Relative weightings (PD vs T1 vs T2) can be numerically calculated for a given sequence (TR, TE) and tissue type (PD, T1, T2). For this analysis we use the logarithmc axis where contrast is defined as the change in signal for a fractional change in a tissue parameter.

The sequence weighting describes what tissue property (PD, T1, or T2) is be most responsible for signal changes in a specific tissue. The image weighting describes what tissue property (PD, T1, or T2) is most responsible for the contrast, or difference in signal, between two different tissues in the image. These are two different things.

The sequence weighting is useful for thinking about which tissue properties contribute to detecting small changes from normal in a tissue. For example, if amyloid increases the T1 value of otherwise normal myocardium then a heavily T1 weighted image for myocardium would be useful for detecting amyloid. Or, if T1 and T2 increase in subtle neuroinflammation then a sequence with synergistic positive T1 and T2 weighting for white matter would be useful for early detection. The sequence weightings depend on the TR and TE of the sequence as well as the T1, T2, and PD of the tissues being looked at.

The sequence weighting for each tissue property is the slope of the tissue filter at a given value of the tissue property. The relative sequence weighting is the slope of the filter at at a given value of the tissue property normalised by the signal at that tissue property value. Mathematically, this is the slope of the filter divided by the filter and is derived mathematically in Appendix 1.

For the PD filter the relative sequence weighting using the logarithmic axis is 1.

For the T1 filter the relative sequence weighting using the logarithmic axis is $-\frac{\mathrm{TR}}{\mathrm{T1}}x\frac{e^{\frac{\mathrm{-TR}}{\mathrm{T1}}}}{1-e^{\frac{\mathrm{-TR}}{\mathrm{T1}}}}$

For the T2 filter the relative sequence weighting using the logarithmic axis is $\frac{\mathrm{TE}}{\mathrm{T2}}$

Image weighing is useful for thinking about which tissue properties contribute to specific tissues having different signal on an image. For example, what contributes to grey matter looking different than white matter, or a tendon/muscle different than a fluid filled tear, or a colon cancer metastasis looking different than liver parenchyma. In addition to the parameters of the pulse sequence and values of a single tissue's tissue properties, image weighting depends on the difference in tissue properties between two specific tissues. A sequence can have overall T2 weighting for a given tissue but if disease changes T1 much more than T2 the image will actually be T1 weighted.

Relative image weighting is approximated by calculating the relative difference in signal between two tissues and normalising by the signal for a hypothetical tissue whose tissue property is the average of the two tissue in question. This is derived mathematically in Appendix 1.

For tissues a and b:

The PD filter relative image weighing is $\frac{{\mathrm{2PD}}_b-{\mathrm{2PD}}_a}{{\mathrm{PD}}_a+{\mathrm{PD}}_b}$

The T1 filter relative image weighting is $\frac{e^{\frac{\mathrm{-TR}}{{\mathrm{T1}}_a}}-e^{\frac{\mathrm{-TR}}{{\mathrm{T1}}_b}}}{1-e^{\frac{\mathrm{-2TR}}{{\mathrm{T1}}_a+{\mathrm{T1}}_b}}}$.

The T2 filter relative imaging weighting is $\frac{e^{\frac{\mathrm{-TE}}{{\mathrm{T2}}_b}}-e^{\frac{\mathrm{-TE}}{{\mathrm{T2}}_a}}}{e^{\frac{\mathrm{-2TE}}{{\mathrm{T2}}_a+{\mathrm{T2}}_b}}}$

There are two tissue drop down menus in the middle of the right hand side of the screen. Beneath the menues are relative sequence and imaging weightings. The sequence weighting (SW) displays the relative weightings of each tissue property filter for Tissue 1. The image weighting (IW) displays the relative contribution of each tissue property filter to the difference in signal between Tissue 1 and Tissue 2. The numbers are generated using the equations above.

------------ FSE T1 BRAIN ------------

For the previously discussed FSE seqeunce with TR = 700 and TE = 10, and for white matter with T1 = 680 ms and T2 = 90 ms:

Select white matter as tissue 1 and grey matter as tissue 2.
The relative weightings from PD, T1, and T2 for white matter 1: 56%, -36%. and 8%.
For white matter, the sequence is 56% positively PD weighted, 36% negatively T1 weighted, and 8% positively T2 weighted.

The image weightings reflect the contribution of each tissue filter to the difference in signal between grey and white matter. The relative image weightings for PD : T1 : T2 are 25% : -67% : 8%. T1 weighting accounts for 67% of the signal difference between grey and white matter on this sequence. How do you interpret the sign of the weighting? Because signal from T1 decreases from WM to GM (Tissue 2 is darker than Tissue 1) the sign is negative. If you swap Tissue 1 and Tissue 2 the signs of the weightings will reverse. Because signal from T1 increases from GM to WM (Tissue 2 is brighter than Tissue 1) the sign is positive.

------------ FSE T1 MSK ------------

Select ligament/tendon as Tissue 1 and muscle as Tissue 2. This is now a standard "T1" weighted image for MSK imaging. For ligaments and tendons, however the sequence is primarily T2 weighted (61%) and the contrast between ligament and muscle on the image is also primarily T2 weighted (63%). But we've always called this a T1 weighted image!!! Well, we were wrong. This is a T2 weighted image for ligaments and tendons.

While we are talking about MSK imaging, set fat as Tissue 1 and muscle as Tissue 2. The sequence is primarily proton density weighted (70%) for fat. However, the contrast between fat and muscle has no PD weighting because the PD of fat and muscle are the same. The image contrast between fat and muscle is 77% due to T1 and 10% due to T2.

------------ FSE T2 Brain ------------

Set TR and TE to standard values for a "T2" weighted image. TR = 4000. TE = 80. Set tissue 1 to white matter and tissue 2 to grey matter. The sequence weighting is split almost evenly between PD (46%) and T2 (52%). The contrast between grey and white matter however is much due more to T2 weighting (65%) than PD weighting (26%). We call it T2 but there is a lot of PD weighting, especially in the white matter. The higher the TE the more T2 weighted the images become, but at the expense of low signal.

Note that for most pathologic processes in the brain there is an increase in PD, T1, and T2. However, both the sequence and image are negatively T1 weighted. While the PD and T2 weightings result in increaed signal for pathologic changes, the T1 weighting results in decreased signal. The T1 and T2/PD weightings are working against each other. We really want sequences where the weightings work together to help visualize changes from normal.

------------ FSE T2 MSK ------------

This same T2 sequence for ligaments and muscles (set tissue 1 to ligaments and tissue 2 to muscles) is heavily T2 weighted. And so is the image contrast. Signal changes in ligaments and muscles on a standard T2 weighted sequence are due to changes in tissue T2.

------------ FSE PD MSK ------------

Create a PD sequence. TR = 4000, TE = 20. For imaging tears in muscles (set Tissue 1 to Muscle and Tissue 2 to Fluid) the sequence is PD weighted, but the tissue contrast is more due to T2 weighting. For fluid filled tears in ligaments and tendons (set tissue 1 to Ligament/Tendon), there is more T2 weighting than PD. We still call this a PD sequence. We discussed this previously.

The point is that many of the weightings we've been taught are incorrect. We have learned what pathology looks like on different sequences and that does not change. This helps explain why.