The Larmor Relation 84 Image Quality/Artifacts (MHz) 42 ω = γ X B = 2πf 84 0.0 1.0 2.0 Magnetic Field (Tesla) 1 A 1D Image Magnetic Field Gradients Magnet Field Strength Field Strength / Gradient Coil Position Position MRI Instrument in Cross Section 4
Fourier Series Fourier Series 5 Fourier Transform 6 A 1D Image Field Strength / Position 7 8
Back Projection Fourier Projections Image Domain Gradient Encoding 2D Fourier Transform FFT of Raw Data Raw Data MR Image real imaginary Fourier Domain Paul Lauterbur Syringomyelia The Syringomyelia Epidemic Surgery is usually recommended for syringomyelia patients. The main goal of surgery is to provide more space for the cerebellum (Chiari malformation) at the base of the skull and upper neck, without entering the brain or spinal cord. This results in flattening or disappearance of the primary cavity. If a tumor is causing syringomyelia, removal of the tumor is the treatment of choice and almost always eliminates the syrinx. Source http://gait.aidi.udel.edu/res695/homepage/pd_ortho/educate/clincase/syrsco.htm 11
Fourier Transform Truncated Raw Data This is Equivalent Truncating the Fourier to Data Results Sampling only in adistortions Portion of (edge the Actual ringing) MR Raw of High Data Spatial Frequencies Actual Object The Syringomyelia Epidemic 13 MR Image Truncation in Fourier Domain Original Sample Apparent Signal 14-1 F (s) encoded Signal Truncated Series 16
What is the actual resolution of MRI? Original Data The Actual Resolution of ƒmri MR Image http://ccn.ucla.edu/bmcweb/sharedcode/mrartifacts/mrartifacts.html Single pixel activation An Equation in Resolution Contrast to Noise Ratio Because MR is an emission modality the temporal resolution, spatial resolution and contrast are inter-dependent: Signal = kb0 (voxel size) imaging time contrast where B0 is the field strength.
CNR vs. Resolution CNR vs. Resolution Noise free Imaging time = 1X Signal/Noise Ratio Held Constant 256 X 256 128 X 128 Imaging time = 2X 64 X 64 Imaging time = 4X 64 X 64 Imaging time = 16X 128 X 128 Imaging time = 4X Minimum Imaging Time Imaging time = 1X 256 X 256 CNR vs. Resolution Bandwidth and Readout Noise free 16 averages Position is encoded by FREQUENCY Bandwidth refers to the Difference from the center of the image to its edge: 4 averages per pixel = 1 average 64 X 64 128 X 128 Imaging Time Held Constant 1 2* Bandwidth = readout duration number of pixels Bandwidth decreases with readout duration: Bandwidth = number of pixels 2 * readout duration 256 X 256
Bandwidth Bandwidth and SNR Decreasing the Bandwidth Improves SNR: Imaging Time is INCREASED and high frequency noise is excluded Narrow Wide Bandwidth Bandwidth Signal Intensity Noise TE=11-14 TR=500 BW=8kHz BW=4kHz BW=16kHz NEX=1 Thick=3mm Matrix=256x256 The Origin of Chemical Shift Bandwidth BW=4kHz BW=8kHz BW=16kHz In water, electrons move from Hydrogen towards Oxygen. Electrons in lipid are shared equally between Hydrogen and Oxygen This exposes the Proton to a slightly higher magnetic field. TE=11-14 NEX=1 Thick=3mm TR=500 Matrix=256x256 Water Lipid Resonance Frequencies Higher
Chemical Shift Artifact Chemical Shift Higher The Fat-Water chemical shift is about 3.5 ppm or: Which is: with a 32 khz readout 75 Hz @ 0.5 Tesla < 1 pixel 150 Hz @ 1.0 Tesla 1 pixel 220 Hz @ 1.5 Tesla > 1 pixel 440 Hz @ 3.0 Tesla 3.5 pixels d If the frequency width of each pixel is less than the frequency difference between water and lipid, then water and lipid will appear in separate pixels Water Fat Amplitude frequency Lowering the Bandwidth/pixel increases the Chemical Shift in pixels Distortions are More Severe at High Magnetic Field Strength Shape and Bandwidth Variation in sample magnetization of is proportional to field strength.! High Field images lose more signal from field inhomogeneity
Apodization from Long Readouts EPI Readout Durations 1 MR Signal T2* signal decay (T2* ~ 45 msec) UCLA 64x128 0.5 GE Product 64x128 UCLA 128x128 GE Product 128x128 Stanford Spiral 128x128 0 Phantom Readout = 2T2* 0 Readout = 4T2* Exercise in Afternoon Lab Motion Artifact 20 40 Aliasing http://airto.ccn.ucla.edu/bmcweb/sharedcode/mrartifacts/mrartifacts.html Exercise in Afternoon Lab 60 80 100
Saturation Spikes Exercise in Afternoon Lab Exercise in Afternoon Lab 38 Image Quality Spikes SNR is Very Limited in MRI Feature Detection Falls Rapidly with Loss in Contrast to Noise Ratio Usable Resolution is NOT the Same as Voxel Size Spatial Encoding Artifacts in MRI May Have Complex Appearance Edge Ringing and Blurring are Related to Parameters Such as Contrast Exercise in Afternoon Lab 40
Characterize Your Tools Instrument Variation 1. System Instability Test Statistics are Effect/Variance Variance includes: Intrasubject (motion, attention, physiology, fatigue, ) Intersubject variance (position, morphology, performance, pathology, physiology, ) Experimental Variance (uncontrolled variables, stimulation variance, ) Instrument Variance Sitewise Variance True Random Noise 2 0-2 -4-6 0 6 12 Mean Intensity Variation Scanner Autocorrelation 42 the Weisskoff Plot Scanner B Scanner A 41 The Expected Standard Deviation of the Mean Signal of a Region over Time Falls with the Square Root of the Number of Voxels. 0 Coefficient of Variation 10 Scanner C L Scanner D -1 10-2 10 1 2 5 10 30 ROI Edge Length 43 44
the Weisskoff Plot Weisskoff Plot Weisskoff R. Magn Reson Med 36:643 Coefficient of Variation 0.2 Measured Theoretical 0.1 Deviations from the Theoretical Curve are Evidence of Correlated Noise RDC = 16.6 10 15 20 ROI Edge Length ROI Length RDC (Radius of Decorrelation) is a Single Point Quantification of the Weisskoff Plot Friedman and Glover, JMRI 23:827 45 Scanner Comparisons 46 48 Drift Friedman and Glover, JMRI 23:827 ROI Length 47
Instrument Variation Interpolation 2. The mystery of scanner drift. This location was not acquired Native Resolution 49 Global Mean Scaling - OFF Bilinear Interpolation 50 Global Mean Scaling - ON 51 52
Thermal Noise Parameter Optimization Noise Distribution in MRI is Rician Signal = (ℜ + σ 1 )2 + (ℑ + σ 2 )2 Background should be Rayleigh Noise π σ, expected variance: 2 µ π = variance 4 µ Expected µ: Best BOLD contrast when te=t2* functional contrast (ℜ = ℑ = 0) 4 π 2 σ 2 Deviations from This Model Imply Coherent Artifacts te/t2* 53 Parameter Optimization Exercise in Afternoon Lab 54 Other Parameters Best BOLD contrast when te=t2* Voxels Should be Large enough that: d ln(signal) 1 = d(te) T2* Thermal Noise << Physiological Fluctuations For Best Signal with Arbitrary Slice Orientation: Voxels Should be Isotropic With Gradient Echo Scans (most BOLD): Signal Falls (much) more than linearly with Slice Thickness Do not Confuse Signal to Noise Ratio with Contrast to Noise Ratio! T2* is both an Instrument Parameter and a Physiological Parameter 55 56