S SaptrishiResearch

A mathematical model of your heart · Research protocol v0.1

Your heart wants to speak. Mathematics can listen.

A resting ECG shows the heart at stillness. A treadmill test shows how it responds to effort and recovery. Together, they can become one traceable account of what was measured—without inventing what the reports cannot prove.

Upload ECG + TMT → See how it works

Research use only · Direct page vision · Typical multi-page processing: 7–10 minutes · No clinical decision output

INPUT / 02 DOCUMENTS PROTOCOL READY
ECG
Resting 12-lead ECGElectrical baseline
01
TMT
Treadmill test reportExercise and recovery response
02
CALIBRATERECONSTRUCTCOMPARE

The idea in plain language

Two familiar reports tell one continuous story.

The system does not ask a machine for a verdict. It asks each page for measurements, checks whether those measurements are trustworthy, and applies declared mathematics that another researcher can reproduce.

01

Your heart speaks

Electrical timing, rhythm, workload, heart rate, blood pressure and recovery leave measurable traces.

02

The reports preserve it

The resting ECG captures the baseline; the TMT records the response as effort rises and then stops.

03

Mathematics listens

Quality rules and fixed equations reconstruct only the values the pages can support.

What the research result contains

A readable summary, backed by an auditable record.

The first view is written for a person. The supporting measurements, equations, source locations and uncertainty flags remain available for technical review.

At restHeart rate, intervals and electrical measurements supported by the ECG.
During effortPeak workload, METs, heart-rate response and recorded blood-pressure response.
During recoveryHow quickly heart rate changes after exercise, when the report contains usable samples.
In contextExercise capacity compared with a published reference—not a diagnosis or biological heart age.
With evidenceEvery accepted value keeps its document, page, stage or lead, and quality status.
With boundariesMissing or unreliable measurements are clearly withheld rather than estimated.

The core principle

Direct page vision reads the report. Mathematics governs the result.

01

Read

Direct page vision examines printed facts, grids and trace coordinates while retaining their source location.

02

Reject

Fixed quality rules exclude ambiguous calibration, incompatible leads and artifact-limited segments.

03

Reconstruct

Versioned equations produce workload, heart-rate, pressure, recovery and lead-wise electrical measurements.

Technical protocol

Every number retains its path back to the page.

The vision layer proposes measurements. Hard rules decide whether they may enter the model. Accepted values retain document, page, lead, stage and confidence provenance.

  1. 01
    Document classificationIdentify resting ECG, TMT summary, stage table and waveform panels.
    layout map
  2. 02
    Calibration recoveryRead paper speed, voltage scale, grid spacing and lead labels.
    mm to ms / mV
  3. 03
    Signal and table extractionTrace waveforms; parse stage, speed, grade, heart rate and blood pressure.
    source tagged
  4. 04
    Compatibility checksReject missing calibration, uncertain leads, clipping, overlap or motion-dominated intervals.
    fail closed
  5. 05
    Fixed computationRun declared equations with units, rounding rules and version identifiers.
    reproducible
  6. 06
    Research outputReturn measurements, quality flags and non-identifiable quantities, not a diagnosis.
    auditable

Objective outputs

Declared equations, not opaque scores.

These formulas describe the intended computation layer. Their use depends on protocol, units and measurement quality encoded in each source report.

01 / External workloadVO₂ = v[0.17 + 0.79G] + 3.5

v in m/min, G as treadmill grade; MET = VO₂ / 3.5

02 / Heart-rate recoveryHRR₁ = HRpeak − HR1min

Reported at one and two minutes when recovery samples are measurable.

03 / Pressure responseRPP = HR × SBP

With MAP = DBP + (SBP − DBP) / 3 for each recorded stage.

04 / Lead-wise ST levelST₆₀,l = Vₗ(J + 60 ms) − baselineₗ

Measured only after grid calibration, lead confirmation and artifact checks.

Baseline rule

The TMT's own pre-exercise trace is the preferred comparator for exercise ST measurements. A separate resting ECG supports morphology, interval and artifact review, but direct voltage subtraction is withheld when resting and exercise lead placements differ.

Functional age, not biological age

A transparent inversion of an exercise-capacity reference equation.

When age, sex, body weight and a measurable peak treadmill workload are present, the model may express achieved capacity as an age-equivalent for cardiorespiratory fitness. It is labelled peak-achieved exercise-capacity-equivalent age. It is not an estimate of coronary anatomy, future disease or remaining lifespan.

  • ✓ Report achieved VO₂ and percent of predicted first
  • ✓ Show the reference equation and every input
  • ✓ Suppress the result when required variables are absent
FRIEND / 2017REFERENCE INVERSION

Predicted exercise capacity

VO₂pred = 79.9 − 0.39A − 13.7S − 0.127Wlb

Age-equivalent at achieved capacity

Aeq = [79.9 − 13.7S − 0.127Wlb − VO₂ach] / 0.39 S = 0 male, 1 female. A reference comparison is meaningful only for populations compatible with the source model.

Identifiable from the reports

What the model can reconstruct.

heart-rate trajectorytreadmill workloadblood-pressure responseheart-rate recoverylead-wise ST measurementsresting intervalsquality flags

Not identifiable

What two scanned reports cannot establish.

  • Ejection fraction or stroke volume
  • Coronary anatomy, stenosis or flow
  • Valve function
  • Directly measured oxygen consumption
  • Presence or absence of cardiac disease

Scientific basis

Built from published components.

The protocol combines established work on ECG image digitisation, exercise testing, functional capacity, recovery and algorithm evaluation. Each source supports a component, not automatic validation of the integrated system.

01 · DigitisationA framework for digitising ECG imagesFortune et al. · Computer Methods and Programs in Biomedicine · 2022↗ 02 · DigitisationECG signal reconstruction from paper recordsCarretti et al. · Sensors · 2022↗ 03 · Exercise testingExercise standards for testing and trainingAmerican Heart Association scientific statement · 2013↗ 04 · ECG standardsRecommendations for ECG standardisationAHA / ACCF / HRS scientific statement · 2007↗ 05 · WorkloadFRIEND treadmill equation for cardiorespiratory fitnessKokkinos et al. · American Journal of Cardiology · 2017↗ 06 · Reference valuesFRIEND registry reference standardsMyers et al. · Progress in Cardiovascular Diseases · 2017↗ 07 · RecoveryHeart-rate recovery after exerciseCole et al. · New England Journal of Medicine · 1999↗ 08 · ValidationAAMI EC57: testing of cardiac rhythm algorithmsANSI / AAMI standard · reaffirmed 2020↗
Additional boundary evidence

Lead-placement effects: Papouchado et al., Mason-Likar modification. Cardiovascular model identifiability: Pironet et al., Medical Engineering & Physics.

Validation status

Scientifically aligned. Not yet clinically validated.

The next phase is prospective evaluation against raw digital ECG and treadmill-system exports, with annotation by independent readers and held-out manufacturers and sites.

Literature specificationComplete
Deterministic equation registryIn design
Scan-to-waveform benchmarkPlanned
External multi-site validationPlanned
Clinical decision useNot authorised
Waveform errorInterval agreementST-level agreementPrinted-field transcription accuracyFailure-rate reportingAAMI EC57-aligned reporting

Research position

“If the page cannot support the number, the model must not produce the number.”

This page documents the intended protocol. The research intake accepts ECG and TMT reports for non-diagnostic processing; the result does not provide medical advice, replace a clinician or certify that an individual is free of disease.

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