WP3: Theory for 360 degree FMTProgress during Year 1

Giannis ZacharakisInstitute for Electronic Structure and Laser (IESL)

Foundation for Research and Technology – Hellas (FORTH)

FMT-XCT First Annual MeetingApril 24 2009

Whole animal imaging

Whole Animal

In Vivo Optical Imaging GroupIESL – FORTH

Cellular and Sub-Cellular

Ballistic Propagation (OPT)

Ballistic Propagation Beer´s Law ~ exp (-a*z)

FMT

Highly Scattering

Fluorescence Molecular Tomography

Diffusion ~ exp (-a*r)/r

2nd generation FMT system

Inverse problem:

F(r) = f-1 [Xinc ; Xprop ]

Forward problem:

Xprop = f [Xinc ; F(r) ]

Tomographic imaging

1[ ] [ ]

W F F Wfl flnB

exc exc

U UU

U U

Iterative Methods (ART), SVD

Normalized Born Approximation + Homogeneous Medium

F

transgenicage ~ 8 weeks

non-transgenic age ~ 8 weeks

Fluorescence

NBornExcitation

Normalized measurements

hCd2-GFP mouse

GFP Control

FORTH’s participation

Objectives

- 2.2.3.1 To implement direct inversion based on boundary removal method for media with arbitrary boundaries

- 2.2.3.2 To research optimal direct inversion approach with simulations and experimental data

- 2.2.3.3 To compare the direct inversion performance with conventional, previously developed FMT inversion methods

- 2.2.3.4. To incorporate algorithms for multi-spectral imaging

- 2.2.3.5. To develop user friendly software for inversion of XCT-FMT data based on direct inversion approaches

- 2.2.3.6. To invert training data acquired from FMT-XCT system for algorithmic finalization

Objectives

2.2.3.1 To implement direct inversion based on boundary removal method for media with arbitrary boundaries

- 2.2.3.2 To research optimal direct inversion approach with simulations and experimental data

- 2.2.3.3 To compare the direct inversion performance with conventional, previously developed FMT inversion methods

Theory for 360 FMT

Boundary removal

Ripoll and Ntziachristos, PRL 2006.

'1( , ) ( ', ' ) ',

2 'o o

A

gU z U z z dA z z

z

r r

R R

Assuming the interface locally plane at (R,z0), we can propagate the measurement U to anywhere in (diffuse) space:

(first Raleigh-Sommerfield integral formula)

(R,z0)

(R,z)

(infinite Diffuse Medium - virtual)

Original Diffuse Volume

Boundary removal

- Use of infinite Green’s functions

- Apply direct inversion

1. Backpropagation2. Complete Fourier Approach

Complete Fourier Approach

flnB s d

s d s d s dinc zL s d d

U (K ,K ) 2 iU (K ,K ) dz exp(i[(q q )(z L)])F(K K ,z)

U (K ,K ) q

[ ]

W Ffl

exc

nB UU

U

[ ]

W F

fl

exc

nB UU

U

Direct Inversion!

Problem in Real space:

Problem in Fourier space:

nBs d s d

2U (K ,K ) exp( L)F(K K , )

/ 2

NnB

s d s d i s di 0

U (K ,K ) 2 W(K ,K ,z )F(K K ,z) z

LIMITATIONS:

1) It can only be used with large numbers of sources Grids of 64x64 sources to obtain relatively good data and are still prone to great Fourier artifacts. This is a great problem since all our FMT setups work with numbers of sources in the 100 range. Having more sources in unpractical, since the experiment times will increase unnecessarily.2) Fluorophore concentration in Fourier space. This means that once inverted the data has to be Inverse-Fourier transformed in 3D. This yields significant Fourier artifacts (seen as 'waves' surrounding the main central points of data) that worsen as the number of sources or detectors gets smaller. This means that in practice even larger numbers of sources need to be used.

Complete Fourier Approach

• After developing and implementing the main features of the direct inversion method, we have decided it is not the method to pursue for our FMT setups.

• Clearly we need a method that can solve fast the inversion needed but can work with small numbers of sources, in the  order of <100 sources.

• We therefore opted to change this deliverable, DIRECT INVERSION method to a deliverable called 'ULTRA FAST INVERSION for FMT' that will be delivered on the next reporting period.

• In the meantime, the partners have access to an inversion method which is significantly faster that the currently existing ones, based on:

Boundary removal and ART inversion on the infinite homogeneous data.

Conclusion

Objective 2.2.3.4. To incorporate algorithms for multi-spectral imaging

Multi-color imaging

- A multispectral algorithm has been developed and tested for simultaneous detection of multiple fluorophores and absorbers.

- It will be incorporated in the FMT software in the next reporting period according to the time schedule.

1 1 1

2 2 2

n n n

G R M G1

G R M2 R

n MG R M

s s ... s CI

s s ... sI C

I Cs s ... s

• Two or more fluorophores with overlapping emissions• Detect fluorescence in equal number of channels

1 1 1

2 2 2

n n n

1 G G R R M M

2 G G R R M M

n G G R R M M

I s C s C ... s C

I s C s C ... s C

I s C s C ... s C

• In microscopy it is performed pixel-by-pixel on the so-called spectral cube

• In tomography we must perform it voxel-by-voxel on the Reconstructed Data

Multi-color imaging

Multi-color imaging

nB flfl

exc

UU W fluo(r)

U

mua excabs

inc

UU W abs(r)

U

log / mua abs dz

Hb Hb HbO HbOmua C C

Tomographic calculations

Fluorescence reconstruction Absorption reconstruction

1 1

2 2

G R G1

2 G R R

s s Cfluo

fluo s s C

In the case of two fluorophores

Hb1 HbO1 Hb1

Hb2 HbO2 HbO2

Cmua

Cmua

Slab phantom:Intralipid + ink + Agarμs = 16 cm-1, μa = 1.5 cm-1

1 1

2 2

G R G1

2 G R R

s s CI

I s s C

Phantom study

Phantom study

Multicolor Quantification studyCFSE: 4μMATTO590: 5μM, 10μM and 15μM

Recover the correct concentrations only when applied on reconstructions

In vivo tissue phantom

CFSE: 4μMATTO590: 5μM, 10μM and 15μM

0log

Ic d

I

Hb HbOBV C C

100

HbO

HbT

COxySat

C

Hb1 HbO1 Hb1

Hb2 HbO2 HbO2

Cmua

Cmua

Tissue oxygenation

Use fluorec to segment the oxyrec data

• Image concurrently in 3D - Fluorescence activity - Oxygenation in hypoxic regions - Neo-vascular factors related to tumor proliferation - Measure dynamic parameters (BV and OxySat) - Identify cancer stage and phenotype (benign or malignant)

Tissue oxygenation

Objective 2.2.3.5. To develop user friendly software for inversion of XCT-FMT data based on direct inversion approaches

Software development

• Custom developed software based on Labview suitable for: 1. Data acquisition2. Data analysis (OPT and FMT)

• Automated user-friendly software for data analysisUses open source application for visualizatione.g. ImageJ, Amide, Osirix

Software development

Software development

Mini-FMT

Automated software for FMT acquisition and analysisThe main goal of the FMT software is to provide a user-friendly interface to take the measurement data and later perform the 3D reconstruction providing an image that can be analyzed with Open Source applications. e.g. ImageJ, Amide, Osirix

There is a complete manual available to the partners with detailed information and guidance for all the functions and parameters.

12 3

4 5

6

7 8 9

10 11 12

13

One button reconstruction

Mini-FMT

FMT data to be shared

Objective 2.2.3.6. To invert training data acquired from FMT-XCT system for algorithmic finalization

A large number of experimental measurements have been acquired that are available to all partners for optimization and finalization of algorithms. These measurements involve phantoms as well as in vivo experiments:

• Quantification• Resolution• Multispectral• In vivo studies (lymph nodes, tumor progression, oxygenation)

FMT data to be shared

FMT data to be shared

FMT data to be shared

FMT – TOAST comparison

Exchange of data with Partner 4UCLReconstructions by: Athanasios Zacharopoulos

FORTH – LIME dataExperiments performed with FORTH-FMT for comparison with LIME-FMT

Visit of Anikitos Garofalakis to FORTH

FORTH – LIME data

FORTH – LIME data

Second Year

• Ultra fast inversion for FMT (new Deliverable)

• Test and compare the performance

• Optimize and finalize Mini-FMT (feedback from Partners)

• Incorporate the multispectral algorithm (absorption & fluorescence)

• Increase the exchange of data! (essential for joint progress)

Vasilis Ntziachristos

FundingE.U. Integrated Project - “Molecular Imaging” E.U. STREP - “TRANS-REG” E.U. EST – MOLEC IMAGE.U. Collaborative Project – “FMT-XCT”

Dimitris Kioussis

IN-VIVO IMAGING GROUPJorge RipollGiannis Zacharakis (Post-doc)Ana Sarasa (Post-doc)Udo Birk (Post-doc)Rosy Favicchio (PhD student)Alex Darell (PhD student)Maria Simantiraki (Msc)

FORTH – IESL/IMBB:E. N. Economou

Clio MamalakiSifis Papamatheakis

Nektarios Tavernarakis

Past membersJuan Aguirre

Abraham MartinAnikitos Garofalakis

Heiko MeyerStelios Psycharakis

Sascha Atrops (EST trainee)Olga Kravtsenyuk (Post-doc)Lucie Lambert (EST trainee)

In vivo Imaging Group

Simon ArridgeAthanasios Zacharopoulos

Bertrand TAvitianAnikitos Garofalakis

LIME - CEA

Collaborations

Geometry

Inversion: • Use spectra• Wavelength dependent W• Depth dependent W• Spectral unmixing

On going

CFSE (20μM)

ATTO590 (20μM)

In vivo tissue phantom

Same number of GFP & DsRed T-cells injectedOnly DsRed cells recognize an antigen peptideRepetitive imaging of cervical lymph nodes

Following T-cell numbers