Principles of the MRI Signal Contrast Mechanisms MR Image Formation John VanMeter, Ph.D. Center for Functional and Molecular Imaging Georgetown University Medical Center

Outline Physics behind MRI Basis of the MRI signal Tissue Contrast Examples Spatial Localization

Properties of Electrical Fields N S +-+- N S

Properties of Magnetic Fields N S

N S + spinning proton bar magnet Hydrogen protons spin producing a magnetic field A magnetic field creates an electrical charge when it rotates past a coil of wire Magnetic Resonance Imaging

Similarity between a proton and a bar magnet

net magnetic moment is zero Randomly oriented protons B o net magnetic moment is positive Protons aligned with a strong magnetic field MoMo

N S The MRI Measurement +

B o Effect of Static Field on Protons

Net magnetization

Precession in Magnetic Field

The Zeeman effect

BoBo

Head Coil (Birdcage)

Spin Excitation Tipping Protons into the Imaging Plane

90 o pulse

90 o Radiofrequency Pulse used to “tip” protons into X-Y plane. x y z Flip Angle - Degree of Deflection from Z-axis

Following an RF pulse the protons precess in the x-y plane B o M o Magnetic Moment Measurable After RF Pulse

The MRI Measurement (Up to this point) In the presence of the static magnetic field –Protons align with the field –Protons precess about the magnetic Briefly turn on RF pulse –Provides energy to tip the protons at least partially into the imaging plane What happens to the protons next?

Types of Relaxation Longitudinal – precessing protons are pulled back into alignment with main magnetic field of the scanner (B o ) reducing size of the magnetic moment vector in the x-y plane Transverse – precessing protons become out of phase leading to a drop in the net magnetic moment vector (M o ) Transverse relaxation occurs much faster than Longitudinal relaxation Tissue contrast is determined by differences in these two types of relaxation

Longitudinal Relaxation in 3D

Free Induction Decay x y z 90 o Longitudinal Relaxation in 2D

Transverse Relaxation Wait time TE after excitation before measuring M when the shorter T2 spins have dephased. x y z x y z x y z vector sum initiallyat t= TE

Transverse Relaxation M o B o

M o B o

M o B o

T 1 and T 2 relaxation

The MRI Measurement (Sans Spatial Localization) RF time Voltage (Signal) time MoMo t x y z x y z x y z M o 90° V(t) BoBo Mo

Main Tissue Contrast Controls Echo Time (TE) – time after 90 o RF pulse until readout. Determines how much transverse relaxation will occur before reading one row of the image. Repetition Time (TR) – time between successive 90 o RF pulses. Determines how much longitudinal relaxation will occur before constructing the next row of the image.

T1 Curve T2 Curve Intensity Time Tissue Contrast Every tissue has a different affect on longitudinal (T1) and transverse (T2) relaxation.

TR (milliseconds) Signal gray matter T1 = 1000 CSF T1 = 3000 white matter T1 = 600 Contrast in MRI: T1-Weighting

Optimizing TR Value for T 1 Contrast

Effect of Varying TR

T1-Weighting CSF dark WM bright GM gray

TE (milliseconds) 5010 Contrast in MRI: T2-Weighting

Optimizing TE Value for T 2 Contrast

Effect of Varying TE

T2-Weighting CSF (fluid) bright GM gray WM dark

Contrast in MRI: Proton Density Tissue with most protons has highest signal and is thus brightest in the image Proton Density Weighted aka PDW

Summarizing Contrast Two main “knobs”: –TR controls T1 weighting –TE controls T2 weighting Longitudinal relaxation determines T1 contrast Transverse relaxation determines T2 contrast

But Wait How do you set TE to generate a T1 weighted image? How do you set TR to generate a T2 weighted image? How do you set TR & TE to generate a proton density weighted image?

Mixing T1 & T2 Contrast What do you get if you use the optimal TR setting for T1 contrast and the optimal TE setting for T2 contrast? T3 contrast? No contrast!!

Tissue Contrast Dependence on TR, TE TR Long Short Long TE PDW T1 poor! T2 (time in 10’s of ms) ( time in 1000’s of ms )

Damadian’s Discovery Differential longitudinal relaxation between healthy and tumorous tissue in the rat Walker sarcoma had longer T1 relaxation time than healthy brain Novikoff Hepatoma had shorter T2 relaxation time than healthy liver

Two Main Classes of Pulse Sequence Spin Echo (SE) - uses a second RF- pulse to refocus spins –TR & TE control T1 and T2 contrast Gradient Echo (GE) - uses a gradient to refocus spins –Flip Angle & TE control T1 and T2* contrast –Used in EPI (fMRI) sequences

T2*-Weighting (GE) Refer to T2-weighting in a gradient echo sequence as T2*-weighting Because of inhomogeneities in the B 0 magnetic field T2 relaxation occurs faster using a gradient echo sequence than ‘true T2 relaxation’ as measured with a spin-echo sequence The greater the inhomogeneity the faster T2 decay occurs

T2*-Weighting (GE) vs T2-Weighting (SE)

T2* Effect Well shimmed Poorly shimmed

T2-WeightedT1-WeightedPD-Weighted Venous Infarct

Glioblastoma Multiforme T2-Weighted T1-Weighted

Cerebral Lymphoma T2-Weighted T1-Weighted

Anaplastic Astrocytoma T2-Weighted T1-Weighted

Multiple Sclerosis

The MRI Experiment x y z RF time x y z Voltage (Signal) time MoMo t x y z M o 90° V(t) BoBo Mo

The MRI Sequence (Sans Spatial Localization) 1)Equilibrium (magnetization points along Bo) 2)RF Excitation (tip magnetization away from equilibrium) 3)Precession produces signal, dephasing starts 4)Readout signal from precession of the magnetization vector (TE) 5)Return to equilibrium and reapply RF Excitation ( TR )

Spatial Localization Gradients, linear change in magnetic field, will provide additional information needed to localize signal Makes imaging possible/practical –Remember the Indomitable? –Couldn’t spatially localize MRI signal instead moved subject to get each voxel Nobel prize awarded for this idea!

Larmor Equation Frequency (rate) of precession is proportional to the strength of magnetic field   =  * B

Dissecting Larmor Equation  =  * B Gyromagnetic Constant Rate of precession Magnetic field

Center Frequency Center frequency is the frequency (i.e. rate) at which protons spin (precess) with just the static magnetic field If the center frequency of a 1.5T scanner is 63MHz what it the center frequency of our 3.0T scanner?

Center Frequency  B 63MHzIf B = 1.5T 2 * 63MHzIf B = 3.0T 126MHz

Gradients A gradient is simply a deliberate change in the magnetic field Gradients are used in MRI to linearly modify the magnetic field from one point in space to another Gradients are applied along an axis (i.e. G x along the x-axis, G y along the y-axis, G z along the z-axis) What happens to the frequency at which the precess when we turn on a gradient?

 B B= B 0 + B 1 +r0-r Effect of Gradient on Rate of Precession

Effect of a Gradient

From Proton Signal to Pixel Intensities Amplitude of the sinusoidal wave at a pixel used to determine the brightness of the pixel (i.e. color)

Net Signal at Coil Signal from Multiple Pixels Pixel 1. Pixel n +

Decomposing Received Signal Left unchanged the signal received cannot be broken down by location of individual pixels Need method for efficiently pulling out the signal from many pixels at once Gradients used to relate where a particular signal is coming from

Frequency Encoding Use a gradient to modify the rate at which the protons spin based on location of the proton Requires the gradient to remain on

Prior to Gradient Col 1 Col 2 Col 3 Uniform Field

Gradient Applied Col 1 Col 2 Col 3 Lower Field Higher Field

Frequency Encoding Apply gradient in one direction and leave it on Result:  Protons that experience a decrease in the net magnetic field precess slower  Protons that experience an increase in the net magnetic field precess faster

Side-Effect of Gradient Gradient also causes phase of the protons to change Application of a second gradient of opposite polarity will undo this

Frequency Encode Gradient The area under the second gradient must be equal to that of the first gradient

Phase Encoding Turn gradient on briefly then turn it off Turning on the gradient will cause some protons to spin faster others to spin slower depending on where they are located Turning off the gradient will make them all spin at the same rate again BUT they will be out of ‘phase’ with one another based on where they are located

Phase Encoding

Prior to Gradient Row 1 Row 2 Row 3 Uniform Field

Gradient Applied Row 1 Row 2 Row 3 Lower Field Higher Field

Gradient Turned Off Row 1 Row 2 Row 3 Uniform Field

Phase Encoding Apply gradient in one direction briefly and then turn off Result:  Protons initially decrease or increase their rate of precession  After the gradient is turned off all of the protons will again precess at the same rate  Difference is that they will be out phase with one another

Combining Phase & Frequency Encoding Row 1, Col 1 Row 2, Col 2 Row 3, Col 3

Sum Corresponds to Received Signal ++++ Row 1, Col 1 Row 2, Col 2 Row 3, Col 3

Converting Received Signal into an Image Signal produced using both frequency and phase encoding can be decomposed using a mathematical technique called the Inverse Fourier Transform Result is the signal (sinusoidal squiggles) produced at each individual pixel

From Signal to Image Row 1, Col 1 Row 2, Col 2 Row 3, Col 3 Inv FFT Pixels

Lauterbur’s Insight Use of gradients to provide spatial encoding Frequency and Phase - was Lauterbur’s contribution Awarded Nobel prize for this work

Pseudo Time k-space

Components of Frequency Domain Three components to a signal in the frequency domain: –Amplitudecomes from contrast –Frequencyrate at which protons spin –Phasedirection of proton’s spin Inverse Fourier Transform (IFT) is a mathematical tool for converting data from frequency domain to ‘image’ domain

k-space Frequency increases from the center out in all directions Phase varies by angle

Images From k-space K-space is turned into an image using a Fourier Transformation 2D-IFT

Center of k-space 2D-IFT

Everything Else 2D-IFT

Full Frequency – Half Phase 2D-IFT

Selecting a Slice Again use gradient to modify frequency of the proton’s spin Slice select gradient is positive on one side of the slice and negative on the other side At the desired slice location the slice select gradient is zero Thus, protons in this slice and only this slice will be spinning at the center frequency of the scanner! If this gradient is on when we apply RF pulse only protons in the slice will be tipped into x- y plane and thus measurable

Slice Select Gradient

Slice Thickness vs Gradient Strength

Slice Orientation

Mansfield’s Contribution Slice selection was Mansfield’s major contribution to MRI Awarded Nobel prize for this work

Putting it All Together Basic Pulse Sequence Diagram

EPI pulse sequence and k- space trajectory

Signal loss due to susceptibility artifacts in GRE EPI images

Magnetic Susceptibility Greater on T2* than T2 Images Oxygenated Hemoglobin Deoxygenated Hemoglobin Spin Gradient Echo (T2)Echo (T2*)

Effects of field variation upon EPI images

Spiral imaging

Susceptibility artifacts in spiral images

Effects of field variation on spiral images

Acquisition Matrix Size 64 x 64 Matrix Isotropic (square) Relative SNR = 1 64 x 128 Matrix Anisotropic (oblong) Relative SNR = x 128 Matrix Isotropic (square) Relative SNR = 0.25

Signal to Noise Ratio Spatial Resolution Temporal Resolution MRI Image Acquisition Constraints