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Correction of Artifacts in Functional MRIs By Olga Lyandres and Jen Nelson Introduction 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 brain. 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. 1 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 including 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 include 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 2 Design 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 = (4kTRcoilf) where Rcoil is the resistance of the coil, T is the absolute temperature in K, and f is the bandwidth of the received signal. 3 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 Calculation 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 Fourier Image Transformation 4 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 Field 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 5 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 data. Verification 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 6 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 Labor: 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 Parts: 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 7 Schedule: 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 (Olga) - 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) 8

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