Exercise 2-4 · T2 Mapping

Quantitative MRI mOOC

T₂ Mapping · Exercise 2-4

Myelin water

A T₂ distribution in every pixel

Two components: which part of the decay does each T₂ component contribute to?
A pixel’s T₂ distribution: how does white matter differ from grey matter?
MWF map: which T₂ ranges best match the published map, and why?

Data: human brain at 3 T, Dvorak et al., CALIPR Framework Myelin Water Imaging Supporting Data, Zenodo, doi:10.5281/zenodo.8049179, CC BY 4.0. Changed: one slice, cropped, 8-bit; T₂ fits added.

Two components in one voxel

(a) These echoes come from one voxel with two components. What is the T₂ of each, and what share of the signal does each have?

Drag each arrow: left or right sets its T₂, up or down its share of the signal (the other takes the rest).

Log scale

A voxel with two water compartments: 32 echoes, 10 ms apart, made with S(TE) = 0.25 e^(−TE/18 ms) + 0.75 e^(−TE/78 ms) (S0 = 1) plus a little Gaussian noise (SD 0.002, seeded, so it is the same every time). Each component is an arrow on the T2 plot: drag it left or right to set its T2, up or down to set its share of the signal; the other arrow takes the rest, as the shares add up to 100% (S0 = 1). The red curve is the model, the dashed curves its two parts, and the fit error is the RMS difference from the echoes (the noise alone gives about 0.2%). Fit one exponential overlays the best single exponential: about T2 = 69 ms here (S0 = 0.89), it cannot follow the data: it starts too low and cuts through the echoes. With Log scale, a single exponential is a straight line, and the two-component data bend: a fast drop (component 1) then a slower slope (component 2). The answer: component 1 is myelin water (18 ms, 25%), component 2 intra/extracellular water (78 ms, 75%), so MWF = 25%. Show answer draws them as dashed arrows. Fairly different pairs can still draw a similar curve: look at the residuals strip under the decay. The true values leave random scatter around zero; a wrong pair leaves a systematic wave. This is why real MWF fits need many echoes and a high SNR, and fit a whole T2 distribution, as on the next slides.

What we saw · 1

Two components shape different parts of the decay

The short component (myelin water) makes the fast drop of the first ~50 ms; the long one sets the slope of the tail.
One exponential cannot follow both: its best fit (about 69 ms) misses the early echoes.
Different pairs can draw almost the same curve: only the residuals tell them apart, so separating components needs many echoes and a high SNR.

The T₂ distribution of a pixel

(b) Compare a white-matter and a grey-matter pixel, then leave a white-matter one picked: the next slide uses it.

Echo

Click a pixel to see its T₂ distribution.

Data: human brain at 3 T, Dvorak et al., CALIPR Framework Myelin Water Imaging Supporting Data, Zenodo, doi:10.5281/zenodo.8049179, CC BY 4.0. Changed: one slice, cropped, 8-bit; T₂ fits added.

One axial slice of a healthy volunteer’s brain, through the genu and splenium of the corpus callosum: a 3D multi-echo spin echo at 3 T (the CALIPR protocol of Dvorak et al. 2023), 56 echoes 6 ms apart (TE = 6 to 336 ms), TR = 1252 ms, acquired at 1.7 mm and reconstructed at 1 mm. The slider picks the echo shown (each echo with its own grey scale, as the late ones are much darker); a click picks a pixel. Top right: that pixel’s T2 distribution, the amount of signal at each T2 (60 values, 4 ms to 2 s, log scale). Bottom right: its 56 echoes, with the decay the distribution predicts in red, and the echo on screen marked. The distributions were fitted offline (tools/prep_mwf_calipr.py): non-negative least squares on an extended phase graph basis, with the refocusing angle fitted per pixel and then smoothed over the brain (about 140° to 175°, as B1 varies), and a constant for the noise floor, lightly smoothed. The slide starts in the splenium: two peaks, myelin water near 14 ms and intra/extracellular water near 90 ms. In grey matter the short peak is small or absent. In some white-matter pixels the short peak sits at the very bottom of the range (4 ms): with this much noise the fit cannot place it more precisely. Data: Dvorak et al., CALIPR Framework Myelin Water Imaging Supporting Data, Zenodo, doi:10.5281/zenodo.8049179, CC BY 4.0 (volunteer 2, first brain scan, slice 22; cropped, 8-bit; T2 fits added).

What we saw · 2

A T₂ distribution in every pixel

White matter: two peaks, myelin water below 40 ms and intra/extracellular water near 70 ms.
Grey matter: one main peak (near 75 ms), with little or no myelin water. Fluid (CSF): its signal sits at the long end, above 1 s.
The distribution is a fit to noisy echoes: in some pixels the short peak lands at the bottom of the range.

From T₂ distributions to an MWF map

Drag a rectangle to move it; drag its left or right edge to stretch or shrink it.
Put MW (myelin water) and IEW (intra/extracellular water) on the two components.
Click Generate MWF map: at every pixel, $$\mathrm{MWF} = \frac{S_{MW}}{S_{MW} + S_{IEW}}$$ with S the area of that pixel’s distribution inside each rectangle.

Your pixel (click the map for another) ·

The MWF map appears here.

Data: human brain at 3 T, Dvorak et al., CALIPR Framework Myelin Water Imaging Supporting Data, Zenodo, doi:10.5281/zenodo.8049179, CC BY 4.0. Changed: one slice, cropped, 8-bit; T₂ fits added.

The pixel picked on the previous slide, with two rectangles on its T2 distribution: MW (myelin water) and IEW (intra/extracellular water), the book’s names. Each spans the full height; drag to move, drag an edge to stretch or shrink (they start off target, MW at 30–50 ms and IEW at 150–400 ms). Each rectangle’s ends are written above it, and in the line above the plot, which follows the drag live. Generate MWF map then computes, at every pixel of the slice, MWF = S_MW / (S_MW + S_IEW), the book’s Eq. 3.8, with S the area of the pixel’s distribution inside each rectangle, and draws the map on a fixed colour scale, 0 to 30% (pixels with most of their signal outside both rectangles, the fluid in the ventricles and sulci, are grey: a tiny MW over an even tinier IEW would mean nothing). Hover for values; the saved pixel is outlined in red, with ticks pointing at it (dark on the Difference tab), and its hover says “your pixel”. Above the map: the pixel’s MWF, the previous map’s value, and the published value; then the mean difference from the published map over the brain, in MWF points (a grey fluid pixel counts as 0), with the previous map’s. Once a map is drawn, a click on it picks another pixel, on any tab: its distribution replaces the one on the left, and the readout follows. The tabs switch between your map, the authors’ own map of the same slice (Published: their regularized NNLS, myelin water below 40 ms; resampled from the volunteer’s T1-weighted space), and the Difference, yours minus theirs (blue: yours lower, red: yours higher, ±15 points). The question, with answers: the lowest mean difference is about 3.0%, with MW from the bottom of the range up to about 35–40 ms (the gap between the two peaks) and IEW from there to the end of the range (2 s). Why: MW must take the whole short peak and nothing of the long one, and the cut sits in the gap between them, where the authors also put it (40 ms). The IEW rectangle does best when it takes all the rest of the signal, because their MWF divides the myelin water by the pixel’s whole signal; IEW 40–200 ms, their window for the IEW T2, gives 3.2%. Starting MW above the bottom (8 ms: 4.4%) or ending it at 50 ms (5.5%) does worse. Why it cannot reach zero (the note under the distribution, on the Difference tab): (1) their fit is regularized in space, each pixel’s T2 distribution and refocusing angle pulled towards its neighbours’, while ours fits each pixel on its own (the salt-and-pepper differences); (2) other fit settings (40 T2 values from 4 ms to 10 s, against our 60 from 4 ms to 2 s, and their own regularization); (3) their map was computed on the echo images, registered to the volunteer’s T1-weighted image, and resampled back here, which blurs it slightly, so even an identical fit would not match pixel for pixel. Region averages agree well: white matter about 12% here against 11% in theirs, and 18% against 17% at the starting pixel in the splenium. Data: Dvorak et al., CALIPR Framework Myelin Water Imaging Supporting Data, Zenodo, doi:10.5281/zenodo.8049179, CC BY 4.0.

What we saw · 3

An MWF map depends on how it is made

MWF is highest in white matter: the corpus callosum and the internal capsules, about 12% here.
Closest to the published map (mean difference about 3%): MW ending in the gap between the peaks (35–40 ms), IEW taking everything after it.
It cannot reach zero: their fit pulls each pixel towards its neighbours. Compare MWF values only between maps made the same way, and over regions rather than single pixels.

Lessons

Myelin water

Two components: the short one shapes the early echoes, the long one the tail; one exponential cannot follow both.
Separating them takes many echoes and a high SNR: different pairs can fit almost equally well.
A T₂ distribution per pixel: two peaks in white matter, one in grey matter, a long tail in fluid.
MWF: the share of signal in the short peak, highest in white matter (about 12% here).
Method matters: windows and regularization change MWF; compare maps made the same way, over regions.

Myelin water

Two components in one voxel

Two components shape different parts of the decay

The T2 distribution of a pixel

A T2 distribution in every pixel

From T2 distributions to an MWF map

An MWF map depends on how it is made

Myelin water

The T₂ distribution of a pixel

A T₂ distribution in every pixel

From T₂ distributions to an MWF map