In vivo evidence of blood flow slippage: failure of the no-slip boundary condition assumption

TL;DR

The study tests the no-slip assumption for arterial blood flow in vivo by combining 3D Navier–Stokes modeling with a Navier slip boundary and a data-assimilation framework that fits an inlet velocity field and a slip parameter from seven 4D flow MRI datasets. By introducing the auxiliary variable $K=\ln\kappa$, the approach can handle spatially varying slip and produce an optimal $\kappa_{opt}$ that better matches measurements than no-slip. Across datasets, clear wall slip is observed, with average wall tangential velocities constituting a substantial fraction of the lumen speed, and corresponding reductions in wall shear stress. These findings imply that boundary conditions critically influence predicted pressure drops, vorticity, and energy dissipation, with broad implications for cardiovascular modeling and disease interpretation.

Abstract

The assumption that blood adheres to vessel walls, the ``no-slip'' boundary condition, is an essential premise of cardiovascular fluid dynamics. Yet, whether it holds true \emph{in vivo} has not been established. Using 4D flow magnetic resonance imaging of the human thoracic aorta and modeling blood as a Navier--Stokes fluid, we quantify the velocity of blood at the wall. We find tangential wall velocities of about 30--80\% of the mean luminal velocity, providing clear evidence of blood slippage. To our knowledge, this is the first demonstration that the no-slip condition does not apply to blood flow \emph{in vivo}. This finding challenges a fundamental assumption in cardiovascular modeling and directly affects key blood flow characteristics such as pressure drop, vorticity, wall shear stress, and energy dissipation, all of which play important roles across a wide range of cardiovascular conditions.

Figures (6)

• Figure 1: A scheme of a simple vessel with marked boundary types.
• Figure 2: Comparison between the manual segmentation (left), automatic segmentation using Total Segmentator (middle) and automatic segmentation with an additional layer of pixels (right) on a cross-section in the middle of the geometry.
• Figure 3: Comparison of the velocity fields for Dataset 1: The velocity field obtained from MRI data (left); the velocity field obtained from MRI data interpolated into a computational mesh, here based on manual segmentation method (middle); the velocity field obtained from numerical simulation with the optimal slip parameter $\kappa_{\rm opt} = \qty{3.89}{Pa.s/m}$ (right).
• Figure 4: Time-dependence of the average tangential velocity over the wall domain $\Gamma_{\rm wall}$ and the average velocity over the entire domain $\Omega$ for all seven MRI datasets and three segmentation methods. Each row corresponds to one dataset. The percentages shown below the graphs represent the ratio of the average tangential velocity along the wall to the velocity averaged over the entire domain, averaged over both space and time.
• Figure 5: Comparison of velocity reconstructions across different boundary condition models for all datasets using the manual segmentation method. Each column corresponds to one dataset, while the rows (top to bottom) show: interpolated 4DMRI velocity data, velocity reconstruction with a no-slip boundary condition, reconstruction with a constant slip parameter $\kappa_{\rm opt}$, reconstruction with a spatially varying slip parameter $\kappa_{\rm opt}(x)$, and the corresponding spatial distribution of $\kappa_{\rm opt}(x)$.