Aptitude Test For Dtu Course 31547, Medical MRI

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.

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.

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.

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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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.

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.

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.

The expression evaluates to 0.

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.

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.

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)).

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.

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.

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.

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.

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.

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.

It should have been "r" to the left in the assignments.

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.

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.

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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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.

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.

Not all functions can be written as a discrete sum of complex exponentials (sines and cosines).

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.

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.

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.

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.

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.

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.

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.

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.