Inversion Time TI
Solve an ideal repeated inversion-recovery null TI=T1·ln[2/(1+exp(−TR/T1))]; assumes ideal inversion and saturation/readout convention, not a patient-specific protocol.
Description
Inversion null timing changes when longitudinal recovery is incomplete before the next inversion.
Inversion null timing changes when longitudinal recovery is incomplete before the next inversion. The finite-TR expression differs from the long-TR limit T1 ln2.
The tool returns nullTimeMs (null time ms). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Inversion Time TI
Use Inversion Time TI when you already have t1Ms, trMs and want nullTimeMs. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Inversion Time TI and understand its results
- Enter t1Ms, trMs 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 nullTimeMs. 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 |
|---|---|---|---|
| t1Ms | T1 ms | number | Required |
| trMs | Tr ms | number | Required |
Use positive T1 and TR in the same unit, here ms. Evaluate the ideal finite-repetition expression.
TI = T1×ln(2/(1+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": {
"t1Ms": 1000,
"trMs": 1000
},
"output": {
"nullTimeMs": 379.8854930417225
}
}Limitations and assumptions
Perfect inversion and the stated recovery model are assumed. Inversion efficiency, readout perturbations and tissue mixtures are not included.
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
Double Inversion Black Blood TI: Model ideal fresh-blood single-inversion nulling and resident-tissue recovery after nonselective then selective inversion; flow replacement, TR history and imperfect inversion 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: RAD229: MRI signal and sequence lecture notes.1
References
-
RAD229: MRI signal and sequence lecture notes — Brian Hargreaves and colleagues, Stanford University
Similar or alternative tools
- Double Inversion Black Blood TI
Model ideal fresh-blood single-inversion nulling and resident-tissue recovery after nonselective then selective inversion; flow replacement, TR history and imperfect inversion 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.