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Quantitative Oxygen Imaging with Electron Paramagnetic/Spin Resonance Oxygen Imaging. Howard Halpern. Why EPR?. Bad News: native diffusible unpaired electrons: Rare Good News: rare native electrons mean no background signal - PowerPoint PPT Presentation
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Quantitative Oxygen Imaging with Electron Paramagnetic/Spin
Resonance Oxygen ImagingHoward Halpern
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
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
Why EPR?• Spectroscopic Imaging: Specific quantitative
sensitivity to Oxygen, Temperature, Viscosity, pH, Thiol
• No water background for signal imaging (vs MRI)
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
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.
Basic Interaction
• Magnetic Moment m (let bold indicate vectors)
• Magnetic Field B• Energy of interaction:
– E = -µ∙B = -µB cos(θ)
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
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
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
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
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
Imaging: Basic StrategyConstraint: Electrons relax 106 times faster than water protons
Image Acquisition: Projection Reconstruction: Backprojection
Projection Acquisition in EPR
• Spectral Spatial Object Support ~( ,f B x
0 0,
2 2 xB BB B
( 0app swB x B B G x
TOTh g B
=α
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
More Projection
• The integration of fsw is carried out over the hyperplane in 4-space by
swB B G x
DefiningˆcG x
BcL
with
The hyperplane becomes1ˆ( )sw swB B G G x B c G
with 1tan c G
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
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 B c
Projection acquisition and image reconstructionImage 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 : tan(=G*L/H
The Ultimate Object:Spectral spatial imaging
Preview: Response of Symmetric Trityl (deuterated) to Oxygen
• So measuring the spectrum/spectral width≈relaxation rate measures the oxygen. Imaging the spectrum: Oxygen Image
Why is oxygen importantin cancer?
Known Since 1909 but in 1955Thomlinson and Gray showed
necrosis
viabletissue
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
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)
Intensity Modulated Radiation Therapy
• Sculpts radiation dose over distances of5mm
• Able to spare normal tissues
But tumor volumes are homogeneous; noaccounting for different regions with
different sensitivity
Biological imaging to enhance targeting of radiation therapy: oxygen imaging
• Intensity modulated radiation therapy allows sophisticated control over spatial distribution of radiation dose
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
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
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...
Why use radio-frequency for EPR?
250 MHz ~6 T MRI
S/N ~ w0.8
N~w 1.2
IN LOSSY,CONDUCTIVETISSUE
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
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
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
Major improvement: Synthesis of selectively deuterated OX31
Improves1. Oxygen sensitivity: B /B~R/R2. Spatial resolution for a given gradient:
resolvable x= B/G 3. Sensitivity
d
d
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
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)
1.0 m m
1.0mM1.75mT
1.0mM4.00 Tm
0.5mM2.50 Tm
1.0mM1.63mT
0.5mM1.50 Tm
0.5mM1.63mT
1.0mM2.50 Tm
0.5mM2.00 Tm
0.5mM1.56mT 1.0mM
1.56mT
1.0mM2.00 Tm
1.0mM6.50 Tm
0.5mM1.75mT
Line Width Fidelity: Agreement Between Image and Individually measured line-widths (1.6 mm) heterogeneous phantom. Side lines Approximately ±3 torr.
EPR spectral-spatial 4D imaging
• CW EPR imager at 250 MHz, with a loop-gap resonator
Dimensions of the resonator (1.5 cm thick)Sensitive Region of the resonator (total of just over 2 -2.5 cm)
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
Oxylite probeInto tumor
• Validation with Oxylite fiberoptic probe (measuring fluorescence quenching by oxygen)
Stereotactic PlatformFor Needle Location
Good agreement!
Adjacent tracks in areas of rapid oxygen variationagree with Oxylite
New insight into the oxygen statusof tumors and tissues
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