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.
Description
Rectangular pulsed-gradient spin-echo diffusion weighting depends on gradient strength, pulse duration and leading-edge pulse separation.
Rectangular pulsed-gradient spin-echo diffusion weighting depends on gradient strength, pulse duration and leading-edge pulse separation. The gyromagnetic ratio must be converted to angular units.
The tool returns bSecondsPerSquareMm (b seconds per square mm). 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 B-Value
Use Diffusion B-Value when you already have gammaHzPerTesla, gradientMilliTeslaPerMeter, deltaMs, separationMs and want bSecondsPerSquareMm. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Diffusion B-Value and understand its results
- Enter gammaHzPerTesla, gradientMilliTeslaPerMeter, 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 bSecondsPerSquareMm. 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 |
|---|---|---|---|
| gammaHzPerTesla | Gamma hz per tesla | number | Required |
| gradientMilliTeslaPerMeter | Gradient milli tesla per meter | number | Required |
| deltaMs | Delta ms | number | Required |
| separationMs | Separation ms | number | Required |
Require positive gamma and pulse duration, nonnegative gradient, and separation at least pulse duration.
b[s/mm²] = (2πgammaHz/T)²×(GmT/m×10⁻³)²×(deltaMs×10⁻³)²×((separationMs−deltaMs/3)×10⁻³)/10⁶ The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"gammaHzPerTesla": 1000000,
"gradientMilliTeslaPerMeter": 10,
"deltaMs": 10,
"separationMs": 30
},
"output": {
"bSecondsPerSquareMm": 0.01052757802782865
}
}Limitations and assumptions
Ramps, imaging gradients and cross terms are excluded. Separation means leading-edge to leading-edge, not the silent gap.
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 Gradient Strength: Invert ideal rectangular PGSE b for gradient magnitude at supplied timing; hardware capability, cross-terms and safety are not inferred. 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 Gradient Strength
Invert ideal rectangular PGSE b for gradient magnitude at supplied timing; hardware capability, cross-terms and safety are not inferred.
- 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.