# HRV Formula Sheet

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## Data Path - input stream: accepted RR intervals from live BLE heart-rate measurement packets - physical H10: RR intervals are derived inside the strap from ECG beat timing - synthetic transport: RR remains the source for the HRV solve, while synthetic PMD ECG is emitted on the same synthetic beat schedule for operator review ## Rolling Short-Term Window The app uses a rolling RR window with a default length of `300 s`. That default tracks the conventional short-term setting discussed by Shaffer and Ginsberg. The first solve is intentionally delayed until the rolling window is nearly full enough to avoid publishing an early headline value from a partial capture. ## Time-Domain Formulas For accepted RR intervals `NN_1 ... NN_n`: Here `NN_i` means the `i`-th accepted beat interval in milliseconds, `n` is the number of accepted intervals in the current rolling window, and an overline means a window average. These formulas are applied to the accepted short-term series the tracker keeps for the HRV solve, not to every raw packet value. ```latex \overline{NN} = \frac{1}{n}\sum_{i=1}^{n} NN_i ``` This is the average accepted beat interval over the current short-term window. ```latex \overline{HR} = \frac{60000}{\overline{NN}} ``` This converts the mean interval into beats per minute using `60000 ms = 1 min`. ```latex SDNN = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(NN_i - \overline{NN})^2} ``` `SDNN` measures how widely the accepted intervals are spread across the whole window. ```latex RMSSD = \sqrt{\frac{1}{n-1}\sum_{i=2}^{n}(NN_i - NN_{i-1})^2} ``` `RMSSD` focuses on beat-to-beat change by differencing neighboring intervals before averaging. ```latex \ln RMSSD = \ln(RMSSD) ``` `\ln RMSSD` is the natural-log form of `RMSSD`; it compresses the scale and is often easier to compare across sessions. ```latex pNN50 = 100 \times \frac{\#\left\{|NN_i - NN_{i-1}| > 50\,ms\right\}}{n-1} ``` `pNN50` is the percentage of adjacent interval pairs whose absolute difference exceeds `50 ms`. ```latex SD1 = \frac{RMSSD}{\sqrt{2}} ``` `SD1` is the short-axis Poincare equivalent of short-term variability and is shown because many readers know HRV through that geometric view. ## Alignment Status The implementation is aligned to the cited short-term HRV guidance for: - `RMSSD` as the headline short-term vagally weighted metric - `SDNN` as sample standard deviation over the accepted short-term window - `pNN50` with a fixed `50 ms` threshold - `SD1 = RMSSD / sqrt(2)` - `mean NN`, `mean HR`, and `lnRMSSD` The app does not claim to reproduce: - `24 h` norms - clinical artifact adjudication - full Holter-style NN editing It is therefore documented as short-term RR-derived telemetry rather than a clinical HRV workstation. ## References - [HRV Workflow](hrv-workflow.md) - [References](references.md) - Shaffer and Ginsberg, "An Overview of Heart Rate Variability Metrics and Norms" (2017). [DOI: 10.3389/fpubh.2017.00258](https://doi.org/10.3389/fpubh.2017.00258)