Exercise 4-6 · B1 Mapping

Quantitative MRI mOOC

B₁ Mapping · Exercise 4-6

Filtering B₁ maps: why, how, and what can go wrong?

What’s wrong with unfiltered DA, AFI and BS maps, and why?
Which filters are used on B₁ maps?
Median or Gaussian: which one, and where do errors appear?
Can filtering make three B₁ mapping methods agree?
How would you filter a map with bright vessels?
What should you report when you filter?

Exercise 4-6

Unfiltered B₁ maps, and the images they came from

DA EPI, 60° / 120°AFI S₁ / S₂BS phase at ±4 kHz Acq. 1

Acq. 2

B₁ map

B₁ 0.71.3phase −ππ

B₁ maps are expected to be smooth, slowly varying fields, but measurements have flaws.

Can you identify some in each map? What might their cause be?

Click any image to enlarge it. DA is a slice through the ventricles; AFI and BS are one slice higher up.

Exercise 4-6

Some flaws, and their causes

DA: long T₁

Sensitive to long T₁, e.g. CSF in the ventricles: it hasn’t recovered between shots (T₁ ≈ 4 s ≈ TR), so B₁ reads too low there.

AFI: Gibbs ringing

Sensitive to Gibbs ringing / truncation: ringing from sharp edges (scalp, skull) runs into the brain as streaks.

BS: phase artefacts

Sensitive to phase artefacts, e.g. fringe lines and phase poles, where the phase can’t be unwrapped cleanly. More on phase in the B₀ chapter (next week, or in the mOOC).

B₁ 0.71.3

Exercise 4-6 · quiz

In practice, B₁ maps are often filtered

$$\hat B_1(\mathbf r)=\sum_{\mathbf r'} w(\mathbf r-\mathbf r')\,B_1(\mathbf r')$$ $$w(\mathbf d)\propto e^{-|\mathbf d|^2/2\sigma^2}$$

$$\hat B_1(\mathbf r)=\operatorname{med}\{\,B_1(\mathbf r') : \mathbf r' \in N(\mathbf r)\,\}$$

A 3 × 3 window N(r) of a B₁ map. What does the centre pixel become?

1.01	0.98	1.03
0.99	1.62	1.00
1.02	0.97	1.01

$$\hat B_1=\arg\min_f\ \sum_i\big(B_1(\mathbf r_i)-f(\mathbf r_i)\big)^2$$ $$+\ \lambda\!\int\!\big|\nabla^2 f\big|^2$$

Exercise 4-6 · which filter?

Which filter would you use?

A 1D B₁ profile through the brain. Which filter would you use on it?

Exercise 4-6 · your filters

Which filter, and what size, for each map?

DAAFIBS

width –

difference from the mean of the three

The same slice, three methods. Pick a filter and a size for each map, to make the three agree as closely as possible.

Spread between the three maps

B₁ 0.71.3

difference −10 %+10 %

Filters work inside the brain only. Width = window width in pixels; Gaussian σ = width / 4. DA here is the chapter’s TSE double angle, on the same slice as AFI and BS.

Exercise 4-6 · (a)

Filter the map, without a mask

You are given B₁ mapping data that is very sensitive to the motion of blood in the vessels: you see bright spots in the B₁ maps. The researcher doesn’t need accurate B₁ inside these regions, but would like to filter the maps in the brain tissue.

Measured B₁

Filtered

Error in tissue

0.7B₁1.3

−10 %error+10 %

rms error in the tissue (vessels not scored)

–

Filter

Width

Without a mask, which filter should you use, and how wide? Why?

Exercise 4-6 · (b)

Mask the vessels, then filter

Measured B₁ (orange: masked)

Filtered

Error in tissue

0.7B₁1.3

−10 %error+10 %

rms error in the tissue (vessels not scored)

–

Filter

Width

Vessel mask

Threshold

How would you create a mask for the vessels? With a mask, which filter should you use? Why?

Exercise 4-6 · Summary

Filtering B₁ maps

B₁ maps can be inaccurate too, and have artefacts: long T₁ (DA), Gibbs ringing (AFI), phase errors (BS).
Filtering is often done, but it can spread errors too: a Gaussian smears one bad voxel over its neighbours, and every filter blurs edges and real variation.
Filtering can’t remove a bias: here BS reads about 2 % higher than DA and AFI everywhere, and more smoothing makes the maps agree without making them right.
Share the raw maps as well as the filtered ones, and be detailed on how you filtered: the filter, its size (or σ), the mask, how edges were handled, and the software.

Filtering B1 maps: why, how, and what can go wrong?

Unfiltered B1 maps, and the images they came from