Simulate Doppler ultrasound (PW and CW) for non-invasive blood-flow measurement in the carotid, cardiac and cerebral circulation. Vary the transmit frequency, insonification angle and PRF to see the Doppler shift, Nyquist velocity, aliasing condition and maximum imaging depth update in real time, and design clinically realistic measurement settings.
Parameters
Transmit frequency f0
MHz
Higher = better resolution but more attenuation
Blood velocity v
cm/s
Carotid ~100, MCA ~55, femoral ~90, AS jet ~400
Insonification angle theta
deg
Beam-to-flow angle. Errors blow up above 60 deg
PRF
Hz
Pulse repetition frequency. Nyquist = PRF/2
Speed of sound c
m/s
Typical value in soft tissue is 1540 m/s
Gate depth
mm
Depth of the vessel being interrogated
Vessel type
Sets a typical Pulsatility Index (PI)
Results
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Doppler shift (kHz)
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Nyquist frequency (kHz)
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Nyquist velocity (cm/s)
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Max imaging depth (cm)
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Angle error sensitivity (%/deg)
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Aliasing
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Probe, vessel and Doppler trace
The probe transmits a beam that meets the vessel at angle theta. Red blood cells back-scatter the wave with the Doppler shift f_d. The lower panel shows the spectral trace with the Nyquist limit (red dashed).
Maximum imaging depth d_max and the Nyquist limit (PRF/2). Raising PRF lifts Nyquist but lowers d_max — the classical PW Doppler trade-off.
Ultrasound Doppler Blood Flow — Aliasing and PSV/EDV
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When the echo machine in the hospital makes that "whoosh, whoosh" sound, is that actually the sound of blood flowing?
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Good question. It is not the blood itself making sound — it is the shift in frequency between the transmitted ultrasound and the wave that bounces back off moving red blood cells, played out loud. That is the Doppler effect: an ambulance siren sounds higher when it approaches and lower when it recedes, and blood does the same thing. The equation is f_d = 2 f0 v cos(theta) / c, and with the defaults the tool reports about 3.25 kHz — right in the audible range, which is why those waveforms are also fed to a loudspeaker.
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I see. But if I push the beam angle from 60 to 70 degrees on the left, the numbers jump. Why?
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It is cos(theta) at work. At theta = 0 the cosine is 1 and the shift is maximum; at theta = 90 deg it is zero, so a beam perpendicular to flow shows no Doppler signal at all. The painful part is the inversion v = f_d c / (2 f0 cos(theta)) where 1/cos(theta) amplifies any pointing error. At 60 deg, tan = 1.732 so a 1 degree mis-aim is about 3% velocity error; at 70 deg about 5%; at 80 deg roughly 10%. That is why every clinical guideline writes "keep theta no more than 60 degrees" in bold.
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The "Aliasing" cell reads "yes" with the defaults. What is actually happening to the signal?
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PW Doppler is not continuous — it fires short pulses at a rate PRF. By the sampling theorem you can only measure frequencies up to PRF/2 (the Nyquist limit). With f_d = 3.25 kHz but Nyquist = 2.5 kHz the spectrum wraps around the baseline and the trace looks like flow has suddenly reversed. In an echocardiogram you see a jet that was pointed right suddenly pointing left — almost always a PRF problem, not a real flow reversal.
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So just crank up the PRF and we are done, right? Sounds easy.
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Ultrasound never gives you something for free. A pulse has to make its round trip before the next pulse fires, so d_max = c / (2 PRF). Double the PRF and you halve the maximum depth. For a deep fetal heart you cannot crank PRF; for the superficial carotid you can push it up to 10 kHz and beat the aliasing. The last resort is CW Doppler — continuous wave, no velocity limit, but no range resolution, so you only get "the fastest flow somewhere along the beam". For severe aortic stenosis CW is mandatory.
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People keep saying PSV and EDV. What are they?
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PSV is Peak Systolic Velocity — the per-beat peak — and EDV is End Diastolic Velocity — the minimum near end-diastole. For the internal carotid, PSV > 230 cm/s and EDV > 100 cm/s suggest >=70% stenosis, which is the trigger for carotid endarterectomy. The Pulsatility Index PI = (PSV - EDV)/Vmean is the pulsatility marker: about 1.5 in the carotid, about 0.8 in the low-resistance MCA, about 4.0 in the high-resistance femoral artery. That is why the tool sets a typical PI for the vessel you pick.
Frequently Asked Questions
Pulsed-wave (PW) Doppler samples the returning echo at the pulse repetition frequency PRF, so by the Nyquist sampling theorem the highest detectable frequency is PRF/2 (the Nyquist limit). When the Doppler shift f_d = 2f0 v cos(theta)/c exceeds PRF/2, the spectral trace wraps around the baseline and appears to reverse direction — this is aliasing. Common remedies are: (1) raise the PRF (at the cost of shallower maximum depth), (2) switch to a lower-frequency probe, (3) shift the spectral baseline, or (4) switch to continuous-wave (CW) Doppler, which has no velocity limit.
Inverting the Doppler equation to obtain velocity gives v proportional to 1/cos(theta), so the smaller cos(theta) is (the larger theta is), the more a 1-degree pointing error is magnified into a velocity error. At theta = 60 deg (cos=0.5, tan=1.732) a 1-degree error gives about 3% velocity error, at 70 deg about 5%, and at 80 deg roughly 10%. Clinical guidelines therefore recommend theta no more than 60 deg. Theta = 0 (beam parallel to flow) is theoretically optimal but rarely possible for superficial vessels like the carotid; practical scans use 45-60 deg.
PSV (Peak Systolic Velocity) is the per-beat peak flow speed; EDV (End Diastolic Velocity) is the minimum speed at end of diastole. In the internal carotid artery, PSV > 125 cm/s suggests >=50% stenosis, and PSV > 230 cm/s with EDV > 100 cm/s suggests >=70% high-grade stenosis, directly informing the decision for carotid endarterectomy (CEA) or stenting. In the heart, the simplified Bernoulli equation deltaP = 4 v^2 (mmHg) converts the peak velocity across a stenotic aortic valve into a pressure gradient and is the cornerstone of valve-stenosis grading.
Each pulse must complete a round trip through tissue before the next pulse is fired, so the maximum unambiguous depth is d_max = c / (2 PRF) with c about 1540 m/s. PRF = 5 kHz gives d_max about 15.4 cm; doubling PRF to 10 kHz cuts it to 7.7 cm. Deep vessels (portal vein, abdominal aorta) therefore force a low PRF and a low Nyquist limit, making aliasing more likely for fast jets. This is the fundamental limit of PW Doppler; for deep high-velocity flow (e.g. severe aortic stenosis) one switches to CW Doppler, which has no velocity ceiling but no range resolution.
Real-World Applications
Carotid ultrasound (stroke screening): Estimating the degree of carotid stenosis from common and internal carotid PSV/EDV is the standard non-invasive method for assessing stroke risk. PSV > 230 cm/s combined with EDV > 100 cm/s flags >=70% high-grade stenosis and drives the decision for carotid endarterectomy (CEA) or stenting. The carotid is shallow (depth 2-4 cm), so 7.5-10 MHz probes give the high spatial resolution required.
Echocardiography (valve function): In aortic stenosis (AS) grading, CW Doppler measures the peak jet velocity v across the valve, and the simplified Bernoulli equation deltaP = 4 v^2 yields the pressure gradient. v = 4 m/s gives deltaP = 64 mmHg, a marker of severe AS. The same principle drives mitral-regurgitation jet evaluation, PDA/VSD shunt assessment, and the estimation of pulmonary pressures from tricuspid regurgitation.
Fetal Doppler (fetal wellbeing): Doppler traces from the umbilical artery, middle cerebral artery (MCA) and ductus venosus characterise fetal circulation. Absent or reversed end-diastolic flow in the umbilical artery (AEDV/REDV) signals severe placental insufficiency, often triggering early delivery for fetal growth restriction. The fetus sits deep (5-15 cm), so 3.5-5 MHz probes are used.
Intra-operative imaging and dialysis-access monitoring: During vascular anastomosis or kidney transplantation, high-frequency intra-operative probes (10-15 MHz) check flow across the new join in real time, catching narrowing or thrombus immediately. In dialysis patients, fistula flow Qa below 500 mL/min signals impending occlusion and is the standard Doppler indication for percutaneous transluminal angioplasty (PTA).
Common Misconceptions and Pitfalls
The biggest pitfall is reading a velocity without correctly aligning the angle-correction cursor with the vessel. The machine computes v = f_d c / (2 f0 cos(theta)), and theta is set by you, on screen, by drawing a cursor along "the flow direction" — it is not measured automatically. A few degrees of misalignment can throw the displayed velocity off enough to push PSV above or below the 230 cm/s threshold and invert the CEA decision. Always align the cursor against the colour-Doppler flow direction (not against the vessel wall), and keep theta no more than 60 deg. This is the number-one error for new sonographers.
Second, "hiding" aliasing by widening the velocity range. Shifting the baseline or switching to HPRF (High PRF) mode removes the wrap-around from the picture, but only at the cost of losing the true velocity. HPRF in particular generates multiple range gates, so signal from a depth other than the displayed gate can leak in (range ambiguity) — you can mix up flow from a superficial and a deep vessel. The safe priority is: (1) drop to a lower-frequency probe to lower f_d itself, (2) reduce the angle, (3) shift the baseline, (4) switch to CW if nothing else works.
Third, treating PI or RI as an absolute number. Pulsatility Index (PI) and Resistance Index (RI) are popular markers of vascular resistance, but they swing with heart rate, blood pressure, age and drugs (beta-blockers, vasodilators). Jumping from "fetal MCA PI rose from 0.8 to 1.2" to "placental function has improved" is dangerous without also accounting for changes in maternal heart rate and pressure. Clinically, PI/RI are interpreted by their trend over time (compared with the prior study) or by ratios across vessels (e.g. MCA/UA ratio), not by a single absolute value.
How to Use
Select ultrasound transducer frequency (2–14 MHz typical for vascular imaging; 5 MHz for carotid, 7–10 MHz for cardiac).
Enter blood velocity in cm/s (normal carotid systolic: 80–120 cm/s; diastolic: 20–40 cm/s).
Set insonification angle in degrees (0° = optimal parallel flow; maximum 60° to avoid cosine error exceeding 50%).
Adjust pulse repetition frequency (PRF in Hz; higher PRF extends Nyquist velocity but reduces penetration depth).
Read Doppler shift in kHz, Nyquist limits, and aliasing warnings to confirm measurement validity.
Worked Example
Carotid artery CW Doppler: 7 MHz transducer, blood velocity 95 cm/s, insonification angle 60°, PRF 5 kHz. Calculated Doppler shift = (7×10⁶ Hz × 2 × 95 cm/s × cos(60°)) / 154,000 cm/s ≈ 4.3 kHz. Nyquist frequency = PRF/2 = 2.5 kHz; velocity aliased (4.3 > 2.5). Increase PRF to 10 kHz for Nyquist velocity 97 cm/s, eliminating wrap-around. Max imaging depth ≈ (speed of sound × pulse duration) / 2 = 12 cm at this PRF.