# The Basics of MRI

## IMAGE PRESENTATION

### Image Contrast

In order for pathology or any tissue for that matter to be visible in a magnetic resonance image there must be contrast or a difference in signal intensity between it and the adjacent tissue. The signal intensity, S, is determined by the signal equation for the specific pulse sequence used. Some of the intrinsic variables are the:

 Spin-Lattice Relaxation Time, T1 Spin-Spin Relaxation Time, T2 Spin Density, ρ T2*

The spin density is the concentration of signal bearing spins. The instrumental variables are the:

 Repetition Time, TR Echo Time, TE Inversion Time, TI Rotation Angle, θ T2*

T2* falls on both lists because it contains a component dependent on the homogeneity of the magnetic field and the the molecular motions. The signal equations for the pulse sequences presented thus far are:

Spin-Echo
S = k ρ (1-exp(-TR/T1)) exp(-TE/T2)

Inversion Recovery (180-90)
S = k ρ (1-2exp(-TI/T1)+exp(-TR/T1))

Inversion Recovery (180-90-180)
S = k ρ (1-2exp(-TI/T1)+exp(-TR/T1)) exp(-TE/T2)

S = k ρ (1-exp(-TR/T1)) Sinθ exp(-TE/T2*) / (1 -Cosθ exp(-TR/T1))

In each of these equations, S represents the amplitude of the signal in the frequency domain spectrum. The quantity k is a proportionality constant which depends on the sensitivity of the signal detection circuitry on the imager. The values of T1, T2, and ρ are specific to a tissue or pathology. The following table lists the range of T1, T2, and ρ values at 1.5T for tissues found in a magnetic resonance image of the human head. TissueT1 (s) T2 (ms) ρ*
CSF0.8 - 20 110 - 2000 70-230
White0.76 - 1.08 61-100 70-90
Gray1.09 - 2.15 61 - 109 85 - 125
Meninges0.5 - 2.2 50 - 165 5 - 44
Muscle0.95 - 1.82 20 - 67 45 - 90
Adipose0.2 - 0.75 53 - 94 50 - 100
*Based on ρ=111 for 12mM aqueous NiCl2

The contrast, C, between two tissues A and B will be equal to the difference between the signal for tissue A, SA, and that for tissue B, SB.

C = SA - SB

SA and SB are determined by the signal equations given above. For any two tissues there will be a set of instrumental parameters which yield a maximum contrast. For example in a spin-echo sequence the contrast between two tissues as a function of TR is graphically presented in the accompanying curve. A contrast curve for tissues A and B as a function of TE is presented in the accompanying curve. To assure that signals from all phase encoding steps possess the same signal properties a few equilibrating cycles through the sequence are added to the beginning of every image acquisition. The necessity of this can be seen by examining the MZ and MXY components as a function of time in a 90-FID type sequence. Note that the amount of transverse magnetization from a 90° pulse reaches an equilibrium value after a few TR cycles. This practice lengthens the imaging time by a few TR periods.

The magnetic resonance community has adopted nomenclature to signify the predominant contrast mechanism in an image. Images whose contrast is predominantly caused by differences in T1 of the tissues is called a T1-weighted image. Similarly for T2 and ρ, the images are called T2-weighted and spin density weighted images. The following table contains the set of conditions necessary to produce weighted images.

WeightingTR Value TE Value
T1 < = T1 < < T2
T2 > > T1 > = T2
ρ > > T1 < < T2

It is impressive to see how the choice of the instrumental parameters TR, TE, TI, and θ affect the contrast between the various tissues of the brain. In the accompanying set of graphics you can select an imaging sequence and the imaging parameters, the resultant image will be displayed in the graphics window. The spin-echo images are actual magnetic resonance images of the human brain. The remaining images are calculated images based on the signal equations above and a set of measured overall T1, T2, and ρ images of the human brain. The two bright circles to the bottom right and left sides of each calculated image are spin density standards, or phantoms, placed next to the head.

Spin-Echo Images

Inversion Recovery Images (180-90)

Gradient Recalled Echo Images ( TE=5 ms )

### Image Histogram

A histogram of an image is a plot of the number of pixels with a given data value. This histogram represents an image in which most of its pixels have data values between 0-80, and 600-1000. Image histograms are useful in deciding how to represent the data value associated with a voxel as a pixel intensity on the display device. You will see the importance of a histogram in the following section.

### Image Processing

Thus far in the teaching package we have concentrated on spin physics, pulse sequences, and hardware. A great deal of math occurs between the point that the raw data has been collected and the image is displayed. This section will take you through some of these details.

The raw data, or k-space data as it is sometimes called, is most often 256x256 data points of complex data. Here it is presented as the Mx and My or real (RE) and imaginary (IM) signals from the signal digitizer. The presentation is in the form of an image of the raw data. The data typically has 16 bits of amplitude resolution. It will be beneficial to follow the processing of this 256x256 set of data before proceeding to smaller size matrices.

As was seen in Chapter 5 it is often times useful to smooth a frequency domain spectrum by convolving it with a Lorentzian line shape. Recall that multiplying the time domain spectrum by an exponentially decaying function, which is the Fourier pair of the Lorentzian lineshape, is equivalent to convoluting in the frequency domain. For this reason the raw data is sometimes multiplied by an exponential cone before it is Fourier Transformed. The Fourier transform is performed first in the vertical direction, and then in the horizontal direction. Once the Fourier transforms are performed, the magnitude is calculated. The magnitude calculation cuts the amplitude information down to 15 bits of resolution. Because the magnitude image is used, there will never be negative pixel intensities. The magnitude data is expanded to a 512x512 data matrix by either pixel interpolation or pixel replication. Pixel replication duplicates even numbered pixels with the lower odd numbered pixel. Pixel interpolation inserts even numbered pixels as the average of the adjacent odd numbered pixels.

For those readers interested in working with a set of raw MRI data, the following detail page is provided. The image is typically displayed with an eight bit video display. This means there are 256 possible gray levels with which to display the 32768 possible data values from the 15 bits of magnitude information. A linear look-up table (LUT) is typically used. Here the video intensity between 0 and 255 is set by a linear relationship to the data value. The width of the data values set to the 256 possible gray levels is called the width or contrast. The data value assigned the center of the gray scale is referred to as the level or brightness. Adjusting the width and level allow the viewer to set the image attributes which best display the anatomy and pathology.

Experiment with the concept of width and level by selecting a width and level from the table below. When a given width and level are selected, the spin-echo image of the human head is displayed with the following contrast and brightness.

WidthLevelImage & LUT
1153576    280860    780735    320730    1470    1865    Often times less than 256x256 data points are collected to decrease the imaging time. For example, a 256x192 or 256x128 data matrix can be collected when there are 192 or 128 phase encoding steps. It is preferable to always have the same size matrix for input into the two dimensional Fourier transform.

In the case of a 256x192 or 256x128 acquisition the ends of the matrix are filled with zeroes. This process is called zero filling. The process is equivalent to pixel replication to produce a 256x256 image from 256x128 data. Once filled with zeroes the data is processed as described above. ### Imaging Coordinates

Clinical imagers do not use the XYZ magnetic resonance coordinate system for collection and presentation of images. Instead the anatomic coordinate system is used. In this system the axes are referenced to the body.

The three axes are left-right (L/R), superior-inferior (S/I), and anterior-posterior (A/P). ### Imaging Planes

Similarly, on clinical imagers the terminology XY, XZ, and YZ are not used to indicate the imaged planes. An imaged plane perpendicular to the long axis of the body is called an axial plane. The sides of this plane are L/R and A/P.

A plane bisecting the front of the body from the back is referred to as a coronal plane. The sides of this plane are L/R and S/I.

A plane bisecting the left and right sides of the body is called a sagittal plane. The sides of this plane are S/I and A/P.

### Signal Averaging

The signal-to-noise ratio (SNR) of a tissue in an image is the ratio of the average signal for the tissue to the standard deviation of the noise in the background of the image. The signal-to-noise ratio may be improved by performing signal averaging. Signal averaging is the collection and averaging together of several images. The signals are present in each of the averaged images so their contribution to the resultant image add. Noise is random so it does not add, but begins to cancel as the number of spectra averaged increases. The signal-to-noise improvement from signal averaging is proportional to the square root of the number of images averaged (Nex). Nex is more commonly referred to as the number of excitations.

SNR ∝ Nex1/2

Increasing Nex increases the acquisition time linearly. For example, increasing Nex from 1 to 2 doubles the acquisition time. The SNR is increased by a factor of the square root of 2.

Compare the results of averaging together the following number of images of a bottle of water.

NexNex1/2Image
11.00 21.41 42.00 164.00 ### Problems

1. There are two adjacent tissues in an image with a T2 of 30 and 50 ms. You wish to produce a spin-echo image of the tissues such that the contrast between the tissues is maximized. What TE should be used? 2. There are two adjacent tissues in an image with T1a = 300 ms, T2a* = 20 ms, ρa = 50 ASDU, and T1b = 150 ms, T2b* = 20 ms, ρb = 50 ASDU. (ASDU = arbitrary spin density units.) You wish to produce a 90° gradient-echo image of the tissues such that the contrast between the tissues is maximized. What TR should be used?

3. What are the four directions in a sagittal imaging plane called? 4. Refer to the following magnetic resonance image and corresponding histogram when answering the following questions.  What features in the image correspond to the peaks at 0-60, 720-865, and 865-1000 most likely represent? What would be a good width and level to use to display an image of the data represented by the histogram? 5. What are the four directions in a coronal imaging plane called?

6. What are the four directions in a axial imaging plane called?

7. What TR and TE values might have been used to produce the image in question #4?

8. A spin-echo imaging sequence produces an image with a SNR=90 for muscle tissue when Nex=2. What SNR is expected when Nex=3? 