Diffusione e perfusione in risonanza magnetica E. Pagani, M. Filippi
DW-MRI
DIFFUSION-WEIGHTED MRI Principles Diffusion results from a microspic random motion known as Brownian motion
THE RANDOM WALK How the position of a jiggling molecule should change with time? After a given time, how far is it likely to be from where it began? The collisions are all random, so that we do not know! A? B
DIFFUSION ON A MACROSCOPIC SCALE The net displacements of molecules over time are randomly distributed if we consider a large population of molecules. We can only calculate the probability that a molecule travels a distance r in a time t. For a simple liquid such probability has a gaussian distribution with zero mean (the probability of moving in any direction is the same!).
DIFFUSION DISTANCE The variance of the travelled distance is given by Einstein s equation: <r 2 > = 6Dt The mean square distance is proportional to time, in other words, the mean molecular displacement, the diffusion distance, increases linearly with the square root of time. The diffusion coefficient, D, depends on the temperature, and characterizes the mobility of the molecules in the medium.
DIFFUSION AND MRI MRI is naturally sensitive to motion. With the use of strong gradients, the effect of the very small movement of diffusing particles becomes visible. 90 180 G TE Carr, H.Y., Purcell, E.M., 1954. Phys Rev 94, 630.
The random motion of the diffusing protons in the presence of a magnetic field gradient results in a random distribution of the phase shifts within the spins This leads to an imperfect refocusing of the spin echo, i.e. to a reduced amplitude of the MR signal. Voxel Random Motion Phase distribution Signal attenuation Gradient Statistical effect
DIFFUSION AND MRI 0 Pulsed gradient Spin echo 90 180 Nearly istantaneus phase shift Nucleus which has not moved is refocused. TE We have a procedure for detecting net motion during a controlled interval E.O. Stejskal. J Chem Phys 1965; 43(10), 3597-3603
FREE vs. RESTRICTED DIFFUSION Obtaining a precise period of time for observation of diffusion is important Diffusion distance FREE DIFFUSION HINDERED DIFFUSION RESTRICTED DIFFUSION Sqrt(diffusion time) For long diffusion times, the measured diffusion coefficient asymptotically approaches a new value, the apparent diffusion coefficient (ADC).
ANALYTIC EXPRESSION Relating spin echo intensity and D A 0 : echo intensity with no gradients ln (A/A 0 )= -b.adc ADC A b depends on the integral of the applied magnetic field gradients
Pulsed gradient Spin echo 90 180 b factor TE b = 2 G 2 [ 2 ( - /3) + 3 /30-2 /6] In the mammalian brain the linear range ln (A/A0) = -b.adc is for 0 > b > 2000
ANISOTROPIC DIFFUSION Control subject In the white matter diffusion is anisotropic
DIFFUSION ANISOTROPY IN THE WHITE MATTER axon myelin sheath IN WHITE MATTER DIFFUSION IS MUCH GREATER ALONG THAN ACROSS AXONS: WHY? myelin sheath axonal membrane neurofilamentous cytoskeleton axonal transport
DIFFUSION ANISOTROPY IN THE WHITE MATTER myelin axon
ANALYTIC EXPRESSION ln (A/A 0 )= - b ij D ij D: Diffusion Tensor (3x3 matrix) 6 unknown components At least 6 measurements with gradients + 1 without Basser PJ, et al. 1994. Biophysical Journal 66, 259-267.
DT INTERPRETATION D can be interpreted as the covariance matrix of a gaussian distribution which characterises the diffusion process. A surface of constant probability takes the form of an ellipsoid in 3D space Linear case Planar case Spherical case
Size Quantitative indexes - Mean Diffusivity D xx + 1/3 D yy D zz D
Size Quantitative indexes - Mean Diffusivity - Principal diffusivities: diffusivities along the three principal directions 1 2 3
Diffusion Anisotropy - Fractional anisotropy index (FA): this is a measure of the deviation from isotropy and is defined to be proportional to the ratio between the magnitude of the anisotropic part to the magnitude of the DT.
IMAGES OF ANISOTROPY corpus callosum subcortical WM internal capsule FA images show high contrast between the strongly anisotropic WM and the virtually isotropic CSF and GM.
IMAGES OF ANISOTROPY parallel fiber arrangement Anisotropy is highly variable in different white matter regions depending on the degree of coherence of fiber tract directions. fibers with different orientations
Orientation Principal directions e1,e2 and e3 x z y - Color-coded principal diffusion direction
Orientation Fiber Tractography Follow the direction along which the voxelaveraged diffusivity is maximum.
Orientation Fiber Tractography
Beyond the diffusion tensor More complex models Model free Fourier inversion: q-space formalism, high angular resolution approach, q-ball approach. P.T. Callaghan, et al. 1991. Nature 351:467-9. L.R. Frank, et al. 2001. Magn Reson Med 45:935-9 D.S. Tuch, 2004. Magn Reson Med 52:1358-72
Perfusion
PERFUSION Can be measured in two ways: 1. MRI contrast agents as a bolus: bolus tracking 2. blood as an endogenous contrast agent: arterial spin labelling (ASL)
BOLUS TRACKING 1. contrast agent is injected over a short time (5 s) 2. images are acquired rapidly 3. echo-planar sequence to give good time resolution 4. signal reduction used to estimate concentration of contrast agent from the relaxivity and echo time
BOLUS TRACKING Baseline signal intensity Injection t
Log Transformation c(t) -ln( I(t) / I 0 ) -ln(i/i 0 ) Injection t
Take account of shape of bolus 1. Want a graph that is independent of the quality of the contrast injection 2. Mathematically form an idealised tissue response curve c(t) Response to real bolus c m (t) Response to idealised bolus c(t) t t
Take account of shape of bolus 3. Arterial input function can be measured from the carotid artery or from a large enough vessel in the image plane. c(t) Response to idealised bolus t
Physiologically meaningful parameters 1. Cerebral blood flow (CBF) 2. Cerebral blood volume (CBV) 3. Mean transit time (MTT) CBV = (k/ )( c m (t)dt / AIF(t)dt CBV / CBF = c(t)dt / c max MTT = CBV / CBF t
ARTERIAL SPIN LABELLING Acquire two images: 1. blood is labelled before it moves into the imaged slice. Acquisition starts after an estimate of the mean transit time ( 1 s ) 2. control image difference between the two images
ARTERIAL SPIN LABELLING blood volume fraction is small low SNR higher field strength non-invasive repeated measures