Model documentation

Standard 73

A model coupling myocardium, chamber geometry and vessels to calculate pressure and blood flow.

Research and education · static anatomy

Overview

This 0D model replaces spatial distributions with representative compartment pressures, flows and volumes. Muscle tension generates pressure; pressure drives flow; changing volume feeds back into muscle length and pressure. Waveforms emerge from this interaction.

The design considers responses to changed loading as well as blood pressure and output, aiming to balance case expressiveness, numerical robustness and simplicity.

Connection schematic, grouping vessel compartments and omitting coronary branches and external pressures. PV denotes the pulmonary valve; PVn denotes pulmonary veins.

The model explores pressure and flow over time, not local jets or travelling/reflected waves. AoP/PAP are representative model pressures, not one-to-one reproductions of specific measurement sites.

Detailed circuit and compartments (nodes)

Four cavities and eleven main-circuit vascular compartments connect to sixteen coronary compartments. Compartments store blood; links carry hydraulic losses. Names denote lumped regions, not exact catheter positions. The septum is a material wall, not a blood-storage node.

Systemic path

Left ventricle (LV)
Proximal aorta (Ao)
Systemic arteries (SA)
Systemic resistance-vessel side (Art)
Systemic capillary bed (Cap)
Systemic veins (SV)
Vena cava (VC)
Right atrium (RA)

Pulmonary path

Right ventricle (RV)
Proximal pulmonary artery (PA)
Pulmonary resistance-vessel side (PArt)
Pulmonary capillary bed (PCap)
Pulmonary venular side (PVen)
Pulmonary vein / LA inlet (PVein)
Left atrium (LA)

LA —MV→ LV and RA —TV→ RV close the circuit. Arrows define positive flow; permitted reverse flow enters continuity with its sign. Coronaries branch from Ao and return to RA.

Ao/SA/Art separate proximal storage from pressure loss toward the periphery, without representing pulse transit or reflection between compartments. SV is the main venous reservoir; VC is the thoracic-pressure-exposed compartment before RA. PCap receives alveolar pressure, while PVen/PVein receive thoracic pressure, separating pulmonary storage and resistance along the path to LA. This is a functional partition, not a vessel-by-vessel anatomical reconstruction.

All main-circuit compartments: law and pressure reference
Compartment	Pressure relation	External pressure	Displayed counterpart
Left ventricle (LV)	Material / geometry balance	$P_{\mathrm{th}}+P_{\mathrm{peri}}$	LVP
Left atrium (LA)	Material / geometry balance	$P_{\mathrm{th}}+P_{\mathrm{peri}}$	LAP
Right ventricle (RV)	Material / geometry balance	$P_{\mathrm{th}}+P_{\mathrm{peri}}$	RVP
Right atrium (RA)	Material / geometry balance	$P_{\mathrm{th}}+P_{\mathrm{peri}}$	RAP / CVP
Proximal aorta (Ao)	Exponential arterial	0 (reference)	AoP
Systemic arteries (SA)	Exponential arterial	0 (reference)	ABP
Systemic resistance-vessel side (Art)	Exponential arterial	0 (reference)	—
Systemic capillary bed (Cap)	Linear storage	0 (reference)	—
Systemic veins (SV)	Nonlinear venous-type	0 (reference)	—
Vena cava (VC)	Nonlinear venous-type	$P_{\mathrm{th}}$	—
Proximal pulmonary artery (PA)	Exponential arterial	$P_{\mathrm{th}}$	PAP
Pulmonary resistance-vessel side (PArt)	Exponential arterial	$P_{\mathrm{th}}$	—
Pulmonary capillary bed (PCap)	Nonlinear venous-type	$P_{\mathrm{alv}}$	—
Pulmonary venular side (PVen)	Nonlinear venous-type	$P_{\mathrm{th}}$	—
Pulmonary vein / LA inlet (PVein)	Nonlinear venous-type	$P_{\mathrm{th}}$	—

AoP/PAP are Ao/PA intravascular pressures, with no display-only ZcQ. ABP is SA pressure, not a simulated brachial cuff. CVP uses mean RA; PCWP uses mean LA as a proxy, without simulating catheter wedging. PV loops use ventricular transmural pressure.

\dot V_i=\sum_j N_{ij}Q_j,\qquad N_{ij}=\begin{cases}+1&j\text{ enters }i\\-1&j\text{ leaves }i\\0&\text{otherwise}\end{cases},\qquad\sum_{i=1}^{31}V_i=TBV

The link tables define incidence matrix N. Each flow leaves one compartment and enters another, conserving total blood. Myocardium and pericardial fluid are excluded. Blood is not added or removed to match pressure or output at fixed TBV.

Reading the equations and numerical assumptions

Volumes, calcium and crossbridge populations evolve as states. Resistances, areas and rate coefficients are parameters. Some pressures and flows follow algebraic balance equations at each time.

Dots denote time derivatives and Δ differences. Sections specify the regular-sinus, unassisted equations, closure/collapse branches, coefficients and initial state. Symbols are local to each section. Circulation uses mmHg/mL/s; mechanics uses Pa/m/s. Convert with 1 mmHg=133.322387415 Pa and 1 mL=10⁻⁶ m³.

Mechanics and circulation are coupled, with implicit time integration for components including viscoelasticity. Baseline starts from a periodically settled state. Stored 2 and 1 ms records are compared below; their agreement is not proof of convergence in every condition.

Mechanisms

Swipe horizontally to read wide equations and tables.

Activation / CaMyofilament tensionGeometry / pressureValves / flow / volume

Volume feeds back through length and shortening velocity into tension. Arrows show interactions.

Activation and calcium

Atrial and ventricular activation events drive calcium transients. Calcium generates pressure through myofilaments and chamber mechanics, not through a prescribed pressure waveform.

Equations and assumptions

Regular sinus rhythm includes atrial capture and ventricular conduction. Ventricles use a calibrated biexponential event source; atria retain a separate source. This is not a full action-potential or intracellular calcium-cycling model. Ca₀ is the long event-free limit, not the periodic trough.

\dot x_r=-x_r/\tau_r,\quad \dot x_d=-x_d/\tau_d,\qquad [Ca]=\mathrm{Ca}_0+g(x_d-x_r)

Implemented subset for distinct time constants. Events increment both drives equally; their difference gives a rise and subsequent decay.

$x_r,\;x_d$: Dimensionless calcium-drive states
$\tau_r,\;\tau_d$: Decay time constants (s)
$\mathrm{Ca}_0,\;g$: Event-free calcium limit and amplitude coefficient (µM)

Activation times and state updates

Time is in seconds. In regular sinus rhythm T=60/HR; ventricular activation follows atrial activation by 120 ms (80 ms AV + 40 ms distal conduction). Calcium deposits occur another 12 ms after the corresponding activation. Each wall has two calcium states.

q is deposit strength, equal to 1 for all five walls at baseline. States decay analytically between events and both receive q at an event. The periodic formula below is for regular unit deposits; it does not initialize chamber volumes or Land states.

t_{A,k}=t_{A,0}+kT,\quad t_{V,k}=t_{A,k}+0.120,\quad t_{Ca,w,k}=t_{A\text{ or }V,k}+0.012

x_j(t+\Delta t)=x_j(t)e^{-\Delta t/\tau_j},\quad x_j(t_k^+)=x_j(t_k^-)+q_k\quad(j=r,d)

x_j(t_k^+)=\frac{1}{1-e^{-T/\tau_j}}\quad\text{(periodic, }q_k=1\text{)}

Interval-dependent calcium strength

Ventricles carry a discrete interval-dependent normalized load L, not measured SR calcium concentration. I is the preceding ventricular interval, a recovery and q the next calcium deposit. Coefficients and reference states are tabulated below. L and a at the reference heart rate form a fixed point with q=1.

The construction specified here is regular sinus rhythm without mechanical support. Optional ectopy, pacing and support-device modes are not included in this baseline equation system.

a_k=1-e^{-I_k/\tau_{\mathrm{rec}}},\quad q_k=a_k\beta L_k,\qquad L_{k+1}=L_k-(1-r)q_k+\gamma(1-ha_k)

Adopted calcium source
Wall	$\tau_r$ (s)	$\tau_d$ (s)	$\mathrm{Ca}_0$ (µM)	g (µM)
Left atrium (LA)	0.0125	0.3	0.0631545706813	0.604696429446
LV free wall (LVFW)	0.11853637422	0.131707082467	0.120706159272	12.0780349398
Ventricular septum (SEP)	0.11853637422	0.131707082467	0.120706159272	12.0780349398
RV free wall (RVFW)	0.11853637422	0.131707082467	0.120706159272	12.0780349398
Right atrium (RA)	0.0125	0.3	0.0631545706813	0.604696429446

Interval-strength coefficients and reference state
Symbol / meaning	Adopted value
τrec (s)	0.5
β	0.8
r	0.5
h	0.2
γ	0.598072916413
$T_{\mathrm{ref}}$ (s)	0.857142857143
aref	0.819907687852
Lref	1.52456187266

Myofilaments: calcium to tension

Calcium binding, crossbridge populations, stretch and shortening velocity determine active tension. Force depends on length and loading history even at the same calcium level.

Equations and assumptions

Based on Land 2017, but not an unchanged reproduction. Ventricular stress scale, calcium affinity and transition rates are calibrated. An extension returns excess strong-bound population to the unbound pool at low calcium. Population conservation does not transfer the original paper's validation to this extension. Passive and viscoelastic components complete wall stress.

T_a=\frac{h(\lambda)T_{\mathrm{ref}}}{r_s}\left[S(1+\zeta_s)+W\zeta_w\right]

Land-derived active fiber stress output (Pa): W/S are weak/strong populations, ζ their distortions and h a length-dependent factor. This is not cavity pressure.

$T_a,\;T_{\mathrm{ref}}$: Active fiber stress and its scale (Pa)
$\lambda,\;h(\lambda)$: Fiber stretch and length-dependent factor (dimensionless)
$W,\;S,\;r_s$: Weak/strong populations and reference strong fraction
$\zeta_w,\;\zeta_s$: Dimensionless crossbridge distortions, dependent on shortening and history

J_{\mathrm{exit}}=k_{\mathrm{max}}\left(\frac{\theta^n}{\theta^n+c^n}\right)^p\max(S-rW,0),\quad \dot S|_{\mathrm{exit}}=-J_{\mathrm{exit}},\quad \dot U|_{\mathrm{exit}}=J_{\mathrm{exit}}

Added exit flux: c is calcium-bound troponin fraction, θ its reference, n/p exponents, kmax a rate (s⁻¹), r=kws/ksu the zero-distortion strong/weak ratio, and U the unbound fraction. Only positive excess is transferred.

Six states and conservation

Each wall has c (Ca-bound troponin), b (blocked), W/S (weak/strong binding) and distortions ζw/ζs. U=1−b−W−S is dependent. Valid states require 0<c≤1 and b,U,W,S≥0. b is unrelated to a hydraulic quadratic coefficient.

Ca is free calcium (µM); λ is the Land stretch. gwu/gsu are distortion-dependent detachment rates (s⁻¹). The added exit flux above applies to ventricular walls; Jexit=0 in atria. Detached population returns to U.

\begin{aligned}\dot c&=k_{\mathrm{TRPN}}\{(\mathrm{Ca}/\mathrm{Ca}_{50})^{n_{\mathrm{TRPN}}}(1-c)-c\},\\\dot b&=k_b\min(c^{-n_{\mathrm{Tm}}/2},100)U-k_u c^{n_{\mathrm{Tm}}/2}b,\\\dot W&=k_{\mathrm{uw}}U-(k_{\mathrm{wu}}+k_{\mathrm{ws}}+g_{\mathrm{wu}})W,\\\dot S&=k_{\mathrm{ws}}W-(k_{\mathrm{su}}+g_{\mathrm{su}})S-J_{\mathrm{exit}},\\\dot\zeta_w&=A_w\dot\lambda-c_w\zeta_w,\qquad\dot\zeta_s=A_s\dot\lambda-c_s\zeta_s.\end{aligned}

\begin{aligned}\lambda_c&=\min(\lambda,1.2),\\\mathrm{Ca}_{50}&=\mathrm{Ca}_{50,\mathrm{ref}}+\beta_1(\lambda_c-1),\\h(\lambda)&=\max\{0,1+\beta_0[\lambda_c+\min(\lambda_c,0.87)-1.87]\},\\g_{\mathrm{wu}}&=\gamma_w|\zeta_w|,\quad g_{\mathrm{su}}=\gamma_s\max(-\zeta_s-1,\zeta_s,0).\end{aligned}

Derived rates and wall coupling

The following rates derive from the independent parameters below. rₛ/r𝓌 are reference fractions, θ=TRPN50. k/c rates are in s⁻¹ and A is dimensionless. Ca50 must remain positive. The λ=1.2 saturation and factor limit 100 are part of the adopted law.

With geometric log strain e, λ=s₀ exp(e), where s₀=1 for all baseline walls. The discrete velocity is (λn+1−λn)/Δt. Land Tₐ is multiplied by λ, orientation fo and active fraction fa to obtain Kirchhoff stress. fo=fa=1. Active controls scale Tref; passive controls scale passive stress and viscous modulus.

\begin{aligned}k_b&=\frac{k_u\theta^{n_{\mathrm{Tm}}}}{(1-r_s)(1-r_w)},\quad k_{\mathrm{wu}}=k_{\mathrm{uw}}(1/r_w-1)-k_{\mathrm{ws}},\\k_{\mathrm{su}}&=k_{\mathrm{ws}}r_w(1/r_s-1),\quad A_w=A_s=\frac{A_{\mathrm{eff}}r_s}{(1-r_s)r_w+r_s},\\c_w&=\frac{\phi k_{\mathrm{uw}}(1-r_w)}{r_w},\quad c_s=\frac{\phi k_{\mathrm{ws}}(1-r_s)r_w}{r_s},\\\tau_f&=\lambda f_o f_aT_a+\tau_{\mathrm{pass}}+\tau_{\mathrm{vis}}.\end{aligned}

These are model reference coefficients. Active multipliers apply to each wall's Tref; effective values are also tabulated in the passive/viscoelastic section.

Independent Land parameters: ventricles and atria
Symbol / meaning	Ventricular walls	Atria	Unit
$k_{\mathrm{TRPN}}$ Troponin rate	100	100	s⁻¹
$n_{\mathrm{TRPN}}$ Ca binding exponent	2	2	1
$\mathrm{Ca}_{50,\mathrm{ref}}$ Ca50,ref	0.6	0.86	µM
$k_u$ Thin-filament activation rate	1000	1000	s⁻¹
$n_{\mathrm{Tm}}$ Thin-filament exponent	5	5	1
$\theta$ reference bound fraction	0.35	0.35	1
$k_{\mathrm{uw}}$ Unbound→weak	104	182	s⁻¹
$k_{\mathrm{ws}}$ Weak→strong	4.8	36	s⁻¹
$r_w$ reference weak fraction	0.5	0.5	1
$r_s$ reference strong fraction	0.25	0.25	1
$\gamma_s$ strong distortion detachment	8.5	8.5	s⁻¹
$\gamma_w$ weak distortion detachment	615	615	s⁻¹
$\phi$ distortion relaxation scale	2.23	2.23	1
$A_{\mathrm{eff}}$ velocity sensitivity	26.5	25	1
$\beta_0$ force-length dependence	2.3	2.3	1
$\beta_1$ affinity-length dependence	-1.2	-2.4	µM
$T_{\mathrm{ref}}$ tension scale	238816.546281	11661.1510106	Pa
$T$ Source temperature (not a variable kinetic factor)	310.15	310.15	K

Derived Land coefficients
	Ventricle	Atrium
$k_b$	14.0058333333	14.0058333333
$A_w$	10.6	10
$A_s$	10.6	10
$k_{\mathrm{wu}}$	99.2	146
$k_{\mathrm{su}}$	7.2	54
$c_w$	231.92	405.86
$c_s$	16.056	120.42

Ventricular added exit: kmax=60 s⁻¹, p=16; atria have no added exit. Baseline settings compare adopted values with source values and calibration provenance. These are not independently measured constants from one subject.

Land et al. 2017

Passive mechanics and deformation history

Passive stretch resistance and time-dependent viscoelastic relaxation contribute to diastolic pressure alongside active stress.

Equations and assumptions

Ventricular passive stress derives from convex strain energy; atria use a separate law. A one-state Maxwell branch represents viscoelastic history. The ventricular prior references organ-level Klotz EDPVR, not direct tissue measurements.

e=\ln\lambda_g,\quad \tau_{\mathrm{pass}}=\frac{d\Psi}{de},\quad \tau_{\mathrm{vis}}=E_v(e-\alpha),\quad \dot\alpha=\frac{e-\alpha}{\tau_v}

Passive and viscous relations. Land active stress is converted using its stretch and orientation/viability fractions before addition in the same stress convention.

$\lambda_g,\;e,\;\alpha$: Geometric stretch, logarithmic strain, and viscous strain
$\Psi,\;\tau_{\mathrm{pass}},\;\tau_{\mathrm{vis}}$: Energy density (J/m³) and passive/viscous Kirchhoff stresses (Pa)
$E_v,\;\tau_v$: Viscoelastic modulus (Pa) and material time constant (s), distinct from pressure-derived LV τ

Ventricular elastic energy

Let e=ln λg, p=Hδ(e), q=Hδ(−e). K0 is central stiffness; Kt/a govern tensile stiffening; Kc adds compression stiffness. Hδ is a smooth positive part with u=z/δ. The three ventricular walls share this law; energy and derivatives are multiplied by each wall's passive scale sₚ,ｗ, listed in the baseline settings.

H_\delta(z)=\begin{cases}0&z\le0\\\delta(u^3-\tfrac12u^4)&0<z<\delta\\z-\delta/2&z\ge\delta\end{cases}

\Psi(e)=\tfrac12K_0e^2+\frac{K_t}{a^2}(e^{ap}-1-ap)+\tfrac12K_cq^2,\qquad \tau_{\mathrm{pass}}=s_{p,w}\,\frac{d\Psi}{de}

Atrial passive law and viscoelasticity

Atria use a separate equibiaxial reduction; sₚ,ｗ below is each wall's passive multiplier. λg=exp(e); C1/C2/C3 are Pa, C4 dimensionless. The fiber term is tension-only. Energy is Ψ(e)=∫₀ᵉτpass(s)ds. Supported strain is −0.5≤e≤0.5; applying the LA-derived material to RA is an extrapolation.

Each wall has a one-state Maxwell branch: α is viscous strain, Ev modulus, τv relaxation time. The implemented backward-Euler update below is applied once per mechanics step. Listed Ev already includes the passive scale.

\tau_{\mathrm{pass}}=s_{p,w}\left[4C_1(\lambda_g^2-\lambda_g^{-4})+4C_2(\lambda_g^4-\lambda_g^{-2})+\begin{cases}C_3(e^{C_4(\lambda_g-1)}-1)&e>0\\0&e\le0\end{cases}\right]

\alpha_{n+1}=\frac{\alpha_n+(\Delta t/\tau_v)e_{n+1}}{1+\Delta t/\tau_v},\qquad \tau_{vis,n+1}=E_v(e_{n+1}-\alpha_{n+1})

Reference passive coefficients (wall multipliers applied separately)
Symbol / meaning	Adopted value
$K_0$ (Pa)	1200
$K_t$ (Pa)	22345.9396953
a	18
$K_c$ (Pa)	0
δ	0.001
$C_1$ (Pa)	1650
$C_2$ (Pa)	0
$C_3$ (Pa)	15
$C_4$	13.37

Wall multipliers and effective material coefficients
Wall	Active scale	Passive scale	$T_{\mathrm{ref}}$ (Pa)	$E_v$ (Pa)	$\tau_v$ (s)
Left atrium (LA)	1	1	11661.1510106	5947	0.3
LV free wall (LVFW)	1	1.04	238816.546281	19307.6	0.3
Ventricular septum (SEP)	1	1.04	238816.546281	19307.6	0.3
RV free wall (RVFW)	1	1.04	238816.546281	19307.6	0.3
Right atrium (RA)	1	1	11661.1510106	5947	0.3

The 0.3 s branch is a reduction informed by healthy ovine RV Prony data, not identified in every human wall. Acta Biomaterialia 2022

Klotz et al. 2006Organ EDPVR context, not the source of the adopted tissue constitutive law.

Moyer et al. 2015Starting point for atrial passive material, reduced here to equibiaxial deformation.

Chambers: tension to pressure

LV free wall, septum and RV free wall interact through shared geometry, with two atrial walls completing the five-wall model. Pressure follows stress and geometry, rather than a prescribed time waveform.

Equations and assumptions

Ventricles use spherical-cap TriSeg geometry and an energy-conjugate pressure mapping. Pericardial/thoracic external pressure is distinct from transmural pressure. Geometry is not patient-specific 3D imaging and does not resolve local stress or torsion. PV loops use transmural pressure while pressure waveforms use cavity pressure, so they differ when external pressure is present.

\delta W=\sum_w V_{\mathrm{m},w}\tau_{\mathrm{f},w}\,\delta\ln\lambda_w,\qquad P_{\mathrm{cavity}}=P_{\mathrm{tm}}+P_{\mathrm{ext}}

Wall virtual work is matched to cavity pressure–volume work. Septal position and junction radius also satisfy force balance.

$\delta W,\;V_{\mathrm{m},w}$: Virtual work (J) and material volume of wall w (m³)
$\tau_{\mathrm{f},w},\;\lambda_w$: Fiber Kirchhoff stress (Pa) and geometric stretch; this stress τ is distinct from the LVP relaxation time
$P_{\mathrm{cavity}},\;P_{\mathrm{tm}},\;P_{\mathrm{ext}}$: Cavity, transmural, and external pressures, added in the same units

Schematic of spherical caps sharing a junction circle, not measured geometry or wall thickness. h is signed height from the junction plane to each cap apex.

Three spherical caps and fiber length

Mechanics uses SI units: m, m², m³, Pa. VL/VR are cavity blood volumes, Mw wall material volumes, vS the signed septal cap volume, y>0 the junction-circle radius. Wall material is not part of TBV. Cap height h is positive toward RV, usually negative for LV free wall.

For each wall solve h from cap volume, then area Aw, curvature κw and thickness correction zw. Aref,w is reference midwall area. zw is unrelated to Land crossbridge distortion ζ. Geometric ew enters the material law.

v_L=-V_L-\tfrac12(M_L+M_S)+v_S,\qquad v_R=V_R+\tfrac12(M_R+M_S)+v_S

v_w=\frac{\pi h_w(h_w^2+3y^2)}6,\quad A_w=\pi(h_w^2+y^2),\quad\kappa_w=\frac{2h_w}{h_w^2+y^2}

z_w=\frac{3\kappa_wM_w}{2A_w},\qquad e_w=\frac12\ln\frac{A_w}{A_{\mathrm{ref},w}}-\frac{z_w^2}{12}-0.019z_w^4

Internal balance and cavity pressures

F/G are generalized forces for cap volume and junction radius. Multiply each current material stress by geometric strain derivatives; do not differentiate active stress as though it were a conservative potential.

For supplied cavity volumes solve vS/y simultaneously from force balance, then obtain LV/RV transmural pressures. Atria use a spherical one-fiber reduction with reference cavity volume Vref. No prescribed pressure waveform or wall-specific pressure gain is added.

F_w=M_w\tau_{\mathrm{f},w}\left.\frac{\partial e_w}{\partial v_w}\right|_y,\qquad G_w=M_w\tau_{\mathrm{f},w}\left.\frac{\partial e_w}{\partial y}\right|_{v_w}

F_L+F_S+F_R=0,\quad G_L+G_S+G_R=0,\qquad P_{\mathrm{tm},L}=-F_L,\quad P_{\mathrm{tm},R}=F_R

e_A=\frac13\ln\frac{V_A+M_A/2}{V_{\mathrm{ref},A}+M_A/2},\qquad P_{\mathrm{tm},A}=\frac{M_A\tau_{\mathrm{f},A}}{3(V_A+M_A/2)}

Thoracic and pericardial pressure

Occupied heart volume VH sums four cavity blood volumes, five wall volumes and prescribed pericardial fluid. Coronary blood is not added again to this occupancy formula. All cavities share the same external pressure. V0 is reference capacity, P* pressure scale and k stiffness.

H smooths engagement, δ=0.001 and u=(x+δ)/(2δ). H′ differentiates with respect to x. Baseline pressure offset/fluid/respiratory amplitudes are zero. With no engagement and zero thoracic pressure, cavity and transmural pressures coincide.

V_H=\sum_{c=LA,LV,RA,RV}V_c+\sum_w M_w+V_{\mathrm{fluid}},\quad x=(V_H-V_0)/V_0

H(x)=\begin{cases}0&x\le-\delta\\\delta(2u^3-u^4)&|x|<\delta\\x&x\ge\delta\end{cases}

P_{peri}=P_{\mathrm{offset}}+P_*[e^{kH(x)}-1]H'(x),\qquad P_c=P_{\mathrm{tm},c}+P_{\mathrm{th}}+P_{peri}

Ventricular wall geometry constants
Wall	M (m³)	$A_{\mathrm{ref}}$ (m²)
LV free wall (LVFW)	0.0000670754366407	0.00935435289387
Ventricular septum (SEP)	0.0000357735662083	0.00396508199259
RV free wall (RVFW)	0.0000360873694207	0.012911294586

Atrial geometry constants
Wall	M (mL)	$V_{\mathrm{ref}}$ (mL)
Left atrium (LA)	25.9829059829	22.8900425619
Right atrium (RA)	23.3998100665	32.5968711181

Pericardial constants
Symbol / meaning	Adopted value
$V_0$ (m³)	0.000600126542735
$P_*$ (Pa)	500
k	8
$P_{\mathrm{offset}}$ (Pa)	0
$V_{\mathrm{fluid}}$ (m³)	0

BSA is 1.9 m² and tissue density 1053 kg/m³. Geometry combines population imaging/mass data, not one subject's complete measurements. Reference areas use a construction stretch of 1.1 at the loaded reference. Pericardial constants are mechanism-test choices, not identified human normal intervals.

Lumens et al. 2009 · TriSegBasis for three-wall geometry; the present constitutive laws and pressure mapping are not a reproduction of the entire original model.

Four valves: pressure difference to flow

Mitral, aortic, tricuspid and pulmonary valves share an opening and pressure-loss structure, with valve-specific forward and regurgitant areas.

Equations and assumptions

Flow is solved algebraically without a separate inertial flow state, while a bounded leaflet-opening memory remains. EOA already accounts for contraction/discharge; no extra Cd is applied. This construction has no local pressure-recovery correction. Raw AV/PV node differences are not Doppler maximum-jet or catheter peak-to-peak gradients.

\Delta P=R Q+B(A)Q|Q|,\qquad B(A)\propto \rho/A^2

Constitutive law on the flowing branch; coefficients include unit conversions. Exact closure supports a pressure difference at Q=0, so this equation alone does not describe every branch.

$\Delta P,\;Q$: Simultaneous upstream-minus-downstream pressure (mmHg) and forward-positive flow (mL/s)
$A,\;\rho$: Current effective orifice area and blood density; area depends on maximum area and opening fraction
$R,\;B$: Linear resistance (mmHg·s/mL) and quadratic loss coefficient (mmHg·s²/mL²)

Opening-state dynamics

ξ is opening fraction (0–1), ΔP upstream minus downstream pressure, d deadband, pₒ offset (0 mmHg in all baseline valves) and kₒ opening sensitivity. Fε smooths positive opening drive with ε=0.1 mmHg. Use the opening time constant when target exceeds previous ξ, otherwise the closing constant.

F_\epsilon(z)=\begin{cases}0&z\le0\\z^2/(2\epsilon)&0<z<\epsilon\\z-\epsilon/2&z\ge\epsilon\end{cases},\quad \xi_\infty=1-e^{-k_oF_\epsilon(\Delta P-d-p_o)}

\dot\xi=\frac{\xi_\infty-\xi}{\tau_\xi},\qquad \xi_{n+1}=\frac{\xi_n+(\Delta t/\tau_\xi)\xi_\infty(\Delta P_{n+1})}{1+\Delta t/\tau_\xi}

Area, direction and exact closure

Amax is maximal forward EOA; Ar closed regurgitant EOA. Forward area includes the residual gap plus the opening-dependent part; reverse area is Ar independent of ξ. Changing Ar also affects near-closure forward flow. Baseline Ar=0 in all valves.

Q is mL/s, A cm², pressure mmHg, ρ=1060 kg/m³, cP=133.322387415 Pa/mmHg. Zero area gives exactly Q=0 with supported pressure difference. No area floor or flow smoothing is introduced. R is not rescaled with area.

A=\begin{cases}A_r+\xi(A_{\mathrm{max}}-A_r)&\Delta P\ge0\\A_r&\Delta P<0\end{cases},\quad B(A)=\frac{\rho}{2c_P}\left(\frac{10^{-6}}{10^{-4}A}\right)^2

Q=\begin{cases}0&A=0\text{ or }\Delta P=0\\\operatorname{sgn}(\Delta P)\frac{2|\Delta P|}{R+\sqrt{R^2+4B(A)|\Delta P|}}&\text{otherwise}\end{cases}

Four-valve coefficients (L=0)
Valve	R (mmHg·s/mL)	$A_{\mathrm{max}}$ (cm²)	$k_o$ (mmHg⁻¹)	d (mmHg)	$\tau_{\mathrm{open}}$ (s)	$\tau_{\mathrm{close}}$ (s)
MV	0.0027	5.5	2	0.6	0.024	0.016
AV	0.0015	3.5	3	0	0.006	0.008
TV	0.0035	8	2	0	0.018	0.01
PV	0.005	4	2	0	0.01	0.006

Vessels: storage and flow

Compliance stores blood and resistance opposes flow. Systemic and pulmonary vessels form a closed circuit in which volume and pressure are solved together.

Equations and assumptions

Aortic and pulmonary roots use algebraic flow without local L. AoP and PAP are the Ao and PA node pressures, without a displayed ZcQ addition; SA is a downstream systemic-arterial compartment. Travelling/reflected waves, propagation delay and particular cuff/arterial-line sites are not simulated. Venous tone and TBV are not interchangeable controls: they affect filling and blood distribution.

\frac{dV_i}{dt}=\sum Q_{\mathrm{in},i}-\sum Q_{\mathrm{out},i},\qquad C_i(P_{\mathrm{tm}})=\frac{dV_i}{dP_{\mathrm{tm},i}}

Volume conservation and differential compliance. Pressure–volume relations, including venous vessels, need not be linear with constant C.

$V_i,\;Q_{\mathrm{in}},\;Q_{\mathrm{out}}$: Compartment volume (mL) and inflow/outflow (mL/s)
$C_i,\;P_{\mathrm{tm},i}$: Pressure-dependent compliance (mL/mmHg) and transmural vascular pressure (mmHg)

Compartment pressure–volume laws

Pressure is mmHg, volume mL and flow mL/s. p=P−Pext is transmural pressure. Vu is volume at p=0; V−Vu is stressed volume. Listed Vs includes stiffness/compliance scaling: original Vs×0.65/1.42 for Ao/SA/Art, original Vs/1.42 for PA/PArt.

Venous-type compartments join collapsed Cc, open Co and distended Cd smoothly. S(z)=ln(1+exp z), σ(z)=1/(1+exp(−z)); ΔS(p;a,d)=S((p−a)/d)−S(−a/d). Tone u changes Vu=Vu,original−G u. The table includes baseline u=0.15.

The venous inverse saturates at −20/45 mmHg; arterial strain is bounded below by ln(0.05). These are numerical boundaries, not normal ranges; saturated results must not be extrapolated physiologically. Compliance readback is floored at 10⁻⁴ mL/mmHg without replacing V(p).

p=P_0\left(e^{\max[(V-V_u)/V_s,\ln0.05]}-1\right)\quad\text{(arterial)},\qquad p=(V-V_u)/C\quad\text{(linear)}

V(p)=V_u+C_cp+(C_o-C_c)d_o\Delta S(p;p_o,d_o)-(C_o-C_d)d_s\Delta S(p;p_s,d_s)

\frac{dV}{dp}=C_c+(C_o-C_c)\sigma\left(\frac{p-p_o}{d_o}\right)-(C_o-C_d)\sigma\left(\frac{p-p_s}{d_s}\right)

Link flow, collapse and external pressure

Non-valve links solve ΔP=RQ+BQ|Q|. Current baseline links have B=0 and L=0, normally Q=(Pup−Pdown)/R. Systemic/pulmonary multipliers apply only to the listed groups, not all venous resistances.

VC→RA and PCap→PVen use a waterfall and collapse-dependent resistance. M± are smooth max/min with ε=0.25 mmHg; χmin=0.08, w=1 mmHg, pc=0. χ uses raw endpoint pressures, not the already modified downstream pressure.

The node table distinguishes thoracic Pth from alveolar Palv exposure. fresp is Hz and amplitudes mmHg. Workbench PEEP is cmH₂O and is multiplied by 0.7355592401 for these mmHg equations. All respiratory inputs are zero at baseline.

M_\pm(a,b)=\frac{a+b\pm\sqrt{(a-b)^2+\epsilon^2}}2

\begin{aligned}P_{\mathrm{down,eff}}&=M_+(P_{\mathrm{down}},P_{\mathrm{ext}}+p_c),\\\chi&=\chi_{\mathrm{min}}+(1-\chi_{\mathrm{min}})\sigma\left(\frac{M_-(P_{\mathrm{up}}-P_{\mathrm{ext}},P_{\mathrm{down}}-P_{\mathrm{ext}})-p_c}{w}\right),\\Q&=\frac{P_{\mathrm{up}}-P_{\mathrm{down,eff}}}{R/\chi^2}.\end{aligned}

P_{\mathrm{th}}=P_{th,0}+0.20\,PEEP+A_{\mathrm{th}}\sin(2\pi f_{\mathrm{resp}}t),\quad P_{\mathrm{alv}}=PEEP+A_{\mathrm{alv}}\sin(2\pi f_{\mathrm{resp}}t)

Effective arterial and linear coefficients
Compartment	$P_0$ (mmHg)	$V_s$ (mL)	C (mL/mmHg)
Proximal aorta (Ao)	50	68.661971831	—
Systemic arteries (SA)	50	183.098591549	—
Systemic resistance-vessel side (Art)	45	54.9295774648	—
Systemic capillary bed (Cap)	—	—	15
Proximal pulmonary artery (PA)	20	42.2535211268	—
Pulmonary resistance-vessel side (PArt)	20	63.3802816901	—

Effective venous-type coefficients
Compartment	$V_u$ (mL)	$C_c / C_o / C_d$ (mL/mmHg)	$p_o / p_s$ (mmHg)	$d_o / d_s$ (mmHg)	Vu,元 / G (mL)
Systemic veins (SV)	1538.409	15 / 130 / 35	-2 / 16	1.5 / 4	1653.909 / 770
Vena cava (VC)	150.091	5 / 45 / 12	-1 / 12	1 / 3	169.591 / 130
Pulmonary capillary bed (PCap)	105	1 / 2 / 1	0 / 14	1 / 3	105 / 0
Pulmonary venular side (PVen)	160	1.2 / 3 / 1.2	-1 / 14	1 / 3	160 / 0
Pulmonary vein / LA inlet (PVein)	215	1.5 / 4 / 1.5	-1 / 14	1 / 3	215 / 0

Main-circuit links and effective non-valve resistance
Link: positive direction	R (mmHg·s/mL)	Multiplier group	Additional law
Left atrium (LA) → Left ventricle (LV)	See valve table	—	Valve opening / direction
Left ventricle (LV) → Proximal aorta (Ao)	See valve table	—	Valve opening / direction
Right atrium (RA) → Right ventricle (RV)	See valve table	—	Valve opening / direction
Right ventricle (RV) → Proximal pulmonary artery (PA)	See valve table	—	Valve opening / direction
Proximal aorta (Ao) → Systemic arteries (SA)	0.048369152	Systemic ×1.04	—
Systemic arteries (SA) → Systemic resistance-vessel side (Art)	0.0773906432	Systemic ×1.04	—
Systemic resistance-vessel side (Art) → Systemic capillary bed (Cap)	0.628798976	Systemic ×1.04	—
Systemic capillary bed (Cap) → Systemic veins (SV)	0.15	—	—
Systemic veins (SV) → Vena cava (VC)	0.05	—	—
Vena cava (VC) → Right atrium (RA)	0.04	—	waterfall + χ (Pth)
Proximal pulmonary artery (PA) → Pulmonary resistance-vessel side (PArt)	0.00625	Pulmonary ×0.625	—
Pulmonary resistance-vessel side (PArt) → Pulmonary capillary bed (PCap)	0.025	Pulmonary ×0.625	—
Pulmonary capillary bed (PCap) → Pulmonary venular side (PVen)	0.03	—	waterfall + χ (Palv)
Pulmonary venular side (PVen) → Pulmonary vein / LA inlet (PVein)	0.01	—	—
Pulmonary vein / LA inlet (PVein) → Left atrium (LA)	0.03025	—	—

Vascular coefficients and resistance partition are lumped construction/calibration values, not direct measurements at specified human vascular sites. Do not apply baseline multipliers a second time to the listed R.

Coronary and external-pressure coupling

Coronary inflow and venous return contribute to global volume balance. Myocardial compression modulates coronary flow, while pericardial and thoracic pressures load cavities and vessels externally.

Equations and assumptions

Coronary territories and layers include resistance/storage, intramyocardial pressure, collapse and autoregulation, some with provisional adult priors. Baseline has no mechanical support, valve regurgitation or respiratory oscillation. Fixed-control preload testing holds HR and tone fixed; it is not a bedside fluid challenge with autonomic and whole-body responses.

This branch is repeated for LAD/LCx/RCA, sharing only CV. Art/CV receive common cardiac external pressure; C1/C2 receive territory/layer-specific intramyocardial pressure.

Coronary storage and resistance

Each territory has one large-arterial Art reservoir, splitting into epi/endo paths with proximal C1 and distal C2 storage, then merging into common venous CV and RA. C1/C2 name compartments, not numerical compliances. Sixteen coronary volumes contribute to TBV without duplication.

All coronary storage uses v=V/Vref, m=4, n=2; Cref is tangent compliance at Vref. Collapse resistance uses a different hydraulic reference Vh. With a=0.67, x=min(1,max(0,V/Vh)), compute f below.

Branch flow is pressure difference divided by effective resistance. R1 uses tone θ and C1 collapse; Rm the geometric mean of C1/C2 collapse; R2 C2 collapse. Structural multipliers are 1 and focal stenosis additions 0 at baseline.

p=P_*(v^m-v^{-n}),\quad P_*=\frac{V_{\mathrm{ref}}}{C_{\mathrm{ref}}(m+n)},\quad V>0

f(V)=\{a+(1-a)x^2(3-2x)\}^{-2}

R_{1,eff}=R_1\theta f(V_{C1}),\quad R_{\mathrm{m},eff}=R_m\sqrt{f(V_{C1})f(V_{C2})},\quad R_{2,eff}=R_2f(V_{C2})

Intramyocardial pressure and beat-wise regulation

Art/CV external pressure is Pe=Pth+Pperi; C1/C2 use PIM. Weights wL/wS/wR, depth d and shortening gain K are tabulated. Septal depth s=d for LAD/LCx, 1−d for RCA. eMVC,w updates at the previous accepted mitral closure. F is the valve-section positive part with width 0.005.

The shortening reference updates when accepted MV flow changes from >1 to ≤1 mL/s, using that endpoint's strains for subsequent steps. This is not an imaging leaflet-contact time or an interpolated metric closure time.

Tone is held within a cycle and updated at completion. Q̄m is signed cycle-mean flow through Rm; Qtarget is the resting target. ℓ=ln θ, T cycle length, τa=25 s, θmin=4/45 and θmax=2. Baseline demand=1 and hyperemia=0 give the update below. It does not autonomously alter contractility from oxygen demand.

P_{\mathrm{IM}}=P_e+(w_Ld+w_Ss)P_{\mathrm{tm},L}+[w_Rd+w_S(1-s)]P_{\mathrm{tm},R}+K\sum_w w_wF_{0.005}(1-e^{e_w-e_{\mathrm{MVC},w}})

\bar Q_{\mathrm{m},k}=\frac{1}{T}\sum_{n\text{ in cycle }k}\Delta t_n Q_{m,n+1}

\ell_{k+1}=\operatorname{clip}_{\ln\theta_{\mathrm{min}},\ln\theta_{\mathrm{max}}}\left[\ell_k+\frac{T}{\tau_a}\ln\max\left(\frac{\bar Q_{\mathrm{m},k}}{Q_{\mathrm{target}}},0.05\right)\right]

Coronary compartment PV constants
Compartment	$V_{\mathrm{ref}}$ (mL)	$C_{\mathrm{ref}}$ (mL/mmHg)	$P_*$ (mmHg)	$V_h$ (mL)
LAD large arterial storage (Art)	1.43391058398	0.00153221919053	155.973178516	1.53221919053
LAD epi C1	0.48107452286	0.0030959673913	25.8979107366	0.496293624668
LAD epi C2	0.276429025657	0.0928790217391	0.496037785643	0.496293624668
LAD endo C1	0.48107452286	0.0030959673913	25.8979107366	0.496293624668
LAD endo C2	0.276429025657	0.0928790217391	0.496037785643	0.496293624668
LCx large arterial storage (Art)	0.943218749158	0.00100788562723	155.973178516	1.00788562723
LCx epi C1	0.316448260285	0.00203651086957	25.8979107366	0.32645930444
LCx epi C2	0.181833541592	0.061095326087	0.496037785643	0.32645930444
LCx endo C1	0.316448260285	0.00203651086957	25.8979107366	0.32645930444
LCx endo C2	0.181833541592	0.061095326087	0.496037785643	0.32645930444
RCA large arterial storage (Art)	1.01084431002	0.00108014758225	155.973178516	1.08014758225
RCA epi C1	0.339136519084	0.00218252173913	25.8979107366	0.349865320892
RCA epi C2	0.194870385107	0.0654756521739	0.496037785643	0.349865320892
RCA endo C1	0.339136519084	0.00218252173913	25.8979107366	0.349865320892
RCA endo C2	0.194870385107	0.0654756521739	0.496037785643	0.349865320892
Common coronary venous storage (CV)	4.12994828733	0.098037492	7.0210355295	4.9018746

All coronary links and reference resistance (before tone / collapse)
Link: positive direction	R (mmHg·s/mL)
Proximal aorta (Ao) → LAD large arterial storage (Art)	20.749926765
LAD large arterial storage (Art) → LAD epi C1	58.0014068184
LAD epi C1 → LAD epi C2	35.7263939068
LAD epi C2 → Common coronary venous storage (CV)	11.9087979689
LAD large arterial storage (Art) → LAD endo C1	42.2821588661
LAD endo C1 → LAD endo C2	32.1859404566
LAD endo C2 → Common coronary venous storage (CV)	10.7286468189
Proximal aorta (Ao) → LCx large arterial storage (Art)	31.1248901474
LCx large arterial storage (Art) → LCx epi C1	94.8761406353
LCx epi C1 → LCx epi C2	53.5895908603
LCx epi C2 → Common coronary venous storage (CV)	17.8631969534
LCx large arterial storage (Art) → LCx endo C1	64.2296097205
LCx endo C1 → LCx endo C2	48.2789106849
LCx endo C2 → Common coronary venous storage (CV)	16.0929702283
Proximal aorta (Ao) → RCA large arterial storage (Art)	29.049897471
RCA large arterial storage (Art) → RCA epi C1	89.1455943902
RCA epi C1 → RCA epi C2	50.0169514696
RCA epi C2 → Common coronary venous storage (CV)	16.6723171565
RCA large arterial storage (Art) → RCA endo C1	74.0663831102
RCA endo C1 → RCA endo C2	45.0603166393
RCA endo C2 → Common coronary venous storage (CV)	15.0201055464
Common coronary venous storage (CV) → Right atrium (RA)	2.44019138756

Coronary coupling weights and shortening gain
Territory	$w_L / w_S / w_R$	K (mmHg)	Rest Qtarget: epi / endo (mL/s)
LAD	0.75 / 0.25 / 0	81.1546499712	0.485355450237 / 0.538744549763
LCx	1 / 0 / 0	79.6541200248	0.323570300158 / 0.359163033175
RCA	0 / 0.2 / 0.8	84.2078441934	0.346682464455 / 0.384817535545

Layer depths are 0.25 (epi) and 0.75 (endo). Volume allocation starts from porcine morphometry and C1/C2 from canine effective compliance, with selected adjustments from beating-boundary checks. This is not a uniquely identified human circuit.

Kassab et al. 1994 · Spaan et al. 2000

Oxygen supply and consumption

Beat-mean flow, hemoglobin, inspired oxygen and prescribed consumption determine systemic oxygen balance separately from myocardial contraction.

Equations and assumptions

Alveolar gas, oxygen dissociation and shunt mixing determine arterial content. Fick balance gives required mixed-venous content; negative required content is infeasible. Local diffusion and full metabolic adaptation are not resolved.

\dot D_{\mathrm{O_2}}=10\,\mathrm{CO}\,C_{\mathrm{aO}_2},\qquad \dot V_{\mathrm{O_2}}=10\,\mathrm{CO}(C_{\mathrm{aO}_2}-C_{\mathrm{vO}_2})

$\mathrm{\mathrm{CO}}$: Beat-mean systemic flow (L/min)
$C_{\mathrm{aO}_2},\;C_{\mathrm{vO}_2}$: Arterial and mixed-venous oxygen content (mL O₂/dL)
$\dot D_{\mathrm{O}_2},\;\dot V_{\mathrm{O}_2}$: Oxygen delivery and prescribed consumption (mL O₂/min); 10 converts L to dL

Beat-mean oxygen balance

Oxygen transport is an algebraic beat-mean readout without feedback to blood volume or tension. P is O₂ pressure (mmHg), S saturation, Hb g/dL, C mL O₂/dL. Alveolar and end-capillary PO₂ are equated. PB is barometric pressure and R respiratory exchange ratio.

CO is L/min, VO₂ mL/min and s an oxygen-mixing shunt fraction, not an added hydraulic connection. End-capillary Cc, venous Cv and arterial Ca satisfy Fick balance and content mixing. Nonpositive flow or negative required content makes the evaluation unavailable.

P_{\mathrm{AO}_2}=F_{\mathrm{IO}_2}(P_B-47)-P_{\mathrm{aCO}_2}/R>0,\quad S(P)=\frac{P^{2.7}}{26.8^{2.7}+P^{2.7}}

C(P)=1.34\,Hb\,S(P)+0.0031P,\quad D=\frac{VO_2}{10\mathrm{CO}},\quad C_a=C_c-\frac{s}{1-s}D,\quad C_v=C_a-D

Analysis: relationships beyond one loop

A PV loop is the simulated beat trajectory. ESPVR, EDPVR, Starling/Guyton curves and PVA/PE are derived through separate loading protocols.

Equations and assumptions

Analyses branch without mutating the live simulation. ESPVR uses the reduced-preload limb through baseline; EDPVR and Starling retain high-volume conditions too. Estimates depend on the finite loading range, settlement and event definitions; linearity and load independence are not guaranteed. Unavailable analysis stays unassessed, not an exact-output placeholder.

Assembling the coupled circulation model

Coupling the connections, constitutive laws and evolving states, with conditions for starting from the saved baseline.

Coupled equations and initial conditions

Blood occupies 31 compartments, constrained by fixed TBV (30 independent volume degrees of freedom). Each wall has six Land states, one viscous strain and two calcium states; four valves have opening states. Six coronary tones and event/load/previous-MVC memories are retained. Pressures, flows and internal geometry follow simultaneous algebraic constraints.

\begin{aligned}V_{n+1}-V_n&=\Delta t\,NQ_{n+1},\\z_{n+1}-z_n&=\Delta t\,f(z_{n+1},Ca_{n+1},\lambda_{n+1},\dot\lambda_{n+1}),\\0&=g(V_{n+1},z_{n+1},P_{n+1},Q_{n+1},v_{S,n+1},y_{n+1}).\end{aligned}

z collects Land/viscous/opening states; f is the documented evolution and g the constitutive, hydraulic and force-balance constraints. The coupled system uses backward Euler, with exact inter-event calcium propagation. Candidate volume, geometry, stress, pressure and flow must satisfy continuity together; vascular updates do not keep stale cavity pressures.

Nominal step is 2 ms, split at activation, calcium and control-window boundaries. Coronary tone updates from completed-cycle flow integrals. Invalid populations, nonfinite states, volume imbalance or failed nonlinear solves are not accepted. Another integrator may approximate the same continuous equations, but finite-step peaks/events and saved baseline parity require separate checks.

Saved setting's initial conditions

The settled launch state below is at t₀=46.286 s。If shifting time to zero, shift event and control times equally. Keeping volumes but zeroing material/Ca states is not equivalent. Display uses 12 significant digits; CSV retains full stored precision.

Initial blood volume (mL)
Compartment	$V(t_0)$
Proximal aorta (Ao)	65.4367287014
Systemic resistance-vessel side (Art)	53.4074756823
Systemic capillary bed (Cap)	373.824096768
Left atrium (LA)	25.7898122897
Left ventricle (LV)	143.711071184
Proximal pulmonary artery (PA)	20.3142440781
Pulmonary resistance-vessel side (PArt)	30.3820470937
Pulmonary capillary bed (PCap)	126.862424703
Pulmonary vein / LA inlet (PVein)	255.714506561
Pulmonary venular side (PVen)	191.350541007
Right atrium (RA)	31.2031541035
Right ventricle (RV)	140.092672085
Systemic arteries (SA)	173.420546231
Systemic veins (SV)	2869.19213711
Vena cava (VC)	422.030448572
Common coronary venous storage (CV)	4.49848733008
LAD large arterial storage (Art)	1.52008136721
LAD endo C1	0.54601764284
LAD epi C1	0.542581530948
LAD endo C2	0.247668811702
LAD epi C2	0.340467873509
LCx large arterial storage (Art)	1.00015438503
LCx endo C1	0.359081996138
LCx epi C1	0.355306395262
LCx endo C2	0.167814565593
LCx epi C2	0.25717706142
RCA large arterial storage (Art)	1.07191786674
RCA endo C1	0.381977788163
RCA epi C1	0.380987565009
RCA endo C2	0.299665178334
RCA epi C2	0.298706473768

Initial Land states (dimensionless)
Wall	c	b	W	S	$\zeta_w$	$\zeta_s$
Left atrium (LA)	0.28113915674	0.704874682088	0.102054035966	0.0936506021977	0.013402384343	0.0338115707429
LV free wall (LVFW)	0.0712952557971	0.997572779339	0.000978883693389	0.00048162586185	-0.000156025626448	0.159371858597
Ventricular septum (SEP)	0.0634436395191	0.998179427826	0.000729140483623	0.000368919301831	0.00056671701343	0.159647291732
RV free wall (RVFW)	0.0581013236786	0.998543071477	0.000573074250909	0.000304279966973	0.00241313043082	0.171438507274
Right atrium (RA)	0.240173486467	0.846068649473	0.0529103777129	0.048855794844	0.0158771615395	0.0473305726281

Initial strain / calcium states (dimensionless)
Wall	$e(t_0)$	$\alpha(t_0)$	$x_r(t_0)$	$x_d(t_0)$
Left atrium (LA)	0.0259051860097	0.136283812906	0.0000661982094573	0.71048708409
LV free wall (LVFW)	0.101624278419	0.0379694626707	0.998315089971	0.999323563371
Ventricular septum (SEP)	0.0785520120923	0.0107355090136	0.998315089971	0.999323563371
RV free wall (RVFW)	0.0602577439257	-0.00661841196296	0.998315089971	0.999323563371
Right atrium (RA)	-0.0106562564514	0.040966058947	0.0000661982094573	0.71048708409

Initial opening / geometry
Quantity	Value
AV ξ	3.79608635874e-27
MV ξ	0.053059576747
PV ξ	4.99723843977e-35
TV ξ	0.257165066582
$v_S$ (m³)	0.0000380009976933
y (m)	0.0335157366463

Coronary tone and partial-window integrals
Territory / layer	$\theta(t_0)$	$\int Q_m\,dt$ (mL)
LAD epi	1.13168252266	0.00015300710174
LAD endo	1.14365945334	0.000171660683095
LCx epi	1.12241435777	0.0000968015110365
LCx endo	1.14314290996	0.000114829817841
RCA epi	1.14000395771	0.000101981803205
RCA endo	1.1845135399	0.000116389854937

Retained timing and discrete memory
Quantity	Value
Next atrial activation (s)	47.0108571429
Last ventricular activation (s)	46.2737142857
$L(t_0)$	1.52456187266
Coronary window start (s)	46.2857142857
Elapsed coronary window (s)	0.000285714285717
$e_{\mathrm{MVC},\mathrm{LVFW}}$	0.101690533274
$e_{\mathrm{MVC},\mathrm{RVFW}}$	0.0586290629596
$e_{\mathrm{MVC},\mathrm{SEP}}$	0.0782742972666

There are no pending calcium/conduction events at this instant. Next calcium deposits follow the next atrial activation by 12 ms (atria) or 132 ms (ventricles). Coronary windows are T=60/70 s from original time zero. Recompute several cycles to verify consistency; this table does not establish uniqueness or stability in every scenario.

Save parameter and initial-state tables (CSV)

Baseline settings

A resting, sinus, unassisted operating point at the body size and heart rate shown below, without an assigned age or sex. Its baseline intervals are not automatically imposed on disease presets or patient demos.

HR: 70 bpm
TBV: 4935 mL
BSA: 1.9 m²
Contractility: 1

Constitutive/calcium calibration is separate from day-to-day case controls. Contractility 1 scales this model's reference material; it is not an absolute unit of normal contractility.

Adopted settings and control domains

These saved baseline settings were selected jointly for pressure, output, filling and reserve, not individually identified from measurements. Control usage and accepted domains are explained in the workbench.

Venous tone reduces unstressed venous capacity and redistributes blood rather than adding volume. Resistance and arterial stiffness values are relative scales. The common ventricular control sets both free walls and septum together; it is not another multiplier applied over the individual wall values.

Parameter	baseline
Heart rate (HR)	70 bpm
Total blood volume (TBV)	4,935 mL
Systemic vascular resistance (SVR)	1.04 (dimensionless)
Common ventricular active tension	1 (dimensionless)
Venous tone	0.15 (dimensionless)
PEEP	0 cmH2O
Pulmonary vascular resistance (PVR)	0.625 (dimensionless)
Arterial stiffness	1.42 (dimensionless)
LA active tension	1 (dimensionless)
LV free wall active tension	1 (dimensionless)
Ventricular septum active tension	1 (dimensionless)
RV free wall active tension	1 (dimensionless)
RA active tension	1 (dimensionless)
LA passive stiffness	1 (dimensionless)
LV free wall passive stiffness	1.04 (dimensionless)
Ventricular septum passive stiffness	1.04 (dimensionless)
RV free wall passive stiffness	1.04 (dimensionless)
RA passive stiffness	1 (dimensionless)
Mitral valve (MV) maximum EOA	5.5 cm²
Mitral valve (MV) reverse EROA	0 cm²
Aortic valve (AoV) maximum EOA	3.5 cm²
Aortic valve (AoV) reverse EROA	0 cm²
Tricuspid valve (TV) maximum EOA	8 cm²
Tricuspid valve (TV) reverse EROA	0 cm²
Pulmonary valve (PV) maximum EOA	4 cm²
Pulmonary valve (PV) reverse EROA	0 cm²
Hemoglobin (Hb)	15 g/dL
Inspired oxygen fraction (FiO₂)	0.21 (dimensionless)
Arterial PCO₂ (PaCO₂)	40 mmHg
Respiratory exchange ratio (RER)	0.8 (dimensionless)
Barometric pressure	760 mmHg
True shunt fraction	0.02 (dimensionless)
Target oxygen consumption (VO₂)	250 mL O2/min
Pericardial reference capacity scale	1 (dimensionless)
Pericardial pressure scale	1 (dimensionless)
Pericardial exponential stiffness scale	1 (dimensionless)
Pericardial fluid volume	0 mL
LAD focal diameter loss fraction	0 (dimensionless)
LCx focal diameter loss fraction	0 (dimensionless)
RCA focal diameter loss fraction	0 (dimensionless)
LAD · subepicardial · inlet resistance scale	1 (dimensionless)
LAD · subendocardial · inlet resistance scale	1 (dimensionless)
LCx · subepicardial · inlet resistance scale	1 (dimensionless)
LCx · subendocardial · inlet resistance scale	1 (dimensionless)
RCA · subepicardial · inlet resistance scale	1 (dimensionless)
RCA · subendocardial · inlet resistance scale	1 (dimensionless)
LAD · subepicardial · microvascular resistance scale	1 (dimensionless)
LAD · subendocardial · microvascular resistance scale	1 (dimensionless)
LCx · subepicardial · microvascular resistance scale	1 (dimensionless)
LCx · subendocardial · microvascular resistance scale	1 (dimensionless)
RCA · subepicardial · microvascular resistance scale	1 (dimensionless)
RCA · subendocardial · microvascular resistance scale	1 (dimensionless)
LV contractility	1 (dimensionless)

Fixed material, calcium source and provenance

Ventricular Land-derived coefficients: source and adopted values are distinct; some rows include unit conversion. Changes in tension scale, calcium affinity and binding kinetics are closed-loop calibration, not independent identification of healthy-human coefficients.

Land et al. 2017 · 10.1016/j.yjmcc.2017.03.008

Parameter	Source	Adopted
$k_{\mathrm{TRPN}}$	0.1 1/ms	100 1/s
$n_{\mathrm{TRPN}}$	2 —	2 —
$\mathrm{Ca}_{50,\mathrm{ref}}$	0.805 uM	0.6 uM
$k_u$	1 1/ms	1,000 1/s
$n_{\mathrm{Tm}}$	5 —	5 —
$\theta$	0.35 —	0.35 —
$k_{\mathrm{uw}}$	0.182 1/ms	104 1/s
$k_{\mathrm{ws}}$	0.012 1/ms	4.8 1/s
$r_w$	0.5 —	0.5 —
$r_s$	0.25 —	0.25 —
$\gamma_s$	0.0085 1/ms	8.5 1/s
$\gamma_w$	0.615 1/ms	615 1/s
$\phi$	2.23 —	2.23 —
$A_{\mathrm{eff}}$	25 —	26.5 —
$\beta_0$	2.3 —	2.3 —
$\beta_1$	-2.4 uM	-1.2 uM
$T_{\mathrm{ref}}$	120 kPa	238,816.55 Pa
$T$	37 degC	310.15 K

Non-source strong-bridge exit rate: 60 s⁻¹ · cooperativity p: 16。Ventricular slack-stretch scale: 1。Fixed systemic compliance multiplier: 0.65。

The source Tref comes from the paper's whole-organ column. Affinity, kinetics and tension were adjusted jointly against closed-loop ejection and relaxation. Multiple parameter combinations can reproduce a baseline; this is not a uniquely identified physiological solution.

Adopted ventricular event-source values (shared by ventricular walls): τr = 118.5 ms, τd = 131.7 ms, Ca₀ = 0.120706159272 µM, g = 12.0780349398 µM.

Baseline assessment

This is the saved baseline assessment, not an on-demand assessment of the current workbench scenario. Passing required checks is distinct from matching every source reference interval.

Qualification belongs to this baseline, not application of healthy criteria to HFrEF. Formal adoption, publication and clinical validation are separate.

Reference flags: PAP min / LV +dP/dt / LV −dP/dt / LV ICT / LV Tei

Reference cautions are listed above. Even an in-range value does not establish measurement equivalence or validity across clinical cases.

2 ms · independent cold qualification

Open a row for its measurement method, adopted/source ranges and rationale. Values come from each record's final settled beat. Unsupported thresholds are identified as such.

Operating targets guide baseline admission; construction/load guards check design behavior. References are contextual and do not independently reject a candidate. Numerical quality checks computation.

Pressure, output and valve gradients

CI2.95 L/min/m²2.5 – 4Pass · Operating target

Measurement

Use signed native AoV NET output/BSA under a distinct metric ID. Interpretation as whole-circulation CO requires a settled unassisted nonshunting state; no positive-only flow substitution or distal-CMR-plane equivalence.

Adopted, source-informed: 2.5 – 4 L/min/m²
resting adult RHC reference · published-reference-interval: 2.5 – 4 L/min/m²

Rationale and interpretation

Resting unassisted nonshunting sinus research construction, BSA1.9, HR60 or70, zero intrathoracic reference. Scientific eligibility for exact-model promotion, not public mint or clinical normality.

2022 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertensionTable 11, CI

CVP / mean RAP3.08 mmHg2 – 6Pass · Operating target

Measurement

Absolute lumped pressure, no respiratory cycle; compare with supine end-expiratory catheter values at the specified zero. No catheter transfer function or peripheral waveform is simulated.

Adopted, source-informed: 2 – 6 mmHg
resting adult RHC reference · published-reference-interval: 2 – 6 mmHg

Rationale and interpretation

Resting unassisted nonshunting sinus research construction, BSA1.9, HR60 or70, zero intrathoracic reference. Scientific eligibility for exact-model promotion, not public mint or clinical normality.

2022 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertensionTable 11, mean RAP

mean PAP17.89 mmHg8 – 20Pass · Operating target

Measurement

Absolute lumped pressure, no respiratory cycle; compare with supine end-expiratory catheter values at the specified zero. No catheter transfer function or peripheral waveform is simulated.

Adopted, source-informed: 8 – 20 mmHg
resting adult RHC reference · published-reference-interval: 8 – 20 mmHg

Rationale and interpretation

Resting unassisted nonshunting sinus research construction, BSA1.9, HR60 or70, zero intrathoracic reference. Scientific eligibility for exact-model promotion, not public mint or clinical normality.

2022 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertensionTable 11, mean PAP

AoP max111.3 mmHg90 – 140Pass · Construction / load guard

Measurement

Model Ao root pressure is invasive-like. Source cSBP is cuff-calibrated noninvasive estimation; authors explicitly distinguish it from higher invasive intra-aortic SBP. Published P10/P90 are context, not 95% normal cutoffs or a model calibration target.

Design interval, not a normal range: 90 – 140 mmHg
women 20-29 · published-10th-90th-percentiles: 80 – 110 mmHg
men 20-29 · published-10th-90th-percentiles: 92 – 115 mmHg
women 30-39 · published-10th-90th-percentiles: 84 – 119 mmHg
men 30-39 · published-10th-90th-percentiles: 88 – 120 mmHg
women 40-49 · published-10th-90th-percentiles: 87 – 123 mmHg
men 40-49 · published-10th-90th-percentiles: 90 – 123 mmHg
women 50-59 · published-10th-90th-percentiles: 93 – 127 mmHg
men 50-59 · published-10th-90th-percentiles: 96 – 126 mmHg
women 60-69 · published-10th-90th-percentiles: 97 – 129 mmHg
men 60-69 · published-10th-90th-percentiles: 97 – 128 mmHg
women 70+ · published-10th-90th-percentiles: 100 – 131 mmHg
men 70+ · published-10th-90th-percentiles: 99 – 130 mmHg

Rationale and interpretation

Keep a baseline away from low/high systemic load and high native end-filling pressure. Ao bounds are retained design choices, not derived from Herbert. LV native flow cessation may precede the pressure upstroke; <=16 is an approximate end-filling design ceiling, not validated catheter LVEDP equivalence or a lower normal limit.

Establishing reference values for central blood pressure and its amplification in a general healthy population and according to cardiovascular risk factorsMethods, invasive versus cuff-calibrated pressure distinction

AoP min77.52 mmHg60 – 90Pass · Construction / load guard

Measurement

Source assumes DBP consistency for calibration, but does not publish a central-DBP normal interval. Do not turn the brachial mean +/- SD into a verified Ao-node cutoff.

Design interval, not a normal range: 60 – 90 mmHg

Rationale and interpretation

Establishing reference values for central blood pressure and its amplification in a general healthy population and according to cardiovascular risk factorsMethods, DBP calibration; no central-DBP reference interval

LV end-filling P10.92 mmHg≤ 16Pass · Construction / load guard

Measurement

Native inlet-closure LV pressure; not validated catheter LVEDP equivalence.

Design interval, not a normal range: ≤ 16 mmHg

Rationale and interpretation

Recommendations for the Evaluation of Left Ventricular Diastolic Function by Echocardiography and for Heart Failure With Preserved Ejection Fraction Diagnosis: An Update From the American Society of EchocardiographySection2, Table1 p539 (>16), Figure1 p540

PAP max26.17 mmHg15 – 30Reference

Measurement

Absolute lumped pressure, no respiratory cycle; compare with supine end-expiratory catheter values at the specified zero. No catheter transfer function or peripheral waveform is simulated.

resting adult RHC reference · published-reference-interval: 15 – 30 mmHg

Rationale and interpretation

Source comparison, not an automatic rejection threshold; account for method differences.

2022 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertensionTable 11, systolic PAP; section 5.1.12.1

PAP min12.06 mmHg4 – 12Outside reference · Reference

Measurement

Absolute lumped pressure, no respiratory cycle; compare with supine end-expiratory catheter values at the specified zero. No catheter transfer function or peripheral waveform is simulated.

resting adult RHC reference · published-reference-interval: 4 – 12 mmHg

Rationale and interpretation

Source comparison, not an automatic rejection threshold; account for method differences.

2022 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertensionTable 11, diastolic PAP; section 5.1.12.1

mean LAP (PCWP surrogate)8.4 mmHg≤ 15Reference

Measurement

Observed quantity remains LA mean, not a wedge measurement or LVEDP. PAWP <=15 is the guideline clinical reference upper limit, not a healthy-cohort distribution or a verified model LA-to-PAWP transfer. No lower bound is invented.

adult RHC PAWP clinical reference · clinical-upper-limit: ≤ 15 mmHg

Rationale and interpretation

Source comparison, not an automatic rejection threshold; account for method differences.

2022 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertensionTable 11, PAWP; section 5.1.12.1

SVI42.17 mL/m²33 – 47Reference

Measurement

Signed native AoV NET volume/BSA. CI = HR * SVI / 1000, so this is a coupled comparison, not a second independent fitting objective. The CI-conditional interval is reported separately; it is not this published SVI interval.

resting adult RHC reference · published-reference-interval: 33 – 47 mL/m²

Rationale and interpretation

Source comparison, not an automatic rejection threshold; account for method differences.

2022 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertensionTable 11, SVI; section 5.1.12.1

AV mean ΔP4.19 mmHg0 – 5Pass · Construction / load guard

Measurement

Time-weighted mean and maximum raw LV-minus-Ao node pressure difference during native aortic forward flow. This hydraulic node gradient is neither a Doppler Bernoulli gradient nor a simultaneous catheter LV-to-recovered-aortic pressure difference; pressure recovery and spatial acceleration are not observed.

Design interval, not a normal range: 0 – 5 mmHg

Rationale and interpretation

Constrain the non-stenotic baseline while retaining the model's explicit pressure-station limitation. No matching healthy-population source establishes the exact mean or peak cutoffs for these model pressure stations. Stenosis diagnostic thresholds would not validate them.

No primary source establishes this cutoff as a normal range. It remains a design check or context.

AV peak ΔP7.82 mmHg0 – 10Pass · Construction / load guard

Measurement

Design interval, not a normal range: 0 – 10 mmHg

Rationale and interpretation

No primary source establishes this cutoff as a normal range. It remains a design check or context.

PV mean ΔP4.45 mmHg0 – 5Pass · Construction / load guard

Measurement

Time-weighted mean and maximum raw RV-minus-PA node pressure difference while native PV flow is positive over the completed beat. The model's hydraulic gradient is not a Doppler Bernoulli or recovered catheter gradient; an explicit outlet node does not provide spatial velocity, pressure recovery or an invasive sensor model.

Design interval, not a normal range: 0 – 5 mmHg

Rationale and interpretation

Record the existing Standard70 right-heart gradient sentinels without promoting them to left-objective groups or changing their numerical limits. No source establishes the exact mean and peak healthy cutoffs for these pressure stations. These remain non-stenotic construction guards, not clinical normal-gradient intervals.

No primary source establishes this cutoff as a normal range. It remains a design check or context.

PV peak ΔP7.37 mmHg0 – 10Pass · Construction / load guard

Measurement

Design interval, not a normal range: 0 – 10 mmHg

Rationale and interpretation

No primary source establishes this cutoff as a normal range. It remains a design check or context.

Ventricular volumes and ejection fraction

LV EDVI75.64 mL/m²46 – 91Pass · Operating target

Measurement

Native valve-closure cavity blood volumes, BSA indexed; compared with anatomical bSSFP CMR excluding papillary/trabecular myocardium from the blood pool. No validated image segmentation or age/sex assignment; separate marginal ranges are not a joint distribution. EF is derived from EDV and ESV.

Adopted intersection of both sex strata (design choice): 46 – 91 mL/m²
men, pooled adult ages · published-reference-interval: 46 – 104 mL/m²
women, pooled adult ages · published-reference-interval: 46 – 91 mL/m²

Rationale and interpretation

For this sex-unspecified generic baseline only, automatic eligibility requires all six valid anatomical CMR comparisons inside BOTH declared sex strata. Otherwise require demographic/method review, not automatic disease rejection. This conservative design intersection does not assign sex or claim joint population normality; preset/patient fitting must use its own profile.

Society for Cardiovascular Magnetic Resonance reference values (normal values) in cardiovascular magnetic resonance: 2025 updateTable 2, anatomical segmentation, sex-specific indexed volume/EF rows

LV ESVI33.47 mL/m²11 – 34Pass · Operating target

Measurement

Adopted intersection of both sex strata (design choice): 11 – 34 mL/m²
men, pooled adult ages · published-reference-interval: 11 – 41 mL/m²
women, pooled adult ages · published-reference-interval: 11 – 34 mL/m²

Rationale and interpretation

Society for Cardiovascular Magnetic Resonance reference values (normal values) in cardiovascular magnetic resonance: 2025 updateTable 2, anatomical segmentation, sex-specific indexed volume/EF rows

LVEF55.75 %55 – 79Pass · Operating target

Measurement

Adopted intersection of both sex strata (design choice): 55 – 79 %
men, pooled adult ages · published-reference-interval: 53 – 79 %
women, pooled adult ages · published-reference-interval: 55 – 80 %

Rationale and interpretation

Society for Cardiovascular Magnetic Resonance reference values (normal values) in cardiovascular magnetic resonance: 2025 updateTable 2, anatomical segmentation, sex-specific indexed volume/EF rows

RV EDVI74.09 mL/m²49 – 99Pass · Operating target

Measurement

Adopted intersection of both sex strata (design choice): 49 – 99 mL/m²
men, pooled adult ages · published-reference-interval: 49 – 117 mL/m²
women, pooled adult ages · published-reference-interval: 47 – 99 mL/m²

Rationale and interpretation

Society for Cardiovascular Magnetic Resonance reference values (normal values) in cardiovascular magnetic resonance: 2025 updateTable 8, anatomical segmentation, sex-specific indexed volume/EF rows

RV ESVI31.92 mL/m²12 – 43Pass · Operating target

Measurement

Adopted intersection of both sex strata (design choice): 12 – 43 mL/m²
men, pooled adult ages · published-reference-interval: 12 – 56 mL/m²
women, pooled adult ages · published-reference-interval: 11 – 43 mL/m²

Rationale and interpretation

Society for Cardiovascular Magnetic Resonance reference values (normal values) in cardiovascular magnetic resonance: 2025 updateTable 8, anatomical segmentation, sex-specific indexed volume/EF rows

RVEF56.92 %49 – 77Pass · Operating target

Measurement

Adopted intersection of both sex strata (design choice): 49 – 77 %
men, pooled adult ages · published-reference-interval: 44 – 77 %
women, pooled adult ages · published-reference-interval: 49 – 77 %

Rationale and interpretation

Society for Cardiovascular Magnetic Resonance reference values (normal values) in cardiovascular magnetic resonance: 2025 updateTable 8, anatomical segmentation, sex-specific indexed volume/EF rows

Contraction, relaxation and filling

AV ET258 ms248 – 336Reference

Measurement

Native accumulated positive AoV-flow duration, not mitral-leaflet color-TDI timing. Opening-to-closure interpretation requires the separate morphology/timing observer to establish one forward episode; this comparison does not enforce that condition. No HR correction or method equivalence inferred.

Copenhagen pooled healthy adults; HR 63 +/- 10 · published-reference-interval: 248 – 336 ms

Rationale and interpretation

Source comparison, not an automatic rejection threshold; account for method differences.

Age- and sex-based normal reference ranges of the cardiac time intervals: the Copenhagen City Heart StudyMethods, Cardiac time intervals; Table 2, pooled LVET 95% prediction interval

PV ET258 msNo numeric intervalReference

Measurement

Native accumulated positive PV-flow duration; the separate morphology/timing observer must establish one forward episode. Doppler PA versus RVOT station, respiration and HR differ. No adult ET bounds inferred from acceleration time, tissue S-wave duration or LVET.

Rationale and interpretation

Source comparison, not an automatic rejection threshold; account for method differences.

Reference values for pulsed Doppler signals from the blood flow velocity on both sides of the pulmonary valveAbstract: population and recording stations; no numeric adult ET interval verified

LV +dP/dt2,564.3 mmHg/s1,200 – 2,500Outside reference · Reference

Measurement

Maximum and minimum accepted-step finite-difference derivative of absolute intracavitary LV pressure over the completed beat. Accepted-step bandwidth, pressure loading, HR, preload, medication and catheter filtering affect extrema. Published negative dP/dt is often a positive magnitude, whereas this model stores a signed minimum; this is not a transmural derivative.

Historical corridor, context only: 1,200 – 2,500 mmHg/s

Rationale and interpretation

Retain plausible contraction and relaxation rates while adjusting aortic ejection morphology. The positive corridor overlaps small normal-LV patient series, but the frozen negative corridor excludes their resting means. Neither series supplies a population-normal acceptance interval; keep both corridors as warnings rather than validated pass/fail physiology.

Contractile and relaxation reserve of the left ventricle. I. Normal left ventricleAbstract; resting values before ergometer exercise
A clinical study of left ventricular relaxationMethods p. 757; normal-control table p. 759; abstract

LV −dP/dt-1,538.9 mmHg/s-1,400 – -700Outside reference · Reference

Measurement

Historical corridor, context only: -1,400 – -700 mmHg/s

Rationale and interpretation

Contractile and relaxation reserve of the left ventricle. I. Normal left ventricleAbstract; resting values before ergometer exercise
A clinical study of left ventricular relaxationMethods p. 757; normal-control table p. 759; abstract

MV E/A0.94 0.8 – 2Reference

Measurement

Ratio of peak native mitral forward volume flow in early and atrial filling windows anchored to the observed atrial-capture event. Volume-flow peaks are not leaflet-tip Doppler velocities; varying effective valve area can change their ratio. A complete post-capture inlet closure and identifiable E/A windows are required, and age, rhythm, HR and loading affect interpretation.

Historical corridor, context only: 0.8 – 2

Rationale and interpretation

Retain the recorded corridor as context only: native volumetric E/A is not Doppler velocity E/A. Positive resolved waves remain required; no numeric widening or candidate-specific target change. The fixed corridor is provisional, not an age-specific Doppler normal interval. Better event anchoring does not remove the flow-versus-velocity observation mismatch.

Recommendations for the Evaluation of Left Ventricular Diastolic Function by Echocardiography and for Heart Failure With Preserved Ejection Fraction Diagnosis: An Update From the American Society of EchocardiographyTables 3 and 5 (p. 551)

LV ICT89.14 ms20 – 70Outside reference · Reference

Measurement

ICT from exact MV closure to AoV zero-flow opening, IRT from exact AoV closure to MV zero-flow opening, and (ICT + IRT) divided by the matched aortic ejection duration. Closure landmarks and trace-interpolated openings must describe one complete beat. Tei is algebraically linked to ICT, IRT and the separately checked ejection time, so these are not independent constraints.

Historical corridor, context only: 20 – 70 ms

Rationale and interpretation

Demote method-mismatched ICT/IRT/Tei corridors to context; retain complete ordered hydraulic events, positivity and exact Tei arithmetic. ET remains an explicitly chosen baseline operating target, not proof of a population-normal timing pattern. The intervals remain provisional hydraulic timing targets. Matching some published endpoints does not establish a measurement-equivalence study or historical source derivation.

Age- and sex-based normal reference ranges of the cardiac time intervals: the Copenhagen City Heart StudyTable 2; Methods, Cardiac time intervals

LV IRT92 ms59 – 134Reference

Measurement

Historical corridor, context only: 59 – 134 ms

Rationale and interpretation

Age- and sex-based normal reference ranges of the cardiac time intervals: the Copenhagen City Heart StudyTable 2; Methods, Cardiac time intervals

LV Tei0.7 0.29 – 0.65Outside reference · Reference

Measurement

Historical corridor, context only: 0.29 – 0.65

Rationale and interpretation

Age- and sex-based normal reference ranges of the cardiac time intervals: the Copenhagen City Heart StudyTable 2; Methods, Cardiac time intervals

RV +dP/dt585.6 mmHg/s300 – 1,000Reference

Measurement

Maximum and minimum accepted-step finite-difference derivative of absolute intracavitary RV pressure over the completed beat. These load- and bandwidth-dependent extrema are neither transmural pressure derivatives nor the mean RV-to-RA pressure-gradient rise inferred over a selected TR velocity interval. Signed negative extrema must not be confused with published pressure-fall magnitudes.

Historical corridor, context only: 300 – 1,000 mmHg/s

Rationale and interpretation

Reclassify the existing Standard70 RV derivative corridors as reference warnings without altering the recorded numerical bounds. No verified source establishes either frozen normal corridor. Sparse normal-PAP invasive data and a method-specific abnormal Doppler threshold justify contextual warnings, not hard healthy-population acceptance limits.

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRV dP/dt section, pp. 158-159
Effect of chronic pressure overload on the maximal rate of pressure fall of the right ventricleAbstract; normal-PAP and pulmonary-hypertension groups

RV −dP/dt-371.9 mmHg/s-700 – -150Reference

Measurement

Historical corridor, context only: -700 – -150 mmHg/s

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRV dP/dt section, pp. 158-159
Effect of chronic pressure overload on the maximal rate of pressure fall of the right ventricleAbstract; normal-PAP and pulmonary-hypertension groups

TV E/A1.1 0.8 – 2Reference

Measurement

Ratio of peak native tricuspid forward volume flow in early and atrial filling windows anchored to the observed atrial-capture event. Requires identifiable windows and an observed post-capture inlet closure. Volume-flow peaks do not equal Doppler velocities if effective valve area changes; respiration, HR, rhythm, age and loading remain relevant.

Historical corridor, context only: 0.8 – 2

Rationale and interpretation

Demote the native tricuspid flow-ratio corridor to context because Doppler velocity and respiratory averaging are different observations; resolved positive filling waves remain required. The numerical corridor resembles a guideline Doppler interval but remains provisional for the native-flow observer; the source upper endpoint is exclusive whereas the frozen gate is inclusive.

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyTable 1; RV diastolic function, pp. 168-169

RV ICT28 ms20 – 90Reference

Measurement

ICT from exact TV closure to PV zero-flow opening, IRT from exact PV closure to TV zero-flow opening, and (ICT + IRT) divided by the matched pulmonary ejection duration. One complete valve-event sequence is required. Tei is algebraically linked to ICT, IRT and the separately checked pulmonary ET; PW-Doppler, TDI and hydraulic timings are different observations.

Historical corridor, context only: 20 – 90 ms

Rationale and interpretation

Demote the unsupported hydraulic right ICT/IRT/Tei numeric corridors to context. Ordered complete valve events and algebraic consistency remain mandatory; a short RV isovolumic phase is not automatically pathological. No primary source was identified for the chosen joint ICT/IRT/Tei corridors. The source below supplies method-specific context, not equivalent normal intervals; all three remain provisional physiological targets.

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRV MPI, pp. 158-159; IVRT, pp. 168-169

RV IRT64 ms30 – 120Reference

Measurement

Historical corridor, context only: 30 – 120 ms

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRV MPI, pp. 158-159; IVRT, pp. 168-169

RV Tei0.36 0.25 – 0.65Reference

Measurement

Historical corridor, context only: 0.25 – 0.65

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRV MPI, pp. 158-159; IVRT, pp. 168-169

LV τ (Weiss)32.04 ms≤ 48Reference

Measurement

Time-weighted exponential fit of intracavitary LVP from the minimum-dP/dt midpoint to next EDP +5 mmHg, before MVO; zero asymptote. Not interchangeable with free-asymptote Glantz τ.

Prolongation context, not a normal distribution: ≤ 48 ms

Rationale and interpretation

τ and fit usability, residuals and window sensitivity are separate checks. Source pressure is not smoothed.

Recommendations for the Evaluation of Left Ventricular Diastolic Function by Echocardiography and for Heart Failure With Preserved Ejection Fraction Diagnosis: An Update From the American Society of EchocardiographyInvasive relaxation reference; Weiss asymptote/method must be matched

Numerical and waveform checks

Period-1Met Criteria metPass · Numerical quality

Measurement

Whether the exact periodic classifier established the required period-one terminal state. Period-one settlement is numerical admissibility, not physiological normality or independent model validation.

Design interval, not a normal range: Criteria met

Rationale and interpretation

Fail closed before interpreting any derived baseline measurement. No clinical population interval applies to an exact periodic-classifier contract.

No primary source establishes this cutoff as a normal range. It remains a design check or context.

LVP ringingMet Criteria metPass · Construction / load guard

Measurement

Algorithmic peak count, total variation and episode count of pressure during the associated semilunar-valve forward-flow episode. Prominence and variation depend on accepted sampling and the thresholded forward-flow episode. Real arterial reflection can produce a systolic shoulder or secondary rise; the current lumped model has no explicit propagation/reflection mechanism, so that observation does not explain its numerical or coupled-mode ringing.

Design interval, not a normal range: Criteria met

Rationale and interpretation

Retain the artifact guards motivated by Standard65-to-68 ringing, separately from unvalidated contour reference corridors. This is a current-model construction requirement, not a claim that every healthy human trace has one peak. No primary healthy-cohort distribution supports the exact peak-count or variation cutoffs. They remain transparent construction guards; no clinical normality follows from passing.

No primary source establishes this cutoff as a normal range. It remains a design check or context.

LVP contour20.46 %8 – 35Reference

Measurement

Central accepted-sample-index pressure range divided by full ejection pressure range, jointly with the first maximum's normalized sample index. The check reports peak index when that alone fails; it is not PV-loop curvature or a time-weighted shape measurement. Sample-index phase is not elapsed-time phase on nonuniform accepted steps. Pressure versus time and pressure versus volume have different curvature because ejection flow varies. Resolution, pressure loading and the selected episode affect these summaries; RV and LV cannot be assigned the same physiological contour solely by analogy.

Historical corridor, context only: 8 – 35 %

Rationale and interpretation

Demote the frozen central-range and peak-index corridors to descriptive warnings: no matched normal distribution supports the limits, and a single compound failure previously conflated late pressure peak with flatness. Numerical thresholds are not widened to admit a candidate. No matched healthy LV or RV reference interval was identified for centralRangeFraction 0.08-0.35 or peakPhase01 0.2-0.8. These values remain visible warnings, not independent scientific validation or permission to accept unexplained ringing.

Aortic input impedance in normal man: relationship to pressure wave formsAuthor-institution abstract; ascending aortic pressure waveform groups
The quest for load-independent left ventricular chamber properties: exploring the normalized pressure-volume loopMethods; Tables 1 and 4; Figures 4-5, PDF pp. 6-7

RVP ringingMet Criteria metPass · Construction / load guard

Measurement

Design interval, not a normal range: Criteria met

Rationale and interpretation

No primary source establishes this cutoff as a normal range. It remains a design check or context.

RVP contour18.98 %8 – 35Reference

Measurement

Historical corridor, context only: 8 – 35 %

Rationale and interpretation

Aortic input impedance in normal man: relationship to pressure wave formsAuthor-institution abstract; ascending aortic pressure waveform groups
The quest for load-independent left ventricular chamber properties: exploring the normalized pressure-volume loopMethods; Tables 1 and 4; Figures 4-5, PDF pp. 6-7

PAP peaks1 1 – 1Pass · Construction / load guard

Measurement

Algorithmic full-cycle PA pressure peak count, thresholded PV forward-episode count, primary-episode PV flow peak count and maximal post-episode PA rebound. The episode threshold and peak-prominence algorithm define these observations; the post-episode rebound is not an invasive dicrotic-notch metric. One peak does not characterize the entire pressure or flow contour.

Design interval, not a normal range: 1 – 1

Rationale and interpretation

Record Standard70 pulmonary ringing and re-ejection guards as construction-only waveform criteria. No primary normal distribution supports the exact one-peak, one-episode or rebound cutoffs. A qualitative Doppler flow shape must not be cited as proof of these pressure-waveform thresholds.

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRVOT Doppler flow, p. 158

PV flow episodes1 1 – 1Pass · Construction / load guard

Measurement

Design interval, not a normal range: 1 – 1

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRVOT Doppler flow, p. 158

PV flow peaks1 1 – 1Pass · Construction / load guard

Measurement

Design interval, not a normal range: 1 – 1

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRVOT Doppler flow, p. 158

PAP closure rebound0 mmHg0 – 0.5Pass · Construction / load guard

Measurement

Design interval, not a normal range: 0 – 0.5 mmHg

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRVOT Doppler flow, p. 158

Numerical quality and morphology checks

Settlement checks periodic differences of the full accepted state. Morphology checks do not impose a universal dome on measured PV loops. Peak phase/roundness context is separate from unexplained ringing and closure-rebound guards.

LVP/RVP morphology uses outlet flow above max(1 mL/s, 1% of peak flow), distinct from ET's full positive-flow duration.

Significance is algorithmic, not statistical. Search each side to a higher peak or boundary; count prominence above the higher valley if at least max(0.5 mmHg, 5% of episode pressure range).

\mathrm{variation}=\frac{\sum_i|P_{i+1}-P_i|}{P_{max}-P_{min}}

Variation sums absolute successive pressure changes divided by episode pressure range. Central roundness uses the middle 25–75% sample range divided by full range, with peak phase retained as context.

Period-1: Cycles: 54 · Consecutive passes: 3 · Normalized tolerance: 0.001
LVP / RVP: Significant peaks / variation ratio: 1 / 1.16 · 1 / 1.28. Variation limit: 2.2
LV τ: Weiss 32.04 ms (R² 0.9963), Glantz 52.43 ms (P∞ -20.33 mmHg). 26 samples. Different asymptote models are not judged by the same cutoff.

P(t)=P_{\infty}+A\exp(-(t-t_0)/\tau)

τ fits pressure decay exponentially. A is pressure above the asymptote at t₀. Weiss fixes P∞=0; Glantz fits it. Neither directly measures the material viscoelastic constant.

τ fitting requires at least 6 points, 15 ms, 10 mmHg. Required R²: Weiss 0.97, Glantz 0.95; normalized error ≤ 0.05.

dP/dt sensitivity, 2 ms versus 1 ms (not a full convergence proof): LV +: 1.38% / LV −: 1.12% / RV +: 2.85% / RV −: 1.01%

Low/high-volume preload reserve

Each changed-TBV endpoint is settled at fixed HR/tone controls. Both ventricles are assessed for CO, filling pressure, EDV and transmural end-filling pressure responses. Floors preserve model response headroom; they are not normal saline-response intervals.

TBV (low/baseline/high): 4,342.8 / 4,935 / 5,527.2 mL

Condition	ΔCO	Δ filling P	ΔEDV	Δ end-diastolic Ptm
LV −TBV	−19.96%	−3.41 mmHg	−30.85 mL	−6.41 mmHg
LV +TBV	+15.03%	+4.62 mmHg	+24.76 mL	+9.62 mmHg
RV −TBV	−19.97%	−0.96 mmHg	−30.6 mL	−1.21 mmHg
RV +TBV	+15.01%	+1.63 mmHg	+32.1 mL	+1.9 mmHg

Changes are relative to baseline. Filling pressure uses mean LA for LV and mean RA for RV. Floors apply to decreases on the low-volume limb and increases on the high-volume limb, with margins exceeding grid sensitivity.

Two-grid agreement is not a full convergence proof. Detailed endpoint τ/morphology assessment is outside this admission scope. No afterload test is included.

Kumar 2004, healthy-volunteer saline-loading study; method context only, not our fixed-tone thresholds

Baseline assessment

This is the saved baseline assessment, not an on-demand assessment of the current workbench scenario. Passing required checks is distinct from matching every source reference interval.

Qualification belongs to this baseline, not application of healthy criteria to HFrEF. Formal adoption, publication and clinical validation are separate.

Reference flags: PAP min / LV +dP/dt / LV −dP/dt / LV ICT / LV Tei

Reference cautions are listed above. Even an in-range value does not establish measurement equivalence or validity across clinical cases.

1 ms · independent cold qualification

Open a row for its measurement method, adopted/source ranges and rationale. Values come from each record's final settled beat. Unsupported thresholds are identified as such.

Pressure, output and valve gradients

CI2.95 L/min/m²2.5 – 4Pass · Operating target

Measurement

Adopted, source-informed: 2.5 – 4 L/min/m²
resting adult RHC reference · published-reference-interval: 2.5 – 4 L/min/m²

Rationale and interpretation

Resting unassisted nonshunting sinus research construction, BSA1.9, HR60 or70, zero intrathoracic reference. Scientific eligibility for exact-model promotion, not public mint or clinical normality.

2022 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertensionTable 11, CI

CVP / mean RAP3.08 mmHg2 – 6Pass · Operating target

Measurement

Absolute lumped pressure, no respiratory cycle; compare with supine end-expiratory catheter values at the specified zero. No catheter transfer function or peripheral waveform is simulated.

Adopted, source-informed: 2 – 6 mmHg
resting adult RHC reference · published-reference-interval: 2 – 6 mmHg

Rationale and interpretation

Resting unassisted nonshunting sinus research construction, BSA1.9, HR60 or70, zero intrathoracic reference. Scientific eligibility for exact-model promotion, not public mint or clinical normality.

2022 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertensionTable 11, mean RAP

mean PAP17.87 mmHg8 – 20Pass · Operating target

Measurement

Absolute lumped pressure, no respiratory cycle; compare with supine end-expiratory catheter values at the specified zero. No catheter transfer function or peripheral waveform is simulated.

Adopted, source-informed: 8 – 20 mmHg
resting adult RHC reference · published-reference-interval: 8 – 20 mmHg

Rationale and interpretation

Resting unassisted nonshunting sinus research construction, BSA1.9, HR60 or70, zero intrathoracic reference. Scientific eligibility for exact-model promotion, not public mint or clinical normality.

2022 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertensionTable 11, mean PAP

AoP max111.4 mmHg90 – 140Pass · Construction / load guard

Measurement

Design interval, not a normal range: 90 – 140 mmHg
women 20-29 · published-10th-90th-percentiles: 80 – 110 mmHg
men 20-29 · published-10th-90th-percentiles: 92 – 115 mmHg
women 30-39 · published-10th-90th-percentiles: 84 – 119 mmHg
men 30-39 · published-10th-90th-percentiles: 88 – 120 mmHg
women 40-49 · published-10th-90th-percentiles: 87 – 123 mmHg
men 40-49 · published-10th-90th-percentiles: 90 – 123 mmHg
women 50-59 · published-10th-90th-percentiles: 93 – 127 mmHg
men 50-59 · published-10th-90th-percentiles: 96 – 126 mmHg
women 60-69 · published-10th-90th-percentiles: 97 – 129 mmHg
men 60-69 · published-10th-90th-percentiles: 97 – 128 mmHg
women 70+ · published-10th-90th-percentiles: 100 – 131 mmHg
men 70+ · published-10th-90th-percentiles: 99 – 130 mmHg

Rationale and interpretation

Establishing reference values for central blood pressure and its amplification in a general healthy population and according to cardiovascular risk factorsMethods, invasive versus cuff-calibrated pressure distinction

AoP min77.55 mmHg60 – 90Pass · Construction / load guard

Measurement

Source assumes DBP consistency for calibration, but does not publish a central-DBP normal interval. Do not turn the brachial mean +/- SD into a verified Ao-node cutoff.

Design interval, not a normal range: 60 – 90 mmHg

Rationale and interpretation

Establishing reference values for central blood pressure and its amplification in a general healthy population and according to cardiovascular risk factorsMethods, DBP calibration; no central-DBP reference interval

LV end-filling P10.94 mmHg≤ 16Pass · Construction / load guard

Measurement

Native inlet-closure LV pressure; not validated catheter LVEDP equivalence.

Design interval, not a normal range: ≤ 16 mmHg

Rationale and interpretation

Recommendations for the Evaluation of Left Ventricular Diastolic Function by Echocardiography and for Heart Failure With Preserved Ejection Fraction Diagnosis: An Update From the American Society of EchocardiographySection2, Table1 p539 (>16), Figure1 p540

PAP max26.17 mmHg15 – 30Reference

Measurement

Absolute lumped pressure, no respiratory cycle; compare with supine end-expiratory catheter values at the specified zero. No catheter transfer function or peripheral waveform is simulated.

resting adult RHC reference · published-reference-interval: 15 – 30 mmHg

Rationale and interpretation

Source comparison, not an automatic rejection threshold; account for method differences.

2022 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertensionTable 11, systolic PAP; section 5.1.12.1

PAP min12.03 mmHg4 – 12Outside reference · Reference

Measurement

Absolute lumped pressure, no respiratory cycle; compare with supine end-expiratory catheter values at the specified zero. No catheter transfer function or peripheral waveform is simulated.

resting adult RHC reference · published-reference-interval: 4 – 12 mmHg

Rationale and interpretation

Source comparison, not an automatic rejection threshold; account for method differences.

2022 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertensionTable 11, diastolic PAP; section 5.1.12.1

mean LAP (PCWP surrogate)8.38 mmHg≤ 15Reference

Measurement

adult RHC PAWP clinical reference · clinical-upper-limit: ≤ 15 mmHg

Rationale and interpretation

Source comparison, not an automatic rejection threshold; account for method differences.

2022 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertensionTable 11, PAWP; section 5.1.12.1

SVI42.19 mL/m²33 – 47Reference

Measurement

resting adult RHC reference · published-reference-interval: 33 – 47 mL/m²

Rationale and interpretation

Source comparison, not an automatic rejection threshold; account for method differences.

2022 ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertensionTable 11, SVI; section 5.1.12.1

AV mean ΔP4.27 mmHg0 – 5Pass · Construction / load guard

Measurement

Design interval, not a normal range: 0 – 5 mmHg

Rationale and interpretation

No primary source establishes this cutoff as a normal range. It remains a design check or context.

AV peak ΔP7.86 mmHg0 – 10Pass · Construction / load guard

Measurement

Design interval, not a normal range: 0 – 10 mmHg

Rationale and interpretation

No primary source establishes this cutoff as a normal range. It remains a design check or context.

PV mean ΔP4.45 mmHg0 – 5Pass · Construction / load guard

Measurement

Design interval, not a normal range: 0 – 5 mmHg

Rationale and interpretation

No primary source establishes this cutoff as a normal range. It remains a design check or context.

PV peak ΔP7.42 mmHg0 – 10Pass · Construction / load guard

Measurement

Design interval, not a normal range: 0 – 10 mmHg

Rationale and interpretation

No primary source establishes this cutoff as a normal range. It remains a design check or context.

Ventricular volumes and ejection fraction

LV EDVI75.64 mL/m²46 – 91Pass · Operating target

Measurement

Adopted intersection of both sex strata (design choice): 46 – 91 mL/m²
men, pooled adult ages · published-reference-interval: 46 – 104 mL/m²
women, pooled adult ages · published-reference-interval: 46 – 91 mL/m²

Rationale and interpretation

Society for Cardiovascular Magnetic Resonance reference values (normal values) in cardiovascular magnetic resonance: 2025 updateTable 2, anatomical segmentation, sex-specific indexed volume/EF rows

LV ESVI33.45 mL/m²11 – 34Pass · Operating target

Measurement

Adopted intersection of both sex strata (design choice): 11 – 34 mL/m²
men, pooled adult ages · published-reference-interval: 11 – 41 mL/m²
women, pooled adult ages · published-reference-interval: 11 – 34 mL/m²

Rationale and interpretation

Society for Cardiovascular Magnetic Resonance reference values (normal values) in cardiovascular magnetic resonance: 2025 updateTable 2, anatomical segmentation, sex-specific indexed volume/EF rows

LVEF55.78 %55 – 79Pass · Operating target

Measurement

Adopted intersection of both sex strata (design choice): 55 – 79 %
men, pooled adult ages · published-reference-interval: 53 – 79 %
women, pooled adult ages · published-reference-interval: 55 – 80 %

Rationale and interpretation

Society for Cardiovascular Magnetic Resonance reference values (normal values) in cardiovascular magnetic resonance: 2025 updateTable 2, anatomical segmentation, sex-specific indexed volume/EF rows

RV EDVI74.06 mL/m²49 – 99Pass · Operating target

Measurement

Adopted intersection of both sex strata (design choice): 49 – 99 mL/m²
men, pooled adult ages · published-reference-interval: 49 – 117 mL/m²
women, pooled adult ages · published-reference-interval: 47 – 99 mL/m²

Rationale and interpretation

Society for Cardiovascular Magnetic Resonance reference values (normal values) in cardiovascular magnetic resonance: 2025 updateTable 8, anatomical segmentation, sex-specific indexed volume/EF rows

RV ESVI31.87 mL/m²12 – 43Pass · Operating target

Measurement

Adopted intersection of both sex strata (design choice): 12 – 43 mL/m²
men, pooled adult ages · published-reference-interval: 12 – 56 mL/m²
women, pooled adult ages · published-reference-interval: 11 – 43 mL/m²

Rationale and interpretation

Society for Cardiovascular Magnetic Resonance reference values (normal values) in cardiovascular magnetic resonance: 2025 updateTable 8, anatomical segmentation, sex-specific indexed volume/EF rows

RVEF56.97 %49 – 77Pass · Operating target

Measurement

Adopted intersection of both sex strata (design choice): 49 – 77 %
men, pooled adult ages · published-reference-interval: 44 – 77 %
women, pooled adult ages · published-reference-interval: 49 – 77 %

Rationale and interpretation

Society for Cardiovascular Magnetic Resonance reference values (normal values) in cardiovascular magnetic resonance: 2025 updateTable 8, anatomical segmentation, sex-specific indexed volume/EF rows

Contraction, relaxation and filling

AV ET255 ms248 – 336Reference

Measurement

Copenhagen pooled healthy adults; HR 63 +/- 10 · published-reference-interval: 248 – 336 ms

Rationale and interpretation

Source comparison, not an automatic rejection threshold; account for method differences.

Age- and sex-based normal reference ranges of the cardiac time intervals: the Copenhagen City Heart StudyMethods, Cardiac time intervals; Table 2, pooled LVET 95% prediction interval

PV ET258 msNo numeric intervalReference

Measurement

Rationale and interpretation

Source comparison, not an automatic rejection threshold; account for method differences.

Reference values for pulsed Doppler signals from the blood flow velocity on both sides of the pulmonary valveAbstract: population and recording stations; no numeric adult ET interval verified

LV +dP/dt2,600.1 mmHg/s1,200 – 2,500Outside reference · Reference

Measurement

Historical corridor, context only: 1,200 – 2,500 mmHg/s

Rationale and interpretation

Contractile and relaxation reserve of the left ventricle. I. Normal left ventricleAbstract; resting values before ergometer exercise
A clinical study of left ventricular relaxationMethods p. 757; normal-control table p. 759; abstract

LV −dP/dt-1,556.3 mmHg/s-1,400 – -700Outside reference · Reference

Measurement

Historical corridor, context only: -1,400 – -700 mmHg/s

Rationale and interpretation

Contractile and relaxation reserve of the left ventricle. I. Normal left ventricleAbstract; resting values before ergometer exercise
A clinical study of left ventricular relaxationMethods p. 757; normal-control table p. 759; abstract

MV E/A0.93 0.8 – 2Reference

Measurement

Historical corridor, context only: 0.8 – 2

Rationale and interpretation

Recommendations for the Evaluation of Left Ventricular Diastolic Function by Echocardiography and for Heart Failure With Preserved Ejection Fraction Diagnosis: An Update From the American Society of EchocardiographyTables 3 and 5 (p. 551)

LV ICT93.14 ms20 – 70Outside reference · Reference

Measurement

Historical corridor, context only: 20 – 70 ms

Rationale and interpretation

Age- and sex-based normal reference ranges of the cardiac time intervals: the Copenhagen City Heart StudyTable 2; Methods, Cardiac time intervals

LV IRT94 ms59 – 134Reference

Measurement

Historical corridor, context only: 59 – 134 ms

Rationale and interpretation

Age- and sex-based normal reference ranges of the cardiac time intervals: the Copenhagen City Heart StudyTable 2; Methods, Cardiac time intervals

LV Tei0.73 0.29 – 0.65Outside reference · Reference

Measurement

Historical corridor, context only: 0.29 – 0.65

Rationale and interpretation

Age- and sex-based normal reference ranges of the cardiac time intervals: the Copenhagen City Heart StudyTable 2; Methods, Cardiac time intervals

RV +dP/dt602.8 mmHg/s300 – 1,000Reference

Measurement

Historical corridor, context only: 300 – 1,000 mmHg/s

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRV dP/dt section, pp. 158-159
Effect of chronic pressure overload on the maximal rate of pressure fall of the right ventricleAbstract; normal-PAP and pulmonary-hypertension groups

RV −dP/dt-375.7 mmHg/s-700 – -150Reference

Measurement

Historical corridor, context only: -700 – -150 mmHg/s

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRV dP/dt section, pp. 158-159
Effect of chronic pressure overload on the maximal rate of pressure fall of the right ventricleAbstract; normal-PAP and pulmonary-hypertension groups

TV E/A1.09 0.8 – 2Reference

Measurement

Historical corridor, context only: 0.8 – 2

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyTable 1; RV diastolic function, pp. 168-169

RV ICT28 ms20 – 90Reference

Measurement

Historical corridor, context only: 20 – 90 ms

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRV MPI, pp. 158-159; IVRT, pp. 168-169

RV IRT64 ms30 – 120Reference

Measurement

Historical corridor, context only: 30 – 120 ms

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRV MPI, pp. 158-159; IVRT, pp. 168-169

RV Tei0.36 0.25 – 0.65Reference

Measurement

Historical corridor, context only: 0.25 – 0.65

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRV MPI, pp. 158-159; IVRT, pp. 168-169

LV τ (Weiss)31.74 ms≤ 48Reference

Measurement

Time-weighted exponential fit of intracavitary LVP from the minimum-dP/dt midpoint to next EDP +5 mmHg, before MVO; zero asymptote. Not interchangeable with free-asymptote Glantz τ.

Prolongation context, not a normal distribution: ≤ 48 ms

Rationale and interpretation

τ and fit usability, residuals and window sensitivity are separate checks. Source pressure is not smoothed.

Recommendations for the Evaluation of Left Ventricular Diastolic Function by Echocardiography and for Heart Failure With Preserved Ejection Fraction Diagnosis: An Update From the American Society of EchocardiographyInvasive relaxation reference; Weiss asymptote/method must be matched

Numerical and waveform checks

Period-1Met Criteria metPass · Numerical quality

Measurement

Design interval, not a normal range: Criteria met

Rationale and interpretation

Fail closed before interpreting any derived baseline measurement. No clinical population interval applies to an exact periodic-classifier contract.

No primary source establishes this cutoff as a normal range. It remains a design check or context.

LVP ringingMet Criteria metPass · Construction / load guard

Measurement

Design interval, not a normal range: Criteria met

Rationale and interpretation

No primary source establishes this cutoff as a normal range. It remains a design check or context.

LVP contour20.48 %8 – 35Reference

Measurement

Historical corridor, context only: 8 – 35 %

Rationale and interpretation

Aortic input impedance in normal man: relationship to pressure wave formsAuthor-institution abstract; ascending aortic pressure waveform groups
The quest for load-independent left ventricular chamber properties: exploring the normalized pressure-volume loopMethods; Tables 1 and 4; Figures 4-5, PDF pp. 6-7

RVP ringingMet Criteria metPass · Construction / load guard

Measurement

Design interval, not a normal range: Criteria met

Rationale and interpretation

No primary source establishes this cutoff as a normal range. It remains a design check or context.

RVP contour18.71 %8 – 35Reference

Measurement

Historical corridor, context only: 8 – 35 %

Rationale and interpretation

Aortic input impedance in normal man: relationship to pressure wave formsAuthor-institution abstract; ascending aortic pressure waveform groups
The quest for load-independent left ventricular chamber properties: exploring the normalized pressure-volume loopMethods; Tables 1 and 4; Figures 4-5, PDF pp. 6-7

PAP peaks1 1 – 1Pass · Construction / load guard

Measurement

Design interval, not a normal range: 1 – 1

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRVOT Doppler flow, p. 158

PV flow episodes1 1 – 1Pass · Construction / load guard

Measurement

Design interval, not a normal range: 1 – 1

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRVOT Doppler flow, p. 158

PV flow peaks1 1 – 1Pass · Construction / load guard

Measurement

Design interval, not a normal range: 1 – 1

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRVOT Doppler flow, p. 158

PAP closure rebound0 mmHg0 – 0.5Pass · Construction / load guard

Measurement

Design interval, not a normal range: 0 – 0.5 mmHg

Rationale and interpretation

Guidelines for the Echocardiographic Assessment of the Right Heart in Adults and Special Considerations in Pulmonary Hypertension: Recommendations from the American Society of EchocardiographyRVOT Doppler flow, p. 158

Numerical quality and morphology checks

LVP/RVP morphology uses outlet flow above max(1 mL/s, 1% of peak flow), distinct from ET's full positive-flow duration.

Significance is algorithmic, not statistical. Search each side to a higher peak or boundary; count prominence above the higher valley if at least max(0.5 mmHg, 5% of episode pressure range).

\mathrm{variation}=\frac{\sum_i|P_{i+1}-P_i|}{P_{max}-P_{min}}

Period-1: Cycles: 54 · Consecutive passes: 3 · Normalized tolerance: 0.001
LVP / RVP: Significant peaks / variation ratio: 1 / 1.17 · 1 / 1.29. Variation limit: 2.2
LV τ: Weiss 31.74 ms (R² 0.9961), Glantz 52.75 ms (P∞ -21.35 mmHg). 50 samples. Different asymptote models are not judged by the same cutoff.

P(t)=P_{\infty}+A\exp(-(t-t_0)/\tau)

τ fits pressure decay exponentially. A is pressure above the asymptote at t₀. Weiss fixes P∞=0; Glantz fits it. Neither directly measures the material viscoelastic constant.

τ fitting requires at least 6 points, 15 ms, 10 mmHg. Required R²: Weiss 0.97, Glantz 0.95; normalized error ≤ 0.05.

dP/dt sensitivity, 2 ms versus 1 ms (not a full convergence proof): LV +: 1.38% / LV −: 1.12% / RV +: 2.85% / RV −: 1.01%

Low/high-volume preload reserve

TBV (low/baseline/high): 4,342.8 / 4,935 / 5,527.2 mL

Condition	ΔCO	Δ filling P	ΔEDV	Δ end-diastolic Ptm
LV −TBV	−19.96%	−3.39 mmHg	−30.86 mL	−6.38 mmHg
LV +TBV	+15.05%	+4.62 mmHg	+24.83 mL	+9.46 mmHg
RV −TBV	−19.96%	−0.96 mmHg	−30.58 mL	−1.13 mmHg
RV +TBV	+15.05%	+1.62 mmHg	+32.14 mL	+1.96 mmHg

Two-grid agreement is not a full convergence proof. Detailed endpoint τ/morphology assessment is outside this admission scope. No afterload test is included.

Kumar 2004, healthy-volunteer saline-loading study; method context only, not our fixed-tone thresholds

History and reproducibility

Changes in this version

This model supports two fixed anatomies: baseline and chronic LV-dilated HFrEF. This page describes the shared model and baseline; disease settings and assessments have a separate case document.

Pinned identities and evidence record

The model, presentation/analysis definition (Surface), baseline and admission policy have separate identities. SHA-256 identifies identical records; it is not a quality score.

Model: circleheart.main-wire-integrated-transaction-v3.static-anatomy.standard-73
Surface: circleheart.main-wire.surface.static-anatomy.standard-73.workbench-v1
baseline: standard73-baseline-v1
Policy: main-wire-prospective-baseline-admission-v1
Construction SHA-256: 0ba2640b3dfa59aa23eb260bca23d1fe41ef3a14f5076d9cea716dc80e7779e5
Qualification checkpoint SHA-256: 816ca45e592525aca9501a70a88ac20186f7fc1ee559166b4b325c8a02ea6f79
Launch checkpoint SHA-256: 4b881697899904e7a66fa5095db92208270942ef5734d0cbd2d9b964717ea4bf

Own-model independent cold 2/1 ms runs assess rest and fixed-control low/high preload responses. Baseline starts from its own checkpoint, with 1,000-step source/artifact continuation checked.

Analysis methods pinned by the Surface

analysis/main-wire-integrated-v3-formal-fixed-tbv-pressure-volume-relations-v1
analysis/main-wire-integrated-v3-guyton-starling-structural-orientation-v1
derivation/suga-pva-measured-load-display-exact-anatomy-mvo2-v14

Download presentation and measurement record