Slope-range ECG-derived respiration

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Metadata

Field	Value
Canonical specification ID	ecg.sloperange
Module	ecg
Source JSON	specs/ecg/sloperange/spec.json

Summary

Estimates an ECG-derived respiration amplitude series from derivative ECG morphology around detected R waves.

The slope-range method summarizes beat-to-beat respiratory modulation by comparing the maximum upslope and minimum downslope of a derivative ECG signal in short windows around each R wave.

Keywords

ECG, ECG-derived respiration, EDR, slope range, respiratory modulation

Scientific References

ID	Relation	Note
kontaxis_edr_af_2020	original_method	Primary method and provenance reference for slope-range ECG-derived respiration.
varon_comparative_edr_2020	validation	Comparative EDR context and validation evidence for single-lead ambulatory ECG.

Inputs

id	data_type	shape	unit	allow_nan	allow_inf	constraints
decg	real_vector	vector	a.u.	false	false	minimum_length=2
r_wave_times	real_vector	vector	s	false	false	minimum_length=1
sampling_frequency	real_scalar	scalar	Hz	false	false	exclusive_minimum=0

Parameters

No parameters.

Outputs

id	data_type	shape	unit
edr	real_vector	vector	a.u.

Normative Definitions

Target	Definition	Formula
r_wave_times	ECG R-wave occurrence times in seconds. Values must be finite, one-dimensional, strictly increasing, without repeats, and mappable onto the derivative ECG sample grid using sampling_frequency.
r_wave_samples	Conceptual sample-grid positions derived from r_wave_times and sampling_frequency on the derivative ECG sample grid. Each value must lie within the decg sample grid. The contract does not specify implementation-specific array indexing conventions.
analysis_windows	Set short_window = round(sampling_frequency * 0.015) and long_window = round(sampling_frequency * 0.05). The upslope_window contains integer offsets greater than -long_window and less than or equal to short_window. The downslope_window contains integer offsets greater than or equal to -short_window and less than long_window.
edr	For each R wave with complete analysis windows, compute edr as max(decg over the upslope window) minus min(decg over the downslope window).
boundary_edr	For an R wave whose analysis windows extend outside the derivative ECG signal, preserve output alignment with r_wave_times and set the corresponding edr value to NaN.

Behavior

Nan handling

NaN and infinite values in decg, r_wave_times, or sampling_frequency are invalid inputs. NaN values may appear in edr only to mark R waves whose analysis windows are incomplete at signal boundaries.

Empty input

Empty decg and empty r_wave_times inputs are invalid.

Input orientation

Treat decg and r_wave_times as one-dimensional vectors regardless of row or column orientation. The edr output is a one-dimensional ordered vector aligned with r_wave_times.

Insufficient data

If decg is too short to support complete windows around a beat, the affected boundary edr value is NaN when the corresponding r_wave_samples value is inside the signal. R-wave times that map outside the derivative ECG sample grid are invalid.

Informative Notes

• This first Biosiglib contract makes edr the only normative output.
• Diagnostic arrays exposed by implementations, including upslopes, downslopes, upslope_max_position, and downslope_min_position, are informative implementation details at this stage.
• Implementation-specific array indexing conventions are not part of the Biosiglib contract.

Conformance Cases

Case ID	File
ecg.sloperange.invalid_r_wave_time_out_of_bounds	conformance/ecg/sloperange/invalid_r_wave_time_out_of_bounds.json
ecg.sloperange.invalid_r_wave_times_not_strict	conformance/ecg/sloperange/invalid_r_wave_times_not_strict.json
ecg.sloperange.synthetic_boundary_nan	conformance/ecg/sloperange/synthetic_boundary_nan.json
ecg.sloperange.synthetic_positive	conformance/ecg/sloperange/synthetic_positive.json