27-28/09/2016 ISC Meeting tematico sulla diffusione, Sesto Fiorentino

NMR Anomalous Diffusion Measurements to investigate complex systems:

experiments

Silvia Capuani

*CNR-ISC UOS Roma Dipartimento di Fisica

Sapienza Università di Roma Laboratorio di Risonanza Magnetica Nucleare

Edificio Fermi stanza 319, Edificio Segre’ Laboratorio 5

silvia.capuani@roma1.infn.it

NMR Laboratory

Fundamental physics

Biophysical applications

Translational longitudinal studies in Humans

Transfer of technology

Clinical application

Molecular diffusion in soft condensed matter: porous heterogeneous, complex systems

Experimental corroboration of simulations and theories

NMR Anomalous diffusion Highlights

Why would we want to evaluate the Diffusion parameters of water

in materials and biological Tissue?

Because Diffusion parameters and diffusion-weighted NMR signal

reflect the micro-structural rearrangement of porous materials and tissues

NMR diffusion

We can measure the displacement of the ensemble of spins in our sample and infer the Diffusion Coefficient.

We cannot measure the Diffusion Coefficient of water (or of generic ions and molecules)

using NMR

NMR diffusion

Diffusion MR images can measure water proton displacements at the cellular level

Probing motion at microscopic scale (10 m), orders of magnitude smaller than macroscopic MR resolution (mm)

This has found numerous research and clinical applications

Voxel zoom

NMR diffusion

Can probe diffusion for time scales: 1 ms to seconds length scales of displacements: 100 nm to100 m

NMR diffusion

Porous Media • Intrinsically multiphase materials • Pore fluids for NMR detection Microstructure is important – Rocks, oil and water reservoirs – Soils, unconsolidated formation – Cement and concrete, catalysts – Food stuff, paper, fabric – Plant and animal tissues, bone – Human tissues – Brain

Conventional diffusion

Multiscale

Complex systems

Anomalous diffusion

system constituted by structures at very different levels of hierarchical

organization

NMR diffusion

Anomalous diffusion

Why anomalous diffusion?

Gaussian diffusion: diameter of the spatial range, d, accessible to a water molecule in a given diffusion time t

LD = d (6Dt)1/2

bone

Trabecular bone marrow

Prostate Cancer staging

100 m

50 m

NMR diffusion

NMR principles

9

NMR signal is an electric signal

f.e.m. induced at the radiofrequency (RF) coil

NMR diffusion

Nuclear paramagnetism

RF 1 2 2( ) ( , , , *, , , ,.....)S t f N T T T CS J D

RF pulse sequences

M

21 )1()()( 0 T

T

T

T

xyE

ER

eeMTMtS

RF sequences

1 2 2( ) ( , , , *, , , ,.....)S t f N T T T CS J D Ĥ1 Ĥ2 Ĥn

τ1 τ2 τn

Magnetic gradients: inhomogeneity of the instrument NMR diffusion

0 = H0

(r) = (H0 + Gr)

Spectroscopy

Imaging

Magnetic field gradients: imaging NMR diffusion

RF

MR response

G phase enc.

G frequency enc.

G slice selection

90° 180°

rGr 0)(

Magnetic gradients: imaging NMR diffusion

00

22

03

)1(HH

KT

IINM

In heterogeneous and complex samples at the interface between different tissues or materials

Magnetic field gradients: magnetic susceptibility differences NMR diffusion

Conventional Diffusion NMR: Gaussian diffusion NMR diffusion

< r 2(t) >= 2dDt

Gaussian Motion Propagator

NMR: how to measure diffusion parameters

),(),(),( tqWeRPtqS Rqi

gq

The diffusion weighted signal is proportional to the characteristic function of the diffusion propagator in time

t time diffusion

NMR diffusion

90 ° 180°

TE

ECHO g g

Diffusion weighted: PGSE

NMR: how to measure diffusion parameters NMR diffusion

b factor (s/mm2)

Signal (a.u.)

bDStS exp)( 0

)(3

222 Gb

bDSbS exp)0()(

S(0)

S(b)

3

2 gb

Dttx 2

Gaussian propagator

Conventional Diffusion NMR: Gaussian diffusion NMR diffusion

xx xy xz

yx yy yz

zx zy zz

D D D

D D D D

D D D

1

2

3

0 0

0 0

0 0

D

D D

D

321 ,, cDDD 2

332

222

11

At least six independent parameters are required. At least six no-complanar DWI + one T2w

Gx Gy Gz Gxz Gxy Gyz

DWIx DWIy DWIz DWIxz DWIxy DWIyz

3

, 10

exp ij iji j

S tb D

S

λ3

λ1 λ2

Diffusion tensor Imaging

Basser et al., JMR, 1994 (103) 247

NMR diffusion

MD map

FA map

MD and FA maps

1 2 3

3

D D DD MD

23

22

21

23

22

21

2

3

DDD

DDDDDDFA

Diffusion tensor Imaging NMR diffusion

mean diffusivity

anisotropy

WM GM

CSF

Diffusion Tensor Imaging

MD and FA Quantitative images

Diffusion tensor Imaging

Low sensitivity and specificity

NMR diffusion

Axon mean diameter ≈7µm Microtubulus ≈20nm

< r2 > = 6 D

(< r2 >)1/2 30μm Where: D 1x10-9 m2/s Δ=80ms

Transient anomalous diffusion can be defined when MSD =TD

with < 1 for t<<TCR and MSD =TD for t>> TCR where TCR is the crossover time.

Anomalous Diffusion

<r2(t)> ≈ tν

ν< 1 subdiffusion

ν> 1 superdiffusion

<x

2>

TCR

Anomalous diffusion

How to determine α and

PGSE

Measure of Anomalous diffusion parameters NMR diffusion

2

0qK

eSS

α

Δ (s)

Sign

al

K

q12

tx 2

2

)0()(qK

eSqS

q (m-1)

Sign

al

1

2 tx

q =g

(Bio)-physical interpretation of and parameters

Length scale(s) of magnetic heterogeneity

Disord

er D

egre

e

Anomalous diffusion in 3D porous media: experiments

Palombo M., Gabrielli A., De Santis S., Cametti C., Ruocco G., Capuani S., J. Chem. Phys. 135 (2011)

Highly porous polymeric matrices with randomly oriented interconnected pores obtained from a solution of polyvinyl alcohol and etyltrimethylammonium bromide (PVA scaffolds)

• void size distribution: 10-100 m • interconnection size distribution: 4-50 m • the three scaffolds differ in the roughness of the walls of their voids and interconnections

Application to multiscale porous materials

Barbetta A. et al., Soft Matter,6 (2010)

PVA1 PVA2 PVA3

PVA3

PVA2

PVA1

α parameter

Gaussian approach

Imaging:

PGSTE sequence

TR = (5000 - ) ms

TE = 15 ms;

= 2 ms

g = 74 mT/m

= (20 520) ms

PVA3

PVA1

PVA2

PVA3

PVA1

PVA2 3

α parameter

SA= 45 m2/g

SA= 68 m2/g

SA= 106 m2/g

Palombo M., Barbetta A., Cametti C., Dentini M., Capuani S., in preparation

Imaging:

PGSTE sequence

TR = (5000 - ) ms

TE = 15 ms;

= 2 ms

g = 74 mT/m

= (20 520) ms

PVA3

PVA1

PVA2

PVA3

PVA1

PVA2

3

SA= 45 m2/g

SA= 68 m2/g

SA= 106 m2/g

Anomalous diffusion approach

Palombo M., Barbetta A., Cametti C., Dentini M., Capuani S., in preparation

Application to multiscale porous materials

Palombo M., Barbetta A., Cametti C., Dentini M., Capuani S., in preparation

dw = 2 /a

M.J. Saxton

Biophys, J. 66 (1994) X=S/

fractal dimension of the random path

quantifies global structural complexity

(Bio)-physical interpretation of and parameters

Length scale(s) of magnetic heterogeneity

Disord

er D

egre

e

Anomalous diffusion in 3D porous media: experiments

Palombo M., Gabrielli A., De Santis S., Cametti C., Ruocco G., Capuani S., J. Chem. Phys. 135 (2011)

M

Internal gradient strength (T/m) m

Bind *B*A*cos

M. Palombo et al. JMR 2012

NMR diffusion

Increase of the image contrast Enhanced interface contrast

intravoxel diffusion heterogeneity in space, i.e., water molecules diffuse with considerably different free lengths. due to both water multi-compartmentalization and magnetic susceptibility differences () at the interface between different compartments

multi-compartmentalization

Multi-compartimentalization + magnetic susceptibility differences ()

Pseudo-superdiffusion

NMR diffusion NMR diffusion

Pseudo superdiffusion

Pseudo “Lèvy flights”

Gi

Superdiffusion process ( <1) is spurious, not real but due to

local ΔX (or Gi ) at the interface between beads and water

Δφ ≈|g|

0 Z

Z

Phase Δφ |g|

0

Brownian Diffusion

Without boundary effects (no Gi)

Brownian Diffusion

0

Phase |g|

Z

Brownian Diffusion

Inte

nsi

ty (

A.U

.)

PGSE Echo Signal

Idiff

Spectroscopy, Brownian Diffusion

t 0

Spectroscopy pseudo-superdiffusion

Pseudo-superdiffusion

Gi

With boundary effects: Gi

0

Phase |g|

Z

Spectroscopy pseudo-superdiffusion

Inte

nsi

ty (

A.U

.)

PGSE Echo Signal

Idiff

IGint

Pseudo-Super Diffusion

t 0

Gi

Voxel 2 Voxel 1

Pseudo-Super Diffusion Imaging

Gi

0

Phase |g|

Z

Pseudo-Super Diffusion Imaging

Voxel 1 Voxel 2

Inte

nsi

ty (

A.U

.)

PGSE Echo Signal

Pseudo-Super Diffusion Imaging

t 0

Inte

nsi

ty (

A.U

.)

t 0

Voxel 1 Voxel 2

Diffusion reflect the micro-structural rearrangement of tissues

parameter

BRAIN AGING

Application to clinical diagnostics

Guerreri M., Caporale A., Palombo M., Bozzali M., Capuani S., submitted

Thank you

for your attention

NMR Laboratory

silvia.capuani@roma1.infn.it

To investigate samples… To investigate Human subjects…

NMR Laboratory

NMR laboratory staff

Alessandra Caporale (PhD student) Michele Guerreri (PhD student)

Maria Giovanna Di Trani (MS student)

Guglielmo Genovese (MS student)

Physicist collaborators Andrea Gabrielli, CNR ISC

Vito Servedio, CNR ISC Marco Palombo , CEA Fontenay-aux-

Roses (France) Chemical collaborators

Felix Wehrli, Penn University (USA) Andrea Barbetta, Sapienza

Medical collaborators: Marco Bozzali, Neuorimaging Laboratory, Fondazione Santa Lucia IRCCS, Rome, Italy. Department of Diagnostic and Interventional Radiology, Molecular Imaging and Radiotherapy & Orthopedic and Traumatology Dip. PTV Foundation, ”Tor Vergata” University of Rome,