Fig 1.
Illustration of a EPG derived curve with an FA of 120° (x) and correct 180° FA (line) for a T2 = 100ms, T1 = 3000ms, ESP = 20ms and ETL of 24.
It can be seen that due to the incorrect FA the first echo point is lower than that of the second and the signal seems to oscillate between odd and even echoes.
Fig 2.
EPG simulated curve for T2 = 50ms, T1 = 3000ms, ESP = 20, ETL = 24, and FA = 120°.
Fig 2A illustrates the difference (blue solid line) between the curve simulated at 120° (black dashed line) an optimal 180° pulse (red solid line). Fig 2B illustrates the envelope (black lines) calculated from the odd and even echoes of the signal (blue line).
Table 1.
Fitted results (T2fitted, Sofitted, Offsetfitted) from EPG simulated data of different FAs (T2 = 100ms, ESP = 20ms, ETL = 24, So = 1000 a.u.).
Offsetcalc is the back calculated vertical offset (Eq 3).
Fig 3.
Relative T2 deviation, dT2 (in %), for method 1 (first row), method 2 (second row), method 3 (third row) and method 4 (forth row).
These results are presented for 3 different FA. It is seen that T2 becomes longer as the FA decreases. Closer approximation to the actual T2 are seen when Eq 2 is used and the first point is excluded. Please note that the scales of dT2 are not uniform provide maximum dynamic range for the different ETL and ESP.
Fig 4.
Relative S0 deviation, dS0 (in %), for methods 1–4 corresponding to rows 1–4 respectively.
Closer approximations with little difference are seen for both equations with the first point excluded from the fit. Please note that the scales of dS0 are not uniform and therefore provide maximum dynamic range for the different ETL and ESP.
Fig 5.
Determined offset values for different FAs for method 2 (top row) and method 4 (bottom row).
Distributions remain relatively similar with decreasing values as FA tends to 180°. Note the decreasing offset with increasing FA.
Table 2.
Mean results of T2 fitting for each method per T2 time for an ESP time of 5ms (ETL = 32, FA = 140°).
Simulations were ran 1000 times.
Table 3.
Mean results of simulated signal with added noise fittings for each method per T2 time for an ESP of 5ms (ETL = 32, FA = 140°).
Simulations were ran 1000 times.
Fig 6.
Example of the signal decay curves of the phantom measurements for a defined pixel (shown by the cross section of the lines): Curves are shown for the single spin echo sequence (top right) and the MSE sequences for different FAs (bottom row).
The X-axis represents TE and y-axis the signal (x 106 a.u). It can be noticed that as the FA reduces the first point, in particular, deviates from the expected exponential decay curve. The variation of the refocusing FA was performed by variation of the FA in the sequence protocol. The actual FA at the respective position might even differ from this value due to B1 inhomogeneities and imperfect slice profiles.
Table 4.
Fitted results from phantom measurements a MSE sequence with different FAs as used in the sequence protocol (see Supporting Information, S1 Dataset: MSE datasets) and different fitting methods.
Single spin echo sequence yielded a mean T2 of 67.7 ± 0.60ms. T2 and dT2 relate to the mean and standard deviation over 3 ROIs within the phantom for each measurement.