Frequency-Dependent Impact of Arterial Wall Compliance on Hemodynamic Predictions: A Fluid–Structure Interaction Study

Technical Summary: Frequency-Dependent Impact of Arterial Wall Compliance on Hemodynamic Predictions

Problem Statement
Fluid–structure interaction (FSI) is recognized as the most physiologically realistic approach for simulating arterial hemodynamics, capturing critical phenomena such as pulse-wave propagation and the Windkessel effect. However, due to the high computational cost and complexity of FSI, rigid-wall computational fluid dynamics (CFD) models remain widely employed in both research and clinical applications. While previous studies have discussed the consequences of neglecting arterial compliance regarding pulse-wave velocity, pressure damping, and wall shear stress, there is limited understanding of how the discrepancy between compliant and rigid-wall models depends on the frequency of pulsatile excitation. This is particularly relevant because the characteristic time of pulse-wave propagation is comparable to the duration of the cardiac cycle; thus, as heart rate increases, the interaction between wave propagation, reflection, and transient blood volume storage may become increasingly significant.

Methodology
To isolate the influence of arterial compliance from geometric complexity, the authors developed a fully coupled FSI model of an idealized, straight cylindrical vessel representing the descending thoracic aorta (50 cm length, 2 cm inner diameter, 0.1 cm wall thickness). The study utilized an axisymmetric two-dimensional formulation to balance computational efficiency with physical fidelity.

• Constitutive Modeling: The arterial wall was modeled as an incompressible, anisotropic, hyperelastic material using the Gasser–Ogden–Holzapfel (GOH) model, which accounts for two families of collagen fibers with angular dispersion. Material parameters were adopted from in vivo data. Blood was modeled as an incompressible Newtonian fluid.
• Boundary Conditions: The outer wall was supported by a spring foundation to simulate surrounding tissue. Residual stresses were incorporated via a prestressing procedure. The inlet was driven by a volumetric flow-rate waveform adjusted to represent heart rates of 1, 1.5, 2, and 2.5 Hz (60–150 bpm), maintaining a constant stroke volume of 70 ml. The outlet employed a grille boundary condition to introduce pressure loss dependent on mass flow rate.
• Simulation Protocol: Simulations were performed for four cardiac cycles to eliminate initial condition effects. Results from the compliant FSI model were compared against a corresponding rigid-wall model under identical boundary conditions.

Key Results
The study demonstrated that the hemodynamic discrepancies between compliant and rigid-wall models are strongly frequency-dependent and increase substantially with heart rate.

• Pulse-Wave Velocity (PWV): The model successfully reproduced physiological pulse-wave propagation, yielding a simulated PWV of 2.69 m/s, which aligns closely with the theoretical Bramwell–Hill estimate of 2.56 m/s.
• Transient Fluid Storage: In the compliant model, the finite propagation speed of the pressure wave caused a phase shift between inflow and outflow, resulting in transient storage of blood volume within the vessel. This "buffering" effect, characteristic of the Windkessel function, increased in magnitude with higher heart rates.
• Pressure Predictions: This was the most significant area of divergence. While pressure extrema in the compliant model changed only marginally (approx. 0.5 kPa) across the 1–2.5 Hz range, the rigid-wall model predicted a substantial increase in systolic pressure and a decrease in diastolic pressure (variation exceeding 4 kPa). The rigid-wall model increasingly overestimated the pressure required to generate a prescribed pulsatile flow as heart rate rose.
• Velocity and Wall Shear Stress (WSS): The compliant model exhibited delayed flow development and lower peak velocities compared to the rigid-wall model. While the difference in maximum velocity remained relatively constant, the difference in minimum velocity and WSS grew progressively with frequency. At 2.5 Hz, the divergence in WSS predictions was approximately twice that observed at 1 Hz.

Significance and Claims
The authors conclude that the errors introduced by the rigid-wall assumption are not constant but increase systematically with heart rate. This limitation arises because rigid models cannot reproduce the compliance-driven mechanisms of transient fluid storage and pressure-wave damping.

The study posits that while rigid-wall simulations may yield acceptable errors under resting physiological conditions, their validity cannot be assessed independently of the characteristic frequency of the flow. Consequently, the authors assert that when CFD simulations are applied to conditions involving elevated heart rates, increased physical activity, or heightened cardiovascular demand, the compliance of the arterial system must be explicitly incorporated to ensure accurate hemodynamic predictions. The paper does not claim rigid-wall models are universally invalid but highlights a specific, frequency-dependent limitation that becomes critical under non-resting conditions.