Advanced Hemodynamics: PISA/EROA, Pressure Half-Time, dP/dt, Qp/Qs & RVSP

From Core Flow Math to Advanced Hemodynamics

Building on the modified Bernoulli equation and VTI-based flow calculations from Section 6.4, several derived calculations let sonographers quantify regurgitant lesions, estimate valve area without planimetry, assess ventricular contractility, quantify intracardiac shunts, and estimate pulmonary artery pressure — all non-invasively, at the bedside, without cardiac catheterization. Each formula below builds directly on the modified Bernoulli equation, VTI, and stroke-volume relationships already introduced, so the constants and units are worth memorizing precisely rather than approximating.

PISA and Effective Regurgitant Orifice Area (EROA)

The proximal isovelocity surface area (PISA) method exploits the fact that blood accelerating toward a regurgitant orifice forms concentric, roughly hemispheric shells of equal velocity. Shifting the color Doppler baseline to lower the Nyquist (aliasing) limit — typically to 20–40 cm/s — makes one shell visible as a color aliasing boundary with a measurable radius (r). Because flow through a hemisphere equals its surface area times velocity, the instantaneous flow rate through that shell is 2πr² × Valiasing. Dividing that flow rate by the peak regurgitant jet velocity (from CW Doppler) yields the effective regurgitant orifice area:

EROA = (2πr² × Valiasing) / Peak V (regurgitant jet)

with r and Valiasing in consistent units (typically cm and cm/s) so EROA is in cm². Multiplying EROA by the regurgitant jet's own VTI gives regurgitant volume: RVol = EROA × VTI (regurgitant jet), in mL. Full severity grading using EROA and RVol thresholds is covered with mitral regurgitation in Chapter 7.4.

Pressure Half-Time and Mitral Valve Area

Pressure half-time (PHT) is the time interval, in milliseconds, for the peak transvalvular diastolic gradient to fall to half its initial value — equivalently, the time for the Doppler velocity to decline to Vmax/√2 (since pressure is proportional to velocity squared). Hatle's empirical formula converts PHT to mitral valve area:

MVA = 220 / PHT

PHT is derived from the slope of the mitral E-wave deceleration on CW Doppler and relates to deceleration time (DT) as PHT ≈ 0.29 × DT, giving the equivalent form MVA = 759/DT. PHT-derived MVA is the standard non-invasive method for grading native mitral stenosis severity, but it becomes unreliable immediately after balloon valvuloplasty, with significant coexisting aortic regurgitation, or with arrhythmias/tachycardia that shorten diastolic filling.

dP/dt: Rate of LV Pressure Rise

dP/dt estimates the rate of left ventricular pressure rise during isovolumic contraction — a relatively load-independent index of contractility — from the continuous-wave mitral regurgitation jet. The sonographer measures the time interval (in seconds) for the MR jet velocity to rise from 1 m/s to 3 m/s. By the modified Bernoulli equation, the pressure difference between those two velocities is fixed: 4(3² − 1²) = 4 × 8 = 32 mmHg. So:

dP/dt = 32 mmHg / time (seconds, 1→3 m/s on the MR CW envelope)

Normal LV contractility corresponds to dP/dt ≥1200 mmHg/s; values <1000 mmHg/s indicate impaired systolic function.

Qp/Qs Shunt Ratio

The Qp/Qs ratio compares pulmonary blood flow (Qp), measured at the RVOT, to systemic blood flow (Qs), measured at the LVOT, using the same stroke-volume formula from Section 6.4 at each site:

Qp/Qs = (CSA_RVOT × VTI_RVOT) / (CSA_LVOT × VTI_LVOT)

A ratio of 1.0 indicates no significant shunt. Qp/Qs >1.5 indicates a hemodynamically significant left-to-right shunt (e.g., ASD, VSD, PDA) and is a commonly used threshold when considering closure; a ratio <1.0 suggests a net right-to-left shunt.

RV Systolic Pressure and PA Pressure Estimation

Applying the modified Bernoulli equation to the tricuspid regurgitation (TR) jet, and adding an estimate of right atrial pressure (RAP), gives right ventricular systolic pressure — which, absent pulmonic stenosis or RVOT obstruction, equals pulmonary artery systolic pressure:

RVSP = 4 × (TR Vmax)² + RAP

RAP is estimated from the inferior vena cava, imaged in the subcostal view 1–2 cm from the IVC–RA junction:

An RVSP ≥35–40 mmHg is generally abnormal and, together with a resting TR velocity ≥2.9 m/s plus adjunctive echo signs, raises suspicion for pulmonary hypertension. Mean PA pressure can be estimated similarly from the pulmonic regurgitation end-diastolic velocity: mean PAP = 4 × (PR end-diastolic velocity)² + RAP, when a PR jet is present.

Worked examples:

• PISA/EROA: r = 1.0 cm, Valiasing = 40 cm/s, peak MR velocity = 500 cm/s (5 m/s) → EROA = (6.28 × 1.0² × 40) / 500 = 0.50 cm²
• dP/dt: 1→3 m/s interval = 25 ms (0.025 s) → dP/dt = 32 / 0.025 = 1280 mmHg/s (normal contractility)
• Qp/Qs: RVOT diameter 2.4 cm, RVOT VTI 25 cm (Qp = 0.785×2.4²×25 = 113.1 mL) vs. LVOT diameter 2.0 cm, LVOT VTI 20 cm (Qs = 0.785×2.0²×20 = 62.8 mL) → Qp/Qs = 113.1/62.8 = 1.80 (significant left-to-right shunt)
• RVSP: TR Vmax 3.0 m/s, RAP 8 mmHg → RVSP = 4 × 3.0² + 8 = 36 + 8 = 44 mmHg (elevated, consistent with pulmonary hypertension)