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 for taking the quiz (well spent). You are encouraged to use e. G. Literature from earlier courses when solving the problems, including
A magnet generating a static field â‰¥ 1 Î¤.
A rotating coil generating linear field variations â‰¥ 1 mT across the imaged region.
A coil used for generating magnetic fields oscillating at frequencies â‰¥ 1 MHz.
A coil used for detecting magnetic fields oscillating at frequencies â‰¥ 1 MHz.
The T1 parameter describes how fast the longitudinal magnetization is lost after excitation.
The T1 parameter describes how fast the transversal magnetization is lost after excitation.
The T1 parameter describes how fast the longitudinal magnetization approaches its full magnitude after excitation.
The T1 parameter describes how fast the transversal magnetization approaches its full amplitude after excitation.
A static field and a weaker radio-frequency field oriented perpendicular to the static field.
A static field and a weaker radio-frequency field oriented parallel to the static field.
A static field and a stronger radio-frequency field oriented perpendicular to the static field.
A static field and a stronger radio-frequency field oriented parallel to the static field.
Mz(t) = M0*(1-exp(-t/T1)).
Mz(t) = M0*exp(-t/T1)
Mz(t) = M0*(1-exp(-t/T2))
Mz(t) = M0*exp(-t/T2)
The magnetization vibrates in a plane through the north direction like a normal compass needle in a static magnetic field.
Spin is an apparent rotation of the nuclei that is independent of the magnetic field. It is causing nuclear magnetism.
Spin is an apparent rotation of the nuclei that is independent of the magnetic field. It is caused by nuclear magnetism.
Precession is an apparent rotation of the nuclei that is independent of the magnetic field. It is causing nuclear magnetism.
Precession is an apparent rotation of the nuclei that is independent of the magnetic field. It is caused by nuclear magnetism.
20% of the maximum possible signal for this substance and field.
40% of the maximum possible signal for this substance and field.
60% of the maximum possible signal for this substance and field.
80% of the maximum possible signal for this substance and field.
Precession is a rotation of the nuclear spin axis. It is causing nuclear magnetism.
Precession is a rotation of the nuclear spin axis. It is caused by nuclear magnetism.
Spin is a rotation of the axis of nuclear precession. It is causing nuclear magnetism.
Spin is a rotation of the axis of nuclear precession. It is caused by nuclear magnetism.
Neutrons in oxygen in mobile water molecules in the body.
Neutrons in hydrogen in mobile water molecules in the body.
Protons in oxygen in mobile water molecules in the body.
Protons in hydrogen in mobile water molecules in the body.
Measuring the absorption of radio waves reveals the T1-value.
T1-differences are reflected in measurements of the equilibrium magnetization.
The MR-signal is T1-weighted if it is recorded after repeated excitations, and if the "repetition time" is sufficiently short.
The decay rate of the MR signal recorded after excitation reflects the T1-value.
The T2 parameter describes how fast the longitudinal magnetization is lost after excitation.
The T2 parameter describes how fast the transversal magnetization is lost after excitation.
The T2 parameter describes how fast the transversal magnetization recovers its full amplitude after excitation.
The T2 parameter describes how fast the longitudinal magnetization recovers its full magnitude after excitation.
Projections of the magnetization density are measured using a rotating radiowave coil. Back projection is used to reconstruct images.
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.
Magnetic field gradients are applied to create linear relations between position and Larmor frequency. Frequency analysis is used for image reconstruction.
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.
The top left image
The top right image
The bottom left image
The bottom right image
1 second
1 millisecond
1 microsecond
25 milliseconds
Measuring the absorption of radio waves reveals the T2-value.
The MR-signal is T2-weighted, if it is recorded after repeated excitations, and if the "repetition time" is sufficiently short.
T2-differences are reflected in measurements of the equilibrium magnetization.
The gradual loss of MR signal recorded after excitation reflects the T2-value.
The half life of the transversal magnetization is TÂ½ = ln(2) T2
The half life of the transversal magnetization is TÂ½ = T2 / ln(2)
The half life of the longitudinal magnetization is TÂ½ = ln(2) T1
The half life of the longitudinal magnetization is TÂ½ = T1 / ln(2)
The column vector (MxBz-MzBx, MyBx-MxBy, MzBy-MyBz)
The column vector (MyBz-MzBy, MzBx-MxBz, MxBy-MyBx)
The column vector (MzBx-MxBz, MxBy-MyBz, MyBz-MzBy)
The column vector (MzBy-MyBz, MxBz-MzBx, MyBx-MxBy)
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.
The Fourier transform of any function f(t) can be expressed as a discrete weighted sum of complex exponentials.
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)
The area under a function f is equal to the Fourier transform of f evaluated at zero frequency.
X*Y = a*c*exp(i*b*d)
X*Y = a*c*exp(i*(b - d))
X*Y = a*c*exp(-i*(b + d))
X*Y = a*c*exp(i*(b + d))
Inhomogeneity of the static magnetic field B0.
Inhomogeneity of the oscillating magnetic field B1.
Nuclear interactions.
The mobility of water molecules.
...makes the sequence insentive to T2-relaxation by refocusing the nuclei.
...inverts the phases of the nuclei so that they get back in phase after a refocusing period.
...inverts the frequencies of the nuclei so that they get back in phase after a refocusing period.
...makes the nuclei precess in opposite direction in the rotating frame of reference so they get back in phase after a refocusing period.
...makes the z-component Bz of the magnetic field vary along the x-direction.
...makes the x-component Bx of the magnetic field vary along the x-direction.
...makes the x-component Bx of the magnetic field vary along the y- and z-directions.
...creates a constant field Bx in the in the x-direction.
The gradient strength during excitation.
The readout gradient strength, i.e. the gradient used to change the phase roll while measuring.
The phase-encoding gradient strength, i.e. the gradient used to select a line in k-space.
The slice-selection gradient strength.