Gradient Amplitude Required
Derive constant readout gradient from desired k-space traversal span and duration; prephasers, ramps and gradient hardware feasibility are excluded.
Description
A constant readout gradient traverses a k-space span in a specified duration.
A constant readout gradient traverses a k-space span in a specified duration. K-space is expressed in cycles per metre when gamma is in Hz/T.
The tool returns requiredGradientMilliTeslaPerMeter (required 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 Gradient Amplitude Required
Use Gradient Amplitude Required when you already have kSpaceSpanCyclesPerMeter, readoutDurationMs, gammaHzPerTesla and want requiredGradientMilliTeslaPerMeter. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Gradient Amplitude Required and understand its results
- Enter kSpaceSpanCyclesPerMeter, readoutDurationMs, gammaHzPerTesla 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 requiredGradientMilliTeslaPerMeter. 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 |
|---|---|---|---|
| kSpaceSpanCyclesPerMeter | K space span cycles per meter | number | Required |
| readoutDurationMs | Readout duration ms | number | Required |
| gammaHzPerTesla | Gamma hz per tesla | number | Required |
Require positive span, duration and gamma.
gradient[mT/m] = 10⁶×spanCyclesPerMeter/(gammaHzPerTesla×durationMs) The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"kSpaceSpanCyclesPerMeter": 1000,
"readoutDurationMs": 10,
"gammaHzPerTesla": 1000000
},
"output": {
"requiredGradientMilliTeslaPerMeter": 100
}
}Limitations and assumptions
The constant-gradient model excludes ramps, rewinding, slew limits and hardware feasibility.
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
Cartesian K-Space Trajectory: Integrate two-axis piecewise-linear gradients by trapezoids into Cartesian k-space from a zero origin; refocusing sign changes must already be applied to supplied gradients. Readout Field of View: Derive frequency-encoding FOV from full signed-span receiver bandwidth and constant readout gradient, not a pixels-times-spacing lookup.
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
- Cartesian K-Space Trajectory
Integrate two-axis piecewise-linear gradients by trapezoids into Cartesian k-space from a zero origin; refocusing sign changes must already be applied to supplied gradients.
- Readout Field of View
Derive frequency-encoding FOV from full signed-span receiver bandwidth and constant readout gradient, not a pixels-times-spacing lookup.