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 St.-Petersburg, 02 Mar - 12 Apr 2006 2 of 26

Tomography Tomography (gr. tomos tomos - - layer, layer, grapho grapho - - write) write) (gr. Simple methods: Computer methods: • anatomic • computed (CT, SCT) • linear X-ray • 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: r r r – has a spin momentum I μ = γ ⋅ = h I g I N I = 0; 1/2; 1; 3/2… r = r Electron: h p I – 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 Interaction with external field: r ↑↑ r r z H = − μ = − μ ϑ = − μ E ( , H ) H cos H z r μ μ z r Fixed momentum orientations I z = m I ϑ Discreet energy levels

Energy levels of nucleus Energy levels of nucleus Interaction energy: Energy = − 1 m I 2 = − γ ⋅ = − β h E HI g HI z N N z eh β = nuclear Δ = ω = N β N magneton h 2 Mc E g H N 0 = 1 m 2 I 0 H 0 H

Energy levels of electron Energy levels of electron

MR theory – classification • NMR • EPR • Nuclei with non-zero • Substance with odd number of e ( 1 H) nuclear spin (H) • Ask help • 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 Equation of line l in x-y-frame: ϕ + ϕ − = x cos y sin s 0 = ϕ − ϕ ⎧ x x ' cos y ' sin ⎨ Rotation of axes: = ϕ + ϕ ⎩ y y ' sin y ' cos − s = Equation of line l in new coordinates: x ' 0 ∞ ∫ ϕ = ϕ − ϕ ϕ + ϕ R ( s , ) f ( s cos y ' sin , s sin y ' cos ) dy ' − ∞ Radon image: − 2 2 a s ∫ ϕ = ϕ − ϕ ϕ + ϕ R ( s , ) f ( s cos y ' sin , s sin y ' cos ) dy ' − − 2 2 a s

Radon transformation Radon transformation 2 Gauss impulses: ⎧ ⎫ − + − 2 2 2 ( x x ) ( y y ) ∑ = − ⎨ ⎬ i i f ( x , y ) exp 2 ⎭ ⎩ 2 b = i 1 Radon image of f(x,y) : ⎧ ⎫ ϕ + ϕ − 2 2 ( x cos y sin s ) = ∑ ϕ π − ⎨ ⎬ i i R ( s , ) b 2 exp 2 ⎭ ⎩ 2 b = i 1

Back projection algorithm Back projection algorithm 1. Fixing the angel ϕ in R(s , ϕ ) 2. Stretch 1D function R(s, ϕ ) in x-y -plane Back-projected image: = ϕ + ϕ ϕ R ( x , y ) R ( x cos y sin , ) ϕ Summary image: π ∫ ˆ = ϕ + ϕ ϕ ϕ f on ( x , y ) R ( x cos y sin , ) d 0

Back projection algorithm Back projection algorithm Main disadvantage: I mage contrast is too low :( 1. Original phantom 2. Radon image (180 projection) 3. Back-projected phantom 1 2 3

Deconvolution algorithm algorithm Deconvolution π ~ ∫ - original function = ϕ + ϕ ϕ ϕ f ( x , y ) R ( x cos y sin , ) d 0 a ~ ~ ∫ ϕ + ϕ ϕ = ϕ = − ϕ R ( x cos y sin , ) R ( s , ) h ( s ) R ( s s , ) ds 1 1 1 − a - convolution product ∞ 1 - Fourier image of | ω | ∫ = ω ω ω h ( s ) cos( s ) d π 1 1 2 − ∞ 1 2 3 5 4

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