Diffusion Gradient Strength
Invert ideal rectangular PGSE b for gradient magnitude at supplied timing; hardware capability, cross-terms and safety are not inferred.
Description
In the rectangular PGSE model, b value is proportional to squared gradient amplitude.
In the rectangular PGSE model, b value is proportional to squared gradient amplitude. Taking a square root inverts that dependence.
The tool returns gradientMilliTeslaPerMeter (gradient milli tesla per meter). 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 Strength
Use Diffusion Gradient Strength when you already have targetBSecondsPerSquareMm, gammaHzPerTesla, deltaMs, separationMs and want gradientMilliTeslaPerMeter. 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 Strength and understand its results
- Enter targetBSecondsPerSquareMm, gammaHzPerTesla, deltaMs, 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 gradientMilliTeslaPerMeter. 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 |
| deltaMs | Delta ms | number | Required |
| separationMs | Separation ms | number | Required |
Use nonnegative target b with valid positive gamma and pulse timing. Evaluate the same forward rectangular-pulse model at unit gradient before inversion.
GmT/m = sqrt(targetB / bValueAtOneMilliTeslaPerMeter) The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"targetBSecondsPerSquareMm": 1,
"gammaHzPerTesla": 1000000,
"deltaMs": 10,
"separationMs": 30
},
"output": {
"gradientMilliTeslaPerMeter": 97.46210015420952
}
}Limitations and assumptions
Target zero returns zero gradient. No ramp, cross-term or hardware limit is 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
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 Duration: Solve the monotone rectangular-PGSE timing equation for pulse duration within [0, leading-edge separation]; no hardware optimization or clinical setting is recommended.
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 Duration
Solve the monotone rectangular-PGSE timing equation for pulse duration within [0, leading-edge separation]; no hardware optimization or clinical setting is recommended.