1. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital Diffusion weighted MRI Brian Hansen, PhD brianh@phys.au.dk

2. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 2 Background: The physics of diffusion  Fickian diffusion  Brownian motion  Self diffusion Diffusion measurements  PGSE pulse sequence and spin dynamics  Interpreting the diffusion weighted signal  Diffusion in biological tissues Diffusion MRI in neuroimaging / neuroscience  Diffusion weighted MRI and the ADC map  Other applications: Fibre tracking Lecture outline

3. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 3 Background and motivation Diffusion processes are everywhere in Nature  Gases  Solids (semi-conductors, alloys)  Liquids (chemical reactions, biology, physiology) Diffusion Weighted (DW) MRI is a non-invasive method for measuring diffusion:  Diffusion coefficient (physical or apparent)  Direction of diffusion (preferred direction) From these parameters the state of e.g. tissue can be estimated.

4. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 4 Clinical Application Ischemic infarction is not visible on conventional MRI (T1,T2, PD) DW MRI introduces new sensitivity:

5. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 5 Physical Principles

6. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 6 Fickian diffusion Fick’s two laws describe diffusion driven by a difference in concentration. Fick’s 1st: Fick’s 2nd: C(x,t) x

7. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital Self-diffusion All water molecules perform a thermally driven random walk. We can only describe this motion statistically: H2OH2O For Brownian motion z = 2

8. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 8 Brownian Motion Named after scottish botanist Robert Brown (1773-1858). Explained by Einstein in 1905. The thermal motion of the molecules cause them to collide. Random motion follows. Described by the Stokes-Einstein relation: D is diffusion coefficient, k B is the Boltzmann constant, T is absolute temperature,  is liquid viscosity and r is particle radius.

9. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital Diffusion in biological tissue Diffusion in tissue is resticted by cell membranes, organelles etc: These random trajectories will in time fill the plane and reveal the structure.

10. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 10 Measuring Diffusion The Pulsed Gradient Spin Echo (PGSE) sequence 90  180  time  g 

11. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 11 No diffusion: Spin 1Spin 2Spin 3 Stationary spins are unaffected by diffusion gradient. time

12. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 12 With diffusion: Spin 1Spin 2Spin 3 time

13. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 13 Vector sum + + = + + = No loss of signal in areas with no diffusion. Diffusion introduces a signal loss. High diffusion gives strong signal attenuation.

14. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 14 DW MRI parameters Parameters g, ,  are combined in the b-factor: Here  is the proton gyromagnetic ratio. The b-factor can be varied by varying one of g,  and . For the PGSE sequence the case b = 0 corresponds to the simpel SE sequence. A large b-factor gives a large signal loss in areas with high diffusion. This is called strong diffusion weighting. 90  180   g 

15. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 15 Signal and b-factor I The DWMR signal from simple free diffusion is described by: By ”simple free diffusion” we mean that applies for all times.

16. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 16 Signal and b-factor II On a log-plot this yields a straight line: log(S(b)/S(b=0)) = -b  D The slope of the curve gives us the physical diffusion coefficient.

17. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 17 Measuring D Remember:

18. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 18 Diffusion in tissue Diffusion in biological tissue is not free: Cell membranes, organelles etc. restrict the diffusion of the water molecules. Simple signal behaviour breaks down due to complex tissue structure: Grey matter, ECS in red. This means that no longer applies for all times.

19. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 19 The Apparent Diffusion Coefficient The value we measure is no longer the physical diffusion coefficient:  Instead we get an average over many restricted random walks We introduce the term Apparent Diffusion Coefficient (ADC) Two measurements at b = 0 and b = 1000 s/mm 2 are made: The slope gives the ADC – not the physical diffusion coefficient. Typical ADC values in brain (mm 2 /s) : Normal gray matter: 0.8-1.0  10 -3 Normal white matter: 0.2-1.0  10 -3 Free water (CSF): 2.9  10 -3 Review and references in Journal of Computer Assisted Tomography 25(4):515-519.

20. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 20 Increasing b-values b = 2000 b = 4000b = 7000

21. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 21 DWI and ADC maps DW MRI provides two new image types: The Diffusion Weighted Image (DWI)The ADC map (a calculated image)

22. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 22 Stroke DWI Acute DWI tPA + 2htPA + 24h DWI

23. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital Possible cause of the bright areas in the DWI: Cells in normal tissueCells in infarct (stroke)

24. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 24 Summary: Strength of DWI T2 MRI: Infarct is not visible – brain appears normal DWI: Infarct clearly visible Scan time: 30 sec, EPI No IV contrast agent needed Infarct detectable after few minutes

25. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 25 Summary: Image types Two image types: DWI and ADC map: DWI: Signal is diffusion weighted. High diffusion: signal loss Low diffusion: no signal loss Infarcts are bright ADC map: Calculated image Contrast opposite to DWI Low intensity: low ADC value (low diffusion) High intensity: high ADC (high diffusion)

26. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 26 DWI ADC MTT Osvd

27. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital 27 Diffusion Tensor Imaging Diffusion is often directional – e.g. along fibers: Instead of measuring many b-values we measure along many different directions. Instead of the ADC we obtain the Diffusion Tensor which describes the diffusion coefficient in space. This is the basis of fibre tracking.

28. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital Images courtesy of Jesper Frandsen, CFIN

29. The Danish National Research Foundation’s Center of Functionally Integrative Neuroscience Aarhus University / Aarhus University Hospital Image courtesy of Jesper Frandsen, CFIN