18.3 Cardiac Hemodynamics, Bernoulli, Continuity, Stroke Volume, and Shunts

Treat equations as models with units

CCI task D14 is to evaluate cardiac hemodynamics. Every calculation starts with a verified anatomic site, a clean Doppler envelope, correct units, and a stated assumption. Color locates acceleration, PW samples a discrete level, and CW records the highest velocity along the entire beam. Align as parallel as possible because measured velocity equals true velocity × cos θ; angle error underestimates velocity, and squaring magnifies the gradient error. Average appropriate beats and use matched cycles in irregular rhythm.

Apply Bernoulli to the right question

The simplified Bernoulli equation ΔP = 4V² estimates the peak instantaneous pressure difference across a high-velocity jet. At 4.0 m/s, ΔP is 4 × 16 = 64 mmHg. It is not the same as a catheter peak-to-peak gradient. A Doppler mean gradient is calculated by tracing the velocity envelope so the system integrates instantaneous gradients over ejection; it is not 4 times the square of the mean velocity.

The simplified form neglects proximal velocity. That is usually reasonable when V₁ is below about 1.5 m/s and much smaller than V₂. If V₁ is important, use 4(V₂² − V₁²). With V₂ = 4.0 and V₁ = 1.5 m/s, the corrected gradient is 4(16 − 2.25) = 55 mmHg, not 64 mmHg. Serial obstructions, long tunnels, pressure recovery, poor alignment, high-output states, and very low flow weaken simple interpretations. For MR, TR, VSD, or aortic coarctation, confirm the jet identity and the relevant upstream pressure assumptions before converting velocity to chamber pressure.

Build stroke volume and continuity from one flow cylinder

For laminar flow through a circular site, SV = CSA × VTI. Measure diameter perpendicular to flow at the prescribed anatomic level, square it to obtain area, and place PW at the corresponding flow site without spectral broadening or acceleration. With LVOT diameter 2.0 cm and LVOT VTI 20 cm, CSA = 0.785 × 2.0² = 3.14 cm² and SV = 3.14 × 20 = 62.8 mL/beat. At 75 beats/min, CO = 62.8 × 75 / 1000 = 4.71 L/min. If BSA is 1.8 m², CI = 4.71/1.8 = 2.62 L/min/m².

Diameter is the dominant error because it is squared. A 5% diameter overmeasurement produces 1.05² = 1.1025, about a 10% area and SV overestimate, before VTI error is added. An oval or off-axis outflow tract, calcified border, wrong phase, sample too close to the valve, and mismatched ectopic beats can therefore produce a precise-looking but inaccurate output. VTI tracing should follow the dense modal velocity, not faint noise. Average multiple beats when rhythm or respiration varies.

Continuity assumes that the same volume crosses two sites during the same time interval with no intervening shunt or important regurgitant loss. For aortic stenosis, AVA = CSA LVOT × VTI LVOT / VTI AV. Using the example above and an aortic VTI of 80 cm gives AVA = 3.14 × 20 / 80 = 0.785 cm². The dimensionless index, VTI LVOT/VTI AV = 0.25, removes the LVOT diameter but does not remove sampling or alignment errors. In subaortic obstruction, significant AR, irregular rhythm, or discordant low-flow states, document assumptions and integrate morphology, gradients, SV index, EF, and other evidence.

Quantify shunts without hiding the weak link

For one intracardiac left-to-right shunt with no important semilunar regurgitation, Qp/Qs = (CSA RVOT × VTI RVOT) / (CSA LVOT × VTI LVOT). A ratio above 1 indicates pulmonary flow exceeds systemic flow; below 1 suggests net right-to-left flow or a measurement/problem configuration that must be reconciled. The ratio is unitless because mL/beat divides by mL/beat. Report which pulmonary and systemic sites were used.

Measure RVOT and LVOT diameters and PW VTIs at their matched sites using the same rhythm and comparable beats. Because two squared diameters enter the ratio, small independent errors can produce a large false shunt. Pulmonary or aortic regurgitation, multiple shunts, PDA location, anomalous venous return, cavopulmonary connections, mechanical support, and changing loading violate the simple model. Color and agitated saline define direction or pathway but do not replace quantitative flow when Qp/Qs is needed. Conversely, a calculated ratio must agree with chamber remodeling and defect anatomy. If it does not, remeasure before reporting; use CMR or invasive oximetry when echo remains unreliable.

Regurgitant calculations use the same conservation principle: regurgitant volume equals total SV across the regurgitant valve minus forward SV at a nonregurgitant reference site, in mL/beat; regurgitant fraction is regurgitant volume divided by total SV × 100%. Different annular shapes, rhythm, and more than one regurgitant lesion magnify error. Hemodynamic calculations support severity only after image quality, assumptions, and units survive this audit.