HRF Peak
Evaluate a supplied double-gamma HRF and identify its unique sampled peak; integer gamma shapes and caller scale/undershoot ratio define the model, not a universal response.
Description
A double-gamma HRF combines a positive response and a delayed undershoot.
A double-gamma HRF combines a positive response and a delayed undershoot. Its largest sampled value has a sampled peak time, which can differ from the continuous maximum.
The tool returns hrfValues (hrf values); sampledPeakTimeSeconds (sampled peak time seconds). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use HRF Peak
Use HRF Peak when you already have timesSeconds, peakShape, undershootShape, scaleSeconds, undershootRatio and want hrfValues, sampledPeakTimeSeconds. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use HRF Peak and understand its results
- Enter timesSeconds, peakShape, undershootShape, scaleSeconds, undershootRatio 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 hrfValues, sampledPeakTimeSeconds. 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 |
|---|---|---|---|
| timesSeconds | Times seconds | list of number | Required |
| peakShape | Peak shape | integer | Required |
| undershootShape | Undershoot shape | integer | Required |
| scaleSeconds | Scale seconds | number | Required |
| undershootRatio | Undershoot ratio | number | Required |
Use increasing nonnegative times, positive scale and ratio, integer shapes 1–32 with undershoot shape greater than peak. Reject a tied sampled maximum.
HRF(t) = gammaDensity(t,peakShape,scale)−gammaDensity(t,undershootShape,scale)/ratio The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"timesSeconds": [
0,
1,
2,
3
],
"peakShape": 2,
"undershootShape": 3,
"scaleSeconds": 1,
"undershootRatio": 6
},
"output": {
"hrfValues": [
0,
0.3372228210738221,
0.2255588053943545,
0.11202090382769386
],
"sampledPeakTimeSeconds": 1
}
}Limitations and assumptions
No continuous optimization or unit-area normalization is performed; the model is not fitted to measured BOLD data.
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
Dispersion Derivative HRF: Evaluate the analytic derivative of the caller double-gamma HRF with respect to its common scale parameter; this differs from time-shift differentiation and is not an orthogonalized design column. GLM HRF Convolution: Compute causal same-length discrete convolution with explicit Δt scaling for a sampled stimulus-rate function; event impulses must be converted to rate samples and no GLM is fitted.
Methodological background: fMRI model specification: haemodynamic response functions and derivatives.1
References
-
fMRI model specification: haemodynamic response functions and derivatives — SPM developers, University College London
Similar or alternative tools
- Dispersion Derivative HRF
Evaluate the analytic derivative of the caller double-gamma HRF with respect to its common scale parameter; this differs from time-shift differentiation and is not an orthogonalized design column.
- GLM HRF Convolution
Compute causal same-length discrete convolution with explicit Δt scaling for a sampled stimulus-rate function; event impulses must be converted to rate samples and no GLM is fitted.