Temporal Derivative HRF
Differentiate a supplied HRF with centered interior differences and one-sided endpoints; this is the time derivative, not an automatically orthogonalized GLM basis.
Description
A temporal HRF derivative approximates how a sampled response changes with time.
A temporal HRF derivative approximates how a sampled response changes with time. The supplied spacing determines the derivative units.
The tool returns temporalDerivative (temporal derivative). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Temporal Derivative HRF
Use Temporal Derivative HRF when you already have hrfSamples, sampleIntervalSeconds and want temporalDerivative. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Temporal Derivative HRF and understand its results
- Enter hrfSamples, sampleIntervalSeconds 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 temporalDerivative. 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 |
|---|---|---|---|
| hrfSamples | Hrf samples | list of number | Required |
| sampleIntervalSeconds | Sample interval seconds | number | Required |
Require at least two samples and positive uniform interval in seconds. Use centered differences internally and one-sided differences at both endpoints.
interior derivative[i] = (h[i+1]−h[i−1])/(2×dt) The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"hrfSamples": [
0,
1,
4
],
"sampleIntervalSeconds": 1
},
"output": {
"temporalDerivative": [
1,
2,
3
]
}
}Limitations and assumptions
Uniform sampling is assumed, not verified from timestamps. No smoothing, HRF fitting or basis orthogonalization is performed.
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. 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.
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.
- 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.