Advanced Imaging Techniques · 2018. 11. 27. · 27.11.2018 2 Diffusion MRI I Slide 3/18 I...

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Advanced Imaging TechniquesDiffusion Imaging

Prof. Dr. Frank G. ZöllnerComputer Assisted Clinical MedicineMedical Faculty Mannheim Heidelberg University

Theodor-Kutzer-Ufer 1-3D-68167 Mannheim, Germany

[email protected]/inst/cbtm/ckm

Diffusion MRI I Slide 2/18 I 07.03.2018

Learning Goals

� introduction to perfusion imaging

� basic MRI principles -> Physics of Imaging Techniques

� Goals:

1. How does the technique work ?

2. What kind of images do we receive?

3. Where is this applied to ?

� Slides of the lectures at https://www.umm.uni-heidelberg.de/inst/cbtm/ckm/lehre/index.html

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Reading� Le Bihan D, et al. MR imaging of intravoxel incoherent motions:

application to diffusion and perfusion in neurologic disorders. Radiology. 1986;161(2):401–7.

� Glenn GR, Kuo L-W, Chao Y-P, et al. Mapping the orientation of white matter fiber bundles: a comparative study of diffusion tensor imaging, diffusional kurtosis imaging, and diffusion spectrum imaging. AJNR Am J Neuroradiol 2016; 37:1216-1222.

� Hagmann P, Jonasson L, Maeder P, et al. Understanding diffusion MR imaging techniques: from scalar diffusion-weighted imaging to diffusion tensor imaging and beyond. RadioGraphics 2006; 25:S205-223.

� Hori M, Aoki S, Fukunaga I, et al. A new diffusion metric, diffusion kurtosis imaging, used in the serial examination of a patient with stroke. Acta Radiologica Short Reports 2012;1:2 DOI: 10.1258/arsr.2011.110024

� Jensen JH, Helpern JA, Ramani A, Lu H, Kaczynski K. Diffusional kurtosis imaging: the quantification of non-Gaussian water diffusion by means of magnetic resonance imaging. Magn Reson Med 2005; 53:1432-1440.


Reading� Jensen JH, Helpern JA. MRI quantification of non-gaussian water

diffusion by kurtosis analysis. NMR Biomed 2010; 23:698-710.

� Yablonskiy DA, Sukstanskii AL. Theoretical models of the diffusion weighted MR signal. NMR Biomed 2010; 23:661-681.

� Andrew J. Steven, Jiachen Zhuo, and Elias R. Melhem. Diffusion Kurtosis Imaging: An Emerging Technique for Evaluating the Microstructural Environment of the Brain. Am J Roentgen 2014 202:1, W26-W33

� Johansen-Berg and Behrens. Diffusion MRI, Academic Press, 632 pages, ISBN: 9780123964601

� Jones. Diffusion Mri: Theory, Methods and Applications, Oxford University Press; ISBN: 978-0195369779

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Content

• Principle of Diffusion

• Apparent Diffusion Coefficient (ADC)

• Diffusion Tensor Imaging (DTI)

• Intravoxel Incoherent Motion (IVIM)

• Diffusion Kurtosis Imaging (DKI)


• Diffusion: Random movement ofmolecules/atoms due to Brownian motion(temperature)

• Diffusion coefficient D:

• Measure for amount of movement

• Dwater = 10-3 mm²/s 9 µm „wandering“ in 40 ms

• Diffusion in tissue is complexand holds information abouttissue structure and function

Diagnostic value

Principle of Diffusion

30 µm

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J = diffusion flux [mol/m^2/s]D = diffusion constant [m^2/s]C = concentration [mol/m^3]

Free Diffusion• 1st Fick´s Law

• 2nd Fick´s Law (Diffusion)

• mean square deviation


Principle of DWI by MRI

Phase in the rotating coordinate system is constant

position of spins in the rotatingcoordinate system

after 90°pulse

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1.Gradient � Spins aquire phase relativ t rot. coordinate system

Spin system without diffusion gradient



Spin system without diffusion

2.Gradient � Phase rephased � similar to gradient echo

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Spin system with diffusion

1.Gradient � Spins acquire phase relativ to rot. coordinate system




Diffusion occurs in between gradientplayout� Spins changelocation

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2.Gradient � Spins not completely rephased � Signal loss



• Gradients G make rotation frequencydependend on spatial position

� � � ∙ � � � ∙ �

• If spins change position (diffusion) firstand second gradient have different effects

Signal attenuation/loss

Apparent Diffusion Coefficient (ADC) Model

x

�

�

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Bloch Equations with Diffusion

(without relaxation)

(isotrop and homogen.)Equation of transport


Bloch Equations with Diffusion

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Signal loss and b-value

Strength of diffusions weighting:

B-value a sequence parameter

Integral devided into 3 parts


DWI Imaging Sequence

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DWI Imaging Sequence - EPI


DWI Imaging Sequence - EPI

Friedli et al. Scientific Reports volume 6 , 30088 (2016)

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• Gradients G make rotation frequencydependend on spatial position

� � � ∙ � � � ∙ �

• If spins change position (diffusion) firstand second gradient have different effects

Signal attenuation/loss


• „b-value“ = b(G, δ, ∆) determinesimpact of signal loss due todiffusion

• assuming equal diffusion in all directions (isotropic)

� � ∙ ��∙��

⇒ �� / � � �� ∙ ��

with Apparent Diffusion CoefficientADC



� � ∙ ��∙��

�� / � � �� ∙ ��

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White Matter

• Consists of highly directional neurion fibres (anisotropic)

Anisotropic Diffusion

Mosby's Medical Dictionary, 8th edition. © 2009, Elsevier.


White Matter

• Diffusion along fibres easier than across myelinsheath

Anisotropic Diffusion

axon0,5 µm

1 µm

Beaulieu. NMR Biomed 2005

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Diffusion Tensor Imaging (DTI)

Diffusion ellipsoid

Diffusion tensor

Water molecule


Diffusion Tensor Imaging (DTI)

Diffusion Tensor

ADC = �

��

Fractional Anisotropy (FA):• Amount of anisotropy• Main direction• 0 " #$ " 1

https://www.intechopen.com/books/novel-frontiers-of-advanced-neuroimaging/brain-structure-mr-imaging-methods-morphometry-and-tractography

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Diffusion Tensor Modell

coordinate system,Eigen system

DTI equation

isotropicdiffusion

anisotropicdiffusion


Diffusions - Tensor Modell

world coordinate system Eigensystem

in general:

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Diffusions - Tensor Modell

� Eigen system

� major Eigen value:&1

� major Eigen vector: [V1 V2 V3]


Diffusions – Tensor Modell

rotation matrix

Eigenvectors invariant to rotation� derived quantities (z.B. Trace, fractional anisotropy (FA))

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Fractional anisotropy

FA Colormap


• Investigation of main diffusion axis of neighbouring voxels

• Similar directions can indicate fibre structures

DTI Fibretracking

https://www.cnet.com/news/hi-def-fiber-tracking-helps-pinpoint-brain-damage/

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Fiber tracking ( naive approach)

• Fiber tracking using the given 3D vector field• start at (1,1)• discrete iteration of the fibers voxel by voxel

� too simple, not working


FACT Algorithmus

� FACT = fibre assignment bycontinuous tracking

� start at (1.5,1.5)

� continuious iteration

� stopping criteria

� border of image reached

� FA < 0.2 ~ FA of grey matter

� curvature too big

Rong et al., „MRM 42:1123-1127 (1999)

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Euler und Runge-Kutta Algortihmengiven: discretes stanionary image, vector field / Tensor field� Fiber track trajectors represented as 3D space curve� vector r(s) parametrised by the arc length s� Evolution of r(s) by Frenet equation dr(rs)/ds= t(s)� T(s) identified by the largest eigenvector ε(r(s))

associated with the largets eigenvalue of D

� Euler / Runge-Kutta algorithm Basser at al. , MRM 44:625-632 (2000)


Comparison of Fiber Tracking approaches

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Fiber tracking

Stieltjes et al, Neuroimage, 2001

Post mortem AtlasIn Vivo DTI


Corpus Callosum

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Fornix


Fiber tracks in Tumors

Capsula internaanterior

Schlüter et al., CURAC 2005

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Risk assessment of structures?


• Fiberkissing/Crossing

• Fibertracking: choice of parameters

ROIs Tracking FA

Fib

ers

Stieltjes B et al., Neuroimage, 2001

Problems of Fiber Tracking

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Noise & Accuracy of Fiber tracks

� Image data generally noisy

� errors of noise add up

� smoothing reduces noise but blurrs the image

Basser et al., MRM 44:625-632 (2000)


Fiber Tractography : Seeding points

� Seed location� Regional seed methods

To extract a specificpathway or mappingtracts from a specificregion

� Whole-brain seedmethods

To generate nearly all possible pathways

Higher redundancy in the pathways

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• Histogram analysis

• Voxel based analysis (VBA)

• ROI analysis

Qunatification in DTI


• a lot of work for larger patient groups/ cohorts

• structures are not alwayseasy to define

• poor reproducibility, inter-and intrareader variability

• meaningful, if it is knownwhere the pathology is to beexpected

• can be used for welldelimited structures

• simple, transparent methodology

-

ROI-Analyse (1)

+

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FA = 0.76

FA = 0.64

ROI-Analyse (2)


Schlüter et al., IEEE 2004

multivariate Gaussian


Ev 1

Ev 2

Ev 3 multivariate Gaussian


equally distributed linear mixture

equally distributed linear mixture

Semi-automatic ROI-Analysis

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fiber density at CC (1)

1Schlüter et al., IEEE 2004


Stieltjes et al., ECR 2005

fiber density in CC (2)

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Water moves inside capillary bed (perfusion)

Randomly orientedcapillaries

Same effect on the MRI signal as diffusion in the tissue

• Two compartments: inside and outside vascular system (both free diffusion)

• Resulting motion referred to aspseudo-diffusion (D* > ADC)

Intravoxel Incoherent Motion (IVIM) Model

[image from: Le Bihan et al.,Radiology, 1988, 168, 497-505]


Water moves inside capillary bed (perfusion)

Randomly orientedcapillaries

Same effect on the MRI signal as diffusion in the tissue

• Two compartments: inside and outside vascular system (both free diffusion)

• Resulting motion referred to aspseudo-diffusion (D* > ADC)

Intravoxel Incoherent Motion (IVIM) Model

Effectprimarily

present forlow b-values

IVIM

Range

ADC

Range

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IVIM (Intravoxel Incoherent Motion) theory

• perfusion influences the DWI signal decay

• IVIM: Perfusion can be described as a pseudo diffusion process

• under following conditions:

• several capillaries in a voxel

• random orientation of the capillaries

• long diffusion time compared to the travel time in a capillary segment


IVIM in the past

• The IVIM theory was first introduced in 1988 by Le Bihan

• Studies were focused on the brain and the IVIM effect was minimal (low perfusion fraction f≈5 %)

• The origin of the biexponential signal decay was discussed controversially

• “Diffusion, Perfusion=Confusion?”

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IVIM in the present

t [years]2000 2008

Liver: Luciani, RadiologyWake up call: Le Bihan

Pancreas: Lee, MRI

Kidney: Theony, Radiology

Pancreas: Lemke, Invest. Rad.

Liver: Patel, JMRI

Muscle: Karampinos, JMRI

Kidney: Zhang, Radiology

Abdomen: Yamada, MRI

Prostate: Riches, RadiologyAnimals: Duong, MRM

2004

IVIM technique can help differentiating lesions from benign tissue in the abdomen

however

IVIM perfusion parameters are not in agreement with parameters obtained from other imaging techniques (DCE, Ultrasound, CT)

The question of the optimal b-value distribution is not answered yet


IVIM equation

• both the diffusion and the pseudodiffusion due to perfusion contibute to the signal attenuation

D: Diffusion constant

D*: Pseudodiffusion coefficient du to perfusion

f: Perfusion fraction

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IVIM in the abdomen

Blood Suppression Lemke et al., submitted. in MRM


IVIM in pancreas carcinoma

Healthy pancreas:

Patient with pancreas carcinoma:

Lemke et al., Invest. Radiology, 2009

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Errors due to bad choice of b-values

b-values too low:

• Curve „fits well to data“, but only because ofextra degree of freedom

• No reasonable signal course

• Fit parameters strongly deviate from groundtruth

SNR for high b-values not sufficient:

• No reasonable signal course (noise corrupts fit)

• Fit parameters strongly deviate from ground truth


Optimization of the b-value distribution

•IVIM parameters of the liver, kidney, brain were used

• Rician noise was added to the simulated signal

• Process was repeated N=5000 times and σ was calculated

• serial optimization approach starting with 3 b-values{b=0, 40, 1000 s/mm²}

• distribution with minimal σ was chosen as the newoptimal distribution and iterated consecutively up to100 b-values

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Comparison to recently used b-value distributions(in vivo)

b=0 s/mm² D f D*

{bsum }

{blit }

• In agreement with the simulations, the D*-map suffers from low image quality due to a high variance

• However, the image quality of the D-, f-, and D*-map calculated from the distribution bsum show an improved image quality compared to the corresponding maps calculated from blit


Diffusion Kurtosis Imaging (DKI)

� standard diffusion weighted imaging (DWI) assume that diffusionwater molecules follows a Gaussian (normal) distribution.

� true for pure liquids and gels

� incorrect for complex biological tissues with cell membranes thatcreate compartments and barriers to diffusion

� Non-Gaussian behavior becomes more noticeable when strongergradients (higher b-values) and longer echo times are used

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� Non-Gaussian behavior becomes more noticeable when strongergradients (higher b-values) and longer echo times are used

� dimensionless parameter K, is a long recognized statistical metric forquantifying the shape of a probability distribution

� Gaussian distribution has K = 0

� more "peaked" and with less weighton their "shoulders" typically have a positive kurtosis (K>0)



� Comparison of b-value range for different DWI measurements

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� Imaging procedure

� similar to DWI, but employ higher b-values >= 1500 s/mm^2

� SNR an issue at high b-values -> averaging

� increased TEs needed to run diffusion gradients

� Data processing

S = Soe−bD + b²D²K/6


Clinical Application of ADC Model

Stroke

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DWI of pancreas – healthy volunteer

b = 400 s/mm²b = 0 s/mm²

ADC [µm²/s]

ADC = 1650 µm²/s


DWI of patient with pancreas ca

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IVIM Application - Brain

Cancer: Glioblastoma

[Federau, Christian and Kieran O'Brien. NMR in Biomedicine 28.1 (2015): 9-16.]

Stroke

[Federau, C., Kieran O‘Brien, et al. Neuroradiology 56.8 (2014): 629-635.]


Registration Segmentation

Applications of IVIM - Body

ProstatePancreatitis

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DKI Application - Brain

traumtic brain injury Grade 2 astrocytoma (AS 2), grade 3 astrocytoma (AS 3), andglioblastoma multiforme (GBM)

Steven et al. Am J Roentgen 2014


DKI Application - Body

Prostate bladder CA

Rosenkrantz et al. J Magn Reson Image 2015

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DKI Application

Rosenkrantz et al. J Magn Reson Image 2015

First author Year Maximal b‐valuea Organ Pathology Comment

Quentin 2012 800 Prostate CancerRosenkrantz 2012 2000 Prostate CancerRosenkrantz 2013 2000 Prostate CancerBourne 2014 2104 Prostate — Ex vivoMazzoni 2014 2300 Prostate CancerQuentin 2014 1000 Prostate CancerSuo 2014 2000 Prostate CancerTamura 2014 1500 Prostate CancerToivonen 2014 2000 Prostate CancerRoethke 2015 2000 Prostate CancerJambor 2015 2000 Prostate CancerPanagiotaki 2015 3000 Prostate CancerMerisaari 2015 2000 Prostate CancerJansen 2010 1500 Head and neck SCCLu 2012 1448 Head and neck SCC nodal

metastasesYuan 2014 1500 Head and neck Nasopharyngeal

carcinomaChen 2015 1500 Head and neck Nasopharyngeal

carcinomaIima 2014 2500 Breast Cancer; other

benign lesions

Nogueira 2014 3000 Breast Cancer; other benign lesions

Wu 2014 2000 Breast Cancer; other benign lesions

Trampel 2006 0.15 Lung Small airway disease

Used hyperpolarized

3He

Heusch 2013 2000 Lung Nonsmall‐cell lung cancer

Part of18

F‐FDG PET/MRI

Pentang 2014 600 Kidney —Huang 2015 1000 Kidney —Rosenkrantz 2012 2000 Liver Hepatocellular

carcinomaEx vivo liver explants

Anderson 2014 3500 Liver Fibrosis Ex vivo murine specimens

Goshima 2015 2000 Liver Hepatocellular carcinoma

Suo 2015 2000 Bladder CancerMarschar 2015 5600 Calf muscle —Lohezic 2014 10000 Myocardium Ex vivo rat

specimens; Q‐space imaging

Yamada 2015 7163 Esophagus Cancer Ex vivo; Q‐space imaging

Filli 2014 800 Whole body —


Summary

� DWI measures water movement in tissue by MRI

� change in signal due to uncomplete rephasing of the moving spins

� structural restrictions reflected by higher signal loss

� properties of DW gradients given by b-value (“diffusion strength”)

� different models to evaluate the diffusion

� ADC

� IVIM

� Kurtosis

� choice of b-values must match quantification

� DTI, diffusion weighted imaging combined with weighting of spatial direction

� allows to tract structures

� broad range of clinical applications

Advanced Imaging Techniques · 2018. 11. 27. · 27.11.2018 2 Diffusion MRI I Slide 3/18 I...

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