Chapter 4: Basic Principles of MR Image Formation

 

Study Questions

 

 

1. What is an image? What do MR images represent?

An image is a “visual description of how one or more quantities vary over space.” MR images depicts the spatial distribution of some property of related to the spins of the atoms within a given sample.

 

2. Explain the following equation in simple language: Mz = Mo + (Mzo - Mo)e^(-t/T1) 

This equation provides a formula for us to figure out what the longitudinal magnetization of a solution is after time ‘t’. Mz represents the desired magnetization value at a certain time. Mo represents the initial magnetization when the atom is fully relaxed and has not received any excitation pulse. The important concept behind this equation is that as the ‘t’ value increases Mz will begin to reach Mo which signifies that the spins states is going from the transverse to the longitudinal plane.

 

3. What happens to transverse magnetization over time as a result of T2 decay?

T2 decay represents the decreasing transverse magnetization over time as it returns to its longitudinal position.  The magnetism vector in the transverse plane follows a circular path with constant angular velocity (ω) and its magnitude decays based on time constant T2.  The net result is an "inward spiral" path towards the longitudinal axis.  Essentially, the net magnetism, once tipped towards the transverse axis, precesses around the longitudinal axis at the Larmor frequency.

 

4. Why is it desirable to collect images at intermediate times of T1 recovery and T2 decay? That is, why can’t we collect our images immediately following excitation (or a very long time after excitation) and still get T1 or T2 contrast?

You cannot collect the images immediately after excitation because it takes a few seconds for the signal to transition from the transversal to longitudinal plane- and this is exactly what you want to measure. If you collect images a long time after excitation then the signal will have already made the transition.  Essentially, at the time of excitation (or a long time after excitation) there will be no contrast between different tissue types because all the spins will be aligned.  At intermediate times, different tissue types will have relaxed at different rates, so T1 recovery and T2 decay contrasts can be measured.

 

5. Explain the following sentence:  “The total signal measured in MRI combines the changes in net magnetization generated by every excited voxel.”

This explains how a single MRI signal actually contains the various signals of every voxel in the brain. Intuitively, it seems that every voxel should have its own recorded signal. In reality, however, it is the combined signal from all the voxels that goes into creating just one MRI signal.

 

6. Why are magnetic field gradients important for image formation?

It is only because of field gradients that we are able to find the location of individual particles. If there were no gradient then all the particles of a given kind would precess at the same rate everywhere it is present in the solution. The gradient provides us with an address of where each particle is.

 

7. What are some gradients called “phase encoding gradients” and others called “frequency encoding gradients”?

The distinction between these two terms are significant in filling a k-space diagram. Phase encoding gradients are put into place BEFORE data acquisition and is responsible for introducing a variety of phases to a given number of spins in the slice. This is used to control the Gy gradient which is responsible for the y-axis intervals in k-space.

Frequency encoding gradients, on the other hand, are responsible for creating a spin precession gradient. This is turned on during data acquisition and contributes to the Gx gradient which, in turn, determines the x-axis of k-space.

 

8. What is the Fourier transform, and when is it used in MRI?

A mathematical equation capable of changing a frequency domain into a time domain and vice versa. In fMRI, it is used to convert data in the time domain    to data in a frequency domain. This frequency domain is referred to as the power spectrum. Raw fMRI data show the relative intensity of the signal at each   time sample. The power spectrum represents this same data, but in a frequency domain, meaning that the power spectrum indicates the intensity of the signal at each component frequency.

 

 

A Fourier transform is the conversion of data in the time domain (which is how it is collected), into the frequency domain, by modeling it as a sine wave. The magnetic gradients and RF pulses focused on a slice allow differentiation of locations based on the phase and the frequency data collected from each coordinate. The Fourier transform is needed to convert the raw values into phase and frequency information that can be displayed as a wave. 

 

 

A Fourier transform can be used to convert MR data into a K-space, which is a frequency representation of the data.

 

 

9. What is slice selection? How is it typically accomplished in MRI?

Slice selection is based on the fact that the brain can be divided into an infinite number of axial slices. In performing a scan, however, we only want to view a given axial slice. This is accomplished by controlling three variables: 1) excitation pulse 2) bandwith of excitation field and 3) the strength of Gz.

 

10. Why must excitation pulses have the form of a sinc function to excite a rectangular slice?

Excitation pulses are only useful if they are controlled. That is, they can only excite the particles that we want them to. Only when we have pulses in the form of a sinc function do we see, after a fourier transformation, that we will have a uniform frequency value (ω).

 

11. What is k-space? How is k-space different from normal image space?

K-space is the first depiction of the fMRI signal.  Changes in k-space over time ("k-space trajectories") are given by time integrals of gradient waveforms (Gx, Gy) multiplied by the gyromagnetic ratio. K-space is different from a normal image in that there is no direct relationship between a given set of coordinates in k-space and an image of the actual object scanned. In other words, the center of k-space does not represent the center of the brain.

 

12. How does the center of k-space contribute to an image? How does the periphery of k-space contribute to an image?

The center of k-space contains all of the low-spatial-freuquency data (signal-to-noise and contrast information for the image). The periphery of k-space contains all of the high-spatial-frequency data (image resolution information). With just the center the image will appear blurry but will still contain all of the signal. With just the periphery, the image will contain all of the finer details but there will not be as much signal.

 

13. What is reconstruction?

Reconstruction is the process of converting k-space into 2D/3D images.

 

14. If we want an image with a higher spatial resolution, how must we change our sampling of k-space? What if we want an image with a larger field of view?

In order to increase spatial resolution there must be a wider range of coverage in k-space. In order to increase the FOV, there must be a increased sampling rate of k-space.

 

15. Why do most fMRI imaging sequences use interleaved slice acquisition?

Excitation pulses rarely affect ONLY the desired slice due to off-resonance effects. It is more likely that the pulses will go beyond the scope of the desired slice and actually excited adjacent slices. In order to avoid this “bleeding of excitation”, researches choose to scan every other slice to ensure there is no affect from a previous excitation.

 

16. How is spatial information encoded within a single slice?

Spatial information is encoded into a single slice based on the fact that both the Kx and Ky coordinates are representing what happens when a given region is placed under several combinations of Gx and Gy gradients. Exactly what type of image results from a given combination of Gx and Gy gradients will determine the phase changes of the particles in the object.

 

17. Why do gradient inhomogeneities cause stretching or skewing of images? Refer to the concept of k-space in your answer.

K-space is determined by gradients along the x-axis and y-axis. If either of these gradients is distorted there will not be an accurate translation of the MRI signal to k-space. If, for example, the Gx is distorted then the length of the x-axis of the k-space diagram will be either shortened or stretched. This will result in a distorted image. The same concept is applied to distortions in Gy which can cause the y-axis of the k-space to be either extended or compressed.