11/14/2012

1

X-ray and optical microtomography

Alexandra Pacureanu

Instrumental for life science research

Dream:

Visualize the internal structure

without damaging the sample or

altering the observed phenomena

with high accuracy,

high speed at

low cost

Three dimensional imaging

Confocal microscopy versus microtomography

xy

xz

xy

xz

Confocal Micro-CT

Same specimen

0.2x0.2x0.3 μm 0.3 μm isotropic

Stain: FITC No stain

FOV (μm) 200x200x18

FOV (μm) 580x580x580

Note the difference in depth of field (xz)

xy xz

xy xz yz

xy

xz

xy

xz

Co

nfo

cal m

icro

sco

py

X-r

ay m

icro

tom

ogr

aph

y

A closer look: Detailed view of a cell (white cercles) in 3 orthogonal planes.

From literature – images of the same structure

[Ciani, Doty, et al., 2009]

Lin & Xu, 2010

Kubek et al., 2010

SEM

AFM

Confocal

11/14/2012

2

Today: 3D isotropic tomographic imaging

Tomography – imaging by sectioning, using a penetrating wave

Hard X-rays (~10-10 m) Visible light (~10-7 m)

1895 – Röntgen – X-rays penetrate matter with weak interaction

1917 – Radon – mathematical basis A function can be retrieved from its line integrals

1964 – Cormack – theoretical basis for CT – X-rays

1973 – Hounsfield – built the first CT machine

1973: 1st brain scanner (Massachusetts General Hospital)

1974: 1st body scanner X (Georgetown Univ Med Center)

1979: The Nobel Prize in Physiology and Medicine awarded jointly to Allan M. Cormack and Godfrey N. Hounsfield "for the development of computer assisted tomography“

The beginnings of computed tomography

Interaction wave - matter

𝑛 = 1 − 𝛿+ 𝑖𝛽

Refractive index decrement – phase shift Local electron density

Absorption index – attenuation Local attenuation coefficient:

Interaction of electromagnetic waves with matter: Complex refractive index

4

Attenuation / Absorption Phase shift

Photoelectric effect an X-ray photon gives all its energy to an atom which ejects an e--. Other X-rays are emitted isotropically (fluorescence).

Elastic (Rayleigh) scattering: the X-ray

wave induces a vibration of the e-

of the matter, the X-rays keep the

same energy - elastic scattering

Inelastic (Compton) scattering: a X-ray

photon gives part of its energy to an e-,

it is deflected and continues its

trajectory with a different energy -

inelastic scattering

Interactions causing attenuation of the X-ray beam How is the X-ray beam attenuated: Beer-Lambert law

A monochromatic X-ray beam, with wavelength and intensity I0, passing through a

uniform material is attenuated exponentially:

I0

I

L I = I0 exp (- µ L)

4

µ - linear attenuation coefficient of the material for the wavelength λ

µtotal = µphotoelectric + µRayleigh + µCompton

µ - is function of energy E (wavelength)

of the X-ray beam, density and atomic number Z of the material

[cm-1] µmass = µ/ρ [cm2/g]

11/14/2012

3

How is the X-ray beam attenuated: Beer-Lambert law

http://www.ndt-ed.org/EducationResources/CommunityCollege/Radiography/Physics

I1 = I0 exp (- 1 y1)

I2 = I1 exp (- 2 y2)

.

.

.

In = In-1 exp (- n yn)

In = I0 exp (- i yi)

1

2

n

I

I

0

n

y

y

y

2

n

1

Generalization of the Beer-Lambert law: Object with different materials

1 2 3 0

S D

Polychromatic case

Example : E=13 keV Absorption of 10 cm of air Absorption of 200 nm of Pb

Generalization of the Beer-Lambert law

Monochromatic case

In practice: “flatfield” image

I0

I

Detector

Source

(D)

Summation on the straigth line (D):

projection information

ln (I0 /I ) = (D) (x,y) ds

Measure I & I0 - then take logarithm Image without the beam (dark): d(x,y)

Image with the beam and without the object (reference): I0(x,y)

Image with the beam and the object: I(x,y)

Flatfield image: F(x,y) = ( I(x,y) - d(x,y) ) / ( I0(x,y) - d(x,y) )

Flatfield = ln

Flatfield and Beer-Lambert law

I0

I

d

d

Tomographic reconstruction

11/14/2012

4

Reconstruct a stack of transverse slices

Parallel beam geometry

Record a set of angular projections (radiographs)

X-ray beam

Beam

Rotation + Spreading + sum+ filter

Rotation + Spreading + sum+ filter

Rotation + Spreading + sum+ filter

Rotation + Spreading + sum+ filter

Rotation + Spreading + sum+ filter

Rotation + Spreading + sum+ filter

Independent 2D reconstruction = 3D reconstruction

Fourier slice theorem

We consider a 2D object as the cross-section of a 3D object

f(x,y) - 2D object (slice in the specimen) R f(, ) - 1D projection or radiograph of f(x,y) at the angle (Radon Transform) F f (,) - 2D Fourier transform of f(x,y) in polar coordinates F R f (,) - 1D Fourier transform of the projection R f(, ) in polar coordinates at the angle Fourier slice theorem F R f (,) = F f (,)

In other words : One can reconstruct the object from its radiographs just by using Fourier transform Collecting projections at a number of angles fills the Fourier space along radial lines

In the central area of the 2D Fourier transform corresponding to the low frequencies, the various spokes are close to each other – more informatuion. At the periphery (the high frequencies area), the spokes are distant – less information. In other words, we have more missing data at the periphery than at the center -> blurring. => Some high pass filter is useful

However, some information is lost

Passing from polar to cartesian grid requires interpolation

q

0°

180°

0,6 0,9 0,3

0

1 circle 2 circles 3 circles

Radon transform - sinogram

A sinogram is an image respresenting the Radon space (i.e. the projection space) Direct space : image (x,y ) Radon space : image (, )

Creating a sinogram

Sinogram

Radon space

Direct space

More about sinograms

x

y

x

y

Rotation axis

Rotation axis

11/14/2012

5

More about sinograms

Sinogram = set of projections

x

y

Acquisition

Reconstruction Reconstruct a stack of transverse slices

Parallel beam geometry

Record a set of angular projections (radiographs)

X-ray beam

For each horizontal line in the projection image, take all corresponding lines from all recorded angles.

This creates the sinogram for the transverse slice corresponding to that 1D projection

From each sinogram, reconstruct the transverse slice How? With Filtered Backprojection (FBP)

2 projections 0, 90 ° 1000 projections 3 projections 0, 45, 90 ° 30 projections

Use of a high-pass filter to suppress background Intuitively: Rotation, Spreading, Sum and Filter

Filtered backprojection

M=8 M=16 M=32

M=1 M=2 M=4

Backprojection example

Relation Fourier slice theorem - filtered backprojection algorithm

dRfFFyxf

).,(2

1),(

1

Ramp filter

Projection Object

“Spreading+sum” = backprojection

Inverse FFT f(x,y)

Rf(x,y) Data

FR f (,)

| | | |.FR f (,)

F-1[| |.FR f (,)]

Backprojection

Using all angles

Reconstruction steps

11/14/2012

6

The number of projections

• Number of projections per turn : Fourier slice theorem

– Collecting projections at a number of angles fills the Fourier space along radial lines

1000 projections 30 projections

x

y 20º

40º

60º

80º

100º

120º

140º

160º 180º

Sampling in the Fourier domain .CCD_Size

2Nb_Proj

Nb_ProjPixel_Size2

1

CCD_SizePixel_Size

1

Roughly, one wants =

Synchrotron micro-CT

• Developed in the 1980’s [Flannery et al., 1987]

• Synchrotron light is electromagnetic radiation produced when charged particles are deviated from a circular trajectory (by magnetic fields)

• Synchrotron radiation was first observed in the 1940s and produced in the 1960s by the bending magnets of accelerators built for high energy nuclear physics research (undesired effect). In the 1970s it has been realized that synchrotron radiation can be used as a versatile and highly intense source of X-rays

• Electrons accelerated to nearly speed of light

• High brilliance X-ray beam enables high spatial resolution imaging (1012 times brighter)

• A monochromatic beam can be selected --> quantitative imaging

• Enables 3D studies with unprecedented details

ESRF, Grenoble, France

Electrons are first accelerated in a linear accelerator (Linac), followed by acceleration in a booster synchrotron. Subsequently they circulate with a constant speed in a storage ring from where the synchrotron light is generated through insertion devices. Image credits: ESRF.

Design of a typical beamline at a synchrotron facility. Dedicated hutches are built for the instruments preparing the beam and for the sample and detector stages. The beamline is controlled remotely from the control room. Image credits: Timm Weitkamp, Soleil

In the experimental hutch of a beamline at ESRF

35

Tomography setup at beamline ID19

• Long beamline – larger beam at the sample • Parallel beam tomography is possible – reconstruction is exact

• 3 insertion devices and 2 monochromators

• Energy range 12-80 keV

• Spatial resolution 280 nm – 30 µm

Beam hardening

Distortions

Smoothing

1mm

SR-µCT versus Commercial µCT

Commercial µCT: Skyscan, Scanco, Xradia,

Human iliac crest biopsy

11/14/2012

7

Voxel: 10 µm, 500 views

Acq time < 5 min

Voxel: 10 µm, 500 views

Acq time ~ 150 min

Desktop µCT SR µCT

SR-µCT versus Commercial µCT: in vivo Drawbacks: Radiation damage

Radiation dose damage (MGy)

~ 70 µm

Requires accurate knowledeg of the acquisition geometry

rotation center, angles....

Shift + Shift - Original

Bad rotation center

Attenuation SR X-ray microtomography Osteocyte cell network 300 nm

Phase imaging

• Interaction with matter induces a “phase shift” (slowing down the wave velocity)

• A more sensitive contrast mechanism (1-3 orders of magnitude)

• Reconstruct phase maps from projection images: phase differences are converted into amplitude differences and observed as intensity contrast

• FBP to reconstruct slices

𝑛 = 1 − 𝛿+ 𝑖𝛽

Refractive index decrement – phase shift Local electron density

Absorption index – attenuation Local attenuation coefficient:

4

Attenuation / Absorption Phase shift

11/14/2012

8

Attenuation and phase shift of electromagnetic wave propagating in medium with complex index of refraction n An interference pattern with "Fresnel

fringes" is created. The recorded interference fringes proportional to the second derivative of the phase.

Phase SR X-ray microtomography Brain imaging

Free space propagation Ischemia – Stroke

Free space propagation phase SR μCT - 2 µm Study bone and blood vessels simultaneously

Phase SR X-ray microtomography Rat testis imaging

Gratings interferometry [Zanette et al. 2012]

Free space propagation phase SR nanoCT 60 nm

Magnified holotomography – magnification by divergent beam

11/14/2012

9

Synchrotron Source ~100 million Euros/year ~ 5 000 Euros / 8 hours OR apply for beamtime

Many specimens relevant to life science are transparent to visible light

• Zebra fish embryos – used as model organisms for disease

studies and drug discovery

• 3D cell cultures – Bridge the gap between cell culture and

live tissue

– Greater similarity with the living organism

• Drosophila melanogaster, etc.

[Pampaloni et al., 2007]

Optical Projection Tomography (OPT) • Same principle as X-ray CT but

– Much more difficult to model than X-rays

– A lot of scattering

– 3 types of photon paths, arriving to the detector at 3 different times (depending of the path length)

• Ballistic (straight line, arrive first)

• Snake (zig zag paths, arrive secong)

• Diffuse (random walks, arrive last)

– Beer Lambert law remains valid

[Arridge 1997, Sharpe 2002]

[Sharpe et al., 2002]

T-Y Chang, C Pardo-Martin, A Allalou, C Wählby,

and MF Yanik, Lab on a Chip, 2012, 12, 711

Optical

Projection

Tomography

in HTS

1 fish processed every 18s

Image pre-processing for

OPT optimization raw

Illumination correction

Vertical and horizontal alignment and

compensation for

change of perspective

Refraction correction

Center of rotation correction

(FBP minimize

entropy).

Final resolution < 10μm Final reconstruction using OSEM,

Hudson & Larkin, IEEE TMI 1994

OPT system for Zebrafish screening at MIT Fairly sophisticated and costly

11/14/2012

10

In-house optical tomography system

• Microscope ~250 EUR • Programmable rotation motor & sample stage ~250 EUR

Imaging zebrafish embryos with our in-house microtomography system

Angular projection 3D rendering of the reconstructed image

Thank you! Acknowledgments: Francoise Peyrin Pierre Bleuet Peter Cloetens Max Langer Amin Allaou