Restrictive vs Unrestrictive

The definition of "restriction" in the context of patent ductus arteriosus (PDA) remains somewhat ambiguous, as no universally accepted criteria exist. However, it is generally understood that a "restrictive" structure limits the transmission of flow or pressure. This concept can be simplified as follows:

Unrestrictive PDA: This allows pressure to equalize across both sides of the connected structure, similar to two boxes connected by a large channel.
Restrictive PDA: This limits the amount of pressure or flow, akin to nearly closing off a garden hose.
The "Most" Restrictive PDA is theoretically the one that is closed. Hence, there is no flow through it and no pressure transmission across it. Sometimes, the duct is on the verge of closing, where minimal or no blood flow is observed, especially during diastole when pressure in the aorta and pulmonary artery decreases. During systole, there may be some "stenting" of the lumen of the duct with some flow, which closes of in Diastole. We often call this "closing pattern".

Article https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7717963/ mentions: "Non-restrictive shunts have a low peak systolic velocity with a high systolic to end-diastolic velocity gradient while restrictive shunts have a high peak systolic velocity and a low systolic to diastolic velocity gradient. If the ratio between peak systolic and end-diastolic velocity is >2 then it is considered as a pulsatile flow pattern while a ratio of <2 is described as restrictive shunt suggestive of a closing PDA".

Important caveats:

"High-Velocity Flow": A restrictive PDA typically shows high-velocity flow due to the narrowed ductal lumen. Doppler studies often demonstrate peak systolic velocities greater than 2.5 m/s and sometimes exceeding 3.5 m/s.
"Continuous Flow Pattern": The flow across a restrictive PDA is typically continuous throughout the cardiac cycle, with a high-velocity systolic jet and less pronounced diastolic flow. A restrictive PDA often presents with a significant pressure gradient between the pulmonary artery and the aorta, which can be calculated using the peak Doppler velocity (using the modified Bernoulli equation). A high gradient (e.g., >20 mmHg) suggests a restrictive flow.
The velocity criteria depend on the pressure (and/or resistence) differences between the aorta (AO) and the pulmonary artery (PA). For example, you can have a very small duct that restricts red blood cells from passing through, but if the AO and PA pressures are nearly equal, the flow will be of low velocity. Consider a situation where systolic blood pressure (sBP) is 100 mmHg and systolic pulmonary arterial pressure (sPAP) is 98 mmHg. In this case, very little flow will pass through the ductus (even if it is very tiny), but since sBP is slightly higher than sPAP, the flow will still be left-to-right. However, with only a 2 mmHg difference between the two arteries, the flow will be minimal. If the PDA is extremely narrow, such as (hypothetically) 0.001 mm, it becomes "restrictive" in that it doesn't transmit flow or pressure effectively, but the flow remains of very low velocity. Typically, at this stage, the flow contour would be continuous and non-pulsatile due to the Windkessel Effect.
- The gradient between PA and AO also depends on their respective pressures. For instance, consider a PDA connecting an aorta with pressures of 50/30 mmHg and a pulmonary artery with pressures of 20/10 mmHg. The pressure gradient across the PDA would be a peak of 30 mmHg and an end value of 20 mmHg. The flow would appear continuous and non-pulsatile, yet with a relatively high velocity, such as during systole, where the velocity might reach 2.7 m/s (30 mmHg ~ 4V^2).
- Let's consider an unrestrictive scenario: in this case, all pressure is transmitted across both ends, and the flow will depend on the pulmonary vascular resistance (PVR) to systemic vascular resistance (SVR) ratio. If the aortic pressure is 45/25 mmHg and the pulmonary artery pressure is also 45/25 mmHg, the flow will be from left to right. Unlike the previous example of 50/30 mmHg, this pressure is slightly lower, likely due to the loss of a few mmHg as the flow needs to fill a much larger vascular network, with both the pulmonary and systemic systems being connected.

In life, very few things are absolute. The PDA is a dynamic structure that gradually becomes more restrictive as it closes. As it narrows, it increasingly limits pressure transmission, much like a hose that becomes progressively occluded, restricting the flow.

Some Criteria for a restrictive ductus:

Peak Doppler velocity > 2 m/s
Ductal diameter < 1.5 mm
High pressure gradient across the ductus (>20-30 mmHg)
Continuous Doppler flow with a “sawtooth” appearance on spectral Doppler.

This paper: https://www.ahajournals.org/doi/full/10.1161/CIRCULATIONAHA.105.592063 says "If the ductus is large and offers minimal resistance to flow (nonrestrictive), the degree of shunting depends on the status of the pulmonary vascular resistance. In many children with moderate or large patent ductus, pulmonary vascular resistance remains modestly elevated, which limits the shunting sufficiently to lessen the physiological impact and permit survival and growth"

This paper https://onlinelibrary.wiley.com/doi/10.1097/MPG.0000000000002420 says: "Ductal flow pattern was evaluated from the parasternal short axis using continuous-wave Doppler and, based on the ratio of end-diastolic to peak-systolic velocity, was defined as pulsatile (≥0.5) or restrictive (<0.5)"

This paper https://jamanetwork.com/journals/jamapediatrics/article-abstract/2375129 says: "For a PDA to cause significant shunting from systemic to pulmonary circulation, the flow needs to be unrestrictive and completely or almost completely left to right; the latter is sometimes referred to as a growing pattern. The PDAs of less than 1.5 mm in diameter are considered small because they are commonly restrictive, cause a mild increase in pulmonary circulation, and are rarely associated with echocardiographic markers of a high-volume shunt.12,13 Further subclassification of PDAs of at least 1.5 mm as moderate or large is based on incremental probability of a high-volume shunt. Although the diameter correlates well with shunt volume, using an absolute cutoff to describe hemodynamic significance may be misleading given the interobserver measurement variability (10%-15%) and its dynamic nature."

This paper https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1720677/ says: "The closing pattern suggests a restrictive PDA small enough to prevent a clinically significant left to right shunt. The growing and pulsatile patterns reflect falling pulmonary artery resistance in the presence of a large ductus with clinically significant left to right shunt, and are an indicator for risk of developing clinically significant PDA. Clinicians need to recognise that once pulmonary artery resistance has fallen, if the closing pattern has not developed, the ductus is large enough to create problems."

When there is pressure build-up in the hose, the water comes out with a high velocity, outlining the high pressure gradient between the inside (hose) and the outside (environment / air). Same as the PDA becoming restrictive.

When there is no restriction, the velocity is low and the water drips out. There is no pressure build-up and the pressure on both side are equalizing (i.e. within the garden hose and the environment)

Unrestrictive left to right (pulsatile)

Low diastolic velocity outlining the pressure are equalizing in diastole between the PA and AO. The Flow is pulsatile. There is no Windkessel Effect in the duct itself.

Restrictive left to right (continuous / saw-tooth)

High systolic and diastolic velocities outlining the pressure are being tapered off in systole and diastole across the ductus. There is a Windkessel Effect in the duct itself that creates this continuous flow pattern / sawtooth pattern.

Closing left to right

Closing ductus (the PDA is almost closed, there are moments in the cardiac cycle where there may not be even flow through it).

Colour clip of the "closing ductus"

This is a small, restrictive patent ductus arteriosus (PDA) exhibiting a closing pattern. The PDA is in the process of closing, with detectable high-velocity flow (3.67 m/s) during systole when its caliber is stretched. However, no flow is observed in diastole and early systole when the caliber collapses. Peak velocities may be underestimated, potentially affecting the accurate assessment of the aorto-pulmonary pressure gradient.

Small left to right restrictive

Restrictive L to R low-velocity PDA, gradient of 6 mmHg at peak of systole. PA pressure infra-systemic but 6 mmHg less than systemic. This may be secondary to systemic low pressures, increased pulmonary pressures, or a mix. The PDA is restrictive in the sense there is a continuous sawtooth pattern with systolic and diastolic velocities that are similar.

Small restrictive PDA left to right but with low velocities of flow through it due to near similar AP and AO pressures.

Bidirectional

Bidirectional PDA that is unrestrictive. In this case, the velocities are low and there is rapid equalization of pressure on both end of the duct with low systolic Right to Left velocities (50 cm/s) and low diastolic velocities (60-75 cm/s).

Bidirectional PDA that is restrictive (subjective interpretation). There is a relatively higher systolic right to left component at 2 m/s, outlining that there is some pressure difference between the PA and the Ao in systole (at least 16 mmHg). The diastolic component is also more restrictive with a left to right shunt at 80 cm/s, outlining some restriction to pressure transmission.

Right to left

Right to left ductus (unrestrictive). Here the duct is large and will let pressure transmit from the PA to the Aorta. The flow is right to left. It is likely that the

Doppler (right to left) - Continuous Wave. We see that the velocities in diastole are verly low (close to the baseline, outlining rapid pressure equalization. The peak systolic velocity is around 80 cm/s, also outlining rapid pressure equalization with low velocity of flow in systole (right to left).

Right to left PDA indicating that there is supra-systemic PA pressure. This could be due to increased PA pressure, low systemic pressure or a mix of both component. The PDA is small, there is aliasing by colour. This Duct is restricting flow/pressure transmission.

Example of CW-Doppler in the Right to Left PDA, indicating that the PA pressure is 46 mmHg above the Ao pressure at peak of systole (3.4 m/s). Because of its restriction, there is significant pressure build up within the duct with some flow in diastole. The velocity of flow gets close to baseline before the end of the cardiac cycle, possibly because PA pressures are getting closer to diastolic pressure at that timepoint, or the duct lumen is closing towards end of diastole (if it is quite small) not letting much pass through it before the next systolic phase.