Aptitude Test For Dtu Course 31547, Medical MRI

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).

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.

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.

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.

 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)

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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.

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)

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)

• A.
• B.
• C.
• D.

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)

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.

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))

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.

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.

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.

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.

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.

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.

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.

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

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.

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)))

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

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.

What does the following expression evaluate to?

• A.
• B.
• C.
• D.

  0

What does the  following expression evaluate to?   

• A.
• B.
• C.
• D.