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27.11.2018
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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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Diffusion MRI I Slide 3/18 I 07.03.2018
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.
Diffusion MRI I Slide 4/18 I 07.03.2018
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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Diffusion MRI I Slide 5/18 I 07.03.2018
Content
• Principle of Diffusion
• Apparent Diffusion Coefficient (ADC)
• Diffusion Tensor Imaging (DTI)
• Intravoxel Incoherent Motion (IVIM)
• Diffusion Kurtosis Imaging (DKI)
Diffusion MRI I Slide 6/18 I 07.03.2018
• 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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Diffusion MRI I Slide 7/18 I 07.03.2018
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
Diffusion MRI I Slide 8/18 I 07.03.2018
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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Diffusion MRI I Slide 9/18 I 07.03.2018
Principle of DWI by MRI
1.Gradient � Spins aquire phase relativ t rot. coordinate system
Spin system without diffusion gradient
Diffusion MRI I Slide 10/18 I 07.03.2018
Principle of DWI by MRI
Spin system without diffusion
2.Gradient � Phase rephased � similar to gradient echo
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Diffusion MRI I Slide 11/18 I 07.03.2018
Principle of DWI by MRI
Spin system with diffusion
1.Gradient � Spins acquire phase relativ to rot. coordinate system
Diffusion MRI I Slide 12/18 I 07.03.2018
Principle of DWI by MRI
Spin system with diffusion
Diffusion occurs in between gradientplayout� Spins changelocation
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Diffusion MRI I Slide 13/18 I 07.03.2018
Principle of DWI by MRI
2.Gradient � Spins not completely rephased � Signal loss
Spin system with diffusion
Diffusion MRI I Slide 14/18 I 07.03.2018
• 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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Diffusion MRI I Slide 15/18 I 07.03.2018
Bloch Equations with Diffusion
(without relaxation)
(isotrop and homogen.)Equation of transport
Diffusion MRI I Slide 16/18 I 07.03.2018
Bloch Equations with Diffusion
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Diffusion MRI I Slide 17/18 I 07.03.2018
Signal loss and b-value
Strength of diffusions weighting:
B-value a sequence parameter
Integral devided into 3 parts
Diffusion MRI I Slide 18/18 I 07.03.2018
DWI Imaging Sequence
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Diffusion MRI I Slide 19/18 I 07.03.2018
DWI Imaging Sequence - EPI
Diffusion MRI I Slide 20/18 I 07.03.2018
DWI Imaging Sequence - EPI
Friedli et al. Scientific Reports volume 6 , 30088 (2016)
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Diffusion MRI I Slide 21/18 I 07.03.2018
• 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
• „b-value“ = b(G, δ, ∆) determinesimpact of signal loss due todiffusion
• assuming equal diffusion in all directions (isotropic)
� � ∙ ���∙���
⇒ �� / � � �� ∙ ���
with Apparent Diffusion CoefficientADC
Diffusion MRI I Slide 22/18 I 07.03.2018
Apparent Diffusion Coefficient (ADC) Model
� � ∙ ���∙���
�� / � � �� ∙ ���
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Diffusion MRI I Slide 23/18 I 07.03.2018
White Matter
• Consists of highly directional neurion fibres (anisotropic)
Anisotropic Diffusion
Mosby's Medical Dictionary, 8th edition. © 2009, Elsevier.
Diffusion MRI I Slide 24/18 I 07.03.2018
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 MRI I Slide 25/18 I 07.03.2018
Diffusion Tensor Imaging (DTI)
Diffusion ellipsoid
Diffusion tensor
Water molecule
Diffusion MRI I Slide 26/18 I 07.03.2018
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 MRI I Slide 27/18 I 07.03.2018
Diffusion Tensor Modell
coordinate system,Eigen system
DTI equation
isotropicdiffusion
anisotropicdiffusion
Diffusion MRI I Slide 28/18 I 07.03.2018
Diffusions - Tensor Modell
world coordinate system Eigensystem
in general:
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Diffusion MRI I Slide 29/18 I 07.03.2018
Diffusions - Tensor Modell
� Eigen system
� major Eigen value:&1
� major Eigen vector: [V1 V2 V3]
Diffusion MRI I Slide 30/18 I 07.03.2018
Diffusions – Tensor Modell
rotation matrix
Eigenvectors invariant to rotation� derived quantities (z.B. Trace, fractional anisotropy (FA))
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Diffusion MRI I Slide 31/18 I 07.03.2018
Fractional anisotropy
FA Colormap
Diffusion MRI I Slide 32/18 I 07.03.2018
• 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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Diffusion MRI I Slide 33/18 I 07.03.2018
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
Diffusion MRI I Slide 34/18 I 07.03.2018
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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Diffusion MRI I Slide 35/18 I 07.03.2018
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)
Diffusion MRI I Slide 36/18 I 07.03.2018
Comparison of Fiber Tracking approaches
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Diffusion MRI I Slide 37/18 I 07.03.2018
Fiber tracking
Stieltjes et al, Neuroimage, 2001
Post mortem AtlasIn Vivo DTI
Diffusion MRI I Slide 38/18 I 07.03.2018
Corpus Callosum
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Diffusion MRI I Slide 39/18 I 07.03.2018
Fornix
Diffusion MRI I Slide 40/18 I 07.03.2018
Fiber tracks in Tumors
Capsula internaanterior
Schlüter et al., CURAC 2005
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Diffusion MRI I Slide 41/18 I 07.03.2018
Risk assessment of structures?
Diffusion MRI I Slide 42/18 I 07.03.2018
• 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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Diffusion MRI I Slide 43/18 I 07.03.2018
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)
Diffusion MRI I Slide 44/18 I 07.03.2018
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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Diffusion MRI I Slide 45/18 I 07.03.2018
• Histogram analysis
• Voxel based analysis (VBA)
• ROI analysis
Qunatification in DTI
Diffusion MRI I Slide 46/18 I 07.03.2018
• 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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Diffusion MRI I Slide 47/18 I 07.03.2018
FA = 0.76
FA = 0.64
ROI-Analyse (2)
Diffusion MRI I Slide 48/18 I 07.03.2018
Schlüter et al., IEEE 2004
multivariate Gaussian
multivariate Gaussian
Ev 1
Ev 2
Ev 3 multivariate Gaussian
multivariate Gaussian
equally distributed linear mixture
equally distributed linear mixture
Semi-automatic ROI-Analysis
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Diffusion MRI I Slide 49/18 I 07.03.2018
fiber density at CC (1)
1Schlüter et al., IEEE 2004
Diffusion MRI I Slide 50/18 I 07.03.2018
Stieltjes et al., ECR 2005
fiber density in CC (2)
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Diffusion MRI I Slide 51/18 I 07.03.2018
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]
Diffusion MRI I Slide 52/18 I 07.03.2018
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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Diffusion MRI I Slide 53/18 I 07.03.2018
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
Diffusion MRI I Slide 54/18 I 07.03.2018
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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Diffusion MRI I Slide 55/18 I 07.03.2018
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
Diffusion MRI I Slide 56/18 I 07.03.2018
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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Diffusion MRI I Slide 57/18 I 07.03.2018
IVIM in the abdomen
Blood Suppression Lemke et al., submitted. in MRM
Diffusion MRI I Slide 58/18 I 07.03.2018
IVIM in pancreas carcinoma
Healthy pancreas:
Patient with pancreas carcinoma:
Lemke et al., Invest. Radiology, 2009
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Diffusion MRI I Slide 59/18 I 07.03.2018
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
Diffusion MRI I Slide 60/18 I 07.03.2018
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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Diffusion MRI I Slide 61/18 I 07.03.2018
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 MRI I Slide 62/18 I 07.03.2018
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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Diffusion MRI I Slide 63/18 I 07.03.2018
Diffusion Kurtosis Imaging (DKI)
� 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)
Diffusion MRI I Slide 64/18 I 07.03.2018
Diffusion Kurtosis Imaging (DKI)
� Comparison of b-value range for different DWI measurements
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Diffusion MRI I Slide 65/18 I 07.03.2018
Diffusion Kurtosis Imaging (DKI)
� 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
Diffusion MRI I Slide 66/18 I 07.03.2018
Clinical Application of ADC Model
Stroke
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Diffusion MRI I Slide 67/18 I 07.03.2018
DWI of pancreas – healthy volunteer
b = 400 s/mm²b = 0 s/mm²
ADC [µm²/s]
ADC = 1650 µm²/s
Diffusion MRI I Slide 68/18 I 07.03.2018
DWI of patient with pancreas ca
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Diffusion MRI I Slide 69/18 I 07.03.2018
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.]
Diffusion MRI I Slide 70/18 I 07.03.2018
Registration Segmentation
Applications of IVIM - Body
ProstatePancreatitis
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Diffusion MRI I Slide 71/18 I 07.03.2018
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
Diffusion MRI I Slide 72/18 I 07.03.2018
DKI Application - Body
Prostate bladder CA
Rosenkrantz et al. J Magn Reson Image 2015
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Diffusion MRI I Slide 73/18 I 07.03.2018
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 —
Diffusion MRI I Slide 74/18 I 07.03.2018
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