quantitative oxygen imaging with electron paramagnetic/spin resonance oxygen imaging howard halpern
TRANSCRIPT
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Quantitative Oxygen Imaging with Electron Paramagnetic/Spin
Resonance Oxygen Imaging
Howard Halpern
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Why EPR?
Bad News: native diffusible unpaired electrons: Rare
• Good News: rare native electrons mean no background signal
• Bad News: Need to infuse subjects with materials with stable unpaired electrons
• Good News: Can infuse materials which target pharmacologic compartments
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Why EPR?• Spectroscopic Imaging: Specific quantitative
sensitivity to Oxygen, Temperature, Viscosity, pH, Thiol
Each property of interest is measured with a specifically designed probe.
Free Radicals can bedetected as well
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Why EPR?• Spectroscopic Imaging: Specific quantitative
sensitivity to Oxygen, Temperature, Viscosity, pH, Thiol
• No water background for signal imaging (vs MRI)
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Why EPR?• Spectroscopic Imaging: Specific quantitative
sensitivity to Oxygen, Temperature, Viscosity, pH, Thiol
• No water background for signal imaging (vs MRI)
• Deep sensitivity at lower frequency (vs optical)• 250 MHz vs 600 THz, 6 orders of magnitude lower• 7 cm skin depth vs < 1 mm
• Vs typical EPR (0.009T vs 0.33T electromagnet)• 250 MHz vs 10 GHz, factor of 40 lower• 7 cm skin depth
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Why Electron Paramagnetic (Spin) Resonance Imaging?
• More sensitive and specific reporter of characteristics of the solvent environment of a paramagnetic reporter
• The reporter can be designed to report (mostly) only one characteristic of the environment
• E.G.: oxygen concentration, pH, thiol concentrations
• We have chosen to image molecular oxygen.
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Basic Interaction
• Magnetic Moment m (let bold indicate vectors)
• Magnetic Field B• Energy of interaction:
– E = -µ∙B = -µB cos(θ)
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Magnetic Moment
• ~ Classical Orbital Dipole– Orbit with diameter r, area a = πr2
– Charge q moves with velocity v; Current is qv/2πr– Moment µ = a∙I = πr2∙qv/2πr = qvr/2 = qmvr/2m
• mv×r ~ angular momentum: let mvr “=“ S• β = q/2m; for electron, βe = -e/2me (negative for e)
• µB = βe S ; S is in units of ħ
–Key 1/m relationship between µ and m• µB (the electron Bohr Magneton) = -9.27 10-24 J/T
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Magnitude of the Dipole Moments
• Key relationship: |µ| ~ 1/m• Source of principle difference between
– EPR experiment– NMR experiment
• This is why EPR can be done with cheap electromagnets and magnetic fields ~ 10mT not requiring superconducting magnets
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Major consequence on image technique
• µelectron=658 µproton (its not quite 1/m);• Proton has anomalous magnetic moment
due to “non point like” charge distribution (strong interaction effects)
• mproton= 1836 melectron
• Anomalous effect multiplies the magnetic moment of the proton by 2.79 so the moment ratio is 658
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The Damping Term (Redfield)
• ∂ρ*/∂t=1/iћ [H*(t’)1, ρ*(0)]+ 0
(1/iћ)2 ∫dt’[H*1(t),[H*1(t-t’), ρ*(t’)]
• Each of the H*1 has a term in it with H= -µ∙Br and µ ~ q/m
• ∂ρ*/∂t~ (-) µ2 ρ* This is the damping term:• ρ*~exp(- µ2t with other terms)• Thus, state lifetimes, e.g. T2, are inversely
proportional to the square of the coupling constant, µ2
• The state lifetimes, e.g. T2 are proportional to the square of the mass, m2
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Consequences of the Damping Term
• The coupling of the electron to the magnetic field is 103 times larger than that of a water proton so that the states relax 106 times faster
• No time for Fourier Imaging techniques• For CW we must use
1. Fixed stepped gradients 1. Vary both gradient direction & magnitude (3 angles)
2. Back projection reconstruction in 4-D
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Imaging: Basic Strategy
Constraint: Electrons relax 106 times faster than water protons
Image Acquisition: Projection Reconstruction: Backprojection
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Projection Acquisition in EPR
• Spectral Spatial Object Support ~
,f B x
0 0,
2 2 x
B BB B
0app swB x B B G x
TOTh g B
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=α
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Projection Description
• With s(Bsw, Ĝ) defined as the spectrum we get with gradients imposed
2
2
, ,x
B
sw sw swB
s B G f B x B B G x dxdB
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More Projection
• The integration of fsw is carried out over the hyperplane in 4-space by
swB B G x
DefiningˆcG x
Bc
L
with
The hyperplane becomes1ˆ( )sw swB B G G x B c G
with 1tan c G
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And a Little More
2
2
ˆ, cos , cos cos sinx
B
sw sw swB
s B G f B x B B cG x dxdB
So we can write B = Bsw + c tanα Ĝ∙x
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So finally it’s a Projection
ˆ, cosr
sw r Gs B G f r r dr
with
cos
,
ˆˆ cos ,sin
, .2 2
sw
G
r x
B
r B c x
G
B Bc
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Projection acquisition and image reconstruction
Image reconstruction: backprojections in spectral-spatial space
Resolution: δx=δB/Gmax THUS THE RESOLUTION OF THE IMAGE PROPORTIONAL TO δB
each projection filtered and subsampled;
Interpolation of Projections: number of projections x 4 with sinc(?) interpolation,Enabling for fitting
Spectral Spatial ObjectAcquisition: Magnetic field sweep w stepped gradients (G)Projections: Angle a: tan( )a =G*DL/DH
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The Ultimate Object:Spectral spatial imaging
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Preview: Response of Symmetric Trityl (deuterated) to Oxygen
• So measuring the spectrum/spectral width≈relaxation rate measures the oxygen. Imaging the spectrum: Oxygen Image
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Why is oxygen importantin cancer?
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Known Since 1909 but in 1955Thomlinson and Gray showed
necrosis
viabletissue
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Dramatic differences in survival for patients with cervicalcancer treated with radiation depending on mean tumor
oxygenation: > or < 10 torr
Hockel, et al, Ca Res 56 (1996), p 4509
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This was thought to be the
source of radiation resistance
•Hyperbaric oxygen trials √ (in human trials)
•Oxygen mimetic radiosensitizers √ (in animals only due to toxicity)
•Eppendorf electrode measurements (humans)
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Intensity Modulated Radiation Therapy
• Sculpts radiation dose over distances of
5mm• Able to spare normal tissues
But tumor volumes are homogeneous; no
accounting for different regions with
different sensitivity
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Biological imaging to enhance targeting of radiation therapy: oxygen imaging
• Intensity modulated radiation therapy allows sophisticated control over spatial distribution of radiation dose
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Biological imaging to enhance targeting of radiation therapy: oxygen imaging
• Intensity modulated radiation therapy allows sophisticated control over spatial distribution of radiation dose
• But: some regions may contain hypoxic cells
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Biological imaging to enhance targeting of radiation therapy: oxygen imaging
• Hypoxic cells are known to be radioresistant
0.0076 torr0.075 torr
0.25 torr
1.7 torr
Air
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Biological imaging to enhance targeting of radiation therapy: oxygen imaging
• Intensity modulated radiation therapy allows sophisticated control over spatial distribution of radiation dose
• Areas of hypoxia could be given extra dose if only we could identify them!
So...
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Why use radio-frequency for EPR?
250 MHz ~6 T MRI
S/N ~ w0.8
N~w 1.2
IN LOSSY,CONDUCTIVETISSUE
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Aim:
Image crucial physiologic information:oxygen
Information:
Communicated by reporter molecules which are injected into
animals/humans.
Communication through EPR spectrum.
Simple spectrum in a complex biological system
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Response of Symmetric Trityl (deuterated) to Oxygen
• No temp. dependence: < 0.05 mG/K• Low viscosity dependence ~1mG/cP• Self quenching a potential confounding
variable -- Solved with Longitudinal Relaxation Rate Imaging
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Information about fluid in which reporter molecule dissolved obtained
from Spectral Parameters4
0
datai
fiti
9287 Bi
Spectral parameters extracted from spectral data using Spectral/Relaxation Rate FittingBonus: Fitting gives parameter uncertainties
Standard penalty for deviation:χ2=(yi-fit(xi, aj))2 minimize this penalty byadjusting the Spectral Parameters aj e.g., spectral width
…
spectralwidth
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Major improvement: Synthesis of selectively deuterated OX31
Improves1. Oxygen sensitivity: d DB / ~DB dR/R2. Spatial resolution for a given gradient:
resolvable Dx= DB/G 3. Sensitivity
d
d
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Line widths pO2 calibration
Oxygen dependence of spin packet width obtained in a series of homogenous solutions of OX31:Since minimal viscosity dependence, aqueous=tissue
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CW 4D IMAGE LINEWIDTH RESOLUTION
A measure of the line width resolution is the distribution of linewidths from a homogeneous
phantom. Here, the s of the distribution is 0.17 mT, or ~ 3 torr pO2 (8x8x8,projections in 20 minutes)
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1.0 m m
1.0mM1.75T
1.0mM4.00 T
0.5mM2.50 T
1.0mM1.63T
0.5mM1.50 T
0.5mM1.63T
1.0mM2.50 T
0.5mM2.00 T
0.5mM1.56T 1.0mM
1.56T
1.0mM2.00 T
1.0mM6.50 T
0.5mM1.75T
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Line Width Fidelity: Agreement Between Image and Individually measured line-widths (1.6 mm) heterogeneous phantom. Side lines Approximately ±3 torr.
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EPR spectral-spatial 4D imaging
• CW EPR imager at 250 MHz, with a loop-gap resonator
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Dimensions of the resonator (1.5 cm thick)Sensitive Region of the resonator (total of just over 2 -2.5 cm)
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Mouse Image (OX063)
XY
YZ
• PC3 tumor with 3D intensity image (Note no artifacts surrounding surface)
• XY and YZ pO2 slices corresponding to the slices in the volume
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Oxylite probeInto tumor
• Validation with Oxylite fiberoptic probe (measuring fluorescence quenching by oxygen)
Stereotactic PlatformFor Needle Location
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Good agreement!
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Adjacent tracks in areas of rapid oxygen variationagree with Oxylite
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New insight into the oxygen statusof tumors and tissues