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