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ELG7173 - Final Exam Winter 2003

You have 3 hours to complete this exam. The exam has six questions; you are required to answer any three of them. Each question is worth equal marks. This is a closed book exam; however, you are permitted to bring two 8.5" × 11" sheets of notes into the exam. You are permitted to use a calculator. You may not communicate with anyone during the exam except the instructor.

  1. Display of Medical Image Data

    2. Software for viewing of medical images typically provides a "windowing" function. Windowing performs a linear stretching of the image histogram, in order to better view pixels with values in the "window". For example, if the screen pixels have intensities in the range 0 to 255, a windowing from wmin to wmax will convert a pixel P to a value of 255 × (P - wmin ) / ( wmax − wmin ) on the output display. Values of P above or below this range are "cropped" to a displayed value of 255 or 0, respectively. Windowing serves two important functions: 1) it enhances the visibility of contrasting tissue regions, 2) it allows selection of the tissue type to be viewed (for example, with CT images, windowing can allow viewing of soft tissue while bone regions are "cropped" to the maximum or minimum value)

    1. Describe how "windowing" allows these goals to be achieved

    2. Describe how the visibility of contrasting regions in an image varies with the size of the contrasting region and the SNR.

    3. Describe how "windowing" interacts with the variation in visibility with SNR. Considering these effects, what image conditions (in terms of contrast size and SNR) benefit most from "windowing"?

  2. X-Ray imaging System

    3. A simple X-ray imaging system consists of a source, an object, and a film detector.

    1. Sketch, and describe each component from the point of view of the generation of- and interaction with X-ray photons

    2. Show the convolution form of image formation for this X-ray system. Briefly describe each parameter and how it relates to the physical properties of the system.

    3. For each system component, list the properties that degrade image resolution, and the magnification level of each effect.

  3. C.T. Image Reconstruction

    4. Consider the geometry defined in figure Q3 for a model of a computed tomography system. Seven hexagonal regions, R1 to R7 are defined. Each region is 2 cm wide between parallel faces. Regions R1, R2, R3 R5, R6, and R7 are soft tissue, and region R4 is bone. The attenuation coefficients for these tissues are defined in table Q3:

    Figure Q3: Diagram for question 3.     		   
    Attenuation (cm-1)
    Tissue Eγ = 20 keV Eγ = 50 keV
    Soft Tissue 0.805   0.347  
    Bone 1.956   0.805  

    Table Q3: Tissue attenuation coefficients for question 3.
    Along each projection, 1.39×106 X-ray photons of energy Eγ=20keV and 1.78×105 X-ray photons of energy Eγ=50keV are emitted. The detectors function such that projections P are calculated as follows: P = log10 ∑( Nγ × Eγ)

    1. Calculate the projection data P1 to P9

    2. Calculate the image values (R1 to R7) using simple (unfiltered) backprojection

    3. What is the average contrast between the bone and soft tissue regions? Use the following definition of contrast: C= ( RBone − RS.T.) / RS.T.

  4. MRI Imaging

    5. An MRI system for imaging Hydrogen (of Gryomagnetic ratio 42.58 MHz/T ) has a main magnet with a Magnetic Field B0 of 1.0 T. Gradient fields in the slice selection and frequency encoding directions are of strength 0.5 Gauss/cm. The maximum gradient field in the phase encoding direction is 0.1 Gauss/cm. An 90°−FID pulse sequence is being used, with a slice selection pulse of 5 ms, a phase encoding pulse of 500 µs, and a frequency encoding pulse of 50 ms. The 90°−FID signal is given by: signal = k ρ ( 1 − exp(−TR/T1) )

    1. What is the width of the selected slice? Assume that the Fourier Transform of an RF pulse of duration T has a frequency domain width of 1/T.

    2. The clinical staff are imaging a part of the patients brain. The field of view is desired to be 5 cm (In both phase and frequency encoding directions) What is the maximum phase difference between the tissues at opposite edges of the field of view?

    3. What is the frequency encoding signal bandwidth (from tissues in the field of view)?

    4. The clinical staff are concerned that the patient may have a particular type of cancer, which has a T1 of 0.8 s, and density of 1.0 g/cm3. Assume normal brain tissue has a T1 of 1.2 s, and density of 0.95 g/cm3. What is best choice of TR to optimize contrast between that cancerous region and the normal brain tissue?

    5. Given this choice of TR, and the encoding timings given previously, how many slices can be imaged within the TR interval?

    6. The clinical staff wish to image 15 slices of tissue with a resolution of 1 mm in both the frequency and phase encoding directions. How many RF pulse sequences will be required? Using the value calculated in part E, how long will this take?

  5. Nuclear Medical Imaging

    1. In class we have discussed three kinds of collimation: 1) Pinhole collimation 2) Electronic collimation 3) Parallel hole collimation. Discuss each collimation technology, describing one medical imaging application, and describing any limitations or advantages in terms of efficiency, focus, and spatial uniformity.

    2. Discuss two issues (of the three presented in class) to be considered in the choice of isotopes for nuclear medical imaging.

  6. Ultrasound

    7. A circular ultrasound transducer of diameter 1 cm is being used at a pulse frequency of 1 MHz to image the mitral valve of the heart (mode M imaging). The background tissue (ie. all tissue except the valve) is a mixture of muscle, fat, and blood, with the following average ultrasound parameters: velocity= 1500 m/s, attenuation= 1.5 db/cm, density = 0.95 g/cm3. The mitral valve itself has the following parameters: velocity= 1550 m/s, attenuation= 1.8 db/cm, density = 1.00 g/cm3. Use the weakly reflecting (ie. no reverberations) assumption.

    1. We wish to image a mitral valve at a depth of 6 cm. Is this depth within the near field for this transducer?

    2. What is the minimum pulse length (in µs), such that the pulse length is two times greater than the diffraction limit (ie. such that the received signal at the transducer centre and edge are within the pulse envelope) ?

    3. Consider the body to be 30 cm across. How rapidly can the pulse be repeated (scan rate), in order to avoid contamination with the previous echo signal? At its maximum speed, consider the mitral valve to move 1 cm in 50 ms. How far will the mitral valve move between scans at this maximum rate?

    4. The uncertainty (position estimation error) in the depth of the mitral valve has a contribution from the movement, and from the from the pulse length. Calculate the speed of movement of the mitral valve, at which the uncertainty contribution from the movement and pulse lengths are equal.

    5. What is the reflectivity of the interface between the mitral valve and background tissue?

    6. Two separate echo signals are obtained when the mitral valve is at a depth of 5 cm and 6 cm, respectively. What is the ratio of pulse envelope amplitude between the two echos from the mitral valve?

Last Updated: $Date: 2005-03-03 16:46:17 -0500 (Thu, 03 Mar 2005) $