Fundamental Principles of Hemodynamics #4: Laminar vs Turbulent Flow

1. Core Concept

Blood flow in the cardiovascular system exists along a spectrum from laminar flow to disturbed or turbulent flow. These patterns are not merely theoretical fluid mechanics concepts; they directly influence pressure gradients, energy loss, wall shear stress, thrombosis risk, endothelial biology, and the performance of surgically reconstructed cardiovascular pathways.

In congenital heart disease and cardiac surgery, understanding flow pattern is especially important because many operative results depend not only on an anatomically open pathway, but also on whether that pathway provides efficient, low-resistance, low-energy-loss flow [1].

2. Laminar Flow

Laminar flow is orderly, layered, and directionally organized. In an idealized straight vessel, fluid particles move in parallel layers with minimal transverse mixing.

The velocity profile is classically parabolic:

• Velocity is highest at the center of the vessel.
• Velocity progressively decreases toward the wall.
• Velocity approaches zero at the endothelial surface because of the no-slip boundary condition.

Blood elements are also not distributed randomly across the lumen. Red blood cells tend to migrate centrally, while plasma and platelets are relatively displaced toward the peripheral near-wall zone. This marginal platelet-rich layer becomes clinically relevant in regions of low flow, disturbed flow, prosthetic material, and abnormal wall shear stress.

Key features of laminar flow include:

• Parallel streamlines
• Predictable axial flow
• Minimal flow separation
• Relatively efficient energy transfer
• Lower energy loss compared with disturbed flow
• More physiologic endothelial shear conditions

Normal arterial flow is often predominantly laminar, although secondary flow, curvature, pulsatility, branching, and stenosis can substantially modify the velocity profile [2].

3. Turbulent and Disturbed Flow

Turbulent flow is disorganized and multidirectional. It is characterized by velocity fluctuation, eddies, vortices, flow separation, and increased energy dissipation.

In the cardiovascular system, fully developed turbulence is not the only clinically important abnormal pattern. Disturbed flow, transitional flow, vortical flow, and turbulent-like flow can all be clinically relevant, especially in reconstructed congenital pathways.

Turbulent or disturbed flow may produce:

• Audible murmurs
• Doppler spectral broadening
• Color Doppler aliasing
• Increased pressure gradient
• Flow separation distal to stenosis
• Abnormal wall shear stress
• Endothelial dysfunction
• Platelet activation
• Thrombosis
• Intimal proliferation
• Progressive stenosis or pathway inefficiency

A murmur is therefore not simply the sound of a narrowed valve or vessel. It is the acoustic consequence of vibration and energy dissipation generated by disturbed, high-velocity flow.

4. Reynolds Number

The tendency for laminar flow to become turbulent is estimated by the Reynolds number:

Re = ρvD / μ

where:

• Re = Reynolds number
• ρ = fluid density
• v = mean velocity
• D = vessel diameter
• μ = dynamic viscosity

Reynolds number represents the balance between inertial forces and viscous forces.

Turbulence becomes more likely when:

• Flow velocity increases
• Vessel diameter increases at a given velocity
• Blood viscosity decreases
• Flow passes through a stenosis
• Flow encounters abrupt expansion
• Flow enters a sharp bend or angulation
• A high-velocity jet strikes a vessel wall
• There is geometric irregularity after surgical reconstruction

In classic rigid-tube fluid mechanics, turbulence is often described as becoming likely when Reynolds number exceeds approximately 2000. In cardiovascular physiology, this threshold is not absolute. Blood is pulsatile and non-Newtonian, vessels are compliant, and congenital heart anatomy is frequently curved, narrowed, bifurcated, patched, or reconstructed.

Therefore, Reynolds number should be interpreted as a conceptual index of disturbed-flow tendency, not as a rigid clinical cutoff.

5. Transition from Laminar to Turbulent Flow

The transition from laminar to turbulent flow depends on the interaction between velocity, viscosity, diameter, and geometry.

Computational analysis of stenosed coronary arteries has shown that transitional turbulence may begin when area stenosis exceeds approximately 50%, with more fully turbulent behavior above approximately 70% stenosis. These changes are associated with significant alterations in wall shear stress and oscillatory shear index [3].

Clinical data after coronary angioplasty also support the relationship between disturbed flow and adverse outcomes. In one study of 97 patients, higher coronary flow velocity and higher Reynolds number after intervention were associated with increased risk of adverse clinical events during follow-up [4].

Although these studies are not congenital heart surgery studies, they are useful because they demonstrate a general principle: high velocity and disturbed flow are not benign mechanical findings. They can be linked to clinically important vascular outcomes.

6. Wall Shear Stress

Wall shear stress is the tangential frictional force generated by flowing blood along the endothelial surface.

Physiologic laminar shear stress helps maintain endothelial homeostasis. In contrast, abnormal shear patterns may promote vascular injury or maladaptive remodeling.

Disturbed flow can create several abnormal shear environments:

• High shear at jet impact sites
• Low shear in recirculation zones
• Oscillatory shear near bifurcations
• Excessive shear in curved small-caliber shunts
• Flow separation distal to stenosis
• Nonuniform shear along patch-augmented pathways

These shear abnormalities may contribute to:

• Platelet activation
• Thrombus formation
• Endothelial dysfunction
• Intimal hyperplasia
• Anastomotic stenosis
• Patch or conduit-related remodeling
• Progressive pathway inefficiency

In central aorta-to-pulmonary artery shunt models, angulation was associated with very high wall shear stress and shear rates, sufficient to promote platelet-mediated thrombosis. Reported wall shear stresses reached approximately 80–200 N/m², with shear rates of approximately 16,000–40,000/s at sites of even modest curvature [5].

This has a direct surgical implication: a shunt may be technically patent but still hemodynamically unfavorable if its geometry creates excessive shear and energy loss.

7. Energy Loss

Turbulent and disturbed flow dissipate mechanical energy. Instead of being preserved as organized forward flow, kinetic energy is lost through eddies, vortices, viscous dissipation, and wall shear stress.

Energy loss is particularly important in congenital heart surgery because many reconstructions function under limited driving pressure.

Examples include:

• Systemic-to-pulmonary shunts
• Right ventricle-to-pulmonary artery conduits
• Branch pulmonary artery reconstructions
• Glenn circulation
• Fontan circulation
• Neo-aortic reconstruction after Norwood procedure
• Patch-augmented aortic or pulmonary pathways

In Fontan connections, computational work has identified wall shear stress as a major mechanism of energy loss within the cavopulmonary pathway [6]. This is clinically important because the Fontan circulation lacks a subpulmonary ventricle. Even modest inefficiency can increase central venous pressure, reduce pulmonary blood flow, impair ventricular preload, and limit cardiac output.

Blood viscosity also matters. Patient-specific Fontan modeling has shown that shear-dependent changes in viscosity can increase power loss, particularly under low-cardiac-output conditions [7]. Therefore, Fontan flow efficiency depends not only on conduit geometry, but also on flow rate, viscosity, and the low-shear venous environment.

8. Surgical Relevance in Congenital Heart Disease

8.1 Systemic-to-Pulmonary Shunts

Systemic-to-pulmonary shunts are vulnerable to high-velocity flow, small-caliber geometry, angulation, and abrupt changes in direction.

Important surgical considerations include:

• Avoiding unnecessary angulation
• Avoiding kinking
• Avoiding excessive length
• Avoiding sharp inflow or outflow angles
• Ensuring smooth anastomotic transitions
• Avoiding size mismatch between shunt and target pulmonary artery
• Considering both patency and shear environment

A shunt that is open but highly angulated may generate excessive wall shear stress, platelet activation, thrombosis risk, and energy loss [5].

8.2 Branch Pulmonary Artery Reconstruction

Branch pulmonary artery stenosis produces high-velocity jets, distal flow separation, and pressure loss. Patch reconstruction should aim not only to enlarge the vessel but also to restore a smooth flow path.

Important technical goals include:

• Smooth patch contour
• No residual waist at the suture line
• No abrupt caliber transition
• Avoidance of pouch-like expansion
• Preservation of branch angle
• Balanced distribution to both lungs

Excessive turbulence or energy loss across reconstructed pulmonary arteries may be especially consequential in Glenn or Fontan physiology, where pulmonary blood flow is passive or preload-dependent.

8.3 Glenn Circulation

In the bidirectional Glenn, superior vena caval flow enters the pulmonary arteries without a subpulmonary ventricle. Flow is driven by systemic venous pressure and low pulmonary vascular resistance.

Direct Glenn-specific evidence linking turbulent transition to clinical outcomes is limited, but the same mechanical principles are relevant. The Glenn anastomosis should avoid:

• Anastomotic narrowing
• Sharp offset between SVC and pulmonary artery
• Competitive or colliding flow streams
• Branch PA stenosis
• Excessive energy loss at the cavopulmonary junction

A technically successful Glenn is therefore not only unobstructed, but also geometrically favorable for low-energy venous flow.

8.4 Fontan Circulation

The Fontan circulation is highly sensitive to energy loss because there is no ventricle pumping blood into the pulmonary arteries.

Fontan pathway inefficiency may contribute to:

• Elevated central venous pressure
• Reduced ventricular preload
• Lower cardiac output
• Exercise limitation
• Pleural effusions
• Hepatic congestion
• Protein-losing enteropathy risk
• Long-term Fontan failure

Wall shear stress is a major mechanism of energy loss in Fontan connections [6]. In addition, non-Newtonian viscosity effects may increase power loss in low-flow Fontan states [7]. Therefore, Fontan design should prioritize smooth, nonobstructive, nonkinked, appropriately sized pathways with minimal flow collision and minimal recirculation.

8.5 Norwood Neo-Aorta

After Norwood reconstruction, the neo-aorta may develop abnormal geometry, diameter irregularity, arch distortion, or stenosis. These changes can generate disturbed or turbulent-like flow.

Recent computational work in post-Norwood patients demonstrated turbulent-like flow patterns in abnormal neo-aortic geometries, particularly in the presence of stenosis or irregular diameter transitions [8].

This supports a practical surgical principle: arch reconstruction should aim for more than relief of obstruction. It should create a smooth, durable, energy-efficient systemic outflow pathway.

8.6 Supravalvar Aortic Stenosis and Patch Repair

In congenital arterial stenoses such as supravalvar aortic stenosis, surgical repair changes not only the diameter of the vessel but also the local flow field. Patient-specific computational modeling has been used to assess changes in pressure drop and wall shear stress before and after repair [9].

This reinforces the broader concept that operative reconstruction should be judged by both anatomic and hemodynamic quality.

8.7 Cardiopulmonary Bypass Cannulation

Cannulae generate high-velocity jets. Small cannula size, excessive flow, malposition, or jet impingement against the aortic wall may produce high shear stress, hemolysis, pressure drop, or vascular injury.

Cannulation strategy should consider:

• Cannula size
• Expected flow rate
• Pressure gradient across the cannula
• Jet direction
• Vessel size
• Aortic wall proximity
• Neonatal or infant vessel fragility

The same principles of velocity, diameter, viscosity, and shear apply during extracorporeal circulation.

9. Practical Clinical Interpretation

In congenital heart surgery, the relevant clinical question is rarely whether flow is perfectly laminar or fully turbulent. The more important question is:

Does the anatomy or reconstruction create unnecessary acceleration, separation, shear, and energy loss?

Assessment may include:

• Intraoperative inspection
• Direct pressure measurement
• Transesophageal echocardiography
• Epicardial echocardiography
• Doppler velocity and gradient assessment
• Color flow mapping
• Postoperative CT
• Cardiac MRI
• Catheterization
• Computational fluid dynamics in selected complex reconstructions

A low-gradient reconstruction is not always ideal if it creates a large recirculation zone, blind pouch, abnormal jet, or thrombotic shear environment. Conversely, a visually open pathway may still be physiologically inefficient if the geometry promotes disturbed flow.

10. Surgical Principles

To minimize disturbed flow and energy loss, surgical reconstruction should aim to:

• Preserve smooth vessel curvature
• Avoid abrupt narrowing
• Avoid abrupt expansion
• Avoid sharp angulation
• Avoid kinking or twisting
• Avoid unnecessary pouch formation
• Match vessel and conduit caliber appropriately
• Create smooth patch transitions
• Prevent residual stenosis at suture lines
• Consider downstream flow distribution
• Consider the interaction between flow rate, viscosity, and pathway geometry

The goal is not simply to make a pathway large. The goal is to create a smooth, durable, low-resistance, low-energy-loss pathway.

11. Key Takeaways

Laminar flow is organized, efficient, and parabolic, with the highest velocity at the center of the vessel and near-zero velocity at the wall.

Turbulent and disturbed flow are disorganized, energy-consuming, and clinically relevant because they produce murmurs, pressure loss, abnormal wall shear stress, endothelial injury, and thrombosis risk.

Reynolds number provides a useful framework for understanding the transition from laminar to turbulent flow, but congenital cardiovascular flow requires interpretation beyond a rigid numerical threshold.

In congenital heart surgery, flow geometry matters. Shunt angulation, branch pulmonary artery stenosis, Fontan pathway design, neo-aortic reconstruction, and cannulation strategy can all influence shear stress, turbulence, and energy loss.

A successful reconstruction should therefore be evaluated not only by anatomic patency, but also by hemodynamic efficiency.

References

[1] Gerrah R, Haller SJ, George I. Mechanical concepts applied in congenital heart disease and cardiac surgery. Ann Thorac Surg. 2017. doi:10.1016/j.athoracsur.2017.01.068.

[2] Ku DN. Blood flow in arteries. Annu Rev Fluid Mech. 1997;29:399-434. doi:10.1146/annurev.fluid.29.1.399.

[3] Mahalingam A, Gawandalkar UU, Kini G, Buradi A, Araki T, Ikeda N, Nicolaides A, Laird J, Saba L, Suri J. Numerical analysis of the effect of turbulence transition on the hemodynamic parameters in human coronary arteries. Cardiovasc Diagn Ther. 2016. doi:10.21037/cdt.2016.03.08.

[4] Kinlay S, Grewal J, Manuelin D, Fang J, Selwyn A, Bittl J, Ganz P. Coronary flow velocity and disturbed flow predict adverse clinical outcome after coronary angioplasty. Arterioscler Thromb Vasc Biol. 2002. doi:10.1161/01.ATV.0000024569.80106.B4.

[5] Celestin C, Guillot M, Ross-Ascuitto N, Ascuitto R. Computational fluid dynamics characterization of blood flow in central aorta to pulmonary artery connections: importance of shunt angulation as a determinant of shear stress-induced thrombosis. Pediatr Cardiol. 2015. doi:10.1007/s00246-014-1055-7.

[6] Moyle K, Mallinson G, Occleshaw C, Cowan B, Gentles T. Wall shear stress is the primary mechanism of energy loss in the Fontan connection. Pediatr Cardiol. 2006. doi:10.1007/s00246-005-0918-3.

[7] Wei H, Cao K, Pahlevan N, Cheng AL. Abstract 12955: Shear-dependent changes in blood viscosity negatively affect energetic efficiency in patient-specific models of the Fontan circulation. Circulation. 2023;148(Suppl 1). doi:10.1161/circ.148.suppl_1.12955.

[8] Tan V, Saprungruang A, Peel B, Macgowan CK, Haller C, Barron DJ, Valverde I, Yoo SJ, Khan MO. Turbulent-like blood flow in neo-aorta in post-Norwood patients. Comput Biol Med. 2025. doi:10.1016/j.compbiomed.2025.110083.

[9] Jack JT, Jensen MO, Collins RT, Chan F, Millett PC. Numerical study of hemodynamic flow in the aortic vessel of Williams syndrome patient with congenital heart disease. J Biomech. 2024. doi:10.1016/j.jbiomech.2024.112124.