Sports cardiology with open algorithms. Every zone, threshold, and inference made by the app is anchored in primary literature, with a verifiable DOI.
Project principle. No reference is cited without reading or validating its existence. If a value lacks support in the literature, it is declared as the author's estimate — both in the app and in the report. This page lists the foundation behind every methodological decision.
01Four-layer method
HR Core MK operates on 4 precision levels with automatic promotion as new data arrives:
Layer 1 — Population
Age + sex → appropriate formula
Tanaka (men), Gulati (women), Nes (athletes). Margin ±10–15 bpm.
Layer 2 — Karvonen
+ Resting HR (HRrest)
Zones expressed as % of reserve (HRmax − HRrest). Anchors the base in the individual's true resting state.
Layer 3 — CPET data
+ VT1, VT2, HRmax measured by cardiopulmonary exercise testing
Zones DERIVED from measured thresholds. Clinical gold standard.
Layer 4 — Inference by triangulation
+ Breathing Pattern + RPE + HR curve over N sessions
Thresholds adapt dynamically with training and adaptation. Operational construct of HR Core MK (validation in progress for paper).
02HRmax by profile
There is no universal HRmax formula. The app selects the appropriate equation based on declared profile and adopts the highest HR observed in real sessions when it exceeds the estimate.
Formulas estimate — real tests measure. When the user reaches an HR higher than the estimate in a valid session, the app uses the measured value as reference.
03Zones as % of reserve (Karvonen)
When resting HR (HRrest) is registered, the app calculates zones as % of reserve, not as % of HRmax:
target HR = HRrest + (HRmax − HRrest) × %
This method anchors the calculation base on the individual's real resting state, being more accurate than % HRmax in people with HRrest distant from the population average (athletes, trained subjects).
VT1 and VT2 are physiological points of gas exchange, not arbitrary constructs:
VT1 (aerobic threshold) — point at which ventilation begins to grow disproportionately to VO₂. Marks the start of mouth recruitment and initial compensatory hyperventilation.
VT2 (anaerobic threshold / respiratory compensation point) — point at which hyperventilation accelerates to buffer acidosis. Above it, sustained exercise lasts minutes, not hours.
The app offers 4 behavioral categories, extending the classic 3-level Talk Test (Foster 2008) to capture the respiratory transition with finer granularity:
NOSEnasal · < VT1
NOSE-MOUTHtransition · ≈ VT1
MOUTHoral · VT1–VT2
PANTINGhyperventilation · > VT2
Why 4 markers and not 3?
The intermediate nose-mouth category maps directly to the onset of mouth recruitment, described by Wasserman, Whipp, Koyl & Beaver. J Appl Physiol. 1973. This is the physiological event that defines VT1 in cardiopulmonary exercise testing. Ignoring it loses resolution exactly where the transition matters.
The term "Breathing Pattern" (or "Ventilatory Pattern") is the established term in respiratory physiology (Wasserman, Whipp), and avoids confusion with the strict Talk Test (which measures speech capacity, not breathing pattern).
The app uses 3 levels of Rating of Perceived Exertion (Light · Moderate · Hard), based on the Brazilian clinical CPET simplification. Direct mapping against Borg 6–20:
HR Core MK
Borg 6–20
Associated threshold
1 · Light
9–12
below VT1
2 · Moderate
13–14
≈ VT1
3 · Hard
15–17
≈ VT2
Why a simplified scale?
Eston & Connolly. Sports Med. 1996 — reduced scales (3–5 categories) retain validity in field populations, patients, and clinical contexts. Eston. IJSPP. 2012 — explicit trade-off: lower granularity requires larger n of markings for stable inference, but converges to the same statistical result.
Chen, Fan & Moe. J Sports Sci. 2002 — meta-analysis. RPE 13–14 (Borg 6–20) ≈ VT1 (r = 0.74); RPE 15–17 ≈ VT2 (r = 0.83). This is the basis for inferring thresholds via perception.
07Triangulation · HR Core MK contribution
Combining three markers reduces the individual error of each:
Absolute HR alone ignores interpersonal variability of % HRmax at VT1/VT2
Breathing Pattern in isolation may be biased in former swimmers (increased CO₂ tolerance)
RPE in isolation may be inconsistent in novice users
The HR Core MK algorithm computes the median of the three estimates, weighted by intra-user consistency (RPE ↔ %HRmax correlation). High convergence (SD < 5 bpm) → declared as high confidence. Divergence → app flags for recalibration.
This is the original contribution of HR Core MK — not formally implemented in commercial apps (Polar Flow, Garmin Connect, Strava, Suunto). The methodology will be published after internal validation, at which point the construct BPM (Breath Phase Marker) may be introduced as the operational name of the method.
08HRR and VO₂max
Heart rate recovery (HRR)
Classical prognostic marker. Cole et al. N Engl J Med. 1999 — HRR-60s < 12 bpm associated with increased 12-year mortality. App classification:
Recommended for athletes and active adults. In sedentary populations, performance-based estimation is preferred (Daniels VDOT).
09Verified references
All references below had their DOI or PMID verified at doi.org and PubMed on 2026-05-07. Complete list in Vancouver format (50+ refs) available in REFERENCES.md of the repository.
Universal formula for general population, n=18,712 in meta-analysis.
Gulati M, Shaw LJ, Thisted RA, Black HR, Bairey Merz CN, Arnsdorf MF. Heart rate response to exercise stress testing in asymptomatic women: the St. James Women Take Heart Project.
Task Force of the European Society of Cardiology and NASPE. Heart rate variability: standards of measurement, physiological interpretation, and clinical use.
Consensus standard for RMSSD, SDNN, pNN50 and measurement conditions.
Plews DJ, Laursen PB, Stanley J, Kilding AE, Buchheit M. Training adaptation and heart rate variability in elite endurance athletes: opening the door to effective monitoring.
Ekelund U, Steene-Johannessen J, Brown WJ, et al. Does physical activity attenuate, or even eliminate, the detrimental association of sitting time with mortality? A harmonised meta-analysis.
Declared limitations. This application is a tool for physiological monitoring and screening; it does not replace cardiopulmonary exercise testing (CPET) in a laboratory nor in-person cardiology evaluation. Indirect estimates carry a margin of ±10–15%. In case of symptoms during exertion (chest pain, disproportionate dyspnea, syncope, palpitations), stop immediately and seek medical attention.