Methodology & Computational Model Foundations

1. Purpose and scope of this document

This document outlines the mathematical and biophysical formulation of MioAtlas. In interactive medical and electrocardiographic simulation, algorithmic transparency is essential: each quantitative parameter, lead vector, and propagation constant must be grounded in direct peer-reviewed sources or clearly acknowledged as a geometric simplification.

Publishing this specification allows students, educators, and researchers to verify exactly how 12-lead tracings are synthesized, how activation wave fronts interpolate, and how coronary occlusions correlate with surface ECG patterns.

Development chronology: The initial working version of the simulator—3D heart, coronary arteries, ischemic scenarios, and 12-lead ECG—was built in a single day. The conduction system, 43-arrhythmia catalog, bedside jugular venous pulse and phonocardiogram panel, and augmented reality mode were developed in subsequent days between September 9 and September 12, 2026.

2. Coronary anatomy reconstruction

The coronary vascular tree models 11 arteries on the epicardial surface: left main coronary artery (LM), left anterior descending (LAD), circumflex (LCx), right coronary artery (RCA), first and second diagonals (D1, D2), first and second obtuse marginals (OM1, OM2), acute marginal (AM), posterior descending (PDA), and posterolateral branches (PLB).

To maintain continuous curvature in anatomical sulci, two spline formulations are combined:

• Cubic Bezier splines (LAD and LM): Reconstructed using positional control points (co), incoming tangent handles (handleLeft), and outgoing handles (handleRight), evaluated via THREE.CubicBezierCurve3 aggregated into a smooth THREE.CurvePath.
• Centripetal Catmull-Rom splines (LCx, RCA, and side branches): Interpolated from measured vertex sequences with degenerate point filtering via THREE.CatmullRomCurve3(points, false, 'centripetal'), preventing loop artifacts in high-curvature segments.

Canonical coordinate transformation

Original curves were authored in Blender (+Z up, right-handed rule). For WebGL rendering under the glTF standard (+Y up, right-handed rule), the canonical linear transformation is applied at runtime:

This conversion is verified at simulator initialization via automated assertions (assertCoordinateConversion), ensuring consistent spatial alignment across anatomical axes.

Anatomical validation of ischemic territories

Demarcation of the 6 ST-elevation myocardial infarction (STEMI) territories is based on the AHA/ACC 17-segment model (Cerqueira et al., 2002).

Calibration of ischemic volumes was audited pixel by pixel under standardized conditions: heart paused in end-diastole (0.0 s), 100% myocardial opacity, and fully evolved STEMI phase (intensity 0.98). Ellipsoidal centers and radii for proximal LAD, mid LAD, proximal LCx, proximal RCA, mid RCA, and proximal PDA were optimized using contrast differential maps between baseline and pathological states, ruling out necrosis leakage into adjacent tissue.

3. Conduction system modeling

The cardiac excitation-conduction system is represented in a coronal cut displaying all four chambers and interventricular septum. It comprises:

• 17 anatomically named main trunks: Sinoatrial node (SAN, sulcus terminalis), anterior, middle (Wenckebach), and posterior (Thorel) internodal tracts, Bachmann bundle to left atrium, atrioventricular node (AVN, Koch triangle), slow and fast nodal pathways, His bundle, right bundle branch (RBB), moderator band, left bundle branch trunk (LBB), left anterior (LAF), posterior (LPF), and septal (LSF) fascicles, and Kent accessory pathway.
• 84 Purkinje branches: Subendocardial network distributing impulses into ventricular myocardium across both chambers.

Tissue conduction velocities

Impulse propagation along splines adheres to benchmark electrophysiological conduction velocities:

• Sinoatrial node (exit): 0.05 m/s.
• Atrial myocardium and internodal tracts: 1.0 m/s.
• Atrioventricular node (decremental delay): 0.05 m/s.
• His bundle & His-Purkinje system: 2.0 to 4.0 m/s.
• Ventricular myocardium: 0.4 to 0.5 m/s.

Propagation chronometry (sinus rhythm)

From sinus node initiation (t = 0 ms), the model applies physiological activation timing windows (conductionTimingMs):

4. Mathematical synthesis of the electrocardiogram

The ECG monitor synthesizes 12 standard surface leads (I, II, III, aVR, aVL, aVF, V1–V6) and 5 extended leads (V7–V9, V3R, and V4R) in real time.

Deterministic 120 Hz accumulator

Decoupled from browser refresh rate, the engine runs a fixed 120 Hz temporal accumulator (Δt = 8.333 ms) ensuring clinical calibration precision:

• Paper speed: 25 mm/s (1 mm = 0.04 s; 5 mm = 0.20 s).
• Voltage: 10 mm/mV (1 mm = 0.1 mV; 10 mm = 1.0 mV).
• 12-lead panels: 2.5 seconds (300 samples at 120 Hz, 3.0 cycles at 72 bpm).
• Continuous rhythm strip (II): 10.0 seconds (1,200 samples at 120 Hz).

Model reference intervals

In normal sinus rhythm at 72 bpm, the catalog applies canonical benchmark values (referenceIntervalsMs):

• P wave (p): 90 ms (reference: 80–100 ms).
• PR interval (pr): 160 ms (reference: 120–200 ms).
• QRS complex (qrs): 90 ms (reference: 80–100 ms).
• Baseline QT interval (qt): 390 ms at 72 bpm (reference: 350–430 ms).

QT rate adaptation: Fridericia vs Bazett formula

To adapt QT duration to changing heart rates, the simulator uses Fridericia formula (cube root of RR) instead of Bazett formula (square root):

Rationale: Bazett formula overcorrects at elevated heart rates (generating false QTc prolongations in tachycardia) and underestimates at bradycardic rates. Fridericia formula provides superior physiological stability across the spectrum, bounding dynamic QT between 200 and 600 ms.

3D thoracic vectors and cardiac dipole

Torso electrodes are positioned at real 3D coordinates: RA [-0.080, +0.070, -0.025], LA [+0.080, +0.065, +0.025], LL [0.000, -0.090, +0.055], and precordials V1–V6. Instantaneous lead voltage results from the scalar dot product between the dynamic ventricular electrical dipole and unit lead vectors (Frank theory, 1956).

5. What the simulator does NOT do: physiological simplifications

To ensure smooth 60 FPS performance in standard web browsers, MioAtlas adopts explicit technical simplifications compared to real biological complexity:

7. Editorial status and technical collaboration