On the comparison between pre- and post-surgery nasal anatomies via computational fluid dynamics

Abstract

Nasal breathing difficulties (NBD) are widespread and difficult to diagnose; the failure rate of their surgical corrections is high. Computational fluid dynamics (CFD) enables diagnosis of NBD and surgery planning, by comparing a pre-operative (pre-op) situation with the outcome of virtual surgery (post-op). An equivalent comparison is involved when considering distinct anatomies in the search for the functionally normal nose. Currently, this comparison is carried out in more than one way, under the implicit assumption that results are unchanged, which reflects our limited understanding of the driver of the respiratory function. The study describes how to set up a meaningful comparison. A pre-op anatomy, derived via segmentation from a CT scan, is compared with a post-op anatomy obtained via virtual surgery. State-of-the-art numerical simulations for a steady inspiration carry out the comparison under three types of global constraints, derived from the field of turbulent flow control: a constant pressure drop (CPG) between external ambient and throat, a constant flow rate (CFR) through the airways and a constant power input (CPI) from the lungs can be enforced. A significant difference in the quantities of interest is observed depending on the type of comparison. Global quantities (flow rate, pressure drop and nasal resistance) as well as local ones are affected. The type of flow forcing affects the outcome of the comparison between pre-op and post-op anatomies. Among the three available options, we argue that CPG is the least adequate. Arguments favouring either CFR or CPI are presented.

Keywords: CFD; Constant power input; LES; Nasal flow; Nasal resistance.

Fig. 1

Pre-op (left) and post-op (right) anatomies, including an external spherical volume around the nose tip. In the post-op anatomy, the red circle highlights changes due to the virtual maxillectomy

Fig. 2

Planes used throughout the paper to visualize results. Left: para-sagittal plane SL passing through the unaltered left nostril; centre: para-sagittal oblique plane SR cutting through the operated right nostril and the throat; right: coronal plane C cutting through the maxillary sinuses. The x-axis is normal to the sagittal plane and points to the right; the y-axis is normal to the coronal plane and points towards the nose tip, and the z-axis is normal to the transverse plane and points upwards

Fig. 3

CPG comparison: magnitude U of the mean velocity vector in planes SL and SR

Fig. 4

CPG comparison: sagittal component $U_y$ of the mean velocity in the coronal plane C. The black line represents the zero contour level

Fig. 5

CFR comparison: magnitude U of the mean velocity vector in planes SL and SR

Fig. 6

Post-op changes of the magnitude U of mean velocity between CPG and CFR. Plot of $U_{\text{CPG}}-U_{\text{CFR}}$ in planes SL and SR

Fig. 7

Post-op changes in the magnitude U of mean velocity between CPG and CPI. Plot of $U_{\text{CPG}}-U_{\text{CPI}}$ in planes SL and SR

Fig. 8

Magnitude U of the mean velocity, for all computed cases, in a three-dimensional view. The iso-surfaces correspond to the level of $U=3\text{m/s}$

Fig. 9

Three-dimensional view of the post-op changes in the magnitude U of the mean velocity. Left: $U_{\text{CPG}}-U_{\text{CFR}}$; right: $U_{\text{CPG}}-U_{\text{CPI}}$. The red/blue iso-surfaces correspond to $+0.35\text{m/s}$ (red) and $-0.22\text{m/s}$ (blue), respectively

Fig. 10

Three-dimensional view of the post-op field of turbulent kinetic energy k, computed with CPG (left) and CFR (right), and visualized via the iso-surface at the level k = 0.25m²/s². Zoom in a subregion shown in the inset