Presentation on theme: "Principles of MRI: Image Formation"— Presentation transcript:
1 Principles of MRI: Image Formation Allen W. SongBrain Imaging and Analysis CenterDuke University
2 What is image formation? To define the spatial location of the sourcesthat contribute to the detected signal.
3 But MRI does not use projection, reflection, or refraction mechanisms commonly used in optical imaging methodsto form image. So how are the MR images formed?
4 Frequency and Phase Are Our Friends in MR Imaging wq = wtThe spatial information of the proton pools contributingMR signal is determined by the spatial frequency andphase of their magnetization.
5 Gradient CoilszzzyyyxxxX gradient Y gradient Z gradientGradient coils generate spatially varying magnetic fieldso that spins at different location precess at frequenciesunique to their location, allowing us to reconstruct 2Dor 3D images.
6 A Simple Example of Spatial Encoding 0.8A Simple Example of Spatial EncodingConstantMagneticFieldVaryingMagneticFieldw/o encodingw/ encoding
7 Spatial Decoding of the MR Signal FrequencyDecomposition
8 Steps in 3D Localization Can only detect total RF signal from inside the “RF coil” (the detecting antenna)Excite and receive Mxy in a thin (2D) slice of the subjectThe RF signal we detect must come from this sliceReduce dimension from 3D down to 2DDeliberately make magnetic field strength B depend on location within sliceFrequency of RF signal will depend on where it comes fromBreaking total signal into frequency components will provide more localization informationMake RF signal phase depend on location within slice
9 Exciting and Receiving Mxy in a Thin Slice of Tissue Excite:Source of RF frequency on resonanceAddition of small frequency variationAmplitude modulation with “sinc” functionRF power amplifierRF coil
11 Gradient Fields: Spatially Nonuniform B: During readout (image acquisition) period, turning on gradient field is called frequency encoding --- using a deliberately applied nonuniform field to make the precession frequency depend on locationBefore readout (image acquisition) period, turning on gradient field is called phase encoding --- during the readout (image acquisition) period, the effect of gradient field is no longer time-varying, rather it is a fixed phase accumulation determined by the amplitude and duration of the phase encoding gradient.Centerfrequency[63 MHz at 1.5 T]f60 KHzGx = 1 Gauss/cm = 10 mTesla/m= strength of gradient fieldx-axisLeft = –7 cmRight = +7 cm
12 Exciting and Receiving Mxy in a Thin Slice of Tissue Receive:RF coilRF preamplifierFiltersAnalog-to-Digital ConverterComputer memory
15 Determining slice thickness Resonance frequency range as the resultof slice-selective gradient:DF = gH * Gsl * dslThe bandwidth of the RF excitation pulse:Dw/2pThus the slice thickness can be derived asdsl = Dw / (gH * Gsl * 2p)
16 Changing slice thickness There are two ways to do this:Change the slope of the slice selection gradientChange the bandwidth of the RF excitation pulseBoth are used in practice, with (a) being more popular
18 Selecting different slices In theory, there are two ways to select different slices:Change the position of the zero point of the sliceselection gradient with respect to isocenter(b) Change the center frequency of the RF to correspondto a resonance frequency at the desired sliceF = gH (Bo + Gsl * Lsl )Option (b) is usually used as it is not easy to change theisocenter of a given gradient coil.
20 Readout Localization (frequency encoding) After RF pulse (B1) ends, acquisition (readout) of NMR RF signal beginsDuring readout, gradient field perpendicular to slice selection gradient is turned onSignal is sampled about once every few microseconds, digitized, and stored in a computerReadout window ranges from 5–100 milliseconds (can’t be longer than about 2T2*, since signal dies away after that)Computer breaks measured signal V(t) into frequency components v(f ) — using the Fourier transformSince frequency f varies across subject in a known way, we can assign each component v(f ) to the place it comes from
21 Spatial Encoding of the MR Signal ConstantMagneticFieldVaryingMagneticFieldw/o encodingw/ encoding
22 It’d be easy if we image with only 2 voxels … But often times we have imaging matrix at 256 or higher.
25 After Frequency Encoding A 9×9 casePhysical SpaceMR data spaceBefore EncodingAfter Frequency Encoding(x gradient)So each data point contains information from all the voxels
26 A typical diagram for MRI frequency encoding: Gradient-echo imaging ExcitationSliceSelectionTEFrequencyEncodingreadout………Time point #1Time point #9ReadoutData points collected during thisperiod corrspond to one-line in k-space
27 ……… Phase Evolution of MR Data TE Gradient Phases of spins digitizer onPhases of spinsGradientTE………Time point #1Time point #9
28 A typical diagram for MRI frequency encoding: Spin-echo imagingExcitationSliceSelectionTEFrequencyEncodingreadout………Readout
29 Phase History180oTEPhaseGradient………digitizer on
30 Image Resolution (in Plane) Spatial resolution depends on how well we can separate frequencies in the data V(t)Resolution is proportional to f = frequency accuracyStronger gradients nearby positions are better separated in frequencies resolution can be higher for fixed fLonger readout times can separate nearby frequencies better in V(t) because phases of cos(ft) and cos([f+f]t) will be more different
31 Calculation of the Field of View (FOV) along frequency encoding direction * Gf * FOVf = BW = 1/DtWhich means FOVf = 1/ (g Gf Dt)where BW is the bandwidth for thereceiver digitizer.
32 The Second Dimension: Phase Encoding Slice excitation provides one localization dimensionFrequency encoding provides second dimensionThe third dimension is provided by phase encoding:We make the phase of Mxy (its angle in the xy-plane) signal depend on location in the third directionThis is done by applying a gradient field in the third direction ( to both slice select and frequency encode)Fourier transform measures phase of each v(f ) component of V(t), as well as the frequency fBy collecting data with many different amounts of phase encoding strength, can break each v(f ) into phase components, and so assign them to spatial locations in 3D
33 After Frequency Encoding A 9×9 casePhysical SpaceMR data spaceBefore EncodingAfter Frequency Encodingx gradientAfter Phase Encodingy gradientSo each point contains information from all the voxels
34 A typical diagram for MRI phase encoding: Gradient-echo imaging readoutExcitationSliceSelectionFrequencyEncodingPhaseReadout………
35 A typical diagram for MRI phase encoding: Spin-echo imagingreadoutExcitationSliceSelectionFrequencyEncodingPhaseReadout………
36 Calculation of the Field of View (FOV) along phase encoding direction * Gp * FOVp = Np / TpWhich means FOVp = 1/ (g Gp Tp/Np)= 1/ (g Gp Dt)where Tp is the duration and Np the numberof the phase encoding gradients, Gp is themaximum amplitude of the phase encodinggradient.
37 Part II.2 Introduction to k-space (MR data space) Imagek-space
38 …….. …….. …….. …….. Phase Encode Time Time Time Step 1 point #1
39 .+Gx-Gx+Gy-GyPhysical SpaceK-SpaceContributions of different image locations to the raw k-space data. Each data point in k-space (shown in yellow) consists of the summation of MR signal from all voxels in image space under corresponding gradient fields.
40 Acquired MR Signal Kx = g/2p 0t Gx(t) dt Ky = g/2p 0t Gy(t) dt For a given data point in k-space, say (kx, ky), its signal S(kx, ky) is the sum of all the little signal from each voxel I(x,y) in the physical space, under the gradient field at that particular momentFrom this equation, it can be seen that the acquired MR signal,which is also in a 2-D space (with kx, ky coordinates), is theFourier Transform of the imaged object.Kx = g/2p 0t Gx(t) dtKy = g/2p 0t Gy(t) dt
41 Two Spaces k-space Image space ky y IFT kx x FT Final Image Acquired DataImage spacexyFinal ImageIFTFT