questions Flashcards
NORRIS: Slice selection represents an important step in MRI. Ideally all excitation profiles would be rectangular in form. If you wish to obtain a rectangular profile, then (to a first approximation) what should the modulation function of the corresponding RF pulse be (2)? Explain how you change the position of the slice (2)? For each of the main functions of RF pulses (excitation, refocusing, inversion) the slice selection gradients have to fulfill different conditions: for each of these three cases explain what conditions the slice gradients need to satisfy and give a sketch of the RF pulse and slice gradient waveform (6).
- this is a sinc function as f(t)=sinc(t) sinc(x) = sin(pi x) / pi x
- adjusting the bandwidth of the frequency pulse: modifying the RF pulse bandwidth shifts the central frequency of the excitation pulse. This shifts the slice position along the gradient axis. A higher frequency targets spins at a different position along the gradient.
or by changing the strenght of the slice selection gradient: Adjusting the gradient strength alters the spatial encoding of frequencies. A stronger gradient means a given frequency corresponds to a different position, thus changing the slice position.
excitation: usually a 90degree pulse is applied. The slice gradient applied is one with the rf and a second gradient lobe, applied after the RF pulse. The amplitude and duration of this last pulse are typically half that of the first gradient lobe. This brings magneetisation from the longitudinal plane to the transverse plane.
The main lobe (2A) gradient ensures that the RF pulse frequency matches the Larmor frequency of spins in the selected slice. This induces a linear phase shift across the slice during the RF excitation. This phase shift is necessary for slice selection but leaves the spins within the slice out of phase.
The rephasing lobe (A) is applied immediately after the RF pulse to cancel out the phase shifts induced by the main lobe. By applying a gradient lobe with an area equal to half that of the main lobe but in the opposite direction (negative amplitude), the spins are rephased. This means the total phase shift caused by the gradient pulses is zero.
Refocusing:
Refocusing usually applies a 180d RF pulse. Here, the slice gradient must be applied symmetrical to the centre of RF as magnetisation is initially in the transverse plane and remains transverse after the pulse.
Inversion:
no transverse magnetization generated, thus no additional requirements on the gradient (=not centered)
Sketch them on paper?? Is it correct?
NORRIS:2. Normally we acquire EPI data in a single shot, i.e. one excitation gives one image. However, it is also possible to segment an EPI acquisition, for example so that four shots will give you one image, with each shot acquiring a quarter of k-space. What would the potential advantages and disadvantages (if any) of such an experiment be in terms of: 1. Spatial resolution (3) 2. Distortion (3) When compared to a single-shot acquisition with the same TE. Are there any circumstances in which you would recommend using such a sequence for an fMRI study (4)? Please explain your reasoning!
Spatial Resolution Advantages:
Reduced T2 Blurring: In single-shot EPI, the entire k-space is traversed in one shot, which can lead to T2* blurring, especially in high-resolution images. Segmenting the acquisition reduces the traversal time for each shot, thereby reducing T2* blurring and potentially improving spatial resolution.
*Higher Gradient Strength Utilization: With segmented EPI, gradients do not need to switch as rapidly, allowing for higher gradient strengths and better spatial encoding, which can enhance spatial resolution.
*Increased SNR per Segment: Each segment can be acquired with a slightly higher signal-to-noise ratio (SNR) because the acquisition time for each segment is shorter, reducing the signal decay.
Spatial Resolution Disadvantages:
*Registration Errors: Combining multiple shots requires precise alignment and correction for any motion between shots. Misalignment can degrade spatial resolution.
*Increased Acquisition Time: Overall acquisition time increases because multiple shots are required to cover the entire k-space, potentially leading to more motion artifacts that can affect spatial resolution.
Distortion Advantages:
*Reduced Geometric Distortion: Single-shot EPI is highly susceptible to geometric distortions due to B0 inhomogeneities and susceptibility variations, especially in regions with strong field gradients. Segmenting the acquisition reduces the time between the start and end of k-space traversal, which mitigates these distortions.
*Improved Phase Encoding: With segmented acquisition, phase encoding can be distributed across multiple shots, reducing the susceptibility to distortions that typically affect single-shot EPI.
Distortion Disadvantages:
Phase Inconsistencies: Each segment is acquired at slightly different times and might experience different phase evolution due to B0 inhomogeneities, leading to phase inconsistencies that need to be corrected.
Complex Reconstruction: The reconstruction process becomes more complex due to the need to combine data from multiple shots, potentially introducing artifacts if not done correctly.
Experiment example where segmented is better than single shot
1. Improved Image Quality in High-Resolution fMRI Studies
Reasoning:
Higher Spatial Resolution: For high-resolution fMRI studies, where detailed mapping of brain activity is crucial, segmented EPI can offer better spatial resolution. This is due to reduced T2* blurring, which is more pronounced in single-shot EPI because the entire k-space is acquired in one go. By segmenting the acquisition, each segment is less affected by T2* decay, resulting in sharper images.
Example: Studies focusing on small brain structures, such as the hippocampus or cortical layers, where fine spatial details are critical, would benefit from the enhanced resolution provided by segmented EPI.
2. Reduced Geometric Distortion in Regions with High Susceptibility Variations
Reasoning:
Geometric Distortion: Single-shot EPI is particularly prone to geometric distortions caused by B0 inhomogeneities and susceptibility variations, especially in regions like the orbitofrontal cortex and temporal lobes. Segmented EPI reduces the time between the start and end of k-space traversal, mitigating these distortions.
Example: fMRI studies investigating brain regions near air-tissue interfaces, where susceptibility-induced distortions are problematic, can achieve more accurate localization of brain activity with segmented EPI.
3. Improved Data Quality in Subjects Prone to Motion
Reasoning:
Motion Artifacts: While segmented EPI requires multiple shots and is generally more sensitive to motion, in practice, the shorter acquisition time per segment can reduce intra-shot motion artifacts. Additionally, modern motion correction algorithms can effectively correct for inter-segment motion.
Example: Studies involving populations prone to head movement, such as children or patients with neurological disorders, may benefit from the reduced intra-segment motion artifacts in segmented EPI, assuming good motion correction strategies are employed.
4. Reduced Susceptibility to Physiological Noise
Reasoning:
Physiological Noise: Single-shot EPI can be more susceptible to physiological noise from sources like cardiac pulsation and respiration, which can cause fluctuations in the magnetic field. Segmented EPI, with its shorter acquisition windows for each segment, can help mitigate these effects, leading to cleaner data.
Example: High-resolution fMRI studies aiming to detect subtle changes in brain activity, where minimizing physiological noise is essential, can benefit from the more stable signal provided by segmented EPI.
NORRIS3: What is the mathematical relationship between the k-space coordinate in an imaging experiment and the applied field gradients? Write this as an equation, or explain it in words (4).
DO THE FOLLOWING BY HAND: After excitation all the spins in a sample are aligned along the x-axis. The phase-encoding gradient is applied along the y-axis and the frequency encoding gradient along the x-axis. We consider a basic 2D imaging experiment in which a spin at coordinate (0,1) is rotated 45 degrees clockwise by an increment of the phase-encoding gradient. In the time between sampling data points in the frequency encoding direction a spin at (1,0) will also rotate 45 degrees clockwise. If we consider spins at coordinates: (1,1), (3,-1), (1,0), (-1,2) then: Which of these coordinates will give signal of the same frequency during frequency encoding? (1) If a negative phase-encoding gradient of twice the increment is applied (spin at coordinate (0,1) is rotated 90 degrees anti- clockwise) then what will be the phase change induced for spins at each of the four coordinates by the phase-encoding gradient? (4) Which k-space coordinate does this correspond to? (1)
k(t) = γ ∫0t G(t’) dt’
the k space coordinate of the trajectory at a specific time (t) is proportional to the integral of the gradient form up to that time.
1. k(t) is the k-space coordinate at time 𝑡
2. γ is the gyromagnetic ratio - is a constant specific to the nucleus being imaged (e.g., for hydrogen protons, 𝛾≈42.58 MHz/T). It scales the relationship between the magnetic field gradient and the k-space coordinate.
3. G(t ′) is the applied magnetic field gradient at time 𝑡 - magnetic field gradient applied during the imaging sequence.
The gradient can change over time and is used to encode spatial information into the MRI signal.
4. ∫0t G(t’) dt’ is the integral of the gradient from 0 to 𝑡. It represents the cumulative effect of the gradient field over time.
This integral determines the position in k-space at any given time 𝑡.
Second part needs to be done by hand.
NORRIS:4. Explain briefly how multi-echo EPI works, including a sketch of the pulse sequence (5). What are the potential advantages compared to a standard EPI experiment? (3). One potential disadvantage is that the image signal to noise ratio in a multi-echo image will be lower than for the corresponding standard image. Why is this consideration generally not relevant for fMRI ? (2)
MRI sequence that acquires multiple echoes within a single readout period following a single RF excitation pulse.
-sketch missing - did you draw by hand?
Advantages over standard EPI
1. T2* Mapping Multi-Parameter Mapping: Multi-echo EPI allows for the simultaneous acquisition of images at different echo times (TEs), enabling the estimation of T2* relaxation times. This is useful for quantitative imaging and creating T2* maps.
Improved Image Contrast:
- Enhanced Contrast: Different tissues have different T2* decay rates. Multi-echo EPI captures these variations, leading to improved contrast in the resultant images, which can be beneficial for detecting subtle differences in tissue properties.
Artifact Reduction: - Reduced Susceptibility Artifacts: By acquiring multiple echoes, averaging can be used to reduce susceptibility-induced artifacts, particularly in regions with significant magnetic field inhomogeneities.
Disadvantage: Lower SNR in Multi-Echo Images
Reason for Lower SNR Reduction: The signal-to-noise ratio (SNR) for each individual echo in multi-echo EPI is generally lower than that of a single-shot EPI due to the division of the signal across multiple echoes and the T2* decay that occurs over time.
Why This Consideration Is Generally Not Relevant for fMRI
1. fMRI Signal Sensitivity: BOLD Contrast: Functional MRI (fMRI) primarily relies on blood oxygenation level-dependent (BOLD) contrast, which is inherently sensitive to T2* changes. Multi-echo EPI can enhance the detection of BOLD signals by capturing multiple T2*-weighted images, improving sensitivity to neural activity changes.
2. Post-Processing Techniques: SNR Recovery: Advanced post-processing techniques, such as echo combination methods (e.g., weighted averaging of echoes), can effectively recover SNR and enhance the detection of fMRI signals. These techniques combine information from multiple echoes to improve the overall image quality and robustness of the fMRI data.
NORRIS:5. Four contrast mechanisms contribute to the T2*-weighted BOLD signal. List them, and give a short description of each, explaining how you would expect their relative contribution to the total BOLD signal to change between an fMRI experiment performed using gradient-echo EPI at 3T (TE=35ms) and 7T (TE=25ms) (8). Which of these will also contribute to a T2-weighted BOLD experiment? (2)
- Extravascular diffusion dynamic averaging: diffusion of water molecules around small vessels averages out the local field inhomogenities caused by deoxyhemoglobin - at 7t, its contribution is very large as the bigger the gradient the bigger field inhomogenities get.
- Extravascular static dephasing: field inhomogenities around big vessels cause static dephasing in the sorrounding tissues, causing signal loss -at 7t, its contribution is large, as inhomogenities are bigger
- Intravascular diffusion t2 : deoxyhemoglobin within blood vessels causes faster t2 decay due to its paramagnetic properties, at 7t it’s contribution is lower as susceptibility effects are more pronounced outside the vessels (extravascular) so intravascular contribution decreases for overall bold signal
- vascular dephasing: phase dispersion of spins within blood vessels due to blood flow and magnetic field gradients , at 7t it’s contribution to overall bold signal decreases as the susceptibility induced dephasing in the extravascular space increases, reducing the contribution of intravascular effects.
Out of all, only extravascular diffusion/dynamic averaging and intravascular diffusion contribute to T2 contrast. This is because these mechanisms directly influence the spin-spin relaxation time (T2) through averaging of local field inhomogeneities and paramagnetic effects within blood vessels, respectively.
EXTRA:
All contribute to t2. Static dephasing and vascular dephasing affect T2 by causing additional phase dispersion due to broader magnetic susceptibility variations.
NORRIS:6. High resolution T2-weighted imaging has become an important modality for examining brain morphology. What are the three sources of contrast in T2-weighted images of the brain (3)? By acquiring data at multiple echo times it is possible to follow the evolution of the signal amplitude and phase. Give two examples of how these data can be used to provide specific additional information on the brain (7). Please give a short description of the data used to produce the final image, the way the image is displayed, and the information contained.
The three sources of contrast in t2* weighted imaging are:
1. myelin density
2. Iron
3. deoxygenated blood
TWO EXAMPLES:
1. quantitative t2* maps - data colleced at various echo times used to fit signal decay curve to an exponential model- phase used - t2* relaxation time per each voxel - information on tissue composition and pathology - e.g. iron content, myelination, microbleeds
2. susceptibility weighted imaging - data includes phase and amplitude to find susceptibility - image with enhanced contrast between tissues with different magnetic susceptibilities - shows veins, hemorrages, iron deposits - details vascular architecture and pathology
BOTH: enhance the ability to detect/characterize brain abnormalities by leveraging the temporal info provided by multi-echo imaging
BECK:1. (i) Describe the ‘Intensity Model’ on tissue intensity distribution for tissue-type segmentation. (ii) Describe how the intensity information can be combined with shape information to achieve segmentation of specific structures from a T1-weighted MR image. (iii) Discuss the interaction between slice-timing correction and motion correction. How should these two steps be ordered and why? (iv) A new study in Nijmegen has funding to genotype a large number of patients with a particular disorder. Anatomical MR images (T1 and T2-weighted) are available. We are interested in linking genotype to the Grey Matter density within the anterior cingulate cortex. Sketch a Statistical Analysis Plan: what part of the data is being used, what quantities are being derived per step and how are multiple modalities being combined?
(i) When we record different types of intensities, we obtain an histogram which shows voxel count for intensity. If we assume three tissue types (cerebrospinal fluid, white matter, and gray matter) the simplest model of this histogram will be a mixture of gaugassians. We sum these gaugassians, and if final line/curve has three peaks, segmentation will be easy. But in practice, it’s not as easy because we have bias field, blurring, low resolution noise, head motion, etc.
Histogram = probability distribution function
(ii) Including spatial neighborhood information in order to increase accuracy uses Markov random field. Certain types of configurations of tissue types are more likely to occur than others. For example, clear boundary between white matter and black matter, or if all voxels except one is gray matter, then that voxel might be gray matter too. If this is taken into account, segmentation becomes more robust to noise and gives a more biologically valid segmentation. Simple classifiers, for example k-means, do not use spatial neighborhood information. We need one for intensity and one for spatial neighborhood. And they need to be weighted using log probabilities. For instance, if the probability of the Markov random field is 0.5, then we equally value intensity and spatial information.
(iii) Interaction between slice timing and motion correction. Ideally, they would be performed together. If split, there is no best order.
Issues if Motion Correction is Done Before Slice-Timing Correction:
1. Temporal Inconsistencies: Motion correction aligns volumes spatially but does not account for the temporal differences between slice acquisitions within a volume. This can lead to inaccurate adjustments since each slice’s position may be altered based on the motion of the whole volume, not considering that slices were acquired at different times.
Interpolation Errors:
2. Performing motion correction first may introduce interpolation artifacts that are not temporally consistent across slices. This misalignment could lead to errors when subsequently applying slice-timing correction, as the temporal correction might be applied to slices that are not in their original temporal context.
Issues if Slice-Timing Correction is Done Before Motion Correction:
1. Spatial Misalignments: Slice-timing correction adjusts the data for temporal differences but does not correct for head movements. If significant motion occurred, this can result in slices that are temporally aligned but spatially misaligned. Subsequent motion correction may then incorrectly align these slices, leading to spatial distortions.
2. Compound Errors: Any motion occurring between slice acquisitions will not be corrected before slice-timing, meaning that the slice-timing correction is applied to a spatially inconsistent dataset. This can compound errors and result in inaccurate data correction, making the final dataset less reliable.
(iv) First, we have data collection, genotyping data, blood samples, saliva, and genotyping to identify genetic variants of interest. Then we have T1-weighted plus T2-weighted to better difference tissue types. First, we pre-process the data. We do brain extraction using BET, the brain extraction tool, on both T1 and T2-weighted images to remove non-brain tissue types or the skull. Then we do a bias field correction. We correct homogeneities in the radiofrequency field for both T1 and T2. Then we do a co-registration. We use affline transformations to align T1 and T2. Then we do segmentation, for instance, tissue type segmentation to classify voxels into cerebrospinal fluid, gray matter, and white matter on T1-weighted images. Then we do an anatomical analysis. We estimate gray matter density, calculate gray matter density by partial volume modeling to estimate relative probability of each voxel belonging to gray matter. Then we do a region-of-interest (roi) extraction, where we define the anterior cingulate cortex region using anatomical atlases, such as the MNI-152, and extract gray matter density specific to the ACC. Statistical analysis involves data normalization, so we normalize values within the ACC to account for inter-individual variability with Jacobian modulation. Then we do voxel-wise analysis, statistical maps to identify significant gray matter density differences in the ACC. Also, we can apply minimal smoothing. Then we do a multilevel analysis using fixed effects, as we are only interested in generalizing to the subject tested. This would mean multiple GLMs using ANOVA-T tests. Then we do correction for multiple comparisons using Bonferroni or FDR.
The integration of multimodal data is, first we combine T1 and T2 information. T2 is used to refine segmentation and improve accuracy of gray matter density estimation. We use a joint histogram analysis to integrate density of T1 and T2 for more robust tissue classification. And we could use deformation-based morphometry, DBM, to assess shape-volume differences in ACC.
BECK:(i) Describe the impact of neural activity on cerebral blood flow, blood volume, oxygen concentration, amount of oxygenated haemoglobin, magnetic field and MR signal. (ii) Sketch and describe the key features of the hemodynamic response function (HRF). What different aspects of the biophysical process are modeled by each one of these features? (iii) Describe (using a flow diagram) how the GLM is being used both at the first level and for higher-level GLM analysis (iv) Below is a graphical representation of the higher-level GLM design. Describe this in terms of the explanatory variables and the associated contrasts. What is the role of the final 5 explanatory variables and why do they not enter into a contrast?
(i)Neural activation leads to cerebral blood flow increase. This also increases the cerebral blood volume and oxygenated hemoglobin and also the cerebral metabolic rate of oxygen, so the rate of oxygen consumption by the brain. While the oxygenated hemoglobin goes down and there is a magnetic field change which reduces local magnetic field inhomogeneities, so the field change is decreased while the MRI signal is increased. In other words, neural activation happens when the cerebral blood flow is increased. This brings oxygenated hemoglobin in the activation area, also increasing the cerebral blood volume. Consequently, cerebral metabolic rate of oxygen increases in that area. Due to the oxygenated hemoglobin increase, the deoxygenated hemoglobin decreases. Thanks to this mechanism described above, the magnetic field inhomogeneities are reduced, so homogeneity is increased and MRI signal goes up. Furthermore, we also have that field changes lead to dephasing or a T2 * effect.
(ii)We want to see whether neural activity is increased or decreased in response to a stimulus, so to get the predicted response we use HRF, Hypodynamic Response Function, with the predicted neural activity. The task of MRI analysis is to go through all voxels and model the neural activity, bold response, relative to the predicted response. Then we check how well a voxel’s response matches the predicted response. And a good activation would be when the stimulus was presented. This is analyzed through General Linear Models or GLM.
(iii)We have four different levels. In the first level, we pre-process fMRI data per participant. In the second, we design a metric construction to combine the data for each participant. In the third, we do model fitting and estimate betas by combining all the participants in a group together. In the fourth level, we compare this data to another group.
BECK:3. (i) List and characterize 3 different types of ‘connectivity’ Structural, functional and effective (ii) What is diffusion, and what can diffusion in the brain tell us about tissue and tissue in- tegrity? (iii) Describe the term ‘Apparent Diffusion Coefficient’ and discuss the limitations with respect to measuring ‘instantaneous’ diffusion (iv)Define the diffusion tensor model, the math- ematical principle behind DTI and 2 scalar quantities that form part of the tensor model - write formula on paper(v) Discuss the effect that spatially global confounds have on the ability to characterise functional connectivity.
(i) There are three different types of connectivities. One is functional, and it’s the temporal correlation between spatially remote events derived from functional data, which is mainly resting-state fMRI. We analyzed these data, spatially distributed patterns that look like activation maps. An example would be the resting-state network.
The effective connectivity describes the influence of one neural system over another. It’s derived from functional data. We do its analysis with dynamic causal modeling, DCM.
Lastly, we have structural connectivity, which images anatomical connections between remote areas obtained from diffusion-weighted MRI data and not functional data. The characterization can be of multiple forms, either voxel-wise scalar inferences about the localized integrity of the connectivity or an atomically distributed shape of entire tracts information.
(ii) Diffusion is effectively process of random motion due to thermal energy. In any medium that is above absolute zero in temperature, water molecules collide and experience net displacement. This net displacement can be described by the diffusion coefficient. When we have no boundaries and medium is homogeneous, for example, drop of ink in water diffuses, diffusion is equal in all directions. And this is isotropic and related to Brownian motion.
What can diffusion in the brain tell us about tissue and tissue integrity?
Brain has restricted diffusion by tissue boundaries, membranes, etc. This is anisotropic. This means that our model on homogeneous diffusivity will break down in a localized fashion, telling us about the presence or absence of boundaries. This can be used as a marker for tissue microstructure. Also, if we look at the whole ensemble of particles, we have an ellipsoid. Diffusivity works well along the length of the bundle, but poorly along the width. Thanks to the ellipsoid, we can assess the size of it to use anisotropy, so the non-roundness of this ellipsoid, to tell us about the directionality and orientation and also structural integrity of bundle we are looking at. Diffusivity is defined as anisotropy, which gives rise to structural quantities.
(iii) Apparent diffusion coefficient. Diffusivity is not a state, it’s a process, thus diffusion in tissues depends on time. The presence or absence of barriers becomes evident after a certain amount of time. Location in brain has a certain profile, strength and orientation, which is shown after diffusivity happens. So ADC quantifies a quantity that depends on the experiment itself, represents a flux of water or small particles via Brownian motion across a surface in a given amount of time. As biological tissues are anisotropic, they are better described with diffusion tensor than ADC. There are certain limitations with respect of instantaneous diffusion ADC. It does not measure instantaneous diffusion, but rather an averaged diffusion over time. This can obscure complexities of water movements within heterogeneous anisotropic environments, where instantaneous diffusion can vary greatly due to the cellular barriers, extracellular spaces and so on. ADC may be useful in areas of restricted diffusion, for example in acute stroke, but it lacks temporal resolution to capture rapid changes in diffusion dynamics that occur in shorter timescales.
(iv) The diffusion tensor model. We take a sequence of scans where we switch on different diffusion directions. Then we obtain a sequence of images and these images are then analyzed using diffusion tensor model. There are a number of assumptions for this diffusion tensor model. First, diffusion within tissues is gaugassian, so isotropic. We do not have a scalar variance, isotropic, but a covariance, anisotropic. Thus, we use a diffusion tensor. Diffusion tensor has to be symmetric, so A to B and B to A need to be equal. Diagonal elements are proportional to the diffusion displacement variances, ADCs, along the X, Y, Z axis. Off-diagonal elements are proportional to correlations, covariances of displacements along the X, Y, Z axis. The diffusion tensor is a 3 by 3 matrix describing diffusion along three axes. We do not look at the diffusion coefficient directly, but we use eigen decomposition. So we extract a singular value decomposition to find eigenvectors. So we have an ellipse with gaugassianity assumption and the ellipsoid with three dimensions to describe its position in space and three length scalars describing how the ellipsoid is in each direction. So we have two scalar quantities. We have eigenvectors, which describe axis of ellipsoids, thus the direction of fibers. And then we have eigenvalues, which describe relative size of that axis, thus the strength of the diffusion. Each voxel has three vector quantities and three scalar quantities.
These create three orthogonal independent scalar quantities that we can derive. We have mean diffusivity, MD, Fractional anisotropy (FA) and mode. Mean diffusivity is the average rate of diffusion within a voxel, the overall magnitude of water diffusion. While Fractional anisotropy (FA) measures the degree of anisotropy of water diffusion, which is the coherence of fiber tracts and tissue integrity. -FORMULA MISSING-
(v) Spatially global compounds on the ability to characterize functional connectivity. Spatial global compounds are physiological noise, like respiratory and cardiac cycles, scanner drifts and subject movements. All of these can introduce spurious correlation across brain regions that do not reflect true neural synchrony, but rather artifacts of the measurement process. So these compounds can create synchronized fluctuations in the bold signal, falsely suggesting functional connectivity. To mitigate these effects, pre-processing steps such as global signal regression, motion correction, physiological noise modeling can be employed. However, if these are not applied correctly, then they can introduce further bias or remove the neural signals.
BECK:4.(i) We have a set of primary imaging data consisting of two groups: patients and controls. Within each group, we have 5 subjects. For each subject we have 3 sessions of the same FMRI experiment. Q: Is there a significant difference between mean effects in the patient group and the control group, which is generalisable to the populations from which the subjects are drawn? (ii) How is this modelled within the framework of hierarchical GLMs? How many GLM levels will be combined and how are quantities derived in one level combined in the next level? (iii) Which variance terms are included in this model at each level and why? (iv) Sketch the design and contrast matrices at each level of the hierarchy.- DO THIS ON PAPER- (v) Describe two situations in which it is important to use non-parametric inference because parametric inference may be invalid.
(i) Significant Difference Between Patient and Control Groups
To determine if there is a significant difference between the mean effects in the patient group and the control group that is generalizable to the populations from which the subjects are drawn, we perform a hierarchical analysis using the General Linear Model (GLM).
(ii) Hierarchical GLM Modeling
The analysis is modeled within the framework of hierarchical GLMs, combining multiple levels of GLMs. We typically use a multi-level analysis approach, where the number of GLM levels combined is contingent on the study design. In this case, with three sessions per subject and two groups (patients and controls), we use four levels:
- First-Level Analysis: Individual session analysis for each subject.
- Second-Level Analysis: Combine the three sessions of each subject to obtain a single estimate per subject.
- Third-Level Analysis: Combine the results of all subjects within each group (patients and controls).
- Fourth-Level Analysis: Compare the group means between patients and controls.
At each level, the parameter estimates (β) and variances from one level become the input data for the next level.
(iii) Variance Terms in the Model
At each hierarchical level, different variance terms are included:
- First-Level: Within-subject variance, which captures the residual noise of individual sessions.
- Second-Level: Between-session variance within each subject, which accounts for variability across sessions for the same subject.
- Third-Level: Between-subject variance within each group, which captures the variability between different subjects within each group.
- Fourth-Level: Between-group variance, which captures the variability between the patient and control groups.
Including these variance terms allows us to separate and properly model different sources of variability, enhancing the generalizability of our findings.
(iv) Design and Contrast Matrices
At each level of the hierarchy, design and contrast matrices are constructed to test specific hypotheses:
- First-Level:
Design Matrix: Includes the experimental conditions for each session.
Contrast Matrix: Compares conditions within each session. - Second-Level:
Design Matrix: Combines the session estimates for each subject.
Contrast Matrix: Averages the session effects for each subject. - Third-Level:
Design Matrix: Combines the subject estimates within each group.
Contrast Matrix: Averages the subject effects within each group. - Fourth-Level:
Design Matrix: Compares the average effects between the patient and control groups.
Contrast Matrix: Tests the difference in mean effects between the two groups.
(v) Importance of Non-Parametric Inference
Two situations where non-parametric inference is crucial because parametric inference may be invalid are:
Violation of Assumptions: When the assumptions underlying parametric tests (e.g., normality, homogeneity of variance) are violated, non-parametric tests provide a valid alternative as they do not rely on these assumptions.
Small Sample Sizes: In cases with small sample sizes, parametric tests may not provide reliable results due to limited power. Non-parametric methods are more robust in these scenarios, providing more reliable inferences.
EXTRA1: Compare the benefits of Simultaneous Multi-Slice (SMS) imaging with multi-echo imaging in fMRI. Discuss the potential advantages and disadvantages of each technique.
Simultaneous Multi-Slice (SMS) Imaging:
Advantages:
Increased Temporal Resolution: SMS allows multiple slices to be acquired simultaneously, significantly reducing acquisition time and increasing the temporal resolution, which is crucial for capturing fast neural processes in fMRI.
Reduced Scan Time: Shorter acquisition times improve patient comfort and reduce the likelihood of motion artifacts.
Efficient Data Collection: SMS enables more efficient use of scanner time, allowing more data to be collected within the same timeframe.
Disadvantages:
Complex Reconstruction: The simultaneous acquisition of multiple slices requires advanced reconstruction techniques to separate the slice signals, increasing computational complexity.
Increased Noise: Potential for increased noise levels due to slice separation processes, which can affect image quality if not properly managed.
Multi-Echo (ME) Imaging:
Advantages:
Improved SNR: Combining data from multiple echoes can improve the signal-to-noise ratio (SNR) by averaging out noise.
T2 Mapping:* Allows for the generation of quantitative T2* maps by fitting the signal decay across different echoes, providing detailed tissue characterization.
Reduced Susceptibility Artifacts: By acquiring multiple echoes, ME-EPI can reduce susceptibility artifacts, which is beneficial for imaging areas with high magnetic field inhomogeneities.
Disadvantages:
Longer Acquisition Time: Acquiring multiple echoes increases the total scan time compared to single-echo methods.
Lower SNR for Individual Echoes: Each individual echo has a lower SNR compared to a standard single-echo acquisition, though this is mitigated by combining echoes.
EXTRA2: Describe the Gradient Echo-Echo Planar Imaging (GE-EPI) sequence. Include a sketch of the pulse sequence and explain its typical applications and benefits in fMRI.
GE-EPI Sequence:
Description:
GE-EPI involves the use of a single RF excitation pulse followed by a series of gradient echoes generated by alternating readout gradients. The phase encoding gradient is applied incrementally to traverse k-space.
Pulse Sequence Sketch:
RF Pulse: A single excitation RF pulse flips the spins into the transverse plane.
Readout Gradient: Alternating gradients along the x-axis generate a series of gradient echoes.
Phase Encoding: Incremental phase encoding gradients are applied between echoes.
Applications and Benefits:
fMRI: GE-EPI is widely used in functional MRI due to its high temporal resolution, which is essential for capturing dynamic changes in brain activity.
Dynamic Studies: Suitable for perfusion and diffusion imaging, where rapid acquisition is needed.
Speed: Provides very fast imaging, capturing a complete image in a single shot, which is crucial for dynamic studies.
EXTRA3: Explain the Spin Echo-Echo Planar Imaging (SE-EPI) sequence. Include a sketch of the pulse sequence and discuss its advantages and disadvantages compared to GE-EPI.
SE-EPI Sequence:
Description:
SE-EPI uses a combination of a 90° RF excitation pulse followed by a 180° refocusing pulse to generate a spin echo, which is then sampled using the EPI readout.
Pulse Sequence Sketch:
90° RF Pulse: Excites the spins into the transverse plane.
180° RF Pulse: Refocuses the dephased spins, creating a spin echo.
Readout Gradient: Alternating gradients collect the spin echo.
Advantages Compared to GE-EPI:
Reduced Susceptibility Artifacts: The 180° refocusing pulse reduces susceptibility artifacts, making SE-EPI more suitable for imaging regions with high magnetic field inhomogeneities.
Improved Image Quality: Provides better image quality in areas prone to susceptibility effects.
Disadvantages Compared to GE-EPI:
Longer Acquisition Time: SE-EPI is slower due to the need for a 180° refocusing pulse, which increases the overall scan time.
Lower SNR: The use of a spin echo typically results in a lower SNR compared to gradient echo sequences.
EXTRA4: Describe the Blipped Echo Planar Imaging (Blipped-EPI) sequence. Explain how it differs from standard EPI and discuss its specific advantages and applications in fMRI.
Blipped-EPI Sequence:
Description:
Blipped-EPI involves adding small gradient pulses (blips) to the phase encoding gradient after each readout gradient to incrementally traverse k-space.
Differences from Standard EPI:
Blipped Gradients: Small, controlled gradient blips are applied between readouts to step through k-space more precisely.
Advantages:
Controlled K-Space Traversal: The use of blips allows for more precise control of k-space traversal, reducing certain artifacts.
Improved Image Quality: Enhances image quality by reducing blurring and distortion often seen in standard EPI.
Applications:
fMRI: Useful in functional MRI where high-quality images with reduced artifacts are necessary.
Diffusion Imaging: Suitable for diffusion-weighted imaging, where precise k-space traversal is critical for accurate image reconstruction.
