EPR imaging characterization of natural and synthetic materials - - PowerPoint PPT Presentation

EPR imaging characterization of natural and synthetic materials

Timophey V. Popov Joint Advanced Students School St.-Petersburg - 2006

Contents:

• Introduction
• MR theory
• Mathematical problems of computer-

aided tomography

• EPR imaging
• Conclusion

Joint Advanced Students School 2 of 26 St.-Petersburg, 02 Mar - 12 Apr 2006

Tomography Tomography (gr. (gr. tomos tomos -

• layer,

layer, grapho grapho -

• write)

write)

Simple methods:

• anatomic
• linear X-ray

Computer methods:

• computed (CT, SCT)
• magnetic-resonance (MRT)
• positron-emission (PET)
• ultrasonic (US)
• laser
• electron-impedance

Joint Advanced Students School St.-Petersburg, 02 Mar - 12 Apr 2006

Introduction Introduction

Questions to be answered during report:

• What a magnetic-resonance phenomenon

is?

• How can we obtain useful information

from spectra?

• Which

Intro – subject review

• What is the aim of tomography actually

for living science?

• T is an individual frame of knowledge

with application in medicine, nanotechnology, chemistry and so on

• EPR imaging is the only method of

inspection electron density distribution in a sample

Magnetic properties of atom Magnetic properties of atom

Nucleus: Electron:

I p r h r = I g I

N

r r h r = ⋅ = γ μ

– has a spin momentum I I = 0; 1/2; 1; 3/2… – has a orbital momentum L L = 0; 1; 2; 3… – has a spin momentum S S = 1/2

Magnetic properties of atom Magnetic properties of atom

H z r ↑↑

H H H E

z

μ ϑ μ μ − = − = − = cos ) , ( r r

μ r I r

z

μ m I z = ϑ

Interaction with external field: Fixed momentum orientations Discreet energy levels

Energy levels of nucleus Energy levels of nucleus

2 1 =

I

m 2 1 − =

I

m

z N N z

HI g HI E β γ − = ⋅ − = h

H Energy H0

H g E

N Nβ

ω = = Δ h

Interaction energy:

Mc eh

N

2 = β

nuclear magneton

Energy levels of electron Energy levels of electron

MR theory – classification

• NMR
• Nuclei with non-zero

nuclear spin (H)

• Ask help
• EPR
• Substance with odd

number of e (1H)

• Substance with

unpaired es on valence shell without chem link (VO)

• Free radicals (mithil-

r)

MR theory – absorption line

• Which information can we obtain from

EPR spectra?

• FS & HFS & SHFS
• g-factor
• Line width & line shape
• Integral intensity

MR theory – CW-method

• Block-scheme of spectrometer
• Sweeping magnetic field and

synchronous detecting of signal

• First derivative form of absorption line
• Aims of sweeping field

MR theory – my examples

• Ask S.M. about good examples…
• in progress

Radon transformation Radon transformation

• 1. The methods of projection data acquisition;
• 2. Means of tomographic images reconstruction:

– Back-projection algorithm; – De-convolution algorithm;

• 3. Examples

Radon transformation Radon transformation

sin cos = − + s y x ϕ ϕ

∫

∞ ∞ −

+ − = ' ) cos ' sin , sin ' cos ( ) , ( dy y s y s f s R ϕ ϕ ϕ ϕ ϕ ⎩ ⎨ ⎧ + = − = ϕ ϕ ϕ ϕ cos ' sin ' sin ' cos ' y y y y x x

' = −s x

∫

− − −

+ − =

2 2 2 2

' ) cos ' sin , sin ' cos ( ) , (

s a s a

dy y s y s f s R ϕ ϕ ϕ ϕ ϕ

Radon image: Equation of line l in x-y-frame: Rotation of axes: Equation of line l in new coordinates:

Radon transformation Radon transformation

⎩ ⎨ ⎧ ⎭ ⎬ ⎫ − + − =∑

= 2 2 2 1

2 ) sin cos ( exp 2 ) , ( b s y x b s R

i i i

ϕ ϕ π ϕ

∑

=

⎩ ⎨ ⎧ ⎭ ⎬ ⎫ − + − − =

2 1 2 2 2

2 ) ( ) ( exp ) , (

i i i

b y y x x y x f

2 Gauss impulses: Radon image of f(x,y):

Back projection algorithm Back projection algorithm

) , sin cos ( ) , ( ϕ ϕ ϕ

ϕ

y x R y x R + =

∫

+ =

π

ϕ ϕ ϕ ϕ ) , sin cos ( ) , ( ˆ d y x R y x fon

Summary image: Back-projected image:

• 1. Fixing the angel ϕ in R(s, ϕ)
• 2. Stretch 1D function R(s, ϕ) in

x-y-plane

Back projection algorithm Back projection algorithm

Main disadvantage:

1 2 3

I mage contrast is too low :(

• 1. Original phantom
• 2. Radon image (180 projection)
• 3. Back-projected phantom

Deconvolution Deconvolution algorithm algorithm

∫

+ =

π

ϕ ϕ ϕ ϕ ) , sin cos ( ~ ) , ( d y x R y x f

∫

−

− = = +

a a

ds s s R s h s R y x R

1 1 1

) , ( ) ( ) , ( ~ ) , sin cos ( ~ ϕ ϕ ϕ ϕ ϕ

∫

∞ ∞ −

= ω ω ω π d s s h ) cos( 2 1 ) (

1 1

1 2 4 3 5

• original function
• convolution product
• Fourier image of |ω|

EPR Imaging – experiment

• Summing up 2 theories
• Adding MF gradient
• Spectral line broadening, frequency

coding

• Radon transform application

EPR Imaging - properties

• EPR imaging resolution (compare with

MRI)

• Practical limitations

EPR Imaging – examples

• Radicals
• Applications to mineral samples

(radiation defects)

• Skin experiments

Conclusion

• Development difficulty
• Limitations of using in vivo
• Further perspectives and so on