SPGR Signal Intensity
Evaluate ideal fully spoiled gradient-echo steady-state signal with explicit T2* attenuation; receiver gain is included in caller equilibrium amplitude.
Description
Spoiled gradient-echo signal balances T1 recovery, excitation flip angle and T2* decay.
Spoiled gradient-echo signal balances T1 recovery, excitation flip angle and T2* decay. The expression assumes steady state and complete transverse spoiling.
The tool returns signalAmplitude (signal amplitude). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use SPGR Signal Intensity
Use SPGR Signal Intensity when you already have equilibriumAmplitude, trMs, t1Ms, teMs, t2StarMs, flipDegrees and want signalAmplitude. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use SPGR Signal Intensity and understand its results
- Enter equilibriumAmplitude, trMs, t1Ms, teMs, t2StarMs, flipDegrees using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read signalAmplitude. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| equilibriumAmplitude | Equilibrium amplitude | number | Required |
| trMs | Tr ms | number | Required |
| t1Ms | T1 ms | number | Required |
| teMs | Te ms | number | Required |
| t2StarMs | T2 star ms | number | Required |
| flipDegrees | Flip degrees | number | Required |
Use nonnegative equilibrium amplitude, positive relaxation times and TR, 0≤TE<TR, and a flip angle in (0,180] degrees.
S = M0(1−E1)sinα/(1−E1 cosα) × exp(−TE/T2*); E1=exp(−TR/T1) The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"equilibriumAmplitude": 100,
"trMs": 100,
"t1Ms": 1000,
"teMs": 10,
"t2StarMs": 50,
"flipDegrees": 30
},
"output": {
"signalAmplitude": 18.002985590840964
}
}Limitations and assumptions
The ideal signal excludes B1 variation, imperfect spoiling, flow and multi-compartment effects.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Ernst Flip Angle: Calculate the spoiled steady-state Ernst angle for supplied TR/T1; contrast optimization, B1 inhomogeneity and preparation pulses are excluded. Spin Echo Signal Intensity: Evaluate an ideal saturation-recovery spin-echo signal M0(1−e^(−TR/T1))e^(−TE/T2); refocusing imperfections and stimulated echoes are excluded.
Methodological background: Basic steady-state free-precession sequences and the Ernst equation.1
References
-
Basic steady-state free-precession sequences and the Ernst equation — ISMRM educational proceedings
Similar or alternative tools
- Ernst Flip Angle
Calculate the spoiled steady-state Ernst angle for supplied TR/T1; contrast optimization, B1 inhomogeneity and preparation pulses are excluded.
- Spin Echo Signal Intensity
Evaluate an ideal saturation-recovery spin-echo signal M0(1−e^(−TR/T1))e^(−TE/T2); refocusing imperfections and stimulated echoes are excluded.