Diffusion Gradient Duration
Solve the monotone rectangular-PGSE timing equation for pulse duration within [0, leading-edge separation]; no hardware optimization or clinical setting is recommended.
Description
For fixed gradient and pulse separation, rectangular PGSE b value increases with pulse duration up to the nonoverlap boundary.
For fixed gradient and pulse separation, rectangular PGSE b value increases with pulse duration up to the nonoverlap boundary. A bounded root search determines the duration.
The tool returns gradientDurationMs (gradient duration 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 Diffusion Gradient Duration
Use Diffusion Gradient Duration when you already have targetBSecondsPerSquareMm, gammaHzPerTesla, gradientMilliTeslaPerMeter, separationMs and want gradientDurationMs. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Diffusion Gradient Duration and understand its results
- Enter targetBSecondsPerSquareMm, gammaHzPerTesla, gradientMilliTeslaPerMeter, separationMs 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 gradientDurationMs. 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 |
|---|---|---|---|
| targetBSecondsPerSquareMm | Target b seconds per square mm | number | Required |
| gammaHzPerTesla | Gamma hz per tesla | number | Required |
| gradientMilliTeslaPerMeter | Gradient milli tesla per meter | number | Required |
| separationMs | Separation ms | number | Required |
Require nonnegative target b, positive gradient, separation and gamma. Reject targets above the model maximum, apart from roundoff tolerance; otherwise use 100 bisection steps.
find delta in [0,separation] satisfying targetB = angularGamma²×G²×delta²×(separation−delta/3) The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"targetBSecondsPerSquareMm": 0.01052757802782865,
"gammaHzPerTesla": 1000000,
"gradientMilliTeslaPerMeter": 10,
"separationMs": 30
},
"output": {
"gradientDurationMs": 10
}
}Limitations and assumptions
Zero target returns zero duration and maximum target returns separation. Ramps, pulse constraints and hardware feasibility are excluded.
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
Diffusion B-Value: Compute the Stejskal–Tanner b value for ideal rectangular PGSE pulses in s/mm² with γ supplied in Hz/T; waveform cross-terms and imaging gradients are excluded. Diffusion Gradient Strength: Invert ideal rectangular PGSE b for gradient magnitude at supplied timing; hardware capability, cross-terms and safety are not inferred.
Methodological background: Spin Diffusion Measurements: Spin Echoes in the Presence of a Time-Dependent Field Gradient.1
References
-
Spin Diffusion Measurements: Spin Echoes in the Presence of a Time-Dependent Field Gradient — Stejskal and Tanner; Journal of Chemical Physics
Similar or alternative tools
- Diffusion B-Value
Compute the Stejskal–Tanner b value for ideal rectangular PGSE pulses in s/mm² with γ supplied in Hz/T; waveform cross-terms and imaging gradients are excluded.
- Diffusion Gradient Strength
Invert ideal rectangular PGSE b for gradient magnitude at supplied timing; hardware capability, cross-terms and safety are not inferred.