Table 3. Key definitions: TP-filters.

Univariate (single TP-filter) model (for each filter segment or module)

X axis

1. TP = tissue property e.g., ρm, T1, T2, D*

2. ∆TP = difference or change in TP. Can be absolute ∆TP (linear X axis) or fractional ∆TP/TP (logarithmic, lnX axis)

3. Scale is linear or logarithmic

Y axis

4. S = signal overall, STP = signal for each TP-filter

5. C = contrast, Cab = ∆S (absolute contrast), or Cfr = ∆S/S (fractional contrast)

6. Scale is linear or logarithmic

Filter, sequence parameters, sequence weighting

7. STP = signal; the filter equation comes from the signal equation

8. SP = Sequence Parameters, TR, TI, TE, b, α ....

9. $\frac{\partial {\text{S}}_{\text{TP}}}{\partial \text{TP}}\left(\text{linear}\right)$= first derivative of STP with respect to TP = sWTP/SEQ/SP/lin = sequence weighting = slope of filter

10. $\frac{\partial {\text{S}}_{\text{TP}}}{\partial \left(\text{In TP}\right)}$(logarithmic) = first derivative of STP with respect to lnTP = sWTP/SEQ/SP/log = sequence weighting = slope of filter

Image contrast and image weighting

11. Cab = sWTP/SEQ/SP/lin × ∆TP as % of full scale

12. Cfr = sWTP/SEQ/SP/log ×$\frac{\mathrm{\Delta T}}{\mathrm{TP}}$ as % of full scale

13. iWTP/SEQ/SP = image weighting (for each TP-filter) = 100% i.e., all contrast comes from the same single TP

14. ∆TP can be calculated from the contrast

Multivariate (multiple TP-filter) model (product of two or more filter segments or modules)

Signal and contrast

1. S = signal = Sρm × ST1 × ST2 .... i.e., product of signal from each TP-filter

2. C = contrast, Cab = ∆S, Cfr = ∆S/S

3. sWrSEQ/SP/... (ρm: T1: T2) = e.g., (51: -30: 19) = sequence weighting ratio i.e., ratio of contributions from each TP to sequence weighting.

4. iWrSEQ/SP/... (ρm: T1: T2) = e.g., (27: -61: 12) = image weighting ratio i.e., ratio of contributions from both sequence weighting and difference (or change) in TP to overall contrast for each TP.

5. ∆TP can be calculated from Cab and Cfr