Pulse sequences
Pulse sequences
• A set of RF and gradient pulses applied to a sample to produce a specific form of NMR signal is called a pulse sequence.
• A pulse sequence timing diagram is a multiple axis plot of some aspect of a pulse sequence versus time.
Pulse sequences
• For each line phase encode, the entire pulse sequence is repeated with the phase encoding gradient amplitude incremented. For a 256 x 256 digital MR image, the sequence must be repeated 256 times.
• The time between subsequent 90o pulses is called the repetition time (TR).
TR TR
The spin-echo
• Here we introduce the concept of spin-echo.
• Here a 90o pulse is first applied to the spin system, which rotates the magnetization down into the x – y plane.
• The transverse magnetization begins to dephase.
• At some point in time after the 90o pulse, a 180o pulse is applied along the –x-axis. This pulse rotates the magnetization by 180o about the x axis.
Movie_1
The spin-echo
• The 180o pulse causes the magnetization to at least partially rephase and to produce a signal called an echo.
TE
• The signal equation for a repeated spin echo sequence as a function of the repetition time (TR), and the echo time (TE) defined as the time between the 90o pulse and the maximum amplitude in the echo is:
12 S=kρ(1−e−TR/T )e−TE/T
TR is the duration in seconds of one measurement (i.e. one phase encode)
The spin-echo
•The other alternative is to apply the 180o pulse along the y-axis, which effectively rotates the magnetic moments around the y-axis.
• This practically yields the same echo result.
Movie_2
The spin-echo pulse sequence
• A pulse sequence timing diagram of a typical spin echo imaging sequence is shown below. It is absolutely true that a picture is worth a thousand words in this case.
The spin-echo pulse sequence
• The echo time (TE) for this pulse sequence is twice the timing between the first and second pulse.
• The data acquisition is timed so that it is centred on the echo time. As you can see from the diagram, the frequency encoding gradient is on at the same time.
• Phase encoding is indicated by a sectioned rectangle in this case.
• It can be performed at anytime in the pulse sequence after the RF pulse that provides the time origin of the sequence but before the data acquisition. It should not be performed during an RF pulse either.
• We could move the phase encoding for the sequence shown above to the right of the 180o pulse.
• In order to perform slice selection, we must have a gradient on during the RF pulse. As shown in the above diagram, slice selection is being performed on both the 90o and 180o pulse.
Pulse sequence and k-space trajectory
Description of the previous pulse diagram (for your own reading)
The gradients cause motion through k-space. This follows from the definition of kx and ky: kx =γGxt ky =γGyT =γngyT
The value of kx or ky is proportional to the integral of the amplitude of the respective gradient over the time it is applied. Let us explore the pulse sequence diagram shown in the previous slide and determine the k- space trajectory for the largest negative phase encoding gradient. We will ignore the slice selection gradient. This is correct to do since from the point of phase origin of the magnetization, the centre of the 90o RF pulse, the area of the positive and negative gradients along the slice selection gradient sum to zero. Thus, there is no net motion in k-space along the slice direction. (The slice selection direction in k-space would be perpendicular to the frequency and phase plane.) After the 90o RF pulse, the origin in k-space is at the (0,0) point in k-space, location 1. This is true since no gradients have been applied and only gradients can cause movement in k-space. Then a gradient is turned on positively in the frequency direction.
The area of this gradient is sufficient to move us to some point to the right of the (0,0) point, location 2. A negative phase encoding gradient of (N-1)/2 gy T is applied. This moves the position in k-space to the lower right corner, location 3. The 180o pulse flips our position to the lower left-hand corner, location 4. This is a result of the magical property of the 180o pulse to change the phase difference between the spins. Then the frequency encoding gradient moves the magnetization across k-space from negative to positive in the horizontal direction, location 4-6. Location 5 is made to correspond with the spin echo that occurs from the two RF pulses and is the centre of k-space in the frequency encoding direction. We usually sample the MR signal symmetrically around this point. Our FOV in this direction will be determined by how finely we sample in this direction.
The repetition time (TR)
• For each line encode, the entire pulse sequence is repeated. For N phase encodes, the same sequence is repeated N times (typically N = 128, 256 or 512) whereby the amplitude of the phase encoding gradient is increased from -(N-1)/2 gy to +(N/2) gy in increments of ngy.
TR TR
TR
The echo-planar imaging sequence (EPI)
The echo-planar imaging sequence (EPI)
• Previous slide shows the trajectory through k-space of a fast imaging sequence capable of traversing all of k-space following a single 90o pulse.
• The entire trajectory can be obtained in less than 200 ms. This is called echo planar imaging (EPI) and was described by Sir. Peter Mansfield very early in the history of MRI.
• Unfortunately, this sequence places very stringent requirements on the gradient coil system.
• Only recent hardware is capable of performing this imaging sequence. Acoustics during the EPI sequence
Play ‘epi-accoustics.wav’
Origins of contrast in MR images
• Contrast is the difference in image intensity that reflect some property that we are imaging.
• In order to see different tissues, the tissues themselves must have differences in the property that we are imaging. For instance, in CT we measure differences in attenuation of x-rays. As we noted before, MRI looks at protons in the tissue. In fact, one source of contrast in MR images in the density of protons in the tissue.
• However, MR is a richer imaging modality than that. Other properties of the tissue are able to cause differences in image intensity of tissue. Some of these properties are listed below:
• Density of protons
• T1 relaxation – longitudinal relaxation • T2 relaxation – transverse relaxation
• Flow
• Magnetization transfer
• and others
Contrast in MR images
•Image contrast is achieved through a combination of proton density and the relaxation properties of the different tissue types.
Right: MR images of the same brain:
(a) T1-weighted image;
(b) also T1-weighted but with a T1 contrast
agent on board;
(c) T2 – weighted image.
(d) T2- weighted image acquired with the Flair
pulse sequence designed to attenuate the signal from cerebral spinal fluid;
Description of the four brain images in the previous slide (for your own reading)
Previous slide shows images of the same brain acquired using four different MR imaging sequences. Note that in T1-weighted images (a) and (b) the cerebral spinal fluid (CSF) is dark. In addition, it is difficult to make out any details of the tumour but one can infer its presence because of the asymmetry of the ventricles and the image distortion in the left hemisphere.
Image (b) is a T1-weighted image but after an injection of an MR contrast agent that causes increased T1 relaxation in tissue that takes up the agent. One can see more features of the tumour that can aid in its classification. In addition, just right of the brain midline at the back of the brain, there appears another bright spot that was not apparent at all on the T1-weighted image without contrast.
In the T2-weighted image (c), the ventricles are bright and the tumour has some structure to it. In addition, tissue around the tumour is also brighter than the brain tissue in the opposite hemisphere. Note also, that with this sequence, the second tumour at the bottom of the image is more obvious.
The image (d) is attained with a special sequence called T2 Flair. This is a T2-weighted sequence but a 180o RF pulse has been specifically applied to water prior to the regular image pulse sequence. After a delay time sufficient to allow the CSF to relax its Mz vector until it is exactly at zero, the imaging sequence is run. Thus, the CSF is dark in this T2-weighted sequence and Flair stands for Fluid attenuating inversion recovery. Many MR imaging sequences are given acronyms so that their specific properties can be remembered.
The point to be made by this figure is that a single object can be imaged in several different ways and will result in different image contrast. Some of the art in MR imaging is to pick sequences that help you not only detect abnormalities but also characterize them. Thus, it is fortunate that the tissue relaxation times are related to the local environment.
T2 weighting
• There are two primary parameters in any MR imaging sequence that can be adjusted, the TE time and the TR time.
•Although the spin echo can refocus the signal that was dephased due to magnetic susceptibility and magnetic field inhomogeneities, it cannot refocus T2 relaxation. Thus, any T2 relaxation that occurs during the TE time results in a loss of signal.
• We can choose a TE time such that we maximize the difference in the resulting signal intensities between two tissues with different T2 relaxation times.
The following equation predicts the signal intensity obtained in a T2-weighted sequence:
M =Me−TE s0
i.e. the longer the echo time, TE, the less signal we obtain. But since we want to choose an echo time that maximizes the contrast between tissues of differing T2, we accept the loss of signal.
Left: Ms as a function of TE time for two different tissues.
T2
T1 weighting
• As transverse magnetization decreases, longitudinal magnetization (i.e. along the same axis as the external static field) must increase.
• T1-weigted sequences are those which exploit the difference in T1 relaxation times of the tissue being imaged, by using short TR values.
• On a T1-weighted image, water regains longitudinal magnetization less quickly than fat. After a short TR, the next 90o pulse will flip both fat and water vectors back into the transverse plane. As water now has a smaller transverse component of magnetization than fat, it will produce less signal and thus will be dark on the screen with respect to fat.
The equation that relates TR and T1 to the resulting signal intensity for a sequence with a 90o excitation pulse is:
−TR 1
M =M1−eT s0
Left: Ms as a function of TR time for two tissues, one with a T1 of 600 ms (black, or top line), one with T1 of 800 ms, (blue or middle line) and the difference between them (red, or bottom line).
T1 and T2 weighting (arbitrary flip angle)
• There are pulse sequences that use flip angles for excitation other than a 90o pulse. Thus, there is also a flip angle dependence to the signal intensity of these sequences. For one of these T1 sequences the signal intensity would be the following:
−TR 1
M 1−e T sinθ 0
Ms=
1
−TR
1−eT cosθ
• Almost all sequences have both a TE time and a TR time. Thus, there is both T2- and T1- weighting. In general, T2-weighted imaging sequences will have long TR times in order to minimize the T1-weighting. However, there is always a trade off between the amount of time it takes to get the image and the amount of T1-weighting that will be in the T2-weighted image. In a T1-weighted image, the TE time is set as short as possible but it must be a finite length of time in order to allow for the phase encoding gradient and the RF pulses. Thus, there is some T2- weighting in any sequence. The overall equation is therefore:
−TR 1
M 1−e T sinθ
0 −TE
Ms= eT2 −TR
1 1−eT cosθ
Multiple slice imaging: sequential acquisition
• There are three ways of obtaining multiple slices in MR images, sequentially, interleaved and in a true volume acquisition.
• To perform sequential acquisition of slices, all the phase encodes for the slice at one location are acquired. Then the frequency of the RF pulse is changed so that a new slice location is chosen. Then all the phase encodes at this location are acquired.
•This requires Np*Ns*TR time to acquire. Sequential is used when the TR time is not much longer than TE (up to TR times of 100-200 ms).
Multiple slice imaging: interleaved acquisition
• As the TR time gets long compared to the TE time, interleaved slice acquisition can be performed.
• If we performed sequential acquisition with long TR times, there would be a large amount of time when no RF pulses, gradient pulses or data acquisition was being performed. This can be used to obtain data from another slice.
• So during the TR time of one slice, a phase encode for an(other) slice(s) is obtained.
Time(interleaved) = Np*TR.
Multiple slice imaging: 3D volume acquisition
• True 3D volume acquisitions take the same length of time as sequential acquisition but have the advantage of acquiring signal from the entire volume on each pulse.
• This greatly improves the SNR of the image. In order to do a volume acquisition, phase encoding is performed in two directions.
• As an example, say the phase encoding will be performed in y and z and frequency encoding in x. For each y phase encode, the total number of z phase encodes must be performed.
• Thus, the imaging time is Ny*Nz*TR in order to get the entire volume.
MR imaging
MRI applications
• T1 and T2 weighted imaging (standard MRI) • Magnetic Resonance Angiography (MRA)
• Arterial Spin Labeling (ASL)
• Cardiac MRI
• Chemical Shift Imaging (CSI)
• Contrast Agent Administration
• Diffusion Weighted Imaging (DWI) • Diffusion Tensor Imaging (DTI)
• Parallel Imaging
• Functional MRI – fMRI
• NMR Spectroscopy
• X-Nucleus MRI
• MRI thermometry
among others
T2 and T1 weighted imaging T2 weighted T1 weighted
Axial MR images of the pelvis (top) and sagittal images of the head (bottom). Note that the regions of fluid appear bright and dark in the T2 and T1 weighted images respectively.
Magnetic Resonance Angiography (MRA)
• Magnetic Resonance Angiography (MRA) is the imaging of blood vessels using MRI. MRA is used to create images of the blood vessels in order to assess them for stenosis or aneurysms. MRA is often used to evaluate the arteries of the brain, neck, the thoracic and abdominal aorta, and the legs. A variety of techniques can be used to create the images, such as administration of a paramagnetic contrast agent (gadolinium) or using a technique known as flow-related enhancement, where most of the signal on an image is due to blood which has recently moved into that plane. See example angiograms below.
Magnetic Resonance Angiography (MRA)
(white blood imaging)
• Flow-related enhancement – is an enhancement of flowing blood seen on gradient echo pulse sequences. This enhancement is a result of inflow of unsaturated spins into a slice plane or imaging volume between RF excitations. Stationary spins within the imaging volume will undergo incomplete T1 relaxation between RF excitations resulting in less signal following the next RF pulse when compared to inflowing, completely relaxed spins in flowing blood.
• Angiographic sequences have very fast TR times. Thus, if the velocity of the blood is slow compared to the slice thickness over the TR time, the magnetization in the blood will become saturated and the signal will be dark.
v > ∆z TR
for white blood imaging
Arterial Spin Labeling
• In Arterial Spin Labeling (ASL), the blood in the arteries upstream from the imaging volume is magnetically ‘labeled’. As a consequence, image intensity changes will occur depending on the blood supply to the tissue in the imaged slice. Upon subtraction of an image acquired without spin labeling, the background signal from static spins is removed and the difference image can be used to quantify perfusion.
Cardiac MRI
• The purpose of cardiac MR imaging is to determine the anatomy and the dynamics of 3D heart structures (e.g. walls and cavities). The motion of heart during the acquisition of MR signals can create strong motion artefacts. As small rodents have a very high heart rate cardiac imaging is a challenging task.
• Nevertheless, it is possible to gate the acquisition. For instance, we can obtain an ECG (electrocardiogram) while the patient is in the magnet and use this signal to gate the pulse sequence. We can acquire one phase encode each heart beat. However, we can use our interleaved slice acquisition method to get multiple slices during that heart beat. One problem with this method is that now our TR time is set by the heart rate. Thus, we don’t have a lot of freedom in choosing the TR time.
Cardiac Triggered acquisition The blue line gives the trigger point. The pulse sequence can then be programmed to delay until the motion is the least (diastole) and then phase encodes from multiple slices obtained. For an image with 128 phase encoding steps, 128 heart beats are required to get an image.
Cardiac MRI
Chemical Shift Imaging (CSI)
• The MRI signal for living tissue is largely made up of 1H in water, and the effects on the image from other hydrogen nuclei are typically small. Therefore the chemical shift effect is normally ignored in MRI. The encoding of measurable contributions from different species (such as water, fat, choline, n-acetyl aspartate, lactate) leads to an additional dimension for imaging.
• Chemical Shift Imaging (CSI) sequences are imaging sequences without a frequency encoding gradient. In order to evaluate the CSI data, Fourier Transformations (FT) are performed over the spatial axis in addition to the FT for calculating the spectrum.
Contrast Agent Administration
•Intravenously injected contrast agents like Gadolinium-DTPA (Gadopentetate- Diethylenetriamine Pentaacetic Acid) intensify the signal in pathological regions (e.g. brain tumors with disrupted blood brain barrier).
• Gd-DTPA decreases the relaxation times T1 and T2 resulting in a stronger T1 weighting. Usually, as a reference, a T1-weighted image is acquired just before the administration of the contrast agent.
• Contrast enhanced MRI gives information e. g. about cerebral ischemia (cerebral infarcts) and intra-cranial tumors.
Diffusion Weighted Imaging (DWI)
• Diffusion is the process by which matter is transported from one part of a system to another as result of Brownian motion. The mean square of the distance covered by a diffusing molecule is proportional to the time and the diffusion coefficient of the investigated medium (Fick’s 1st law).
• Magnetic Resonance Imaging (MRI) makes use of magnetic field gradients to detect phase shifts caused by diffusion. For coherent motion in the presence of a gradient pulse there is a phase shift of the received signal. For incoherent motion in presence of a gradient pulse there is an amplitude reduction due to phase dispersion. Consequently, image areas of reduced diffusion show relative signal hyper-intensity.
• Diffusion weighted imaging (DWI) is the only non-invasive and non-contaminating method capable of ‘self-diffusion’ imaging and quantification.
Diffusion Tensor Imaging (DTI)
• When diffusion is anisotropic the diffusion contrast is strongly dependent on the direction of the diffusion-sensitizing field gradients.
• Diffusion Tensor Imaging (DTI) needs a set of diffusion-weighted images, which are acquired with the same diffusion gradient amplitude but with different diffusion gradient directions. This set of images has to be acquired with at least 6 non-collinear directions, preserving uniform space sampling. In parallel one image acquired without diffusion sensitivity is required for the absolute scaling of the diffusion tensor.
Parallel Imaging
• The key element of any Parallel Imaging system is the application of multiple independent receiver coils with distinct sensitivities across the object. Primarily, the main purpose of this so-called phased array technology was to distribute the high SNR performance of their small component coils over a larger area covered by the entire array, with no increase in imaging time. In conventional imaging phased array technology has been used to improve image quality within the same acquisition time, whereas PI techniques use phased array technology to provide a significant reduction of MR scan time and/or improve spatial/temporal resolution.
Angiogram of the rat brain showing nearly same image quality using single (left) and two receiver coils (right). Compared to the left image, the image on the right was obtained in half the time.
Functional MRI
• In functional MRI studies (fMRI), a Blood Oxygen Level Dependant (BOLD) technique is used to demonstrate changes in cerebral blood oxygenation associated with performance of cognitive tasks. As de-oxygenated blood has a considerably higher magnetic susceptibility than oxygenated blood, significant contrast can be obtained.
NMR spectroscopy
• Nuclear magnetic resonance spectroscopy analyses the magnetic properties of certain atomic nuclei to determine different electronic local environments of hydrogen, carbon, or other atoms in an organic compound or other compound. This is used to help determine the structure of the compound.
X-nucleus MRI
• X-nucleus MRI is imaging of nuclei other than protons (1H = hydrogen). Nuclei heavier than Hydrogen that possess angular momentum have γ factors which are an order of magnitude smaller than that of proton. The main characteristics of the most popular X-nuclei are given below.
Imaging of 19F
Nature Neuroscience 8, 527 – 533 (2005)
MRI thermometry
• The non-invasive MR thermometry method is based on the temperature dependence of the proton resonance frequency.
• Good quality temperature images are obtained from phase information of standard sequences with an accuracy as high as 0.2°C in phantoms.
• Two physical tissue properties have been suggested as good candidates for thermal imaging, namely the spin-lattice decay time, T1, and the molecular diffusion coefficient of the water molecules, which quantifies the thermal Brownian motion.
• MRI thermometry is routinely used to monitor the spatial and temporal behaviour of temperature during non-invasive treatment of cancer/tumour with ultrasound or magnetic hyperthermia.
Biomed Eng Online. 2006; 5: 56.
Frequency selective pulses
Introduction
• To acquire a signal in Magnetic Resonance, it is necessary to generate a component of the net magnetization in the transverse plane.
• This is achieved by applying a radiofrequency pulse at the Larmor frequency. But what happens when there is a range of Larmor frequencies?
• In the last lecture we investigated the different reasons why there may be a range of frequencies (i.e. T2* phenomena)
Introduction
• In the following we will investigate how the MRI experiment can use frequency to select different elements of the spin system.
• This may be a chemical or spatial element. The basic principles of frequency selection are the same.
• Remember the electronics is unable to ascertain why a signal has a different Larmor frequency, so will treat chemical and spatial information in the same way. It is only the interpretation of the results that gives the data meaning.
•
•
The first experiments used continuous wave (CW) techniques, which are described on the next page. These were slow, and failed to produce images.
A better solution was found with the advent of pulsed or Fourier transform MRI, in which the complete spectrum (of spin frequencies) was excited simultaneously and the response of the system measured as a free induction decay. This time domain signal could then be transformed to a frequency domain spectrum using the Fourier transform.
Pulsed NMR
Excitation bandwidth of RF pulses
• When an RF wave is switched on and off in a very short period, it actually produces excitation over a range of frequencies.
• In the MR experiment, the pulse is applied at a constant frequency, at approximately the Larmor frequency of the spins under investigation. While RF pulses excite a range of frequencies, the amplitude and phase of the excitation may not be constant over this frequency range.
• The behaviour of the RF pulse as a function of frequency offset is called the excitation profile of the pulse. The RF pulse is amplitude modulated, which means that the RF pulse, while having a constant frequency, will vary in amplitude during the pulse.
Shaped RF pulses
• In MR, it is often necessary to have very well defined excitation profiles.
• This is achieved using amplitude and/or phase modulated RF pulses.
• In the remainder of this module, we will consider only amplitude modulation of RF pulses.
• Amplitude modulated pulses are often referred to as shaped pulses, and within the spectrometer this is achieved in a modulator, where the output of a frequency synthesizer is modulated by a particular low frequency shape. The excitation bandwidth of the RF pulse will be a function of this shape and the length of the pulse.
Fourier pairs
• The excitation profile of an RF pulse is approximated by the Fourier transform of the excitation waveform.
• So we consider these two properties to be a Fourier pair. For example, the Fourier transform of a square pulse in time domain has a sinc shape in frequency domain and vice versa:
sinc(t)=sin(t)/t
•
•
The Fourier pair idea has been extended to produce a wide range of pulses currently used in MRI. We saw how a square pulse produced a sinc shaped frequency excitation profile and vice versa. In most applications, we would actually prefer a square excitation profile. What is the Fourier pair for a square excitation? – A sinc pulse.
So one of the most commonly used pulses in MRI is the sinc(t) pulse. Theoretically, the Fourier transform of a rectangle is an infinitely long sinc pulse which is, naturally, impractical, so the waveform has to be truncated.
• Another commonly used pulse shape is the Gaussian pulse. The excitation profile of a Gaussian is also a Gaussian and it produces a narrower bandwidth in a shorter time than a sinc and requires less peak power, so it also has wide application, especially for highly selective excitation pulses.
Some commonly used RF shapes
Excitation bandwidth
• In most applications, we are interested in exciting a particular bandwidth. This is achieved through a combination of pulse shape and pulse duration.
• As the pulse duration is increased, the width of the excitation profile is reduced.
• For a sinc pulse, the bandwidth is given by the inverse of the time between the centre of the pulse and the first zero-crossing point.
• RF pulses are generated by a RF transmit coil, which we will study in the ‘MR hardware I’.
Excitation bandwidth
• This animation will allow you to investigate the excitation profiles of some common pulses. The bandwidth of the profile is normally defined as the width at half the height.
sinc (ap) where -3 < a < 3 Gaussian (1% truncation)
Truncation effect in RF pulses
• Because RF pulses cannot be infinite in duration, they are truncated, and hence the Fourier transform approximation is modified.
• If the pulse is apodised, by a function that reduces the B1 field smoothly to zero, then the excitation profile is spatially smoother. Note, however, that it is also broader.
• In practice, the developer of the pulses used in commercial MR scanners needs to give details of the excitation bandwidth of the pulses provided.
•The figure on the right shows the excitation profile for a truncated sinc pulse.