Questions and Answers ​in MRI
  • Home
  • Complete List of Questions
  • …Magnets & Scanners
    • Basic Electromagnetism >
      • What causes magnetism?
      • What is a Tesla?
      • Who was Tesla?
      • What is a Gauss?
      • How strong is 3.0T?
      • What is a gradient?
      • Aren't gradients coils?
      • What is susceptibility?
      • How to levitate a frog?
      • What is ferromagnetism?
      • Superparamagnetism?
    • Magnets - Part I >
      • Types of magnets?
      • Brands of scanners?
      • Which way does field point?
      • Which is the north pole?
      • Low v mid v high field?
      • Advantages to low-field?
      • Disadvantages?
      • What is homogeneity?
      • Why homogeneity?
      • Why shimming?
      • Passive shimming?
      • Active shimming?
    • Magnets - Part II >
      • Superconductivity?
      • Perpetual motion?
      • How to ramp?
      • Superconductive design?
      • Room Temp supercon?
      • Liquid helium use?
      • What is a quench?
      • Is field ever turned off?
      • Emergency stop button?
    • Gradients >
      • Gradient coils?
      • How do z-gradients work?
      • X- and Y- gradients?
      • Open scanner gradients?
      • Eddy current problems?
      • Active shielded gradients?
      • Active shield confusion?
      • What is pre-emphasis?
      • Gradient heating?
      • Gradient specifications?
      • Gradient linearity?
    • RF & Coils >
      • Many kinds of coils?
      • Radiofrequency waves?
      • Phase v frequency?
      • RF Coil function(s)?
      • RF-transmit coils?
      • LP vs CP (Quadrature)?
      • Multi-transmit RF?
      • Receive-only coils?
      • Array coils?
      • AIR Coils?
    • Site Planning >
      • MR system layout?
      • What are fringe fields?
      • How to reduce fringe?
      • Magnetic shielding?
      • Need for vibration testing?
      • What's that noise?
      • Why RF Shielding?
      • Wires/tubes thru wall?
  • ...Safety and Screening
    • Overview >
      • ACR Safety Zones?
      • MR safety screening?
      • Incomplete screening?
      • Passive v active implants?
      • Conditional implants?
      • Common safety issues?
      • Projectiles?
      • Metal detectors?
      • Pregnant patients?
      • Postop, ER & ICU patients?
      • Temperature monitoring?
      • Orbital foreign bodies?
      • Bullets and shrapnel?
    • Static Fields >
      • "Dangerous" metals?
      • "Safe" metals?
      • Magnetizing metal?
      • Object shape?
      • Forces on metal?
      • Most dangerous place?
      • Force/torque testing?
      • Static field bioeffects?
      • Dizziness/Vertigo?
      • Flickering lights?
      • Metallic taste?
    • RF Fields >
      • RF safety overview?
      • RF biological effects?
      • What is SAR?
      • SAR limits?
      • Operating modes?
      • How to reduce SAR?
      • RF burns?
      • Estimate implant heating?
      • SED vs SAR?
      • B1+rms vs SAR?
      • Personnel exposure?
      • Cell phones?
    • Gradient Fields >
      • Gradient safety overview
      • Acoustic noise?
      • Nerve stimulation?
      • Gradient vs RF heating?
    • Safety: Neurological >
      • Aneurysm coils/clips?
      • Shunts/drains?
      • Pressure monitors/bolts?
      • Deep brain stimulators?
      • Spinal cord stimulators?
      • Vagal nerve stimulators?
      • Cranial electrodes?
      • Carotid clamps?
      • Peripheral stimulators?
      • Epidural catheters?
    • Safety: Head & Neck >
      • Additional orbit safety?
      • Cochlear Implants?
      • Bone conduction implants?
      • Other ear implants?
      • Dental/facial implants?
      • ET tubes & airways?
    • Safety: Chest & Vascular >
      • Breast tissue expanders?
      • Breast biopsy markers?
      • Airway stents/valves/coils?
      • Respiratory stimulators?
      • Ports/vascular access?
      • Swan-Ganz catheters?
      • IVC filters?
      • Implanted infusion pumps?
      • Insulin pumps & CGMs?
      • Vascular stents/grafts?
      • Sternal wires/implants?
    • Safety: Cardiac >
      • Pacemaker dangers?
      • Pacemaker terminology?
      • New/'Safe" Pacemakers?
      • Old/Legacy Pacemakers?
      • Violating the conditions?
      • Epicardial pacers/leads?
      • Cardiac monitors?
      • Heart valves?
      • Miscellaneous CV devices?
    • Safety: Abdominal >
      • PIllCam and capsules?
      • Gastric pacemakers?
      • Other GI devices?
      • Contraceptive devices?
      • Foley catheters?
      • Incontinence devices?
      • Penile Implants?
      • Sacral nerve stimulators?
      • GU stents and other?
    • Safety: Orthopedic >
      • Orthopedic hardware?
      • External fixators?
      • Traction and halos?
      • Bone stimulators?
      • Magnetic rods?
  • …The NMR Phenomenon
    • Spin >
      • What is spin?
      • Why I = ½, 1, etc?
      • Proton = nucleus = spin?
      • Predict nuclear spin (I)?
      • Magnetic dipole moment?
      • Gyromagnetic ratio (γ)?
      • "Spin" vs "Spin state"?
      • Energy splitting?
      • Fall to lowest state?
      • Quantum "reality"?
    • Precession >
      • Why precession?
      • Who was Larmor?
      • Energy for precession?
      • Chemical shift?
      • Net magnetization (M)?
      • Does M instantly appear?
      • Does M also precess?
      • Does precession = NMR?
    • Resonance >
      • MR vs MRI vs NMR?
      • Who discovered NMR?
      • How does B1 tip M?
      • Why at Larmor frequency?
      • What is flip angle?
      • Spins precess after 180°?
      • Phase coherence?
      • Release of RF energy?
      • Rotating frame?
      • Off-resonance?
      • Adiabatic excitation?
      • Adiabatic pulses?
    • Relaxation - Physics >
      • Bloch equations?
      • What is T1?
      • What is T2?
      • Relaxation rate vs time?
      • Why is T1 > T2?
      • T2 vs T2*?
      • Causes of Relaxation?
      • Dipole-dipole interactions?
      • Chemical Exchange?
      • Spin-Spin interactions?
      • Macromolecule effects?
      • Which H's produce signal?
      • "Invisible" protons?
      • Magnetization Transfer?
      • Bo effect on T1 & T2?
      • How to predict T1 & T2?
    • Relaxation - Clincial >
      • T1 bright? - fat
      • T1 bright? - other oils
      • T1 bright? - cholesterol
      • T1 bright? - calcifications
      • T1 bright? - meconium
      • T1 bright? - melanin
      • T1 bright? - protein/mucin
      • T1 bright? - myelin
      • Magic angle?
      • MT Imaging/Contrast?
  • …Pulse Sequences
    • MR Signals >
      • Origin of MR signal?
      • Free Induction Decay?
      • Gradient echo?
      • TR and TE?
      • Spin echo?
      • 90°-90° Hahn Echo?
      • Stimulated echoes?
      • STEs for imaging?
      • 4 or more RF-pulses?
      • Partial flip angles?
      • How is signal higher?
      • Optimal flip angle?
    • Spin Echo >
      • SE vs Multi-SE vs FSE?
      • Image contrast: TR/TE?
      • Opposite effects ↑T1 ↑T2?
      • Meaning of weighting?
      • Does SE correct for T2?
      • Effect of 180° on Mz?
      • Direction of 180° pulse?
    • Inversion Recovery >
      • What is IR?
      • Why use IR?
      • Phase-sensitive IR?
      • Why not PSIR always?
      • Choice of IR parameters?
      • TI to null a tissue?
      • STIR?
      • T1-FLAIR
      • T2-FLAIR?
      • IR-prepped sequences?
      • Double IR?
    • Gradient Echo >
      • GRE vs SE?
      • Multi-echo GRE?
      • Types of GRE sequences?
      • Commercial Acronyms?
      • Spoiling - what and how?
      • Spoiled-GRE parameters?
      • Spoiled for T1W only?
      • What is SSFP?
      • GRASS/FISP: how?
      • GRASS/FISP: parameters?
      • GRASS vs MPGR?
      • PSIF vs FISP?
      • True FISP/FIESTA?
      • FIESTA v FIESTA-C?
      • DESS?
      • MERGE/MEDIC?
      • GRASE?
      • MP-RAGE v MR2RAGE?
    • Susceptibility Imaging >
      • What is susceptibility (χ)?
      • What's wrong with GRE?
      • Making an SW image?
      • Phase of blood v Ca++?
      • Quantitative susceptibility?
    • Diffusion: Basic >
      • What is diffusion?
      • Iso-/Anisotropic diffusion?
      • "Apparent" diffusion?
      • Making a DW image?
      • What is the b-value?
      • b0 vs b50?
      • Trace vs ADC map?
      • Light/dark reversal?
      • T2 "shine through"?
      • Exponential ADC?
      • T2 "black-out"?
      • DWI bright causes?
    • Diffusion: Advanced >
      • Diffusion Tensor?
      • DTI (tensor imaging)?
      • Whole body DWI?
      • Readout-segmented DWI?
      • Small FOV DWI?
      • IVIM?
      • Diffusion Kurtosis?
    • Fat-Water Imaging >
      • Fat & Water properties?
      • F-W chemical shift?
      • In-phase/out-of-phase?
      • Best method?
      • Dixon method?
      • "Fat-sat" pulses?
      • Water excitation?
      • STIR?
      • SPIR?
      • SPAIR v SPIR?
      • SPIR/SPAIR v STIR?
  • …Making an Image
    • From Signals to Images >
      • Phase v frequency?
      • Angular frequency (ω)?
      • Signal squiggles?
      • Real v Imaginary?
      • Fourier Transform (FT)?
      • What are 2D- & 3D-FTs?
      • Who invented MRI?
      • How to locate signals?
    • Frequency Encoding >
      • Frequency encoding?
      • Receiver bandwidth?
      • Narrow bandwidth?
      • Slice-selective excitation?
      • SS gradient lobes?
      • Cross-talk?
      • Frequency encode all?
      • Mixing of slices?
      • Two slices at once?
      • Simultaneous Multi-Slice?
    • Phase Encoding >
      • Phase-encoding gradient?
      • Single PE step?
      • What is phase-encoding?
      • PE and FE together?
      • 2DFT reconstruction?
      • Choosing PE/FE direction?
    • Performing an MR Scan >
      • What are the steps?
      • Automatic prescan?
      • Routine shimming?
      • Coil tuning/matching?
      • Center frequency?
      • Transmitter gain?
      • Receiver gain?
      • Dummy cycles?
      • Where's my data?
      • MR Tech qualifications?
    • Image Quality Control >
      • Who regulates MRI?
      • Who accredits?
      • Mandatory accreditation?
      • Routine quality control?
      • MR phantoms?
      • Geometric accuracy?
      • Image uniformity?
      • Slice parameters?
      • Image resolution?
      • Signal-to-noise?
      • Ghosting?
  • …K-space & Rapid Imaging
    • K-space (Basic) >
      • What is k-space?
      • Parts of k-space?
      • What does "k" stand for?
      • Spatial frequencies?
      • Locations in k-space?
      • Data for k-space?
      • Why signal ↔ k-space?
      • Spin-warp imaging?
      • Big spot in middle?
      • K-space trajectories?
      • Radial sampling?
    • K-space (Advanced) >
      • K-space grid?
      • Negative frequencies?
      • Field-of-view (FOV)
      • Rectangular FOV?
      • Partial Fourier?
      • Phase symmetry?
      • Read symmetry?
      • Why not use both?
      • ZIP?
    • Rapid Imaging (FSE &EPI) >
      • What is FSE/TSE?
      • FSE parameters?
      • Bright Fat?
      • Other FSE differences?
      • Dual-echo FSE?
      • Driven equilibrium?
      • Reduced flip angle FSE?
      • Hyperechoes?
      • SPACE/CUBE/VISTA?
      • Echo-planar imaging?
      • HASTE/SS-FSE?
    • Parallel Imaging (PI) >
      • What is PI?
      • How is PI different?
      • PI coils and sequences?
      • Why and when to use?
      • Two types of PI?
      • SENSE/ASSET?
      • GRAPPA/ARC?
      • CAIPIRINHA?
      • Compressed sensing?
      • Noise in PI?
      • Artifacts in PI?
  • …Contrast Agents
    • Contrast Agents: Physics >
      • Why Gadolinium?
      • Paramagnetic relaxation?
      • What is relaxivity?
      • Why does Gd shorten T1?
      • Does Gd affect T2?
      • Gd & field strength?
      • Best T1-pulse sequence?
      • Triple dose and MT?
      • Dynamic CE imaging?
      • Gadolinium on CT?
    • Contrast Agents: Clinical >
      • So many Gd agents!
      • Important properties?
      • Ionic v non-ionic?
      • Intra-articular/thecal Gd?
      • Gd liver agents (Eovist)?
      • Mn agents (Teslascan)?
      • Feridex & Liver Agents?
      • Lymph node agents?
      • Ferumoxytol?
      • Blood pool (Ablavar)?
      • Bowel contrast agents?
    • Contrast Agents: Safety >
      • Gadolinium safety?
      • Allergic reactions?
      • Renal toxicity?
      • What is NSF?
      • NSF by agent?
      • Informed consent for Gd?
      • Gd protocol?
      • Is Gd safe in infants?
      • Reduced dose in infants?
      • Gd in breast milk?
      • Gd in pregnancy?
      • Gd accumulation?
      • Gd deposition disease?
  • …Cardiovascular and MRA
    • Flow effects in MRI >
      • Defining flow?
      • Expected velocities?
      • Laminar v turbulent?
      • Predicting MR of flow?
      • Time-of-flight effects?
      • Spin phase effects?
      • Flow void?
      • Why GRE ↑ flow signal?
      • Slow flow v thrombus?
      • Even-echo rephasing?
      • Flow-compensation?
      • Flow misregistration?
    • MR Angiography - I >
      • MRA methods?
      • Dark vs bright blood?
      • Time-of-Flight (TOF) MRA?
      • 2D vs 3D MRA?
      • MRA parameters?
      • Magnetization Transfer?
      • Ramped flip angle?
      • MOTSA?
      • Fat-suppressed MRA?
      • TOF MRA Artifacts?
      • Phase-contrast MRA?
      • What is VENC?
      • Measuring flow?
      • 4D Flow Imaging?
      • How accurate?
    • MR Angiography - II >
      • Gated 3D FSE MRA?
      • 3D FSE MRA parameters?
      • SSFP MRA?
      • Inflow-enhanced SSFP?
      • MRA with ASL?
      • Other MRA methods?
      • Contrast-enhanced MRA?
      • Timing the bolus?
      • View ordering in MRA?
      • Bolus chasing?
      • TRICKS or TWIST?
      • CE-MRA artifacts?
    • Cardiac I - Intro/Anatomy >
      • Cardiac protocols?
      • Patient prep?
      • EKG problems?
      • Magnet changes EKG?
      • Gating v triggering?
      • Gating parameters?
      • Heart navigators?
      • Dark blood/Double IR?
      • Why not single IR?
      • Triple IR?
      • Polar plots?
      • Coronary artery MRA?
    • Cardiac II - Function >
      • Beating heart movies?
      • Cine parameters?
      • Real-time cine?
      • Ventricular function?
      • Tagging/SPAMM?
      • Perfusion: why and how?
      • 1st pass perfusion?
      • Quantifying perfusion?
      • Dark rim artifact
    • Cardiac III - Viability >
      • Gd enhancement?
      • TI to null myocardium?
      • PS (phase-sensitive) IR?
      • Wideband LGE?
      • T1 mapping?
      • Iron/T2*-mapping?
      • Edema/T2-mapping?
      • Why/how stress test?
      • Stess drugs/agents?
      • Stress consent form?
  • …MR Artifacts
    • Tissue-related artifacts >
      • Chemical shift artifact?
      • Chemical shift in phase?
      • Reducing chemical shift?
      • Chemical Shift 2nd Kind?
      • In-phase/out-of phase?
      • IR bounce point?
      • Susceptibility artifact?
      • Metal suppression?
      • Dielectric effect?
      • Dielectric Pads?
    • Motion-related artifacts >
      • Why discrete ghosts?
      • Motion artifact direction?
      • Reducing motion artifacts?
      • Saturation pulses?
      • Gating methods?
      • Respiratory comp?
      • Navigator echoes?
      • PROPELLER/BLADE?
    • Technique-related artifacts >
      • Partial volume effects?
      • Slice overlap?
      • Aliasing?
      • Wrap-around artifact?
      • Eliminate wrap-around?
      • Phase oversampling?
      • Frequency wrap-around?
      • Spiral/radial artifacts?
      • Gibbs artifact?
      • Nyquist (N/2) ghosts?
      • Zipper artifact?
      • Data artifacts?
      • Surface coil flare?
      • MRA Artifacts (TOF)?
      • MRA artifacts (CE)?
  • …Functional Imaging
    • Perfusion I: Intro & DSC >
      • Measuring perfusion?
      • Meaning of CBF, MTT etc?
      • DSC v DCE v ASL?
      • How to perform DSC?
      • Bolus Gd effect?
      • T1 effects on DSC?
      • DSC recirculation?
      • DSC curve analysis?
      • DSC signal v [Gd]
      • Arterial input (AIF)?
      • Quantitative DSC?
    • Perfusion II: DCE >
      • What is DCE?
      • How is DCE performed?
      • How is DCE analyzed?
      • Breast DCE?
      • DCE signal v [Gd]
      • DCE tissue parmeters?
      • Parameters to images?
      • K-trans = permeability?
      • Utility of DCE?
    • Perfusion III: ASL >
      • What is ASL?
      • ASL methods overview?
      • CASL?
      • PASL?
      • pCASL?
      • ASL parameters?
      • ASL artifacts?
      • Gadolinium and ASL?
      • Vascular color maps?
      • Quantifying flow?
    • Functional MRI/BOLD - I >
      • Who invented fMRI?
      • How does fMRI work?
      • BOLD contrast?
      • Why does BOLD ↑ signal?
      • Does BOLD=brain activity?
      • BOLD pulse sequences?
      • fMRI Paradigm design?
      • Why "on-off" comparison?
      • Motor paradigms?
      • Visual?
      • Language?
    • Functional MRI/BOLD - II >
      • Process/analyze fMRI?
      • Best fMRI software?
      • Data pre-processing?
      • Registration/normalization?
      • fMRI statistical analysis?
      • General Linear Model?
      • Activation "blobs"?
      • False activation?
      • Resting state fMRI?
      • Analyze RS-fMRI?
      • Network/Graphs?
      • fMRI at 7T?
      • Mind reading/Lie detector?
      • fMRI critique?
  • …MR Spectroscopy
    • MRS I - Basics >
      • MRI vs MRS?
      • Spectra vs images?
      • Chemical shift (δ)?
      • Measuring δ?
      • Backward δ scale?
      • Predicting δ?
      • Size/shapes of peaks?
      • Splitting of peaks?
      • Localization methods?
      • Single v multi-voxel?
      • PRESS?
      • STEAM?
      • ISIS?
      • CSI?
    • MRS II - Clinical ¹H MRS >
      • How-to: brain MRS?
      • Water suppression?
      • Fat suppression?
      • Normal brain spectra?
      • Choice of TR/TE/etc?
      • Hunter's angle?
      • Lactate inversion?
      • Metabolite mapping?
      • Metabolite quantitation?
      • Breast MRS?
      • Gd effect on MRS?
      • How-to: prostate MRS?
      • Prostate spectra?
      • Muscle ¹H-MRS?
      • Liver ¹H-MRS?
      • MRS artifacts?
    • MRS III - Multi-nuclear >
      • Other nuclei?
      • Why phosphorus?
      • How-to: ³¹P MRS
      • Normal ³¹P spectra?
      • Organ differences?
      • ³¹P measurements?
      • Decoupling?
      • NOE?
      • Carbon MRS?
      • Sodium imaging?
      • Xenon imaging?
  • ...Artificial Intelligence
    • AI Part I: Basics >
      • Artificial Intelligence (AI)?
      • What is a neural network?
      • Machine Learning (ML)?
      • Shallow v Deep ML?
      • Shallow networks?
      • Deep network types?
      • Data prep and fitting?
      • Back-Propagation?
      • DL 'Playground'?
    • AI Part 2: Advanced >
      • What is convolution?
      • Convolutional Network?
      • Softmax?
      • Upsampling?
      • Limitations/Problems of AI?
      • Is the Singularity near?
    • AI Part 3: Image processing >
      • AI in clinical MRI?
      • Super-resolution?
  • ...Tissue Properties Imaging
    • MRI of Hemorrhage >
      • Hematoma overview?
      • Types of Hemoglobin?
      • Hyperacute/Oxy-Hb?
      • Acute/Deoxy-Hb?
      • Subacute/Met-Hb?
      • Deoxy-Hb v Met-Hb?
      • Extracellular met-Hb?
      • Chronic hematomas?
      • Hemichromes?
      • Ferritin/Hemosiderin?
      • Subarachnoid blood?
      • Blood at lower fields?
    • T2 cartilage mapping
    • MR Elastography?
    • Synthetic MRI?
    • Amide Proton Transfer?
    • MR thermography?
    • Electric Properties Imaging?
  • Copyright/Legal
    • Copyright Issues
    • Legal Disclaimers
  • Forums/Blogs/Links
  • What's New
  • Self-test Quizzes - NEW!
    • Magnets & Scanners Quiz
    • Safety & Screening Quiz
    • NMR Phenomenon Quiz
    • Pulse Sequences Quiz
    • Making an Image Quiz
    • K-space & Rapid Quiz
    • Contrast & Blood Quiz
    • Cardiovascular & MRA Quiz

Quantifying Flow

How are ASL methods able to quantify blood flow?  
Picture
Like perfusion metrics obtained other MR methods, quantification of blood flow by ASL is highly desirable but difficult to achieve. The signal intensity difference data (ΔS = Scontrol − Sinversion) provides perfusion-weighted images only. Translating this raw data into absolute blood flow measurements requires three steps: 1) image processing and filtering to remove artifacts; 2) acquisition of a separate proton density (PD) or T1 image map for scaling signal intensities; and 3) fitting of data to a mathematical model to calculate blood flow on a pixel-by-pixel basis. 
Image Processing and Filtering
Before attempting to quantify blood flow, raw data from an ASL study must be "cleaned" up as much as possible. Some degree of patient movement commonly occurs between the tagging and control acquisitions, and so rigid-body motion correction techniques are typically applied with co-registration and "de-noising" using a Gaussian smoothing filter. Segmented gray matter and white matter images may be generated and processed separately to minimize partial volume effects.
More severe and random errors (such as the gradient malfunction shown right) may be identified by outlier analysis, where differences between control and tagged data are discarded when exceeding certain predefined thresholds. Oval "masks" are commonly generated to exclude out-of-brain voxels. Statistical techniques using independent component analysis may be applied to further reduce noise. 
Picture
Temporary gradient malfunction corrupts ASL raw data image
Picture
Corrected by excluding affected data during postprocessing
Calibration Images for Scaling
PicturePD calibration image
For quantification of blood flow, arbitrary ASL signal intensities of perfusion-weighted images must be scaled to M0b, the equilibrium magnetization of arterial blood. In theory, M0b could be measured from a pure arterial voxel, but this is not practical because of the small size of such vessels and associated partial volume effects. Instead, M0b is usually calculated indirectly by measuring the equilibrium magnetization of brain or CSF from a separately acquired proton-density (PD) weighted image. The PD data is converted to M0b using corrections for TR, tissue T1, and the blood-brain partition coefficient (λ).     

Mathematical Modeling and Data Fitting
The final step is to fit the filtered and calibrated ASL data to a mathematical model, computing quantitative blood flow measurements on a voxel-by-voxel basis. The most widely used is Buxton's general kinetic model, a single-compartment, plug-flow model whose parameters are estimated using a linear systems approach and deconvolution similar to those described for DSC imaging in a prior Q&A. 
The final equations for calculating blood flow (F) depend on multiple measured and estimated parameters as well as the precise ASL pulse sequence employed. Just to give the reader a taste of the complexity, here is the equation currently used on GE systems for their 3D pCASL technique based on the work of Alsop et al:  
Picture
The individual terms include: the factor 6000 (to convert units into mL/min/100 g tissue); λ, the blood-tissue partition coefficient (commonly assumed to be 0.9 for brain); TRPD, the repetition time of the saturation recovery proton density calibration sequence; T1T and T1b, the relaxation times of tissue and blood (commonly assumed to be 1.2 sec and 1.6 sec at 3.0T, respectively); SIcont, SIinv, and SIPD, the signal intensities of corresponding control, labeled/inverted, and proton density weighted pixels; PLD, the post labeling delay time between the end of the pCASL inversion component and image acquisition; LT, the labeling time, or duration of the pCASL inversion; α, the labeling efficiency of the pCASL inversion (typically assumed to be 0.8); σ, the suppression efficiency of the background saturation pulses (typically assumed to be about 0.75); KSF, a scaling factor for the perfusion-weighted sequence; and NEXPW, the number of excitations (signals averaged) for the ASL sequence. 
The purpose of providing this equation is not to bewilder the reader, but to illustrate the multiple parameters that must be either assumed or estimated to calculate true blood flows from ASL data. A small error or variance in any of these parameters could easily alter the final calculation by 30% or more. Scaling factors can be empirically adjusted to keep calculated blood flows within expected physiological ranges, but I caution users to maintain a healthy skepticism about accuracy of values so obtained. Like other MR perfusion methods, ASL blood flow measurements remain most useful in a qualitative sense, comparing corresponding regions of the brain (or other organs) relative to one another.

Advanced Discussion (show/hide)»

In their original description of CASL in 1992, Williams et al. laid the foundation for quantitative analysis of ASL by modifying the Bloch equations to account for exchange between longitudinal tissue magnetization (MT) and the magnetization of labeled blood.
Picture

Here F is the blood flow rate, T1 is the longitudinal relaxation time of tissue in the absence of flow or exchange, MT0 is the tissue magnetization under fully relaxed conditions, and Ma and Mv are the time-dependent arterial and venous longitudinal magnetizations respectively.

Assuming the blood-tissue interaction occurs in a single, well-mixed compartment, the magnetization of venous blood exiting the system Mv = MT/λ, where λ is known as the blood-tissue partition coefficient, the fraction of labeled arterial water extracted during passage through the tissue. For brain, the value of λ is generally taken to be about 0.9, an average of gray and white matter obtained from [15O]water-labeled PET studies.

With continuous and complete inversion of arterial spins, the subsequent sampling of MT results in an exponential decrease in MT with an apparent time constant T1app, given by

Picture
and an expression for blood flow (F) can be derived from experimentally measurable quantities
Picture
where Mcont and Minv  are the signal magnitudes of tissue in the control and inverted (tagged) states respectively. Although T1app  is a function of F it can be measured separately/independently, usually by a T1 mapping or estimation procedure.
In 1998 Buxton et al proposed a more sophisticated method, known as the general kinetic model, some version of which remains the most widely used model for ASL analysis. The Buxton analysis is uses a linear systems approach similar to that described for DSC imaging. Before proceeding, the reader is advised to quickly review DSC linear systems analysis summarized in this prior Q&A. 
The basic result of the Buxton method, applicable to both continuous and pulsed ASL techniques, is summarized by the following equation:
Picture
Here ΔM(t) represents the difference in tissue magnetization between the control and labeled states and M0b is the equilibrium magnetization of blood before labeling. The term α is called the labeling efficiency (the fraction of flowing spins inverted, typically 80-95% depending on the ASL method). The factor "2" arises because the spins have been inverted so their change in magnetization between control and labeled states is M0b − (−M0b) = 2M0b. The symbol F represents blood flow, the desired parameter to be measured.
The integral expresses the principle of convolution, a fundamental mathematical method for analyzing linear systems. The first term in the integral, a(τ), is an arterial input function, called by Buxton the tissue delivery function, represents the normalized concentration of labeled magnetization arriving in a voxel of tissue at time (τ) during image readout. R(τ) is known as the residue function, a dimensionless variable similar to that used in DSC imaging, representing the fraction of labeled water molecules still remaining in the imaged voxel at time (τ). A new term not found in DSC but required for ASL analysis is m(τ), the magnetization relaxation function, the fraction of the original inverted magnetization that remains at time (τ).

Several assumptions are implicit in the Buxton model, any of which may be rightfully challenged in part:

  1. Perfect "plug" flow. The labeled magnetization enters as a perfect rectangular bolus with sharp leading and trailing edges. The arterial input function, a(t), is therefore zero except during passage of the bolus, where it takes the form a(t) = αe−t/T1b, where T1b is the relaxation time of blood.  (In real life such a perfect rectangular spin-labeling profile is difficult to achieve, even with techniques like QUIPSS to improve edge definition of the bolus. Having a range of transit times leads to underestimation of blood flow.)
  2. Single compartment kinetics. All labeled water flowing into a voxel instantaneously exchanges into the tissue, a "well-mixed" condition. (However, some labeled spins remain in vessels before being exchanged while others flow out of the imaged slice without exchanging. Both effects lead to an underestimation of perfusion). The true extraction fraction (λ) needs to be measured or estimated, which for human brain tissue at normal flow rates is about 0.9. The usual form of the residue function in the Buxton model is given by R(t) = e−Ft/λ.
  3. Magnetization decay rate reflects tissue T1. As a consequence of assumptions 1 & 2 above, the magnetization relaxation function is assumed to have the form m(t) = e−t/T1t, where T1t is the tissue T1. (Because it ignores flow-though, magnetization transfer effects, and imperfect mixing, this assumption leads to in an overestimation of perfusion).
To overcome these limitations of the Buxton model, more sophisticated analyses have been developed. These include: 1) describing the arterial input as a function with rounder, smoother leading and trailing edges; 2) using a two-compartment model with vascular and tissue components, similar to the Tofts' model for DCE imaging; 3) segmenting gray and white matter data and applying different values for tissue T1 and λ, and 4) changing the magnetization decay function to reflect an initial vascular phase before tissue water exchange occurs. Multi-TI ASL acquisition methods also hold promise to better estimate bolus arrival times and relaxation properties of blood and tissue.


References
     Alsop DC, Detre JA, Gola X, et al. Recommended implementation of arterial spin-labeled
perfusion MRI for clinical applications: A consensus of the ISMRM perfusion study group and the European consortium for ASL in dementia
. Magn Reson Med 2015; 73:102-116.
     Buxton RB, Frank LR, Wong EC, et al. A general kinetic model for quantitative perfusion imaging with arterial spin labeling. Magn Reson Med 1998; 40:383-396.
    Herscovitch P, Raichle ME. What is the correct value for the brain-blood partition coefficient for water? J Cereb Blood Flow Metab 1985; 5:65-69. (Answer: probably about 0.90 ml/g) 
    Mutsaerts HJMM, Steketee RME, Heijtel DFR, et al. Inter-vendor reproducibility of pseudo-continuous arterial spin labeling at 3 Tesla. PLOS One 2014; 9(8):e104108.     
     Petersen ET, Lim T, Golay X. Model-free arterial spin labeling quantification: approach for perfusion MRI. Magn Reson Med 2006; 55:219-232. (QUASAR method) 
     Petersen ET, Zimine I, Ho Y-C L, Golay X. Non-invasive measurement of perfusion: a critical review of arterial spin labelling techniques. Br J Radiol 2006; 79:688-701. 
     Pinto J, Chappell MA, Okell TW, et al. Calibration of arterial spin labeling data — potential pitfalls in post-processing. Magn Reson Med 2020; 83:1222-1234.
     Wang Z. Arterial spin labeling perfusion MRI signal processing toolbox (ASLtbx). Version 1, May 2012. (manual for a freely available MATLAB-based toolbox for processing ASL data).
     Williams DS, Detre JA, Leigh JS, Koretsky AP. Magnetic resonance imaging of perfusion using spin inversion of arterial water. Proc Natl Acad Sci USA 1992; 89:212-216. (derives modified Bloch equations to account for inflow of inverted spins)
     Wong EC. Quantifying CBF with pulsed ASL: technical and pulse sequence factors. J Magn Reson Imaging 2005; 22:727-731.

Related Questions
     How is the arterial input function used to extract more quantitative flow information from the DSC data?
     How should imaging parameters be chosen to optimize an ASL acquisition?  

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