirming
that diffusion measurements are dominated by diffusion within alveoli and the smallest respiratory
bronchioles.
• However, we can also measure the degree of structure of the bronchioles over volume larger than
the observable volume, by calculating the kurtosis of the distribution.

48. Diffusion coefficient can be used to measure the degree of destruction or restriction of the alveoli in
the acini. Higher than normal diffusion coefficient shows increase and destruction of alveoli, whereas
lower than normal diffusion coefficient shows restriction of alveoli.

49. Kurtosis measures can be used to show the degree of destruction or restriction of the bronchioles
in the lungs. Lower than normal values of kurtosis show destruction and increase of the bronchioles,
whereas higher than normal kurtosis shows bronchiole restriction.

50. Modeling destruction and obstruction ofModeling destruction and obstruction of
the airwaysthe airways
• To model the destruction of the airways we increase the diameter of the cylinders whichTo model the destruction of the airways we increase the diameter of the cylinders which
represent each generation of the airways in the simulationrepresent each generation of the airways in the simulation
• To model the obstruction of the airways, we decrease the diameter of the cylinders representingTo model the obstruction of the airways, we decrease the diameter of the cylinders representing
the airwaysthe airways

53. The simulation on the
left shows diffusion
over many generations
of bronchioles, and would
occur over times large compared
with the acquisition time
The simulation on the right
shows diffusion over a few generations
of bronchioles corresponding to
times of the order of data acquisition time

56. Comparing ADC for different lungComparing ADC for different lung
structurestructure
• Histograms of diffusionHistograms of diffusion
coefficients from thecoefficients from the
combined middle thirdscombined middle thirds
(dorsal to ventral) of the right(dorsal to ventral) of the right
and left lung. Representativeand left lung. Representative
animals are shown from theanimals are shown from the
control and elastase-treatedcontrol and elastase-treated
groups at end expiratorygroups at end expiratory
volume (solid line) and heldvolume (solid line) and held
breath (dashed line).breath (dashed line).

57. ADCADC
• These parametric maps show the apparentThese parametric maps show the apparent
diffusion coefficient in the lungs of adiffusion coefficient in the lungs of a
nonsmoker (top left) and a smoker (bottomnonsmoker (top left) and a smoker (bottom
left) with 18 pack years of smoking history. Itleft) with 18 pack years of smoking history. It
is this diffusion parameter that gives us ais this diffusion parameter that gives us a
measure of alveoli that exchange oxygenmeasure of alveoli that exchange oxygen
from the air we breathe into the blood.from the air we breathe into the blood.
Alveoli are increased in size in the smokerAlveoli are increased in size in the smoker
compared to the nonsmoker, as indicated bycompared to the nonsmoker, as indicated by
the warmer colors in the smoker (green andthe warmer colors in the smoker (green and
aqua) compared to the nonsmoker (deepaqua) compared to the nonsmoker (deep
blue). To the right of the maps are histogramblue). To the right of the maps are histogram
plots; they show the distribution of values forplots; they show the distribution of values for
the respective slices more quantitatively.the respective slices more quantitatively.
The mean and standard deviations areThe mean and standard deviations are
increased in the smoker (bottom right)increased in the smoker (bottom right)
compared to the nonsmoker (top right). Thiscompared to the nonsmoker (top right). This
occurs due to destruction of alveolar walls inoccurs due to destruction of alveolar walls in
the lungs of the smoker.the lungs of the smoker.

58. Initial ADC and KurtosisInitial ADC and Kurtosis
• Experimentally determined values of ADC andExperimentally determined values of ADC and
Kurtosis for healthy lungs areKurtosis for healthy lungs are
• ADCADC00 = 0.22 cm^2 /s= 0.22 cm^2 /s
• ADKADK00 = 0.35= 0.35
• Based on these values we determine the initialBased on these values we determine the initial
LL00 and Rand R00 which will correspond to length andwhich will correspond to length and
cross-sectional radius of the first generationcross-sectional radius of the first generation
airway of healthy lungs.airway of healthy lungs.

59. Correlation with KurtosisCorrelation with Kurtosis
• The model shows consistently that value ofThe model shows consistently that value of
Kurtosis of distribution of diffusion distancesKurtosis of distribution of diffusion distances
decreases for increased cross-sectional area ofdecreases for increased cross-sectional area of
airways (airway destruction), and increasesairways (airway destruction), and increases
when the cross-sectional area is decreasedwhen the cross-sectional area is decreased
(airway obstruction)(airway obstruction)

60. Correlation with Diffusion CoefficientCorrelation with Diffusion Coefficient
• The simulation also shows that with increasedThe simulation also shows that with increased
cross-sectional area of the alveoli the ADCcross-sectional area of the alveoli the ADC
increases from its value for the initial alveolarincreases from its value for the initial alveolar
size (destruction of the acini)size (destruction of the acini)
• When the cross-sectional area of the alveoli isWhen the cross-sectional area of the alveoli is
decreased, ADC also decreases from its initialdecreased, ADC also decreases from its initial
value (obstruction of the acini)value (obstruction of the acini)

61. Histograms showing P(Δr) vs. Δr for various geometriesHistograms showing P(Δr) vs. Δr for various geometries
Results of the diffusional kurtosis and diffusion measurements.

62. Experimental DataExperimental Data
 Hyperpolarized He3 is initially in a uniform magnetic field. AnHyperpolarized He3 is initially in a uniform magnetic field. An
RF field pulse is used to achieve an initial orientation of netRF field pulse is used to achieve an initial orientation of net
magnetization.magnetization.
 A gradient field, a non-uniform magnetic field of constantA gradient field, a non-uniform magnetic field of constant
gradient, is used to change the resonant frequencies at differentgradient, is used to change the resonant frequencies at different
spatial locations, which allows to differentiate between signalsspatial locations, which allows to differentiate between signals
obtained from the different spatial locations of He3 atoms.obtained from the different spatial locations of He3 atoms.
 The RF field sweeps through a range of frequencies to findThe RF field sweeps through a range of frequencies to find
resonant signal at all locations in space, thus associating eachresonant signal at all locations in space, thus associating each
spatial location with a particular resonant frequency.spatial location with a particular resonant frequency.

63. Experimental ProcedureExperimental Procedure
 Hyperpolarized He3 is initially in a uniform magneticHyperpolarized He3 is initially in a uniform magnetic
field with spins aligned with the field. An RF field pulsefield with spins aligned with the field. An RF field pulse
flips the spins into the plane perpendicular to theflips the spins into the plane perpendicular to the
uniform field, to begin precession, and with use of auniform field, to begin precession, and with use of a
gradient field, a non-uniform magnetic field of constantgradient field, a non-uniform magnetic field of constant
gradient, signal is acquired during time of re-growth ofgradient, signal is acquired during time of re-growth of
the component of magnetic moment along the uniformthe component of magnetic moment along the uniform
field.field.

64.  Using the data for the signal acquired, diffusionUsing the data for the signal acquired, diffusion
coefficient and kurtosis can be calculated fromcoefficient and kurtosis can be calculated from
S(b)/S(0) = exp( -S(b)/S(0) = exp( -bbD + (1/6)D + (1/6)bbD²K )D²K )
bb = (γδG)²(Δ-δ/3)= (γδG)²(Δ-δ/3)
where G is the gradient strength, Δ the time betweenwhere G is the gradient strength, Δ the time between
pulses, and δ the time of duration of the RF field pulse.pulses, and δ the time of duration of the RF field pulse.
 The differentThe different bb values, depending on the properties ofvalues, depending on the properties of
the signal and field gradient, can be used to findthe signal and field gradient, can be used to find bb--
weighted average signal, and use the result to calculateweighted average signal, and use the result to calculate
D and K.D and K.

65. txG∆=∆ γφ
( )∑ −=
N
itot i
N
S
1
exp
1
φ
∆
δ
δ
-G
G
( )3222
δδγ −∆= Gb
Phase accumulation in gradient
where ∆φ = phase increment; x = position; γ = gyromagnetic ratio; G = gradient; ∆t = time interval.
Total signal (normalized)
where φi
is the phase of the ith
spin and N is the total number of spins.
"b value" (diffusion weighting)
Pulse sequence:
where b = diffusion weighting parameter; γ = gyromagnetic ratio; G = gradient; δ = pulse length;
∆ = time between beginning of each pulse.

66. Signal acquisitionSignal acquisition
 Signal is reconstructed from the equationSignal is reconstructed from the equation
S(t) = ∫ dz exp( i ΦG(z,t) )S(t) = ∫ dz exp( i ΦG(z,t) )
ΦG(z,t) = - γz ∫t dt’ G(t’)ΦG(z,t) = - γz ∫t dt’ G(t’)
ΦG(z,t) = - γzGt for constant gradient GΦG(z,t) = - γzGt for constant gradient G
S(k) = ∫ dz ρ(z) exp( i 2πkz)S(k) = ∫ dz ρ(z) exp( i 2πkz)
where k = (γ/2π)Gtwhere k = (γ/2π)Gt
and ρ(z) = ∫ dk S(k) exp( i 2πkz)and ρ(z) = ∫ dk S(k) exp( i 2πkz)
is the actual density of He3 atoms in the studied volume.is the actual density of He3 atoms in the studied volume.
 By sweeping through the Fourier space k, using gradients alongBy sweeping through the Fourier space k, using gradients along
the three spatial dimensions, we can find the signal S(k) =the three spatial dimensions, we can find the signal S(k) =
S(k(t)) and then reconstruct the density ρ(z), which can be doneS(k(t)) and then reconstruct the density ρ(z), which can be done
for all spatial dimensions.for all spatial dimensions.

67. Results of the diffusional kurtosis andResults of the diffusional kurtosis and
diffusion measurementsdiffusion measurements
Subject
ADK ADC
Volunteer 1 0.321 0.231
Volunteer 2 0.326 0.200
Volunteer 3 0.372 0.242
Volunteer 4 0.377 0.201
Mean 0.343 ± 0.029 0.216 ± 0.020