Interactive Simulation Suite · Cardiovascular Mechanics

Hemodynamic Simulators:
Ventricular & Venous Dynamics

Explore cardiovascular mechanics in real time with first-principles biophysical models—from left ventricular ventriculo-arterial interaction (ESPVR & EDPVR) to right heart central venous pressure (CVP) and atrial pressure-volume loops.

First-Principles Biomechanics

Deriving ESPVR & EDPVR from Spherical Geometry

The left ventricle is approximated as a thick-walled sphere undergoing centrosymmetric radial expansion and contraction with an incompressible myocardium. The relation between intracavity pressure and volume derives directly from the mechanical work principle:

P = dW / dV

where W represents total elastic strain energy stored in the myocardium, calculated by integrating strain energy density functions over the spherical wall domain:

1. Passive Diastolic Mechanics (EDPVR): Characterized by an isotropic exponential strain energy function:

Ψ = (a / b) (e^{b(I₁ − 3)} − 1)

Linear parameter a sets base tissue elasticity; exponent b dictates non-linear stiffening upon stretch (e.g. interstitial fibrosis).

2. Active Systolic Mechanics (ESPVR): Combines passive resistance with active sarcomere contraction via additive stress:

Ψ_a = T_a (λ²/2 − λ₀λ)

T_a represents peak isometric contractility (inotropic state) and λ denotes myocardial fiber strain.

3. Ventriculo-Arterial Coupling: Systemic afterload is coupled as arterial elastance E_a = ESP / SV. The intersection of the E_a line and ESPVR determines stroke volume, ejection fraction, and blood pressure equilibrium.

Clinical Interpretation

Parameter Tuning & Clinical Translation

Translate constitutive physics parameters directly into clinical indices measured at the bedside:

Parameter	Physical Meaning	Clinical Translation	Reference & Pathology
Wall Thickness (Δ)	Normalized wall thickness	Relative Wall Thickness (RWT)	0.27 (Normal) · <0.22 (Eccentric dilation) · >0.35 (Concentric hypertrophy)
Contractility (T_a)	Max active stress	Inotropic State	~77 kPa (Normal) · <50 kPa (HFrEF / Shock) · >100 kPa (Hyperdynamic)
Stiffness (a)	Linear scaling factor	Diastolic Compliance	1.15 kPa (Normal) · >1.8 kPa (Global stiffening / aging)
Fibrosis (b)	Exponential stretch	Restrictive Filling	3.8 (Normal) · 6.0–9.0 (Severe fibrosis / restrictive cardiomyopathy)
Preload (EDV)	End-diastolic volume	Venous Filling	130 mL (Normal) · >180 mL (Volume overload / dilated cardiomyopathy)
Afterload (E_a)	Arterial elastance (ESP/SV)	Effective Systemic Load	1.5 mmHg/mL (Normal) · >2.5 mmHg/mL (Vasoconstriction / severe HTN)
Compliance (C_a)	Arterial tree distensibility	Arterial Capacitance	1.47 mL/mmHg (Normal) · <0.80 mL/mmHg (Arterial stiffness)

INTERACTIVE CLINICAL PV LOOP SIMULATOR (ESPVR & EDPVR MODEL)

SIMULATION ACTIVE

Back to Advanced Hemodynamics

Return to Main Platform

Right Atrial Cardiac Cycle

The Venous Pressure Waveform

In the absence of venous obstruction, pressure measured in the large central veins (the CVP) faithfully reflects pressure and flow changes within the right atrium. The waveform has five distinct phasic events: three positive deflections (the a, c, and v waves) and two descents (x and y).

Component	Timing	Biophysical Mechanism
a wave	End-diastole	Active right atrial contraction. Dominant positive deflection in normal right-heart physiology.
c wave	Early systole	Isovolumic right ventricular contraction; tricuspid valve closure and systolic dome bulging.
x descent	Mid-systole	Atrial relaxation and systolic annular descent pulling the atrial floor toward the apex (caval S wave).
v wave	Late systole	Passive venous inflow against a closed tricuspid valve. Height determined by compliance and inflow volume.
y descent	Early diastole	Tricuspid valve opening and rapid ventricular passive filling down the pressure gradient (caval D wave).

Mechanics & Compliance

The Atrial Pressure-Volume Loop

Like the ventricle, right atrial function can be depicted as a pressure-volume loop, forming a characteristic figure-of-eight on its side:

The A Loop (Left): Initiated by the P wave, running counter-clockwise. Atrial contraction raises pressure while emptying the chamber—the booster pump function, contributing 15–30% of ventricular stroke volume.

The V Loop (Right): Runs clockwise, representing passive filling and emptying. It comprises the reservoir phase (venous return stored while the tricuspid valve is shut) and the conduit phase (blood draining into the ventricle once the tricuspid valve opens).

Static Atrial Compliance: The steepness of the pressure-volume slope from the minimum of the A loop to the maximum of the V loop defines chamber compliance. When stiff or distended, pressure spikes rapidly, producing a tall v wave and exaggerated y descent.

Clinical Scenarios

Three Validated Physiological Archetypes

Use the interactive simulation console below to toggle between these three preloaded states and explore how waveform morphology, tricuspid inflow velocity, and atrial PV loops change in lockstep:

State 01

1. Normal Hemodynamics

The a wave exceeds the v wave; the systolic x descent is the dominant trough. The atrial PV loop shows a balanced figure-of-eight with high compliance and low filling pressures.

State 02

2. Right Ventricular Failure

Blunted systolic annular descent abolishes the x descent. Elevated filling pressures cause a dilated, non-compliant atrium with a towering v wave (> a wave) and rapid, steep y descent into the stiff ventricle.

State 03

3. Constrictive Pericarditis

Both x and y descents are exaggerated; filling into the constrained ventricle is rapid in early diastole but abruptly halted. Markedly elevated pressures throughout, shifting the PV loop upward with steep elastance.

INTERACTIVE CVP EXPLORER & ATRIAL PV LOOP WORKSTATION

SIMULATION READY