Hemodynamics & Doppler Measurements

Laminar vs Turbulent Flow

Laminar flow is orderly: red blood cells move in smooth, parallel layers (streamlines) without significant mixing between layers. On the spectral display, laminar flow produces a narrow, well-defined waveform with a clear spectral window beneath the systolic peak (see 9.6).

Turbulent flow is disorganized: red blood cells move in many directions and at many velocities simultaneously, colliding and mixing chaotically. Turbulence typically develops distal to a stenosis, at a vessel bifurcation, or wherever velocity becomes very high, and it produces spectral broadening — the window fills in because a wide range of velocities and directions are present at the same instant.

Plug vs Parabolic Flow Profiles

Flow profile describes how velocity varies across the width of the vessel lumen, not over time:

Plug flow tends to evolve into a parabolic profile as blood travels farther from the heart and encounters more friction against the vessel wall along its length.

The Simplified Bernoulli Equation

⚠ ΔP = 4v², where ΔP is the pressure gradient in mmHg and v is the peak velocity in m/s measured at, or just downstream of, a stenosis or stenotic valve.

This equation converts a velocity measurement — something ultrasound measures directly and accurately — into a clinically meaningful pressure gradient, without needing an invasive catheter. It is central to echocardiographic grading of valve stenosis, for example estimating the gradient across a stenotic aortic valve, and to grading vascular stenoses elsewhere in the body.

Worked example: a peak velocity of 3 m/s across a stenotic valve gives ΔP = 4 × (3)² = 4 × 9 = 36 mmHg.

Resistive Index & Pulsatility Index

Both indices quantify downstream vascular resistance using only the peak systolic velocity (PSV) and end-diastolic velocity (EDV) read off the spectral waveform — no angle correction is needed for either ratio, because the angle term cancels out of the calculation.

Both indices are used to characterize downstream vascular beds — for example, a high-resistance waveform with little or no diastolic flow (high RI) versus a low-resistance waveform with brisk continuous diastolic flow (low RI) — in applications spanning renal and hepatic transplant surveillance, testicular torsion evaluation, and umbilical artery assessment in obstetrics.

Worked example: PSV = 80 cm/s, EDV = 20 cm/s gives RI = (80 − 20)/80 = 60/80 = 0.75. Using the same values with a mean velocity of 40 cm/s gives PI = (80 − 20)/40 = 60/40 = 1.5.

RI is bounded between 0 and 1 and cannot exceed 1 even when diastolic flow is absent or reversed, so PI is often the more discriminating index in very high-resistance beds where RI would simply flatten near its ceiling. Because both indices are ratios built from the same two velocities read directly off the waveform, neither requires angle correction to calculate — a frequent exam trap pairs RI or PI with a distractor answer that incorrectly invokes cosθ.

Solving the Doppler Equation for Velocity

The Doppler shift equation from 9.1 can be rearranged to solve for the one unknown sonographers actually want: the true blood flow velocity.

⚠ v = (f_D · c) / (2 · f_t · cosθ)

Where f_D is the measured Doppler shift, c is the propagation speed of sound in soft tissue (1540 m/s), f_t is the transducer's transmit frequency, and θ is the Doppler angle between the ultrasound beam and the direction of flow. Because cosθ appears in the denominator, an inaccurate angle estimate directly distorts the calculated velocity — the reason 9.2's 60-degree-or-less angle rule and careful angle-correction cursor placement matter so much for any measurement that depends on this equation.

Formula Reference Table

Why This Matters on the Exam

SPI loves plug-and-chug calculation items built from this exact table: give PSV and EDV and ask for RI or PI, give a peak velocity and ask for the Bernoulli gradient, or give f_D, f_t, and θ and ask for velocity. Also expect conceptual items distinguishing plug from parabolic flow profile and laminar from turbulent flow pattern — these two pairs are frequently confused with each other on the exam despite describing entirely different things: spatial profile across the lumen versus organization of flow over time.