Keywords
computational fluid dynamics - statistical shape model - nasal breathing - flow field
- wall shear stress - intranasal airflow
For successful surgery of the nasal framework, preoperative evaluation of nasal breathing
is essential. At present, however, this only involves assessing the general patency
of the nasal cavity. In the clinical context, objective criteria for distinguishing
between normal and impaired nasal breathing exclusively include global parameters
such as the total nasal resistance measured by rhinomanometry or the inspiratory peak
flow. In addition, cross-sectional areas are examined. The limitations of this relatively
basic approach become evident in practice. Frequently it does not meet the clinical
requirements due to inconsistencies between the patient's complaints, findings, and
the measurement results.[1]
[2]
[3]
[4]
Technological advancements have made it possible to use image data obtained through
radiological diagnostics of the paranasal sinuses for numerical simulation of intranasal
airflow during nasal breathing. This method, known as computational fluid dynamics
(CFD), has been established in the industry for years and is increasingly of interest
in medical research, yet it is finding tentative applications in rhinology.[5]
[6] It allows for calculation of any flow parameters with high spatial and temporal
resolution in complex geometries, such as the nasal cavity.
This article aims to reflect the latest insights on the application of CFD in rhinology,
primarily from the practitioner's perspective. Technical details receive limited attention.
Background
The terms CFD and numerical flow simulation can be used interchangeably. They denote
procedures that enable calculation of flow parameters in tortuous geometries when
analytic solutions are not feasible. Predominantly, a so-called finite volume method
(FVM) is employed.
The mathematical model of CFD refers to a system of partial differential equations,
which are called Navier–Stokes equations. They are based on the conservation laws
of momentum, energy, and mass. To manage computational effort for flows with possible,
not solely, laminar characteristics, turbulence models are commonly utilized.
CFD provides a flow field that can represent any desired parameter with high temporal
and spatial resolution. The subsequent visualization is key for flow analysis and
understanding higher-order relationships in very complex simulations that address
multiple parameters.[7]
The methods of numerical flow simulation have been extensively tested and have demonstrated
reliability and sufficient accuracy in various practical contexts. Thus, when using
software with a well-established reputation, in specific cases valid results can be
accomplished without extensive experimental testing.
CFD Workflow with Respect to Rhinology
The application of CFD in rhinology is appealing because imaging of the paranasal
sinuses, including the nasal cavity, is routinely performed in the cases in which
impaired nasal breathing is the predominant symptom. Subsequently, a complete dataset
representing the considered anatomical structures is available in a Digital Imaging
and Communications in Medicine (DICOM) format.
For reliable simulation outcomes, a minimum image resolution aligning with the requirements
for navigated surgery is recommended.[8]
[9]
The acquired data can be used for three-dimensional reconstruction of the nasal cavity
after semiautomated segmenting of the cross-sectional images from the nasal entrance
to the choanae. This is followed by discretization of the selected flow domain by
creating a mesh comprising polyhedral subdomains. Including the paranasal sinus airway
is generally not necessary, as the flow rate within them is negligibly small. Depending
on the location and the specific application, various types of polyhedra may be used.
The choice of the mesh and its structure plays a crucial role in the accuracy and
stability of the simulation ([Fig. 1]).
Fig. 1 Meshed flow domain of a left nasal cavity.
Prior to calculation, mathematical and physical modeling must be performed, which
includes specifying the boundary conditions. In our experience, it has proven effective
for intranasal airflow simulations to set either a constant driving pressure difference
or a constant flow rate that corresponds to resting respiration. Further assumptions
involve rigid walls, the “no-slip” condition at the wall surface, and incompressible
fluid behavior—justified by a Mach number smaller than 0.1. The assumed air density
is 1.225 kg/m3, and the dynamic air viscosity is set at 1.789 × 10−5 kg/ms.
For simulation, the CFD solver uses iterative approaches to approximate a solution.
During this process, fluid flow parameters are updated continuously until the desired
convergence criteria are met. Based on our observations, we believe that steady-state
calculations in conjunction with a turbulence model can sufficiently reflect the dynamics
of intranasal airflow and meet medical evaluation purposes.[10] Consequently, elaborate advanced procedures such as transient calculation, large
eddy simulation (LES), or direct numerical simulation (DNS) might be dispensable in
the scope of nasal breathing assessment.
Finally, postprocessing including visualization and analysis is performed, which is
crucial for understanding the results. Examination of the velocity and pressure field,
along with the wall shear stress (WSS) pattern, holds special clinical significance
([Fig. 2]). However, in individual cases, it may also be useful to consider the temperature
and humidity of the breathed air.
Fig. 2 Illustrated visualization of color-coded inspiratory flow parameters projected onto
the left lateral nasal wall. From left to right: streamlines with flow velocity, pressure
drop, wall shear stress distribution.
[Fig. 3] provides a graphical overview of the CFD workflow.
Fig. 3 Rhinology-related workflow of computational fluid dynamics.
Rethinking the Characterization of Nasal Airflow
Inextricably linked to assessment of nasal breathing is the question: What constitutes
nasal breathing? As noted earlier, the main criterion defining the quality of nasal
respiration currently hinges on the nasal cavity's total patency. Various methods
such as rhinomanometry, cross-sectional area, and inspiratory peak flow measurements
are employed to quantify this.[2]
[4] Consequently, treatment plans for impaired nasal breathing mainly align with these
metrics despite the inherent limitations of global parameters. The need to broaden
the theoretical framework becomes evident when one takes into account the variety
of anatomical and physiological conditions that facilitate normal nasal breathing.
The key conditions might be outlined as follows[11]:
-
An approximately symmetrical, slitlike flow domain, with a normally configured isthmus
area serving as bulk flow formation structure.
-
Low but sufficient total nasal resistance.
-
Healthy mucous membrane with a normal liquid film.
-
Intact erectile tissues and structures.
-
Optimal support for the flexible nasal sidewalls.
The intricate interplay of numerous conditions can be succinctly encapsulated as an
overall adequate bidirectional interaction between the flowing air and the inner lining,
providing a novel and comprehensive understanding of healthy nasal breathing. We believe
only through this approach can the full diagnostic potential of CFD in rhinology be
unlocked, while, to the best of our knowledge, existing applications of CFD have primarily
focused on examining rather global parameters.
The Simulated Flow Field as a Diagnostic Interface
The simulated flow field within the nasal cavity quantitatively reflects the local
distribution of one or more flow parameters, and visualization displays their correspondence
with the anatomical structures. Of particular interest is the distribution pattern
of WSS. This parameter describes the tangential forces on the nasal wall that are
caused by adhesion of the passing air particles. WSS correlates with interactions
between the flowing air and the mucous membrane in terms of mass and heat transfer
as well as effects on both thermo- and mechanoreceptors. Consequently, the flow field—particularly
the distribution pattern of WSS—may serve as a diagnostic interface for evaluating
a patient's nasal breathing ([Fig. 2]).[12]
[13]
However, this necessitates a point-to-point quantitative comparison with a valid reference
for the flow field, for example, based on a sufficient statistical shape model (SSM).[14] The SSM needs to capture the broad natural variation in nasal cavity morphology,
taking into account both the static geometry and the inner lining's fluctuations.
It should encompass both healthy and symptomatic populations, representing individuals
with either unimpaired or compromised nasal breathing, respectively.
Implementing the SSM would, within certain limits, enable the determination of whether
a specific nasal cavity geometry facilitates normal airflow.[15] If this is confirmed but the patient still perceives nasal breathing problems, clinical
investigation would be required to explore other potential causes, such as mucosal
disease, inadequate structural support of the nasal sidewalls, or perceptual issues.
Discussion
Fluid–Structure Interaction
A central concern in rhinology is the nasal valve, which anatomically corresponds
to the isthmus nasi.[16]
[17] According to Bernoulli's law, the dynamics of the nasal valve during inspiration
are due to the changing relationship between the static pressure inside the nasal
cavity and ambient pressure. The compliance of the nasal sidewalls is governed by
these fluctuating pressure conditions, as well as by their intrinsic mechanical properties.
During inspiration, the airflow acceleration in the nozzle-like constriction of the
isthmus nasi leads to a locally enhanced difference between the decreasing intranasal
static pressure and the constant ambient atmospheric pressure. Therefore, at the isthmus
nasi, the inspiratory resulting inward-directed forces are particularly pronounced.
Known as the Venturi effect, it can lead to a subsequently aggravated constriction
of the isthmus area through the shifting nasal walls. Collectively, this is referred
to as fluid–structure interaction (FSI).
Currently, addressing FSI in simulations of nasal breathing is challenging due to
various technical complexities, most notably the difficulty in obtaining data on the
mechanical properties of the nasal sidewalls. Disregarding FSI might generally be
a minor issue, as exclusive nasal breathing usually occurs during resting respiration
related to low flow rates,[18] which the boundary conditions involve. While at low flow rates the inward inspiratory
shifting of the anterior nasal sidewalls is typically not significant, during intensified
inspiration with elevated flow rates, bilateral inward shifting of the sidewalls serves
as a physiological limiter of inflow, comparable to a Starling resistor. To a certain
extent, this aligns with the intended functioning of the nasal valve.[19]
In contrast, asymmetrical nasal valve dynamics prove to be more critical and, therefore,
require greater attention. Specifically, when one nostril collapses, while the other
remains unaffected, questions arise about the sufficiency of the cartilaginous support
on the affected side. Often, surgical enforcement is the first course of action, frequently
without a comprehensive analysis of the underlying causes. Based on our experience,
corroborated by the opinion of colleagues (Helmut Fischer via e-mail on April 24,
2021), asymmetrical nasal valve dynamics are more attributed to flow domain asymmetry
than to unilateral instability of the nasal sidewall. Therefore, in most cases, correcting
only the flow domain of the nose is already sufficient. Simulating the flow field
under the assumption of rigid walls allows for isolating solely static geometry-related
factors affecting nasal breathing from those concerning the condition of the nasal
sidewall structure, the latter of which must be clinically assessed.
In closing, what appears as a limitation in current rhinologic CFD applications can
conversely also offer advantages.
Nasal Airflow Misperception
The perception of airflow within the nasal cavity is most likely primarily facilitated
by thermoreceptors, activated indirectly through the evaporative cooling of the mucous
membrane during inhalation.[20] Mechanoreceptors, which directly respond to WSS, may also play a significant role.[21] Signals from these receptors are conveyed to the brain via the trigeminal system,
creating the sensation of the intranasal airflow. This is influenced by both the airstream's
distribution pattern and the allocation of receptors within the nose. Perception of
nasal breathing as either impaired or normal is also subject to individual signal
processing. In essence, the trigeminal system mediates the individual perception of
the nasal cavity's patency.
In general, reliably distinguishing between objectively impaired nasal breathing and
airflow misperception is a challenging task, often achievable only by the presence
of unequivocal clinical findings. Due to their inherent limitations, conventional
diagnostic methods like rhinomanometry merely offer marginal improvements to clinical
evaluations. To accurately identify cases of nasal airflow misperception, it is crucial
to verify whether the respective nasal cavity facilitates a normal airflow pattern.
This confirmation might be attained through flow field simulation using CFD, complemented
by comparison with a valid reference for quantitative analysis. In other words, the
application of CFD could enable discrimination of objectively compromised airflow
from solely misperceptions.
Fluctuations of the Flow Domain due to the Nasal Cycle
The nasal cycle is a physiological phenomenon in which the swelling state of the nasal
mucosa periodically changes. Specifically, the inferior turbinates complementarily
congest and decongest in an alternating pattern. Ideally, the overall patency of the
nose remains largely unchanged during this process. The switching itself occurs relatively
quickly compared with the periodicity of its occurrence.[22]
[23]
Due to the nasal cycle, diagnostic imaging may show a significantly changed flow domain
in the same patient depending on the time of examination. Therefore, when applying
CFD for the evaluation of nasal breathing, this temporal physiological variability
in the nasal cavity's morphology should be taken into account by using a reference
that represents these normal fluctuations. An SSM, as mentioned earlier, might be
an appropriate means to address the issue.
Reduced Bias through Comparative Analysis
Assessing nasal breathing using CFD is very complex and inherently carries an elevated
risk of error from multiple sources. These include technical aspects such as the choice
of boundary conditions, computational grid meshing, and selection of a specific turbulence
model, as well as investigator-related factors, particularly in image segmentation.
Employing an SSM to generate referential flow parameters for quantitative evaluation
of the intranasal airstream simultaneously offers additional benefits by mitigating
the aforementioned risks of bias. When a uniform methodology is applied to both the
individual case under investigation and the SSM reference, errors are more likely
to occur consistently. Consequently, these errors can be partially offset through
comparative analysis.
Conclusion
Compared with conventional methods, CFD enables a fundamentally new approach for evaluating
nasal breathing. To unlock the full diagnostic potential of this technology, new foundational
considerations are instrumental, particularly regarding the essence of nasal breathing
and how it can be adequately characterized. The intranasal flow field, specifically
the distribution pattern of WSS, can serve as an interface reflecting the quality
of nasal breathing in terms of bidirectional interactions between airflow and the
mucous membrane. To quantitatively analyze this interaction for individual patients,
reference parameters derived from an appropriate SSM are required. Implementing such
an SSM is a challenge that we are currently working on.
A prerequisite for such nasal breathing assessment is imaging of the paranasal sinuses,
including the nasal cavity, which is routinely performed to rule out mucosal disease
in cases of impaired nasal breathing. The acquired two-dimensional image data not
only provide morphological information but can also be subsequently used to assess
respiratory intranasal airflow when needed. This possible dual use could facilitate
the cost-effective implementation of CFD-based nasal breathing evaluation in clinical
practice. While segmentation of the image data for reconstructing the 3D geometry
of the nasal cavity is not yet fully automatable, artificial intelligence approaches
might tackle this issue in the future.
Using CFD in conjunction with an SSM would enable the differentiation between normal
and impaired nasal breathing and the precise localization of the problem, allowing
for targeted surgical intervention when indicated. Thus, a possible paradigm shift
in nasal breathing assessment may be on the horizon. An advanced model of the airflow-related
intranasal physiology, which compliments the existing one and aligns well with the
capabilities of the CFD methodology, could facilitate this development.[12]
[13]
