Aptitude Test For Dtu Course 31547, Medical MRI

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Aptitude Test For Dtu Course 31547, Medical MRI - Quiz

The following questions are representative of the prerequisites for DTU course 31547, Medical MRI (link below). They are provided as a service to potential participants, and may also be useful for repetition of course 31545, Medical Imaging Systems (exam preparation). The latter is a "qualified prerequisite course" for the MRI course.
All answers are directly relevant to the course 31547, and participants are assumed to know them already, e. G. From earlier DTU courses on signal analysis, linear algebra, programming and MRI. Don't worry, however, if you find some of the questions difficult (they are).
Set aside a few hours Read morefor taking the quiz (well spent). You are encouraged to use e. G. Literature from earlier courses when solving the problems, including slides and other MRI material from course 31545. Do not answer a question until you are sure of the answer - this way you will benefit the most. At the end of the test, you will be told which of your answers were right and wrong. Ask, if you are still puzzled after seeing the answers and reading the background material.
Your identity is not recorded. You can certainly choose to take the course even if you fail this test, but in that case further course preparation is recommended. It is a tough course if you are behind already at the beginning. You are especially encouraged to get acquainted with all all words and concepts appearing in the quiz -- they will be used constantly.
Enjoy,Lars G. Hanson,


Questions and Answers
  • 1. 

    Write a function in Matlab, that implements numerical differentiation for a vector of equidistant samples (first and second derivatives). Unlike Matlab's built-in function diff(), your function should not shift the result vector relative to the input vector (see e.g. first paragraph of http://terpconnect.umd.edu/~toh/spectrum/Differentiation.html).  Check the result in Matlab yourself by comparing to analytical solutions in example cases. You will need the function during course 31547 (and other Matlab programming skills).

  • 2. 

    Which of the following is not part of typical scanners for magnetic resonance imaging?

    • A.

      A magnet generating a static field ≥ 1 Τ.

    • B.

      A rotating coil generating linear field variations ≥ 1 mT across the imaged region.

    • C.

      A coil used for generating magnetic fields oscillating at frequencies ≥ 1 MHz.

    • D.

      A coil used for detecting magnetic fields oscillating at frequencies ≥ 1 MHz.

    Correct Answer
    B. A rotating coil generating linear field variations ≥ 1 mT across the imaged region.
    Explanation
    This answer is correct because a rotating coil generating linear field variations is not typically found in scanners for magnetic resonance imaging. The other options, such as a magnet generating a static field, a coil used for generating magnetic fields oscillating at frequencies, and a coil used for detecting magnetic fields oscillating at frequencies, are all part of typical scanners for MRI.

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  • 3. 

    Which of the following sentences about T1 relaxation is correct?

    • A.

      The T1 parameter describes how fast the longitudinal magnetization is lost after excitation.

    • B.

      The T1 parameter describes how fast the transversal magnetization is lost after excitation.

    • C.

      The T1 parameter describes how fast the longitudinal magnetization approaches its full magnitude after excitation.

    • D.

      The T1 parameter describes how fast the transversal magnetization approaches its full amplitude after excitation.

    Correct Answer
    C. The T1 parameter describes how fast the longitudinal magnetization approaches its full magnitude after excitation.
    Explanation
    The T1 parameter describes how fast the longitudinal magnetization approaches its full magnitude after excitation. This means that T1 relaxation refers to the recovery of the magnetization in the longitudinal direction, which is aligned with the external magnetic field. It measures how quickly the magnetization returns to its original state after being disturbed by excitation. This is in contrast to T2 relaxation, which refers to the decay of transverse magnetization.

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  • 4. 

    Which of the following combinations of static and RF magnetic fields is used for MRI?

    • A.

      A static field and a weaker radio-frequency field oriented perpendicular to the static field.

    • B.

      A static field and a weaker radio-frequency field oriented parallel to the static field.

    • C.

      A static field and a stronger radio-frequency field oriented perpendicular to the static field.

    • D.

      A static field and a stronger radio-frequency field oriented parallel to the static field.

    Correct Answer
    A. A static field and a weaker radio-frequency field oriented perpendicular to the static field.
    Explanation
    MRI (Magnetic Resonance Imaging) uses a combination of a static magnetic field and a weaker radio-frequency (RF) field. The static field is used to align the protons in the body, while the RF field is used to perturb the alignment of the protons. By measuring the response of the protons to the RF field, detailed images of the body can be obtained. The RF field is oriented perpendicular to the static field to ensure that the protons are perturbed in a controlled manner.

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  • 5. 

     Which formula below describes the recovery of magnetization after a 90 degree excitation pulse in the beginning of a magnetic resonance experiment? (Mz is here the magnetization along the B0-field, M0 is the size of the equilibrium magnetization, T1 is the longitudinal relaxation time, T2 is the transversal relaxation time, and t is the time after excitation):

    • A.

      Mz(t) = M0*(1-exp(-t/T1)).

    • B.

      Mz(t) = M0*exp(-t/T1)

    • C.

      Mz(t) = M0*(1-exp(-t/T2))

    • D.

      Mz(t) = M0*exp(-t/T2)

    Correct Answer
    A. Mz(t) = M0*(1-exp(-t/T1)).
    Explanation
    The correct answer is Mz(t) = M0*(1-exp(-t/T1)). This formula describes the recovery of magnetization after a 90 degree excitation pulse in the beginning of a magnetic resonance experiment. It takes into account the equilibrium magnetization (M0), the time after excitation (t), and the longitudinal relaxation time (T1). The formula shows that the magnetization along the B0-field (Mz) increases over time and approaches the equilibrium magnetization (M0) exponentially with a time constant of T1.

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  • 6. 

    The vector equation  describes the time evolution of the total nuclear magnetization  of protons in a static magnetic field where  is the gyromagnetic ratio of hydrogen nuclei. What does the equation predict?

    • A.

      The magnetization gradually aligns along  (they become parallel), so that the tissue is magnetized.

    • B.

      The magnetization vibrates in a plane through the north direction like a normal compass needle in a static magnetic field.

    • C.

      The magnetization  precesses around the magnetic field  at a (angular) frequency

    • D.

      The magnetization precesses around the magnetic field forming an angle   between the two.

    Correct Answer
    C. The magnetization  precesses around the magnetic field  at a (angular) frequency
    Explanation
    The vector equation describes the time evolution of the total nuclear magnetization of protons in a static magnetic field. It predicts that the magnetization will precess around the magnetic field at a (angular) frequency.

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  • 7. 

    The sentences below describe spin or precession. Select the most correct.

    • A.

      Spin is an apparent rotation of the nuclei that is independent of the magnetic field. It is causing nuclear magnetism.

    • B.

      Spin is an apparent rotation of the nuclei that is independent of the magnetic field. It is caused by nuclear magnetism.

    • C.

      Precession is an apparent rotation of the nuclei that is independent of the magnetic field. It is causing nuclear magnetism.

    • D.

      Precession is an apparent rotation of the nuclei that is independent of the magnetic field. It is caused by nuclear magnetism.

    Correct Answer
    A. Spin is an apparent rotation of the nuclei that is independent of the magnetic field. It is causing nuclear magnetism.
    Explanation
    The correct answer is "Spin is an apparent rotation of the nuclei that is independent of the magnetic field. It is caused by nuclear magnetism." This is the most correct statement because spin is indeed an apparent rotation of the nuclei that is independent of the magnetic field. However, it is not causing nuclear magnetism, but rather it is caused by nuclear magnetism.

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  • 8. 

    A substance with relaxation times T1 = 1s and T2= 0.1s has the equilibrium magnetization M0 at 1.5T. The magnetization is rotated by two short (1 ms) 90 degree radio-frequency pulses separated by a 0.5s pause. The signal measured immediately after the second pulse is approximately… (hint: You may find the answer of question 12 helpful).

    • A.

      20% of the maximum possible signal for this substance and field.

    • B.

      40% of the maximum possible signal for this substance and field.

    • C.

      60% of the maximum possible signal for this substance and field.

    • D.

      80% of the maximum possible signal for this substance and field.

    Correct Answer
    B. 40% of the maximum possible signal for this substance and field.
    Explanation
    When a substance with relaxation times T1 = 1s and T2 = 0.1s is subjected to two short 90 degree radio-frequency pulses separated by a 0.5s pause, the magnetization is rotated. After the second pulse, the signal measured is approximately 40% of the maximum possible signal for this substance and field. This can be explained by the fact that T1 relaxation time is longer than the pause between the pulses, allowing the magnetization to recover partially. However, T2 relaxation time is shorter than the pause, causing some loss of signal coherence. This results in a signal that is reduced to 40% of the maximum possible signal.

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  • 9. 

    Select the correct sentence below.

    • A.

      Precession is a rotation of the nuclear spin axis. It is causing nuclear magnetism.

    • B.

      Precession is a rotation of the nuclear spin axis. It is caused by nuclear magnetism.

    • C.

      Spin is a rotation of the axis of nuclear precession. It is causing nuclear magnetism.

    • D.

      Spin is a rotation of the axis of nuclear precession. It is caused by nuclear magnetism.

    Correct Answer
    B. Precession is a rotation of the nuclear spin axis. It is caused by nuclear magnetism.
    Explanation
    The correct sentence is "Precession is a rotation of the nuclear spin axis. It is caused by nuclear magnetism." This sentence accurately explains that precession is a rotation of the nuclear spin axis and that it is caused by nuclear magnetism.

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  • 10. 

    Where is the MR signal coming from during normal MR imaging?

    • A.

      Neutrons in oxygen in mobile water molecules in the body.

    • B.

      Neutrons in hydrogen in mobile water molecules in the body.

    • C.

      Protons in oxygen in mobile water molecules in the body.

    • D.

      Protons in hydrogen in mobile water molecules in the body.

    Correct Answer
    D. Protons in hydrogen in mobile water molecules in the body.
    Explanation
    During normal MR imaging, the MR signal is coming from the protons in hydrogen in mobile water molecules in the body. MR imaging works by using a strong magnetic field to align the hydrogen protons in the body. When a radiofrequency pulse is applied, the protons absorb the energy and then release it as a signal when they return to their original state. This signal is detected by the MR machine and used to create an image.

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  • 11. 

    Which of the following options gives a T1-weighted magnetic resonance (MR) measurement?

    • A.

      Measuring the absorption of radio waves reveals the T1-value.

    • B.

      T1-differences are reflected in measurements of the equilibrium magnetization.

    • C.

      The MR-signal is T1-weighted if it is recorded after repeated excitations, and if the "repetition time" is sufficiently short.

    • D.

      The decay rate of the MR signal recorded after excitation reflects the T1-value.

    Correct Answer
    C. The MR-signal is T1-weighted if it is recorded after repeated excitations, and if the "repetition time" is sufficiently short.
    Explanation
    The MR-signal is T1-weighted if it is recorded after repeated excitations, and if the "repetition time" is sufficiently short. This means that the signal is more sensitive to T1 differences between tissues when it is recorded after multiple excitations and with a short repetition time. T1-weighted measurements are used to highlight differences in tissue relaxation times, providing contrast between different types of tissues in an MR image.

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  • 12. 

    Which of the following sentences about T2-relaxation is correct when field inhomogeneity is insignificant?

    • A.

      The T2 parameter describes how fast the longitudinal magnetization is lost after excitation.

    • B.

      The T2 parameter describes how fast the transversal magnetization is lost after excitation.

    • C.

      The T2 parameter describes how fast the transversal magnetization recovers its full amplitude after excitation.

    • D.

      The T2 parameter describes how fast the longitudinal magnetization recovers its full magnitude after excitation.

    Correct Answer
    B. The T2 parameter describes how fast the transversal magnetization is lost after excitation.
    Explanation
    The T2 parameter describes how fast the transversal magnetization is lost after excitation. This means that after the initial excitation of the magnetic field, the transversal magnetization decreases over time. This is in contrast to the other options, which describe the recovery or magnitude of the longitudinal magnetization.

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  • 13. 

    Which sentence below best characterizes magnetic resonance imaging?

    • A.

      Projections of the magnetization density are measured using a rotating radiowave coil. Back projection is used to reconstruct images.

    • B.

      The strong B0 field is applied in all directions in order to make the nuclear directions depend on position. Image reconstruction is performed by weighted averaging of measurements sensitive to different directions.

    • C.

      Magnetic field gradients are applied to create linear relations between position and Larmor frequency. Frequency analysis is used for image reconstruction.

    • D.

      The frequency of radio waves coming from the body after excitation equals the frequency of spatial phase roll patterns. Reconstruction is done by weighting phase roll patterns with the measured frequencies.

    Correct Answer
    C. Magnetic field gradients are applied to create linear relations between position and Larmor frequency. Frequency analysis is used for image reconstruction.
    Explanation
    Magnetic resonance imaging uses magnetic field gradients to create linear relations between position and Larmor frequency. This allows for frequency analysis to be used in image reconstruction. By analyzing the frequencies of the signals emitted by the body after excitation, the image can be reconstructed.

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  • 14. 

    Eight MR axial brain images are shown above. They are all acquired with a ”spin-echo sequence” with repetition time TR, and echo time TE. The top row of images are aquired with TE=10ms and varying TR. The bottom row of images are aquired with TR=4000ms and varying TE. The units of indicated times are all milliseconds. Which image has the most pure PD-weighting (”proton density weighting”)?

    • A.

      The top left image

    • B.

      The top right image

    • C.

      The bottom left image

    • D.

      The bottom right image

    Correct Answer
    C. The bottom left image
    Explanation
    The bottom left image has the most pure PD-weighting because it has the longest repetition time (TR=4000ms) and a short echo time (TE=10ms). In a spin-echo sequence, a longer TR allows for more recovery of the longitudinal magnetization, which enhances the proton density contrast. A shorter TE also helps to minimize T2 relaxation effects, further emphasizing the proton density weighting. Therefore, the bottom left image is likely to have the highest proton density contrast among all the images.

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  • 15. 

    This question concerns excitation of nuclei in a particular magnetic resonance experiment. A sinusoidal voltage is applied to a particular radio frequency (RF) coil so that it generates an oscillating resonant magnetic field of 1 microtesla amplitude. This B1 field rotates at the Larmor frequency in the transversal plane (it is therefore not generated by a simple loop coil). The gyromagnetic ratio of the considered nuclear species is 10 MHz/T. Relaxation during the excitation pulse is insignificant. How long does it take to do a 90 degree excitation in this situation?

    • A.

      1 second

    • B.

      1 millisecond

    • C.

      1 microsecond

    • D.

      25 milliseconds

    Correct Answer
    D. 25 milliseconds
    Explanation
    In this situation, the gyromagnetic ratio of the nuclear species is given as 10 MHz/T. The Larmor frequency is the frequency at which the nuclei precess in the magnetic field. Since the B1 field generated by the RF coil rotates at the Larmor frequency, it means that the B1 field is rotating at a frequency of 10 MHz.

    To do a 90 degree excitation, the B1 field needs to rotate for a quarter of a cycle. Since the frequency of rotation is 10 MHz, the time taken for a quarter of a cycle (90 degrees) is 1/4 * (1/10 MHz) = 25 milliseconds. Therefore, the correct answer is 25 milliseconds.

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  • 16. 

    In the absence of field inhomogeneity, which of the following options gives a T2-weighted magnetic resonance (MR) measurement? 

    • A.

      Measuring the absorption of radio waves reveals the T2-value.

    • B.

      The MR-signal is T2-weighted, if it is recorded after repeated excitations, and if the "repetition time" is sufficiently short.

    • C.

      T2-differences are reflected in measurements of the equilibrium magnetization.

    • D.

      The gradual loss of MR signal recorded after excitation reflects the T2-value.

    Correct Answer
    D. The gradual loss of MR signal recorded after excitation reflects the T2-value.
    Explanation
    The gradual loss of MR signal recorded after excitation reflects the T2-value because T2 relaxation refers to the time it takes for the protons to lose their phase coherence and return to equilibrium after being excited. In T2-weighted imaging, the signal is measured during this relaxation process, and the rate at which the signal decays reflects the T2 value. Therefore, the gradual loss of MR signal recorded after excitation is a measurement of T2-weighted magnetic resonance.

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  • 17. 

    The ”half life” T½ of an exponentially decaying quantity describes how long it takes for the quantity to be reduced by a factor of two. Which statement below correctly describes the relation between a nuclear relaxation time (defined conventionally) and the corresponding ”half life”?

    • A.

      The half life of the transversal magnetization is T½ = ln(2) T2

    • B.

      The half life of the transversal magnetization is T½ = T2 / ln(2)

    • C.

      The half life of the longitudinal magnetization is T½ = ln(2) T1

    • D.

      The half life of the longitudinal magnetization is T½ = T1 / ln(2)

    Correct Answer
    A. The half life of the transversal magnetization is T½ = ln(2) T2
    Explanation
    The correct answer explains that the half-life of the transversal magnetization is equal to ln(2) multiplied by T2. This means that it takes ln(2) times the nuclear relaxation time (T2) for the transversal magnetization to be reduced by a factor of two.

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  • 18. 

    The vector equation  describes the time evolution of the total nuclear magnetization  of protons in a static magnetic field  chosen along the z-axis.  is the gyromagnetic ratio. Define  to be the Larmor frequency (positive), and define the complex transversal magnetization as Mxy=Mx+i*My where Mx and My are components of  and where "i" is the imaginary unit. Which equation describes the evolution of the transversal magnetization in this case? (do the actual calculation)

    Correct Answer
    B.
  • 19. 

    Which quantity below correctly describes the vector product   ?

    • A.

      The column vector (MxBz-MzBx, MyBx-MxBy, MzBy-MyBz)

    • B.

      The column vector (MyBz-MzBy, MzBx-MxBz, MxBy-MyBx)

    • C.

      The column vector (MzBx-MxBz, MxBy-MyBz, MyBz-MzBy)

    • D.

      The column vector (MzBy-MyBz, MxBz-MzBx, MyBx-MxBy)

    Correct Answer
    B. The column vector (MyBz-MzBy, MzBx-MxBz, MxBy-MyBx)
    Explanation
    The correct answer is the column vector (MyBz-MzBy, MzBx-MxBz, MxBy-MyBx). This is because the vector product, also known as the cross product, is defined as a binary operation on two vectors resulting in a vector that is perpendicular (orthogonal) to both input vectors. The components of the resulting vector are determined by specific formulas, and the given column vector matches those formulas correctly.

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  • 20. 

    Which statement below is false? (you will need the right versions of all 4 during the DTU MRI course 31547)

    • A.

      The Fourier transform F of a real function f(t) has Hermitian symmetry, i.e. F(w)=conj(F(-w)) where conf() denotes complex conjugation, and w is the frequency variable corresponding to time t.

    • B.

      The Fourier transform of any function f(t) can be expressed as a discrete weighted sum of complex exponentials.

    • C.

      The Fourier transform of time shifted function f(t+t0) equals the Fourier transform of f times a phase roll: F(w)exp(i t0 w)

    • D.

      The area under a function f is equal to the Fourier transform of f evaluated at zero frequency.

    Correct Answer
    B. The Fourier transform of any function f(t) can be expressed as a discrete weighted sum of complex exponentials.
    Explanation
    Not all functions can be written as a discrete sum of complex exponentials (sines and cosines).

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  • 21. 

    Let  X=a*exp(i*b) and Y=c*exp(i*d) be two complex numbers where a,b,c,d are real numbers, and i is the imaginary unit. How is the product X*Y calculated?

    • A.

      X*Y = a*c*exp(i*b*d)

    • B.

      X*Y = a*c*exp(i*(b - d))

    • C.

      X*Y = a*c*exp(-i*(b + d))

    • D.

      X*Y = a*c*exp(i*(b + d))

    Correct Answer
    D. X*Y = a*c*exp(i*(b + d))
    Explanation
    The product of two complex numbers is calculated by multiplying their magnitudes and adding their arguments. In this case, the magnitudes of X and Y are a and c respectively. The argument of X is b and the argument of Y is d. Therefore, the product X*Y is equal to a*c*exp(i*(b + d)).

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  • 22. 

    What is the source of shortening of T2* compared to T2?

    • A.

      Inhomogeneity of the static magnetic field B0.

    • B.

      Inhomogeneity of the oscillating magnetic field B1.

    • C.

      Nuclear interactions.

    • D.

      The mobility of water molecules.

    Correct Answer
    A. Inhomogeneity of the static magnetic field B0.
    Explanation
    The source of shortening of T2* compared to T2 is the inhomogeneity of the static magnetic field B0. In a homogeneous magnetic field, the T2 and T2* relaxation times would be equal. However, in the presence of field inhomogeneities, the T2* relaxation time becomes shorter than T2. This is because the inhomogeneities cause variations in the local magnetic field, leading to dephasing of the spins and faster decay of the signal.

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  • 23. 

    Select the right continuation of the following sentence concerning effects of field inhomogeneity: A 180 refocusing pulse following a 90 degree excitation in a spin-echo sequence...

    • A.

      ...makes the sequence insentive to T2-relaxation by refocusing the nuclei.

    • B.

      ...inverts the phases of the nuclei so that they get back in phase after a refocusing period.

    • C.

      ...inverts the frequencies of the nuclei so that they get back in phase after a refocusing period.

    • D.

      ...makes the nuclei precess in opposite direction in the rotating frame of reference so they get back in phase after a refocusing period.

    Correct Answer
    B. ...inverts the pHases of the nuclei so that they get back in pHase after a refocusing period.
    Explanation
    A 180 refocusing pulse following a 90 degree excitation in a spin-echo sequence inverts the phases of the nuclei so that they get back in phase after a refocusing period. This is because the 180 pulse flips the magnetization vector by 180 degrees, causing the spins to precess in the opposite direction. As a result, the spins that were dephased during the 90 degree excitation pulse are rephased during the refocusing pulse, leading to the recovery of the signal and refocusing of the nuclei.

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  • 24. 

    Select the right continuation of the following sentence: Sending a constant current through the gradient coil creating a gradient in the x direction...

    • A.

      ...makes the z-component Bz of the magnetic field vary along the x-direction.

    • B.

      ...makes the x-component Bx of the magnetic field vary along the x-direction.

    • C.

      ...makes the x-component Bx of the magnetic field vary along the y- and z-directions.

    • D.

      ...creates a constant field Bx in the in the x-direction.

    Correct Answer
    A. ...makes the z-component Bz of the magnetic field vary along the x-direction.
    Explanation
    Sending a constant current through the gradient coil creates a magnetic field gradient in the x direction, which causes the z-component Bz of the magnetic field to vary along the x-direction. This is because the gradient coil is responsible for generating the gradient in the magnetic field, and the direction of the gradient determines how the magnetic field component varies. In this case, since the gradient is in the x direction, it affects the z-component of the magnetic field.

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  • 25. 

    The k-space is traversed during MR image acquisition. For a given nucleus, what determines the instantaneous speed at which k-spaced is traversed during a sample period?

    • A.

      The gradient strength during excitation.

    • B.

      The readout gradient strength, i.e. the gradient used to change the phase roll while measuring.

    • C.

      The phase-encoding gradient strength, i.e. the gradient used to select a line in k-space.

    • D.

      The slice-selection gradient strength.

    Correct Answer
    B. The readout gradient strength, i.e. the gradient used to change the pHase roll while measuring.
    Explanation
    The instantaneous speed at which k-space is traversed during a sample period is determined by the readout gradient strength. This gradient is used to change the phase roll while measuring, which affects the position in k-space that is being sampled. By adjusting the strength of the readout gradient, the speed at which k-space is traversed can be controlled, allowing for different sampling rates and image acquisition times.

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  • 26. 

    Suppose you know the detailed sequence diagram for an imaging sequence, and that this includes quantitative gradient specifications. How do you calculate the k-space position at a time t? (except for a scaling by the gyromagnetic ratio)

    • A.

      By temporal integration of gradients from excitation until time t considering only periods where the observed magnetization is transverse, and taking into account refocusing pulses.

    • B.

      By spatial integration of gradients considering only areas where the observed magnetization is transverse, and taking into account refocusing pulses.

    • C.

      By temporal integration of gradients from the last refocusing pulse until time t considering only periods where the observed magnetization is transverse.

    • D.

      By spatial integration of gradients considering only areas where the observed magnetization is transverse.

    Correct Answer
    A. By temporal integration of gradients from excitation until time t considering only periods where the observed magnetization is transverse, and taking into account refocusing pulses.
    Explanation
    The correct answer explains that to calculate the k-space position at a time t, one needs to temporally integrate the gradients from excitation until time t, while considering only periods where the observed magnetization is transverse. Additionally, refocusing pulses should be taken into account. This approach ensures that only relevant information is considered and that the magnetization is properly accounted for during the imaging sequence. Spatial integration of gradients or considering only areas where the observed magnetization is transverse may not provide an accurate calculation of the k-space position at a specific time.

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  • 27. 

    During MRI, so-called "phase rolls" are created in the patient using gradients. If the phase of the nuclei is color-coded, the phase variation can be visualized as stripe patters across the field of view (FOV). It is convenient to introduce a vector space called k-space, where each point corresponds to an associated phase roll  in image space. A phase-roll can be characterized by it's direction in space and by its wavelength. Which sentence below best describes how k-space is structured?

    • A.

      The distance from k-space origin is the wavelength. The phase variation of the phase roll is in the direction of the k-space vector.

    • B.

      The distance from k-space origin is the inverse wavelength. The phase variation of the phase roll is in the direction of the k-space vector.

    • C.

      The distance from k-space origin is the wavelength. The phase variation of the phase roll is orthogonal to the direction of the k-space vector.

    • D.

      The distance from k-space origin is the inverse wavelength. The phase variation of the phase roll is orthogonal to the direction of the k-space vector.

    Correct Answer
    B. The distance from k-space origin is the inverse wavelength. The pHase variation of the pHase roll is in the direction of the k-space vector.
    Explanation
    In k-space, the distance from the origin represents the inverse wavelength. This means that shorter wavelengths are represented by points closer to the origin, while longer wavelengths are represented by points further from the origin. Additionally, the phase variation of the phase roll is in the direction of the k-space vector. This means that the phase of the nuclei changes in the same direction as the k-space vector.

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  • 28. 

    Which of the following statements about MR images is most correct?

    • A.

      The spatial resolution is determined by the k-space sampling density, the FOV by the extent of k-space coverage, and the contrast by the signal in the central k-space region.

    • B.

      The spatial resolution is determined by the extent of k-space coverage, the FOV by the signal in the central k-space region, and the contrast by the k-space sampling density.

    • C.

      The spatial resolution is determined by the signal in the central k-space region, the FOV by the extent of k-space coverage, and the contrast by the k-space sampling density.

    • D.

      The spatial resolution is determined by the extent of k-space coverage, the FOV by the k-space sampling density, and the contrast by the signal in the central k-space region.

    Correct Answer
    D. The spatial resolution is determined by the extent of k-space coverage, the FOV by the k-space sampling density, and the contrast by the signal in the central k-space region.
    Explanation
    The spatial resolution in MR images is determined by the extent of k-space coverage, meaning that the more of k-space that is sampled, the higher the spatial resolution will be. The FOV (Field of View) is determined by the k-space sampling density, meaning that the more densely k-space is sampled, the larger the FOV will be. The contrast in MR images is determined by the signal in the central k-space region, meaning that the strength of the signal in the central region of k-space will determine the contrast in the image.

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  • 29. 

    For which value of the parameter t is the following matrix not invertible?

    • A.

      T=0

    • B.

      T=2/3

    • C.

      T=2

    • D.

      T=3

    Correct Answer
    B. T=2/3
    Explanation
    In order for a matrix to be invertible, its determinant must be non-zero. Thus, we need to find the determinant of the given matrix for each value of t. Evaluating the determinant, we find that for t=2/3, the determinant is 0. Therefore, the matrix is not invertible for t=2/3.

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  • 30. 

    Which sentence is not correctly describing the conditions in a frame of reference that rotates at the common Larmor and radio-wave frequency during on-resonance excitation?

    • A.

      The magnetization precesses around B0.

    • B.

      The magnetization precesses around B1.

    • C.

      The B1 field is stationary and orthogonal to B0.

    • D.

      The B0 field is stationary and orthogonal to B1.

    Correct Answer
    A. The magnetization precesses around B0.
    Explanation
    The correct answer is "The magnetization precesses around B0." This statement is not correct because in a frame of reference that rotates at the common Larmor and radio-wave frequency during on-resonance excitation, the magnetization precesses around B1, not B0.

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  • 31. 

    Which of the following expressions is not a solution to the differential equation  where t is a dimensionless time variable? The function f(t) and the constant k are complex. The imaginary unit is denoted "i" below.

    • A.

      F(t) = |f(t=0)| exp(-kt + i p) where p is the phase angle of f(t=0)

    • B.

      F(t) = f(t=1) exp(-kt) exp(k)

    • C.

      F(t) = i f(t=0) (sin(i k t) - i cos (i k t))

    • D.

      F(t) = i f(t=1) (sin( -i k (t-1)) - i cos( -i k (t-1)))

    Correct Answer
    D. F(t) = i f(t=1) (sin( -i k (t-1)) - i cos( -i k (t-1)))
    Explanation
    The given expression f(t) = i f(t=1) (sin( -i k (t-1)) - i cos( -i k (t-1))) is not a solution to the differential equation. This is because the differential equation involves the exponential function exp(-kt) and its complex conjugate, while the given expression involves trigonometric functions sin and cos. Therefore, the given expression does not satisfy the conditions of the differential equation and is not a solution.

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  • 32. 

    Which of the matlab functions below is not a correct implementation of the factorial of a positive integer? (Reminder: the factorial of 5, for example, is 5! = 5*4*3*2*1. Neither the implementation efficiency, nor the precision for large arguments, is relevant for the answer. Matlab permits recursive functions, i.e. self-referencing functions).

    • A.

      function r = f(x)   if x==1     f(x) = 1;   else     f(x) = x*f(x-1); end

    • B.

      function r = f(x)   r = prod(1:x); end

    • C.

      function r = f(x)   r=1;   for i=1:x      r = i*r;   end end

    • D.

      function r = f(x)   r=1;   for i=2:x     r = i*r;    end end

    Correct Answer
    A. function r = f(x)   if x==1     f(x) = 1;   else     f(x) = x*f(x-1); end
    Explanation
    It should have been "r" to the left in the assignments.

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  • 33. 

    Which properties do normal T1- and T2-weighted MR images reflect:

    • A.

      The protein content since proteins contain large amounts of hydrogen.

    • B.

      The water content and electromagnetic waves from neural activity.

    • C.

      The water content and the mobility of water molecules.

    • D.

      The concentration of injected protons and their relaxation.

    Correct Answer
    C. The water content and the mobility of water molecules.
    Explanation
    T1- and T2-weighted MR images reflect the water content and the mobility of water molecules. T1-weighted images provide information about the water content, while T2-weighted images provide information about the mobility of water molecules. The relaxation times of water molecules in different tissues can be used to differentiate between different types of tissues in the body. The protein content and concentration of injected protons are not directly reflected in T1- and T2-weighted MR images.

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  • 34. 

    What does the following expression evaluate to?

    • A.
    • B.
    • C.
    • D.

      0

    Correct Answer
    B.
    Explanation
    The expression evaluates to 0.

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  • 35. 

    What does the  following expression evaluate to?   

    Correct Answer
    D.

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  • Current Version
  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
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    Larsh
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