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A Computational Investigation of the Effect of Venous Valve Morphology on Flow Conditions Conducive to Thrombus Formation

This computational study utilizing a fluid–solid interaction model reveals that venous valve morphology significantly influences both pumping performance and thrombosis-conducive flow conditions, demonstrating that while shorter, deeper-cut, and more flexible valves generally improve hemodynamics by reducing fluid stasis and shear stress, these modifications must be balanced against the risk of compromising valve closure and allowing backflow.

Original authors: Matthew S. Ballard, Connor Stong, Jacob Biesinger

Published 2026-09-22

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Matthew S. Ballard, Connor Stong, Jacob Biesinger

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Deep within the veins of the legs, a silent and critical struggle takes place every time a person stands or walks. While the heart pumps blood with force through the arteries, it lacks the reach to push that same blood all the way back up from the feet against the pull of gravity. To solve this, the body relies on a chain of tiny, one-way doors called venous valves. These flexible flaps open to let blood flow toward the heart when leg muscles squeeze, and snap shut to stop it from sliding backward. However, these same valves are also the birthplace of a dangerous condition known as deep vein thrombosis, where blood clots form and can travel to the lungs. For decades, doctors have known that these clots often start in the small pockets of fluid trapped behind the valve flaps, but the precise reason why some valves are more likely to cause trouble than others has remained a mystery.

A team of researchers at Utah Valley University has now used a powerful computer simulation to peer inside these microscopic chambers and watch how the shape of the valve itself changes the flow of blood. Instead of working with real patients or physical models, the scientists built a virtual, three-dimensional replica of a vein and a valve, filling it with a digital fluid that behaves like blood. They then ran thousands of simulations, systematically altering the physical properties of the valve to see how each change affected the movement of the fluid. Their goal was to understand how the length of the valve, the depth of the cut at its tip, and its stiffness influence two things: how easily blood can move forward, and how much blood gets stuck in the pockets behind the flaps where clots are likely to form.

The researchers discovered that the geometry of the valve creates a delicate balance between efficiency and safety. When they made the valves longer or cut the tips more shallowly, the valves became very good at stopping blood from flowing backward. However, this came at a cost: the longer, shallower valves created larger pockets of stagnant fluid behind them. In these pockets, the blood moved so slowly that it essentially stopped, creating a perfect environment for a clot to begin forming. Conversely, when the researchers shortened the valves or cut the tips deeper, the blood flowed more freely with less resistance, and the stagnant pockets became smaller. Yet, if the valves were cut too deep or made too short, they failed to seal properly, allowing significant amounts of blood to leak backward, which defeats the purpose of the valve entirely.

Stiffness played an equally vital role in this equation. The simulations showed that valves made of stiffer material struggled to open fully, creating more resistance to forward flow, and they also struggled to close tightly, allowing more backflow. More flexible valves, however, were able to bend easily to let blood through and then snap shut to block it. Crucially, the most flexible valves also created the smallest regions of stagnant fluid. The computer models revealed that the most dangerous areas were always the pockets behind the valve leaflets, where the fluid remained nearly motionless throughout the entire pumping cycle. These stagnant zones were largest when the valves were long, stiff, and had shallow tips.

The study suggests that the risk of clot formation is not just a matter of blood chemistry, but is deeply tied to the physical shape of the valve itself. The findings indicate that valves which are shorter, have deeper cuts at the tips, and are made of more flexible material are less likely to create the stagnant conditions that lead to thrombosis. While the researchers note that their work is based on simulations and that real human veins are more complex, the results point toward a new way of thinking about venous health. By understanding how specific morphological features influence blood flow, doctors may one day be able to look at a patient's valve structure through imaging and predict their risk of developing a clot, potentially leading to better prevention strategies for those most vulnerable to this life-threatening condition.

Technical Summary: A Computational Investigation of the Effect of Venous Valve Morphology on Flow Conditions Conducive to Thrombus Formation

Problem Statement
Venous thromboembolism (VTE), encompassing deep vein thrombosis (DVT) and pulmonary embolism (PE), is a leading cause of preventable death, frequently originating near venous valves. While the role of hypercoagulability is well-studied, the specific influence of venous valve morphology on the hemodynamic conditions that promote thrombosis—specifically fluid stasis and low shear stress—remains under-characterized. Previous computational studies have largely relied on simplified two-dimensional models or limited 3-D simulations that did not systematically vary valve geometry. Consequently, there is a gap in understanding how specific morphological parameters (such as valve length, tip shape, and stiffness) interact to influence both valve pumping performance and the creation of thrombosis-conducive flow environments.

Methodology
The authors employed a fully coupled three-dimensional fluid-solid interaction (FSI) computational model to simulate blood flow through venous valves.

Fluid Mechanics: Blood flow was modeled using the Lattice Boltzmann Method (LBM) with a D3Q19 lattice, treating blood as a Newtonian fluid. This approach is efficient for complex, moving geometries.
Solid Mechanics: The flexible bi-leaflet valve leaflets were modeled using a Lattice Spring Model (LSM), treating the leaflets as thin, linearly elastic plates discretized into mass nodes connected by stretching and bending springs.
Geometry and Parameters: The simulation domain consisted of a rigid venous sinus with a flexible bi-leaflet valve. The study systematically varied three dimensionless parameters:
- Aspect Ratio ( $A$ ): The ratio of valve leaflet length to vein diameter.
- Depth of Cut ( $D_c$ ): A dimensionless measure of the crescent-shaped tip removal (ranging from shallow to deep cuts).
- Dimensionless Bending Stiffness ( $K$ ): Representing the balance between elastic forces and pressure forces.
Simulation Conditions: Both steady-state simulations (forward and reverse flow) and dynamic simulations (oscillating pressure gradients mimicking muscle contractions) were performed. The Reynolds number was kept below 1 to focus on viscous effects.
Metrics: Valve performance was quantified via normalized fluid resistance (forward flow), normalized fluid conductance (reverse flow/leakage), and the volume percentage of fluid experiencing low normalized shear stress ( $P_L$ , defined as regions where $T \leq 0.05$ ).

Key Contributions
This study provides a systematic characterization of how venous valve morphology influences hemodynamics, moving beyond single-geometry analyses to explore the trade-offs between valve competence (blocking backflow) and flow efficiency. The work introduces a comprehensive 3-D FSI framework that isolates the effects of aspect ratio, tip geometry, and stiffness on specific flow conditions known to correlate with thrombus initiation.

Results
The computational investigation yielded several distinct findings regarding the interplay between morphology and flow:

Dynamic Flow Behavior: Dynamic simulations confirmed that valve pockets behind the leaflets maintain persistent regions of low velocity and low shear stress throughout the oscillatory cycle, even when the valve is functioning correctly. These regions represent potential sites for thrombus initiation.
Aspect Ratio ( $A$ ) and Stiffness ( $K$ ):
- Forward Flow: Resistance to forward flow increases monotonically with both higher $A$ (longer valves) and higher $K$ (stiffer valves).
- Reverse Flow: Conductance (leakage) increases with higher $K$ . Stiffer valves are prone to incomplete closure, especially at lower aspect ratios. Effective closure requires valves to be sufficiently long ( $A \gtrsim 1.4$ ) and flexible.
Depth of Cut ( $D_c$ ):
- Forward Flow: Valves with deep cuts (high $D_c$ ) offer minimal resistance to forward flow as they protrude less into the lumen.
- Reverse Flow: However, deep cuts compromise valve competence. As $D_c$ increases, the ability to seal against backflow diminishes, leading to significant leakage. A critical threshold exists (approximately $0.4 \leq D_c \leq 0.5$ for the tested stiffness range) above which valves fail to close effectively.
Shear Stress and Stasis:
- The volume of fluid in low-shear regions ( $P_L$ ) increases with higher aspect ratios ( $A$ ) and higher stiffness ( $K$ ).
- Conversely, $P_L$ decreases as the depth of cut ( $D_c$ ) increases.
- Longer valves and shallower cut tips enlarge regions of low shear stress and fluid stasis within valve pockets. Conversely, shorter valves and deeper cuts reduce resistance and decrease regions of low shear stress and fluid stasis, provided the valve geometry remains within a critical threshold that allows for effective closure. If the valve is too short or the cut is too deep, closure is impaired, allowing substantial backflow which creates distinct flow conditions.

Significance and Claims
The paper concludes that venous valve morphology strongly dictates both pumping performance and the hemodynamic conditions conducive to thrombosis. The authors claim that:

Optimal Morphology for Hemodynamics: Valves with lower aspect ratios ( $A$ ), lower stiffness ( $K$ ), and deeper cuts ( $D_c$ ) minimize regions of fluid stasis and low shear stress, theoretically reducing thrombotic risk.
The Competence Trade-off: While shorter, deeper-cut, and more flexible valves improve hemodynamics, they must remain within specific geometric limits to maintain valve competence (preventing backflow). If $A$ is too low or $D_c$ is too high, the valve fails to close, allowing substantial backflow.
Clinical Implications: The findings suggest that patients with stiff, overly long, or shallow-cut venous valves may be at elevated risk for VTE. The authors posit that this understanding could eventually aid in identifying high-risk patients via imaging prior to prolonged immobility (e.g., hospital stays) and inform the design of prophylactic devices.

The authors maintain a modest tone, acknowledging that their model simplifies physiological conditions (e.g., treating blood as Newtonian and using simplified pressure waveforms) and that predicting actual thrombosis requires further integration of biological factors and residence time kinetics. They view this work as a foundational step toward more complex models and physical validation.

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