nmr diffusion diffraction and diffusion interference from cells

$: NMR Diffusion Diffraction and Diffusion Interference from Cells$
NMR Diffusion Diffraction and Diffusion Interference from Cells

Philip Kuchel & Guilhem Pages

School of Molecular and Microbial Biosciences University of Sydney

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Contents

Red cells…motivation

q-Space analysis

Flow diffraction

Octagon-star model



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Movie showingred blood cell membrane flickering

Echinocytesunder DIC Microscopy

…showingechinocyteto discocytereversionand backagain

0 min 4 min 16 min

56 min

Echinocytesunder DIC microscopy

Movie showing change in shape ofred blood cell

Discocytes

Spherocytes

Tracking red cell shape transformation

in packed samples over time courses of

minutes

University of Sydney

1E-5

1E-4

1E-3

0.01

0.1

1

E [q

, D] 1st diffraction minimum

pore hopping shoulder

2nd diffraction minimum

3rd diffraction minimum

q (105 x m-1) � ��

Ht = 58%48%41%

Secondderivative

Fouriertransform



Unbalanced bipolar pulses in STE…rapid signal acquisition

Pelta et al. (2002) MRChem 40 S147

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q

Movie showing change in shape of the q-spaceplot



z (μm)

Movie showing change in shape of the mean celldiameter

Flow diffraction

g

sliceδz

sliceFlowa

z

xÕyÕ

z

xÕyÕ

−φ1πy

φ1 xÕyÕ

φ2 −φ1

z

π/2x ...δ

= γδgz

γδg(z + δz) = φ2 ...Δ

B0

Flow rate = 0.834 mm s-1

1.32 mm s-1

2.15 mm s-1

Since the uniform linear flow-velocity is a m s-1 then a = z/ ; and by definition q = (1/2 ) g so the change in phase angle brought about by flow is: = 2 q z = 2 q a

Hence, the normalized signal S[q, ] is proportional to, S[q, ] ∝ sin2[2 q a ]/(2 q a )2

qmin,n = n/(2 a )

a = n/(2 qmin,n )

E[q, Δ] = ρ[r0]∫∫ P[r

0 | r

0+ R, Δ] exp[i 2 π q ⋅ R] dr

0dR

P[R, Δ] = ρ[r0] P[r

0|∫ r

0 + R , Δ] dr

0

E[q, Δ] = P[R, Δ] exp[i 2 π q ⋅ R] dR∫P[R, Δ] = E[q, Δ] exp[-i 2 π q ⋅ R] dq∫

E[q, ∞] = ρ[r0] exp[i 2 π q ⋅ r

0] dr

0∫ ρ[r] exp[i 2 π q ⋅ r] dr∫E[q, ∞] = S*[q] S[q] = | S[q] |2

E[g, Δ] = ∫ρ�r� r Δ� exp�i δ g ·(r - r)� drdrγ

A model of variable packing density

q-space plot results

…octagon-star system

x

z

(b, b)

(0, a)

(a, 0)(0, 0)

Construction element for q-space signal intensityfor octagon-star model

z

x

(a/2, a/2)

(0, 0)

(0, a/2)

(a/2, 0)(b, 0)

(0, b)

Construction element for q-space signal intensityfor octagon-star model…90o rotation

Expression for q-space signal intensity from stars alone



q-space plot from octagon-star system as Ht increases

Movie showing change in shape of the q-spaceplot-function as Ht is increased

q-space plot from stars only



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Bill Price is my name!

Thanks to past and present students…

Grazie!


Bill Bubb NMRBob Chapman NMRTom Eykyn NMRDavid Jacques DICTim Larkin MathematicaGuilhem Pages NMR & fast q-spaceDavid Regan NMR & simulationDavid Szekely DIC & Mathematica

Chris GarveyBill PricePeter Stilbs

nmr diffusion diffraction and diffusion interference from cells

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