of 14
Davis, Ramesh et al.
Page
1 of
14
Mapping the Microscale Origins of MRI Contrast with
Subcellular NV Diamond Magnetometry
Hunter C. Davis
1#
, Pradeep Ramesh
2#
, Aadyot Bhatnagar
3
, Audrey Lee
-Gosselin
1
, John F. Barry
4,5,6,7
, David R.
Glenn
4,5,6
, Ronald L. Walsworth
4,5,6
, Mikhail G.
Shapiro
1,
*
1
Division
of Chemistry
and
Chemical
Engineering,
2
Division
of Biology
and
Biological
Engineering,
3
Division
of Engineering
and
Applied
Sciences,
California
Institute
of Technology,
Pasadena,
CA
91125,
USA
4
Harvard
-Smithsonian
Center
for
Astrophysics,
5
Department
of Physics,
6
Center
for
Brain
Science,
Harvard
University,
Cambridge,
MA
02138,
USA
7
MIT
Lincoln
Laboratory,
Lexington,
MA
0242
0, USA
#
Equal
contribution
*Correspondence
should
be addressed
to MGS:
(mikhail@caltech.edu
)
Abstract
Magnetic
resonance
imaging
(MRI)
is a widely
used
biomedical
imaging
modality
that
derives
much
of its contrast
from
microscale
magnetic
field
gradients
in biological
tissues.
However,
the
connection
between
these
sub
-voxel
field
pattern
s and
MRI
contrast
has
not
been
studied
experimentally.
Here,
we
describe
a new
method
to map
subcellular
magnetic
fields
in mammalian
cells
and
tissues
using
nitrogen
vacancy
diamond
magnetometry
and
connect
these
maps
to voxel
-scale
MRI
contrast,
providi
ng
insights
for
in vivo
imaging
and
contrast
agent
design.
Main
Text
Magnetic
resonance
imaging
(MRI)
is a common
biomedical
imaging
modality
whose
contrast
is based
on
the
spatially
and
temporally
varying
behavior
of nuclear
spins.
This
behavior
is influenced
by microscale
magnetic
field
gradients
in cells
and
tissues
produced
by
endogenous
substances
such
as pathological
iron
deposits
[1,
2] or molecular
imaging
agents
such
as iron
oxide
nanoparticles
(IONs)
[3,
4]. The
resulting
image
contrast
is used
to diagnose
diseases
or track
the
in vivo
distribution
of labeled
cells
and
molecules
[5,
6]. The
precise
dependence
of voxel
-scale
(~ 0.5
mm)
MRI
contrast
on
microscale
magnetic
field
gradients
has
been
a hot
topic
of theory
and
simulation
due
to its
importance
for
disease
diagnosis
and
contrast
agent
design
[2,
7-10]
. These
studies
predict,
for
example,
that
the
spatial
frequency
of the
local
magnetic
field
can
significantly
impact
the
T
2
relaxation
rate
of a tissue
and
that
optimizing
contrast
agent
size
can
maximize
T
2
contrast
for
a given
set
of material
and
imaging
parameters.
Despite
the
significance
of the
relationship
between
the
spatial
pattern
of the
local
magnetic
field
and
T
2
relaxation,
this
dependence
has
not
been
studied
experimentally
due
to a lack
of methods
to map
magnetic
fields
at the
micro
scale
under
biologically
relevant
conditions.
Here,
we
present
a method
to study
the
connection
between
subcellular
magnetic
fields
and
MRI
contrast
using
nitrogen
vacancy
(NV)
magnetometry,
a recently
developed
technique
that
enables
the
imaging
of magnetic
fields
with
optical
resolution
using
the
electronic
properties
of fluorescent
NV
quantum
defects
in diamond
[11].
The
electronic
structure
of an
NV
center
forms
a ground
-state
triplet,
with
the
!
=
±
1
states
separated
from
the
!
=
0
state
by 2.87
GHz,
making
ground
-state
spin
transitions
addressable
by standard
electron
spin
resonance
(ESR)
techniques.
The
resonant
freque
ncy
of these
transitions
shifts
linearly
in a magnetic
field
due
to the
Zeeman
effect.
Upon
green
laser
excitation
(532
nm)
, the
!
=
±
1
states
are
more
likely
to undergo
non-
radiative
relaxation
than
the
zero
-spin
state,
so that
microwave
-induced
transitions
from
!
=
0
to
!
=
±
1
cause
a drop
in NV
fluorescence.
Thus,
the
local
magnetic
field
of an
NV
center
can
be easily
extracted
from
the
optically
reported
ground
-state
spin
transition
frequency.
Diamonds
densely
doped
with
NV
centers
make
it
is possible
to optically
image
this
resonant
transition
frequency
over
a wide
field
of view,
thus
providing
an
Abbe
-limited
image
of the
magnetic
field
at the
diamond
surface
[12].
NV
magnetometry
has
recently
been
used
in
proof
-of-concept
biological
applications
such
as imaging
the
magnetic
fields
produced
by magnetotactic
bacteria
[13],
detecting
magnetically
labeled
cancer
cells
[14],
and
measuring
magnetic
fields
produced
by neuron
al
action
potentials
[15].
However,
to date
this
technology
has
not
been
used
to map
sub
-cellular
magnetic
fields
in
living
mammalian
cells
or to connect
these
maps
to
in
vivo
diagnostic
imaging
modalities
such
as MRI.
Doing
so requires
adapting
NV
magnetometry
for
high
-
Davis, Ramesh et al.
Page
2 of
14
sensitivity
imaging
of sparse
magnetic
field
s in cells
and
tissues,
developing
methods
to convert
2-D NV
data
into
the
3-D distribution
of magnetic
field
sources
and
simulating
the
behavior
of nuclear
spins
in the
resulting
magnetic
fields.
In addition,
monitoring
the
evolution
of
magnetic
fields
in live
cells
requires
operating
under
non-
damaging
optical
and
thermal
conditions
with
reduced
available
signal.
In this
work,
we
address
these
challenges
to enable
the
mapping
of sub
-cellular
magnetic
fields
in an
in vitro
model
of macrophage
iron
oxide
endocytosis
and
an
in vivo
model
of liver
iron
overload,
connecting
both
to MRI
contrast.
Our
ho
me
-built
NV
magneto
-microscope
(
Fig.
1a
)
was
optimized
for
both
high
resolution
magnetic
field
imaging
of fixed
samples
and
dynamic
imaging
of
living
cells.
By
virtue
of a relatively
thick
NV
layer
in
our
diamond
(~4
μm)
, we
were
able
to significantly
red
uce
the
applied
laser
power
compared
to shallower
surface-
implanted
NV
diamond
microscopes,
while
maintaining
a strong
NV
fluorescent
signal
for
rapid
imaging.
We
used
a total
internal
reflection
geometry
to
minimize
phototoxicity
[13,
15]
and
bonded
a silicon
carbide
wafer
to the
diamond
base
to improve
thermal
dissipation
[15].
For
cell
imaging
experiments,
we
applied
a moderate
bias
field
(~10
mT)
to magnetize
cell
-internalized
superparamagnetic
IONs
.
As
a first
test
of our
method,
we
imaged
the
magnetic
fields
resulting
from
the
endocytosis
of
superparam
agnetic
IONs
by murine
RAW
264.7
macrophages.
Magnetic
labeling
and
in vivo
imaging
of
macrophages
is under
development
for
a variety
of
diagnostic
and
therapeutic
applications
[4,
16-
18]
,
which
could
benefit
from
an
improved
understanding
of
the
resulting
MRI
contrast.
In particular,
although
labeling
is typically
done
with
dispersed
particles,
their
internalization
and
subsequent
compaction
by the
cell
(
Fig.
1, b-c
) could
produce
radically
different
magnetic
field
profiles
[8-10]
, which
cannot
be directly
observed
by conventio
nal
electron
microscopy
or iron
staining
techniques.
We
performed
vector
magnetometry
on
fixed
macrophages
after
incubating
them
for
one
hour
with
200
nm
IONs
and
allowing
one
additional
hour
for
internalization.
After
measuring
the
magnetic
field
along
each of the
four
NV
orientations
(
Fig.
1d
), we
projected
the
field
maps
along
Cartesian
axes
convenient
for
magnetic
dipole
localization
via
orthogonalization
and
tensor
rotation
(
Fig.
1e
).
To
convert
the
resulting
2-D vector
map
at the
diamond
surface
into
a 3-D model
of magnetic
fields
inside
the
cell,
we
developed
an
algorithm
for
iterative
localization
of
magnetic
dipoles
(
Fig.
1f
,
Supplementary
Fig.
S1
).
First,
the
in-plane
coordinates
of putative
dipole
field
sources
(
e.g.
, clusters
of magnetic
particle
s) were
identified
from
local
minima
in the
x-component
of the
vector
field,
chosen
parallel
to the
projection
of the
bias
field
onto
the
diamond
surface.
Then,
the
off
-diamond
height
(z)
and
magnetic
moment
of each
cluster
were
determined
by fitting
the
local
dipole
field
profile.
After
fitting
the
dipole
at the
strongest
local
minimum,
the
resulting
magnetic
field
pattern
was
subtracted,
and
the
next
strongest
local
minimum
fitted,
with
this
process
repeated
until
all local
minima
were
exhausted.
A global
fit was
then
performed
using
the
results
from
the
local
fits
as starting
parameters.
The
degree
-of-freedom
-adjusted
R
2
for
all
the
global
fits
made
to 6 representative
particle
-
containing
cells
was
greater
than
0.90.
To
translate
sub
-cellular
magnetic
field
maps
into
predictions
about
MRI
contrast,
we
performed
Monte
Carlo
simulations
of
nuclear
spin
T
2
decoherence
in lattices
of representative
cells
. These
cells
contain
ed magnetic
dipole
distributions
and
magnitudes
derived
from
NV
magnetometry
of a
representative
cellular
library
(
Fig.
2a
,
Supplementary
Fig.
S2
). This
simulation
predicted
a
bulk
MRI
T
2
relaxation
time
of 24.3
ms
for
a 1:1
mixture
of supplemented
and
unsupplemented
cells
(
Fig.
2b
). When
compared
to an
experimental
MRI
measurement
of T
2
in macrophages
prepared
as in the
NV
experiment
and
pelleted
in a 1:1
mixture
with
unsupplemented
cells,
the
Monte
Carlo
prediction
was
accurate
to within
2.8%
(
Fig.
2, c-d
). Importantly,
this
relaxation
time
could
not
ha
ve been
predicted
solely
from
the
concentration
of IONs
in the
sample,
as
previous
simulations
have
suggested
a major
influence
of packing
geometry
on
contrast
agent
relaxivity
[8-10]
.
To
establish
that
this
relationship
also
holds
for
our
model
system,
we
performed
MR
I measurements
and
Monte
Carlo
simulations
with
IONs
distributed
in the
extracellular
space
(
Fig.
2e
).
Per
iron
mass,
we
found
that
this
diffuse
extracellular
arrangement
produces
approximately
6.63-
fold
faster
T
2
relaxation
than
do
endocytosed
particles,
underlining
the
importance
of
microscale
magnetic
field
patterns
(
Fig.
2f
).
To
extend
this
technique
to diagnostic
imaging,
we
performed
NV
magnetometry
on
liver
specimens
from
a mouse
model
of hepatic
iron
overload.
The
spatial
distribution
of iron
deposits
in the
liver
and
other
tissues
has
been
a topic
of interest
in clinical
literature
as
an
indicator
of disease
state,
including
efforts
to discern
it
noninvasively
using
MRI
[2].
Iron
overload
was
generated
through
intravenous
administration
of 900
nm
IONs
to C57bl/6
mice
(
Fig.
2g
).
Livers
were
harvested
18
hours
after
injection
and
imaged
with
7T
MRI,
showing
enhanced
mac
roscale
T
2
relaxation
compared
to controls
(
Fig.
2h
).
To
investig
ate
the
microscale
nature
of this
contrast
enhancement,
we
cryosectioned
the
livers
of saline
- and
iron
-injected
mice
Davis, Ramesh et al.
Page
3 of
14
and
imaged
the
magnetic
field
profile
s of these
tissue
sections
on
our
NV
magneto
-microscope
. We measured
the
projection
of the
magnetic
field
along
a single
NV
orientation,
probing
the
!
=
0
to
!
=
+
1
and
!
=
0
to
!
=
1
transitions.
This
revealed
a
punctate
distribution
of magnetic
dipoles
within
the
liver
tissue
of the
iron
-overloaded
mouse
(
Fig.
2i
,
Supplementary
Fig.
S3
). We
confirmed
that
these
magnetic
fields
resulted
from
IONs
using
fluorescent
imaging,
for
which
purpose
the
IO
Ns
were
labeled
with
a fluorescent
dye
. These
results
suggest
that
NV
magnetometry
could
be used
to map
sub
-voxel
magnetic
field
pat
terns
with
in clinical
specimen
s.
Finally,
we
tested
whether
NV
magneto
metry
could
be used
to follow
the
magnetic
consequenc
es of a
dynamic
process
in
living
mammalian
cells.
Macrophages
endocytosing
IONs
go through
several
stages
of internalization,
gradually
reconfiguring
diffuse
particles
into
compacted
lysosomal
clusters
(
Fig.
3a
).
This
process
could
be relevant
to interpre
ting
MRI
data
from
labeled
macrophages
and
to the
development
of
clustering
-based
magnetic
nanoparticle
contrast
agents
[19,
20]
. To
image
living
cells
, we
adjusted
our
NV
methodology
to
minimize
optical
and
thermal
energy
deposition.
We
sub
-sampled
the
NV
spectrum
to probe
only
the
!
=
0
to
!
=
+
1
transition
of one
NV
orientation
and
limited
laser
illumination
to 5 minutes
per
image.
This
allowed
us to generate
time
-lapse
images
of magnetic
fields
coalescing
inside
macrophages
after
ION
internalization
(
Fig.
3, b-c
,
Supplemen
-
tary
Fig
s. S4-S5
). Cell
viability
(assessed
via
a Trypan
Blue
exclusion
assay)
was
~90%.
To
our
knowledge,
this
represents
the
first
magnetic
field
imaging
of a
dynamic
process
in living
mammalian
cells
, and
could
aid
the
development
of dynamic
contrast
agents
for
MRI.
In summary,
this
work
has
established
methods
to experimentally
connect
subcellular
magnetic
field
gradients
to voxel
-scale
MRI
contrast
and
follow
dynamic
processes
within
living
cells
using
NV
diamond
magnetometry.
We
anticipate
that
these
methods
will
enable
the
microscale
sources
of MRI
contrast
to be
studied
in a variety
of biological
contexts
to aid
in the
interpretation
of clinical
images
and
contrast
agent
development.
While
this
study
demonstrated
the
core
capabilities
of this
method
using
iron
-loaded
cells
and
tissues,
future
improvements
should
extend
this
technique
to samples
containing
weaker
and
more
ho
mogeneously
distributed
magnetic
field
sources.
For
example,
employing
diamonds
with
thinner
NV
layers
would
reduce
the
point
spread
function
of NV-
imaged
magnetic
fields,
increasing
the
precision
of source
localization,
while
improved
methods
for
positioning
tissue
sections
flat
on
the
diamond
surface
would
allow
the
mapping
of fields
produced
by smaller,
endogenous
magnetic
inclusions.
Combined
with
ongoing
advances
in NV
diamond
technology,
these
improvements
will
help
subcellular
magnetometry
investigate
the
origins
of
MRI
contrast
in a broad
range
of biological
and
medical
scenarios.
Methods
Nitrogen Vacancy Magneto
-Microscope
The NV
magneto-
microscope
was constructed from a
modified upright Olympus microscope and a 532 nm
laser source.
The diamond used in this work is an
electronic grade (N
< 5ppb) single crystal substrate with
nominal rectangular dimensions of 4.5 mm x 4.5 mm x
500
μ
m, grown using chem
ical vapor deposition (CVD)
by Element Six. The top
-surface NV sensing layer
is
measured to be 3.87
μ
m thick,
consists of 99.999
%
isotopically pure
12
C with 21.4 ppm
14
N
(3.77*10
17
cm
-3
)
incorporated
into the layer during growth
. Layer
thickness and nitrogen concentration were determined
by
secondary ion
mass
spectroscopy.
The diamond was
irradiated with an unknown irradiation dosage and then
annealed first at 800
ºC for twelve hours
followed by
1000
ºC for twelve hours.
This
diamond was affixed to
a silicon carbide wafer (for enhanced heat dissipation)
,
which was in turn affixed to a
pair of triangular prisms
to facilitate a total internal reflection excitation path.
The prisms, silicon carbide wafer and diamond were
fused usi
ng Norland Optical Adhesive
(NOA 71)
. The
diamond assembly was removable to allow live cell
culture on the diamond surface in a cell culture
incubator. Light was collected from the top of the
diamond through a water
-immersion objective. Images
were acquire
d on a
Basler acA2040-
180kmNIR
-
CMV4000
CCD
camera with
2048x2040
5.5
μm
pixels
(we used
256x
1020
pixels
to increase frame rate)
. For
high
-resolution vector magnetometry and tissue
imaging, NV fluorescence was excited using a 100 mW
Coherent OBIS LS 532 nm optically pumped
semiconductor laser. For live cell imaging, we used an
attenuated 2
W 532 nm laser from Changchun New
Industries Optoelectronics. When necessary,
focal
drift
was adjusted for using a piezo
-driven stage (
Thorlabs
).
Microwave pulses were applied through a single turn
copper loop immediately surrounding the diamond.
The microwave signal was generated by a Stanford
Research Systems Inc.
SG384
signal generator
and
amplified by
a ZHL
-16W
-43-
S+ amplifier from
Davis, Ramesh et al.
Page
4 of
14
MiniCircuits
. Experimental timing was controlled by a
National Instruments USB 6363 X Series DAQ.
A bias
magnetic
field was generated by two
NeFeB grade
N52
magnets (1”x2”x.5”, K&J Magnetics) positioned
on
opposite sides of the NV diamond
. The NV setup was
controlled by custom software written in LabView.
Cell Culture
RAW
264.7
cells were cultured at 37º C and
5% CO
2
in DMEM
(Corning Cellgro
) and passaged at or before
70% confluence. For particle labeling, media was
aspirated and replaced with phenol red
-free DMEM
supplemented with
279 ng/ml
IONs (200 nm Super
Mag Amine Beads Ocean Nanotech). After one hour,
the ION solution was aspirated and cells were washed
twice with PBS to remove unbound particles. For fixed
-
cell magnetometry, the cells were trypsinized quenched
with DMEM and deposited on
the diamond surface.
After a 1 hour incubation at
5% CO
2
and 37 ºC, the
cells were fixed with
4 % paraformaldehyde
-zinc
fixative
(Electron Microscopy Services)
and washed
twice with PBS.
For live cell imaging, the cells were cultured as
above until
trypsinization and spotting on the diamond.
Their media was supplemented with 0.1 mM ascorbic
acid to mitigate phototoxicity
[21]. For extended
imaging (Supplementary Fig. S3a), the cells were
maintained on the diamond in DMEM supplemented
with 10 mM HEPES to stabilize pH at 7.4 under
ambient atmosphere.
Vector Magnetometry
The
bias
magnetic field was aligned
close to in
-plane
with the diamond surface while having
sufficient
out
-of-
plane field strength
to resolve all NV resonances
, and
the full NV ODMR spectrum was probed. The
microwave resonance for each pixel in the image was
set as the center of the middle hyperfine peak of the
transition. Spectra were swept at
0.5 Hz with 2000
images acquired per spectrum (
0.9 ms exposure time).
Images were acquired with an Olympus 60x water
immersion objective (NA 1.0). Magnetometry spectra
were acquired for 2 hours each. For a sub
-set of
measurements, this time was extended to 6 hours to
improve SNR.
Projection field maps for each NV orientat
ion
were generated from the corresponding peaks in the NV
ODMR, and a quadratic background subtraction was
performed to remove the magnetic gradient from the
bias magnets. Projection field maps were combined to
form 3 orthogonal field maps with
!
orient
ed normal
to the diamond sensing surface
.
!
is defined as the
projection of the applied field onto the diamond plane
and
!
is defined along the vector
that
completes the
orthogonal set. Pixels were binned 2x2 in post
-
processing to boost SNR.
(This does not cause a
significant reduction in resolution as the binned pixels
in
the object plane are 92 nm on a side, which
oversamples the
Abbe limit of ~340 nm
.) Our sensitivity
for this technique was 17
nT
at 1 μm
in plane resolution
(our out of plan
e resolution was fixed by the
NV layer
depth of 3.87
μ
m). Of particular note, this detection
limit
is sufficient to
detect a single 200 nm ION spaced
10
μm
off of the diamond, where the peak
measured
|
!
|
field would be greater than 200
nT
.
Live Cell
Magnetometry
For live cells, the
bias
magnetic field was aligned along
an arbitrary direction
sufficient to resolve at least one
NV resonance
, and the magnetic field projection along
a single NV orientation was probed using the
!
=
0
!
=
+
1
transition.
T
he
microwave
resonance for each pixel in the image was set as the
center of the middle hyperfine peak of the transition.
Spectra were swept
~10 MHz
at 1 Hz with 200 images
acquired per spectrum (4 ms exposure time).
In order to
limit phototoxicity, each im
age was averaged for only 5
minutes and the laser was shuttered for five minutes in
between images
, resulting in a 50% duty cycle.
Regions
of interest were selected to include all relevant fields for
a given cell.
Optical
power
density was ~40 W/cm
2
.
Images were acquired with a Zeiss 40x near infrared
water immersion objective (NA 0.8).
Cell viability was
assessed by performing a Trypan Blue exclusion assay at
the conclusion of NV measurements.
Field Fitting and Dipole Localization
In-plane dipole coo
rdinates
were identified as local
minima in the
B
x
field map. Before localization, the field
map was
spatially low
-passed
(2D Gaussian filter with
= 0.5 pixels) to eliminate noise
-generated local
minima in the background. A pixel was identified as a
local minimum if and only if its
B
x
field v
alue was
smaller than all of its immediate neighbors (including
diagonals) in the
spatially low
-passed
image.
Starting with the strongest local minimum, the
measured magnetic
field in a 10x10 pixel (~1.8x1.8
μm
)
square surrounding this minimum was fitted to a point
dipole equation and averaged through the full NV
layer
depth
(assuming uniform
NV
density)
, with the
magnetic moment, height off of the diamond, and
dipole orientation as free parameters.
!
,
=
!"
!
,
!
,
,
,
,
푑푏
!
(
!
!
!
)
!
!
where
!"
(
,
)
=
!
4
(
3
(
)
!
!
)
Davis, Ramesh et al.
Page
5 of
14
Here
i’=(i
-i
0
)
and
j’=(j
-j
0
)
where (
i
0
,j
0
) are
the in
-
plane coordinates
of the magnetic dipole
,
and
correspond to the two rotational degrees of freedom
available to a point dipole,
M is the magnetic moment,
z is the height of the dipole over the diamond,
r
is the
displacement vector,
is the
unit
vector along the
projection of the dipole axis onto the
diamond surface
plane
,
=
!
cos
!
sin
, b is a dummy variable
for integration through the NV layer,
and h is the NV
layer thickness.
All parameters are free to fit other than
the
in-plane
dipole coordinates, which are fixed by the
local minimum of the
B
x
field map.
After the strongest minimum has been fitted, the
fitted field from the fit dipole (within the full field of
view) was subtracted from the magnetic field image, to
facilitate th
e fitting of weaker dipoles. The 10x10 pixel
neighborhood of the second strongest dipole was then
fitted in the subtracted image. The fitted field was
subtracted, and the fitting continued until the list of
local minima
had
been exhausted.
A global fit was then performed using the results
from the neighborhood fits as starting parameters. The
global fit function is the sum of N dipoles (where N is
the number of local minima) with the
in-plane
dipole
coordinates
fixed at the local minima.
!
!"!
,
=
!
!
(
,
)
!
Here q is an index that runs from one to N and
indicates the dipole field source.
The precision of this
technique is limited by
the key assumption
that the local
minima are not significantly shifted in the x
-y plane by
neighboring dipoles. The degree of freedom
-adjusted R
2
for each of the four global fits in the cell library was
greater than 0.9. (For 3 of the 6 labeled cells, with
image
acquisition
time
increased from 2 to 6 hours, the R
2
was
greater than 0.95)
While this approach was able to
produce
a
sufficiently
precise
magnetic
field
reconstruction to predict MRI relaxation,
other
methods
are also available
for analytic dipole
localization and m
agnetic field reconstruction
[22].
Monte
Carlo
Simulations
& Cell
Library
Nuclear spin relaxation was simulated by assigning 11
representative cells from vector magnetometry to
random positions in a repeating
face
-centered cubic
lattice containing a total of 108 spherical cells with
periodic boundary conditions.
Cell size was set to match
previously
measured
values
for
RAW
264.7
macrophages
[23].
Water molecules were randomly
assigned initial x, y, and z coordinates
in the
lattice and
allowed to diffuse while their phase in the rotating
frame
evolved
from
0
=
0
by
훿휙
=
훾퐵
,
,
훿푡
, where
(
,
,
)
is the local
nanoparticle-
induced field. Re
-focusing pulses were
simulated at 5.5 ms Carr
-Purcell time by setting
=
훿푡
.
The magnetic field was mapped
within this 3D
-volume using a finite mesh whose mesh
size was inversely proportional to the local field
gradient. If a water molecule moved within a distance
equivalent to six nanoparticle cluster radii of a cluster,
the fiel
d contribution from that cluster was calculated
explicitly.
Background RAW cell relaxation was
accounted for by post
-multiplying the simulated signal
with an exponential decay with time constant set to the
measured relaxation rate of an unlabeled RAW cell
pellet.
Cell membranes were modeled as semi
-
permeable boundaries with a permeability of .01
!"
!"
in
accordance with previously measured values for murine
macrophage
-like cells, adjusted to the temperature in
our magnet bore (12.9 ºC)
[24]. Intracellular and
extracellular water diffusivity were set
, respectively,
to
0.5547 and 1.6642
!"
!
!"
in accordance with previously
established values for water diffusivi
ty at 12.9 ºC
[25].
Bulk spin magnetization in the sample was calculated as
=
cos
[
!
]
!
, where
i
is the index of simulated
water molecules. Nanoparticle clusters were modeled as
spheres packed so as to occupy three times the volume
of their constituent nanoparticles, consistent with other
simulations and grain packing theory
[10]
[26].
To
account for the increase in nanoparticle magnetizations
at 7T compared to our NV bias field, we scaled dipole
magnetization using a SQUID
-measured curve
(Supplementary Fig.
S6). Data presented in the
manuscript represents the output of N=10 sim
ulations,
each containing 20 random arrangements of cells and
2000 water molecules.
To assess the impact of an alternative
nanoparticle distribution (Fig. 2, e
-f), we simulated the
same quantity of nanoparticles, unclustered and
distributed randomly in th
e extracellular space. The
presented data comprises N=10 simulations, each
containing 20 random arrangements of particles and
2000 water molecules.
MR Imaging and Relaxometry
Imaging and relaxometry were performed on a Bruker
7T MRI scanner
. A 72 mm diameter volume coil was
used to both transmit and receive RF signals.
To
measure the T
2
relaxation rate of RAW cells after
nanoparticle labeling, the cells were labeled identically
to their preparation for NV magnetometry, then
trypsonized, quen
ched with 10 mL DMEM
and
pelleted for 5 min at 350 g. DMEM was aspirated and
cells were resuspended in 150 μL PBS. After
transferring
the
cells to a
300 μL centrifuge tube,
they
were pelleted for 5 min at 350 g. These tubes were
Davis, Ramesh et al.
Page
6 of
14
embedded in a phantom compr
ising 1% agarose
dissolved in PBS and imaged using a multi
-echo spin
echo sequence (TR = 4000 ms, TE = 11 ms,
2 averages,
20 echoes
, 273x273x1000 μm voxel size
). T
2
relaxation
was obtained from a monoexponential fit of the first 6
echoes. (The
slower
background relaxation rate
s of four
unsupplemented RAW cell pellets were measured using
the first 20 echoes.)
For the scenario in which nanoparticles are
unclustered in the extracellular space, unsupplemented
RAW cells were pelleted and re
-suspended in P
BS
supplemented
with
100
μg/ml
ION
s.
This
concentration was selected
to ensure a measurable T
2
and allow both
in silico
and
in cellulo
comparison
s
between
the per
-iron relaxation rates of
extracellular
and internalized particle scenarios
. The validity of a
per
-iron comparison
was
confirmed by previous studies
of the linearity of relaxivity for this size of iron oxide
nanoparticles
[27]. After
supplementation, the cells
were re
-pelleted and immediately imaged
as described
above.
Mouse Model of Iron Overload
C57bl/6 m
ice were injected in the tail vein with 10
mg/kg of
dragon green labeled
900 nm ION (Bangs) or
saline. 1
6 hours after injection, the mice were perfused
with
2 mL of 10% formalin,
and their livers were
harvested for MRI or NV magnetometry. MRI was
performed on
livers embedded in 1
% agarose using the
7T scanner described above, using a
spin
-echo pulse
sequence
with TR = 2500
, TE =
11
ms
, 4 averages, and
a 273x273x1000 μm voxel size
. For NV magnetometry,
the liver was
frozen in OCT embedding media
and
sectioned into 10
μm
slices.
Sections
were mounted in
on glass coverslips. We inverted the glass cover slip and
pressed the tissue sample against the NV diamond.
Silicon vacuum grease was applied at the edge of the
cover slip (away from the diamond) to seal the sample
against the diamond. Afte
r this preparation was
complete, PBS was added to the dish to wet the sample.
To compensate for magnetic field sources being further
from the diamond due to tissue thickness and/or folds
in the sections, NV imaging was performed with a
strong (~250 G) bias field applied along a single NV
axis. This strong bias field served to increase the
magnetization of the magnetic inclusions in the liver. As
it was applied along an NV axis, this bias field did not
significantly reduce the contrast of the relevant ODMR
spectral
lines. Images were acquired with a Zeiss 40x
near infrared water immersion objective (NA
0.8).
Software
and
Image
Processing
All
fits
and
plots
were
generated
in MATLAB.
Monte
Carlo
Simulations
were
performed
in C++
on
a Linux
high
performance
computing
cluster.
Acknowledgements
We
acknowledge
Arnab
Mukherjee,
George
Lu,
My
Linh
Pham,
Andrei
Faraon,
Geoffrey
Blake,
Joe
Kirschvink,
Hans
Gruber,
Michael
Tyszka,
Russ
Jacobs,
and
John
Wood
for
helpful
discussions.
This
work
was
supported
by
the
National
Science
Foundation
Graduate
Research
Fellowship
(PR),
Caltech
Center
for
Environmental
-
Microbial
Interactions
(MGS),
the
Burroughs
Wellcome
Fund
(MGS),
the
NSF
EPMD
and
PoLS
programs
(RLW)
and
the
ARO
MURI
program
on
Imaging
and
Control
of Biological
Transduction
using
NV-
Diamond
(RLW).
Research
in the
Shapiro
Laboratory
is also
supported
by the
Heritage
Medical
Research
Institute.
Davis, Ramesh et al.
Page
7 of
14
Figure 1
Sub
-cellular mapping of magnetic
fields in cells labeled for MRI.
(
a
) Schematic of sub
-voxel
magnetic field mapping using a NV
magneto
-microscope. (
b
) Illustration of a cell labeled with IONs and its
expected magnetic field pattern.
(
c
) Brightfield image of RAW 264.7 macrophage labeled wi
th 200 nm IONS.
White arrows point to internalized IONs. A brightfield imaging artifact also appears as black in the upper right
corner of the cell. (
d
) Cartoon representation of each NV orientation and corresponding representative spectra from
fixed cell
experiments. The blue ball represents the nitrogen and the red ball represents the adjacent lattice vacancy.
Highlighted peaks in each
relative fluorescence (RF)
spectrum show the transition corresponding to each of the 4
orientations. (
e
) Magnetic field i
mages of the field projections along each of the 4 NV axes of macrophages 2 hours
after initial exposure to 279 ng/ml 200 nm IONs (left). These images are converted via
Gram
-Schmidt
orthogonalization and
tensor
rotation to field maps along 3 Cartesian coor
dinates with the z
-axis defined
perpendicular to the diamond surface and the x
-axis defined as the projection of the applied bias field onto the
diamond surface plane (right). The y
-axis is defined to complete the orthogonal basis set. (
f
) Representative e
xample
of the procedure for dipole localization in cellular specimens. This procedure comprises three steps: first the local
minima in the field map are identified and ranked; next, in decreasing order of magnitude, the neighborhood of
each local minimum i
s fit to a point dipole equation and the resulting field is subtracted
from
the field map to
reduce the fit
-deleterious effect of overlapping dipole fields; finally, the results of these fits are used as
guess
parameters for a global fit over the full
field
-of-view. The fit shown has a degree
-of-freedom
-adjusted R
2
of 0.97.
Scale bars are 5
μm
.