Exercises - Quantitative MRI mOOC

Exercise 2

a. Using the Plotly figure in the VFA section that displays the signal curves for white matter, gray matter, and CSF, determine the Ernst angle for the following: white matter and a TR of 15 ms, gray matter for a TR of 50 ms, and CSF for a TR of 140 ms.

b. Calculate the Ernst angle for these tissues and TRs with Eq. 2.6. Are they in agreement with the values you estimated with the interactive figure?

c. It’s been shown (Deoni, Rutt, and Peters 2003) that the optimal flip angles for a two-measurement VFA T₁ mapping imaging protocol are located at approximately 70% of the Ernst angle. Find the optimal flip angles to image each tissue above using their respective TRs.

d. For a TR of 30 ms, which flip angle would result in the best contrast between white matter and grey matter in an SPGR image?

Exercise 3

a. The IR signal curves for WM/GM/CSF in Figure 2 were simulated for 3T T₁ tissue values. Using Binder and the notebook that was used to generate that blog post, regenerate that figure for T₁ values at 1.5 T (WM ~ 650 ms and GM ~ 1200 ms as reported by (Wright et al. 2008)). Assume the CSF value does not change.

b. An IR T₁ mapping pulse sequence that a previous student developed and is available at the MRI scanner has a fixed TR of 3 seconds. Could you use a data analysis pipeline that only has the long-TR IR T₁ fitting option available to map T₁ in WM, at 1.5T and/or 3T? Show this visually via simulations.

c. Are there any inversion times you should avoid using when designing an IR T₁ mapping protocol at 1.5T when using this TR? If so, demonstrate why and which one(s) using modified code from one of these notebook figures.

Exercise 4

Imagine you’re a graduate student in a lab that recently transitioned from human imaging to animal imaging (specifically, mouse models of multiple sclerosis). Because there has never been MRI data acquired in your lab in mouse, your advisor asks you to acquire T₁ maps of some healthy mice to get the an estimate of T₁ values in white matter so that you can use this value to optimize other pulse sequence protocols (eg protocol parameters for T₁-weighted images, optimal flip angle for spoiled gradient angle SNR, etc). You do some literature search and find a paper that measured T₁ in mice (Kuo et al. 2005), but using a different pulse sequence.

a. Using qMRLab, determine if the IR imaging protocol (TR = 1000 ms , TI = [100, 300, 600, 900] ms) you used for your previous human study at 1.5 T (where WM has a T₁ of ~600ms) would yield good results if applied to mice (at 9.4 T, (Kuo et al. 2005) reports a WM T₁ of ~1700 ms). Assume an SNR of 100. Explain how you’ve reached your conclusion.

b. If the human T₁ mapping 1.5T protocol is not appropriate to image mice at 9.4T, explain via written arguments why this might be the case. Use simulation figures to support your arguments.

c. Propose a new protocol that might yield more precise and/or accurate T₁ maps. Why did you make those changes? How did you determine the improvement?

Exercise 6

You receive an email from a collaborator in your city asking for help with a T₁ dataset they acquired on their new 3T scanner. They tried fitting the data with qMRLab already, but are getting T₁ values in the brain that are beyond the expected values (eg, WM: 2000ms, GM, 5000 ms). They send you their acquired data.

a. Fit a T₁ map using their data and plot a few voxel signal curves.

b. Luckily, you own a standardized quantitative MRI NIST phantom with known T₁ values, and are able to go to your collaborators scanner to acquire a dataset using their protocol. Here is data you acquired for a region of the phantom with a known T₁ value (900 ms +- 5ms) close to the expected WM values. Plot that data, and simulate the expected signal curve for this T₁ value

c. Comparing the human and phantom data and the simulated curves, what do you notice? What do you think may be the problem?

d. Test your proposed problem with some of your simulation code.

e. What would you propose to your collaborator? Is a new data acquisition protocol required, or can you provide some post-processing corrections prior to fitting the data?