GRAPPA Acceleration

Count unique regularly subsampled phase lines plus a contiguous ACS interval, avoiding double counting; GRAPPA kernel fitting and reconstruction are not performed.

Description

Autocalibration lines add acquisition overhead to a regular phase-line stride.

Autocalibration lines add acquisition overhead to a regular phase-line stride. Taking the union avoids counting a calibration line twice when it already lies on the stride.

The tool returns acquiredLineIndexes (acquired line indexes); acquiredLineCount (acquired line count); effectiveAcceleration (effective acceleration). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use GRAPPA Acceleration

Use GRAPPA Acceleration when you already have fullPhaseLines, nominalStride, acsStartIndex, acsLineCount and want acquiredLineIndexes, acquiredLineCount, effectiveAcceleration. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use GRAPPA Acceleration and understand its results

Enter fullPhaseLines, nominalStride, acsStartIndex, acsLineCount 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 acquiredLineIndexes, acquiredLineCount, effectiveAcceleration. 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
fullPhaseLines	Full phase lines	integer	Required
nominalStride	Nominal stride	integer	Required
acsStartIndex	Acs start index	integer	Required
acsLineCount	Acs line count	integer	Required

Use positive integer full-line count and stride, nonnegative ACS start/count and an in-range ACS interval. Return zero-based acquired indexes.

acquired = indexes divisible by stride UNION [ACSstart,ACSstart+ACScount); acceleration = fullLines/acquiredCount

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "fullPhaseLines": 128,
    "nominalStride": 4,
    "acsStartIndex": 48,
    "acsLineCount": 32
  },
  "output": {
    "acquiredLineIndexes": [
      0,
      4,
      8,
      12,
      16,
      20,
      24,
      28,
      32,
      36,
      40,
      44,
      48,
      49,
      50,
      51,
      52,
      53,
      54,
      55,
      56,
      57,
      58,
      59,
      60,
      61,
      62,
      63,
      64,
      65,
      66,
      67,
      68,
      69,
      70,
      71,
      72,
      73,
      74,
      75,
      76,
      77,
      78,
      79,
      80,
      84,
      88,
      92,
      96,
      100,
      104,
      108,
      112,
      116,
      120,
      124
    ],
    "acquiredLineCount": 56,
    "effectiveAcceleration": 2.2857142857142856
  }
}

Limitations and assumptions

This counts lines only; calibration timing, reconstruction and actual SNR are not modelled. A zero-length ACS interval is allowed.

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

Acceleration Factor Rate: Compare a supplied full acquisition with accelerated readout plus explicit calibration and fixed overhead; effective acceleration can be below one. Compressed Sensing Acceleration: Measure actual 2D sampling-mask acceleration and audit required calibration coverage; mask sparsity is not a compressed-sensing reconstructability guarantee.

Methodological background: SENSE: sensitivity encoding for fast MRI.^[1]

References

SENSE: sensitivity encoding for fast MRI — Pruessmann et al.; Magnetic Resonance in Medicine

Similar or alternative tools

Acceleration Factor Rate
Compare a supplied full acquisition with accelerated readout plus explicit calibration and fixed overhead; effective acceleration can be below one.
Compressed Sensing Acceleration
Measure actual 2D sampling-mask acceleration and audit required calibration coverage; mask sparsity is not a compressed-sensing reconstructability guarantee.