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					              Correction of Artifacts in Functional MRIs

                         By Olga Lyandres and Jen Nelson

The project that we have chosen encompasses both electrical and biomedical engineering.
It is part of the work being done by the Magnetic Resonance Research Laboratory at the
Beckman Institute where, through the collaborative efforts among engineers, biochemists,
and psychologists, the function of the human brain is being studied using MRI.
Specifically, functional MRI (fMRI) techniques are used to obtain the data for the study.

During data acquisition, subjects undergo an alternating sequence of rest and stimuli,
which results in approximately one percent signal differences from active regions of the
brain. Because of this, fast imaging is crucial in order to detect the difference in the
signal. FMRI allows for this fast imaging time and the collection of data that can be
interpreted by superimposing images onto the high-resolution anatomical images of the

However, fMRI typically images typically contain several distortions. These distortions
arise from both, an aliasing artifact known as N/2 ghosts that is caused by fast shifting of
the phase gradient, and from geometric distortions. Our project will seek to eliminate
these distortions, for it is only after correcting them that accurate interpretation of the
data can be made.

This project will have a direct impact on the progress of studies using fMRI. Reduction
of the geometric distortion and N/2 ghosting presently contained in the fMRI images will
be valuable to ongoing research projects conducted at this university. Specifically, the
contribution that we will make by eliminating artifacts in fMRI images will greatly
enhance the study of the brain by producing clearer, more accurate images. As a result,
we are excited that our project will have a direct impact on research and will be used in
the future.

The objective of our project is two-fold. One objective is to implement an algorithm that
will correct for the geometric distortions in fMRI images. Geometric distortions occur in
fMRI images as a result of internal inhomogeneities in the magnetic field. One cause of
variation in the magnetic field is the interactions between air-filled cavities and the white
matter tissue in the brain. As a result, the resonant frequency of the particles is
misrepresented on the acquired images. This gives inaccurate spatial information about
the source of the signal. Thus active areas of brain as seen on the image cannot be
correctly linked to their appropriate locations in the brain.

To correct geometric distortion, a field map can be constructed that indicates the
displacement of the pixels in the distorted image. We need to acquire additional data
while varying a known parameter such as the time between spin echo sequences. From
that information we can determine the variations in the magnetic field and spatial shifts.

The results are encoded into the field map, which is then used to unwarp the image. The
corrected image can be used together with an anatomical image to identify areas of the
brain that are of interest.

The other objective of the project is to eliminate N/2 ghosts from the fMRI image. The
N/2 ghosts arise from the time dependent frequency shift that occurs because of time
dependent eddy currents. Because of the back and forth trajectory in k-space used in
echo planar imaging (which is used in fMRI), the frequency shifts create a phase
difference from line to line in the raw data. As the data is Fourier transformed, the phase
shift creates a phase ambiguity in the image, such that aliasing occurs and part of the
signal appears 90 degrees out of phase.

In fMRI, N/2 ghosts create many problems. Because aliasing occurs as a result of the
N/2 ghost, the image will be warped. In particular, ghosting of activated regions could
lead to apparent activation appearing outside the head. In addition, movement of a
patient’s head can cause interference fringes of overlapping ghost and images to change
drastically, resulting in a large effect from even small displacements.

Finally, another aspect of our project will be the design of a surface radio frequency coil
used to image small areas that are located close to the surface of the body, for example
the eye or a skin tumor. Design of a surface coil is necessary in this project in order to
obtain images that are accurate and clear prior to processing, especially in the region of
the motor cortex, in order to decrease the distortions present after processing occurs.

The achievement of our objectives will lead to many benefits to the end customer

      An improved surface coil capable of producing sharper images prior to
       undergoing processing algorithms to eliminate distortions
      A more spatially correct image of the brain
      Elimination of the N/2 ghost and reduction of aliasing in the final fMRI image
      A higher accuracy in the correlation between the activated region of the brain and
       its function
      Advances in the study of the brain

Some features of the fMRI with correction for geometric distortion and N/2 ghosts

      Construction of a field displacement map
      Unwarping algorithm for echo-planar images
      Calculation of phase angle for correction of the N/2 ghost
      Application of the phase angle correction for the N/2 ghost

The design of our project consists of a hardware component, that of an RF surface coil,
and two software subsystems: the first to remove N/2 ghosts from the fMRI image and
the second to remove geometric distortions from the fMRI image.

RF Surface Coil Design

The hardware component of our project will be the design and implementation of a radio
frequency, or RF, coil. This coil is responsible for supplying magnetic energy to the
protons at the Larmor frequency in order to stimulate transitions between the two nuclear
energy levels, and therefore, produce an MRI signal.

The design of the RF coil will be based on Faraday’s Law, as given in Equation 1.1.

       Equation 1.1: E  -d /dt.

In addition, the RF coil must be capable of storing as much of its magnetic energy as
possible in the near field region (within the patient). As a result, the RF coil acts as a
magnetic field storage device whose design is based on a resonant electric circuit having
a resonant frequency, fr. At fr, the output of the circuit as a function of the input is
maximum. This resonant frequency can be obtained using Equation 1.2.

       Equation 1.2: fr = 1 / (2(LC))

where L is the inductance of the coil and C is the capacitance with contributions from the
intrinsic capacitance of the coil and also capacitance which is added to the circuit for
tuning the resonance, and matching the input impedance of 50 .

Specifically, we will be designing a surface coil to acquire motor cortex data from the
brain. For such a coil, the simplest design is a loop of wire, with additional capacitance
added to resonate at the required frequency.

With respect to the design of the surface coil, considerations must also be made so as to
ensure that the coil will contribute as little noise to the image as possible. The noise
voltage given by the coil can be calculated from Equation 1.3.

       Equation 1.3: Vnoise = (4kTRcoilf)

where Rcoil is the resistance of the coil, T is the absolute temperature in K, and f is the
bandwidth of the received signal.

Overall Block Diagram:

MRI                     P file              Correction               Removal                Corrected
Scanner at              Image                for N/2                  of                     Image
Carle                   Matrix               Ghosts                   Geometric
Hospital                                                              Distortion

Block Description

MRI Scanner
The data is acquired with an MRI scanner located at Carle Hospital.
During the time when the stimulus is applied, 15 slices of data are collected with each
slice represented by a 64X64 data matrix. Furthermore, there are 200 data sets acquired
for each slice.

Data Preparation
The data collected by the scanner is placed into a P-file, which contains header
information specific to the MRI scanner. Data is processed to remove the header
information from the file, process raw image data, and place the data an array of 64X64
matrices. In this format, images can be processed and analyzed.

Correction for N/2 Ghosts

        Images or                   of time-                    Application              Corrected
        reference                   dependent                   of phase shift           Image
        scans                       phase shift                 correction

The basic idea used to eliminate the N/2 ghosts found in fMRI images is seen in the block
diagram above. An image or reference scan is used in order to calculate the resulting
phase shift that is causing the ghost to appear. Once this phase shift is calculated, the N/2
ghost can be eliminated by shifting each line back an appropriate amount, applying a
Fourier transform to the data, and producing the corrected image.

There are several methods for reducing N/2 ghosts. These methods will be researched,
implemented, tested and improved upon in order to not only implement the correction for
N/2 ghosts, but also to optimize that correction. A basic block diagram for one such
method is shown below.

                    Splicing                                                                 Application
Collection          together                              Reversing        Calculation       of phase
of                                 Fourier                of even          of phase
                    of             Transformation                                            correction to
reference           reference                             lines            correction        images
scans               scans

                                                                         Image               Transformation

In the method shown in this detailed block diagram, reference scans are acquired using
reversed switching gradients. In other words, if the first line of the normal image is
acquired under a positive read gradient, then the first line of the reference scan is
acquired under a negative read gradient. Using this, the even lines of a reference scan
can be used to correct for the odd lines of the actual image. Then a Fourier
transformation is performed on all the lines in both the normal and reference scan in the
read direction. The even lines of the reference image are reversed, and a phase correction
is applied using the formulas found in Equations 2.1 – 2.2.

       Equation 2.1: cos  = r1*r2 + i1*i2 / ((r12+i12)*(r22+i22))

       Equation 2.2: sin  = i1*r2 + r1*i2 / ((r12+i12)*(r22+i22)) where r and i
represent the real and imaginary components of each data point and 1 refers to the normal
image and 2 refers to the reference image

After calculation of the phase correction, , the correction is applied using
Equation 2.3 – 2.4.

       Equation 2.3: r’ = r cos  + imag*sin 
       Equation 2.4: imag’ = imag*cos  - r sin 

Finally, the images are Fourier transformed along the phase encode direction to form the
corrected image.

Correction for Geometric Distortions

      Inverse 2-D         Measure              Set up a             Determine
      FFT                 phase shift          system of            spatial
                                               equations            distribution
                                                                    of Magnetic

As mentioned above, data is collected using the MRI scanner. To correct the geometric
distortions, additional data must be acquired. To do this, imaging is performed with
several different Echo Time (TE) values, where TE is the time between the spin-echo
sequences within each slice.

The first step in processing the data is to perform inverse 2-D FFT. That allows the
image to be viewed and visually analyzed.

Once we acquire the images, we can measure the phase shift of the pixels in the data
matrix. The phase shift, , is dependent on the resonant frequency, , and TE value
according to Equation 3.1.

       Equation 3.1:  = *TE

TE is a known parameter set by the user, so the resonant frequency can be found by
setting up a system of equations involving . This system of equations is comprised of
Equation 3.1 (above) and Equation 3.2 .

        Equation 3.2: =*(B0 + Gz*z) where  is the gyromagnetic ratio of the nucleus
and is characteristic of different elements, B0 is the strength of the magnetic field, and Gz
is the magnetic field gradient in z direction.

Then, the strength of the magnetic field and the location in the z direction at which it is
measured. Must be found. With the additional information obtained from the use of
Equations 3.1 – 3.2, for at least 2 different TE values, a system of equations can be
produced and used to solve for the unknowns B0 and z.

After determining the magnetic field and the location, this information is encoded into a
field map, which is the representation of the displacement of pixels in the image. Using
this field map, the pixels can be relocated and the intensity of each pixel adjusted to yield
a corrected image without distortions.

Corrected Image

After applying the corrections from N/2 ghosting and geometric distortion, an image
without any aliasing artifacts or distortions is produced. Spatial information in this image
is accurate and thus, the image can be used to in conjunction with a high-resolution
anatomical image to study the activity of the brain during various cognitive tasks.

Performance Requirements

There are no strict requirements in terms of the implementation and features described
above. The system needs to be able to handle large sets of data, specifically 200 sets of
64X64 image matrices for each slice. In addition, as there are 15 slices of data acquired
every 3 seconds, there must also be a large storage and computational capacity for the


Testing Procedure

Testing procedures will consist of the following.

1. The surface coil will be tested by using it to obtain data and produce an image.

2. Once code for the geometric distortion is written, it will be tested on various sample
   images taken from the MRI scanner at Carle Hospital. Images processed using the
   correction for geometric distortion code will be compared to those processed without

   the correction for geometric distortion code to ensure that spatial deformities have
   been reduced. In addition, multiple data sets will be tested.

3. Similarly, once code for the correction for the N/2 ghost is written, it will be run on
   images obtained from the MRI scanner at Carle hospital. Images processed using this
   correction algorithm will be compared to those processed without it to ensure that
   aliasing has been reduced.

4. The two correction codes will be interfaced and then tested again on images obtained
   from the MRI scanner at Carle Hospital. Again comparisons will be made using
   images processed without the correction and images processed with the correction
   algorithm to ensure that the algorithm is indeed reducing geometric distortion and
   aliasing caused by N/2 ghosts.

5. Finally, the interfaced code will be tested at various noise levels (see below).

Tolerance Analysis:

The element of this design that most affects the performance of our project is the amount
of noise present in the image. Large amounts of noise present in the image will reduce the
signal to noise ratio, and thus produce a poor image. As a result, the completed algorithm
for both the correction of the N/2 ghosting and geometric distortion will be tested using
images containing various noise levels to see at what noise level the correction algorithm
breaks down.

                                  Cost and Schedule

Cost Analysis


         Hourly Wage: $100 / hour per person
         Hours: 10 hours per week * 12 weeks = 120 hours
         Total: $100 * 2.5 * 120 = $30,000
         Total for 2 people = $30,000*2 = $60,000


         RF Coil: Provided by Magnetic Resonance Imaging Lab
         MRI machine: Provided by Carle Hospital
         Parts Cost = 0

Total Cost:

         Labor + Parts = $60,000 + 0 = $60,000


Date                What (Who)

Feb. 6              - Proposal (Olga & Jen)
Feb. 12             - Research on geometric distortion correction complete (Olga)
                    - Research on N/2 ghost correction complete (Jen)
Feb. 16             - RF coil block diagram and schematics complete (Olga & Jen)
Feb. 17             - Detailed software block diagram of geometric distortion
                      correction complete (Olga)
                    - Detailed software block diagram of N/2 ghost correction
                      complete (Jen)
Feb. 19             - Design Review (Olga & Jen)
Feb. 27 – Mar. 29   - Implementation of geometric distortion correction software
                    - Implementation of N/2 ghost correction software (Jen)
                    - Integration of correction software with pre-existing software
                    (Olga & Jen)
Mar. 25 – Mar. 29   - Build RF Coil (Olga & Jen)
Mar. 26             - Mock – Up Demo (Olga & Jen)
Apr. 1 – Apr. 19    - Debugging, testing, and interfacing of geometric distortion
                      correction and N/2 ghost correction (Olga & Jen)
Apr. 22             - Project demo (Olga & Jen)
Apr. 24             - Project Presentation (Olga & Jen)
Apr. 30             - Final paper due (Olga & Jen)


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