Using computational fluid dynamics (CFD) to improve the bi-directional nasal drug delivery conceptM Kleven1,2, MC Melaaen2, M Reimers3, JS Røtnes4,5, L Aurdal5,6, PG Djupesland7

ABSTRACT

Nasal delivery is considered for an increasing number of existing and new drugs and vaccines, but current nasal delivery devices have major disadvantages. The Norwegian company OptiNose AS is developing a novel concept that challenges traditional delivery systems. The patended bi-directional delivery system improves drug and vaccine distribution to the nasal mucous membrane while at the same time preventing lung deposition. It takes advantage of the posterior connection between the nasal passages persisting when the velum automatically closes during oral exhalation. It is the exhalation into the delivery device that triggers the release of particles into an airflow, which enters one nostril via a sealing nozzle and exits through the other nostril.

This paper describes how OptiNose is using Computational Fluid Dynamics (CFD) during the development process for their drug delivery concept. The simulations are used to visualize and demonstrate the basic features of the bi-directional technique and discuss how its design and function could be further optimized. CFD computations thus increase the efficiency of device development and reduce the need for expensive and time consuming laboratory experiments.

To perform successful CFD calculations on the nose, construction of a proper surface grid of the nasal cavity is important. The process of building the surface grid is presented in the paper. The final surface grid was next imported into Tgrid, a volume grid generator, and finally the simulations were carried out by use of the commercial CFD code FLUENT. These steps are described in the paper. Testing of the cell quality, both during surface grid and volume grid generation, is mandatory. The testing procedures are briefly presented in the paper. Finally, to be able to rely on the CFD computations done, one needs thorough validation. This article presents some comparison of the CFD computation results against physical experiments. The comparison analysis shows promising results.

INTRODUCTION

Description of the nose

The apparent external nose surrounds the nostrils and one-third of the nasal cavity, which according to Mygind & Dahl (1998) in its entirety consists of a 5 cm high and 10 cm long chamber. The nose consists of two nasal passages, separated by the nasal septum, each of which opens independently into the upper part of the throat, i.e. nasopharynx. The internal walls opposite the nasal septum have ridges formed of bone, i.e. conchae or turbinate bones. Several of the bones, the frontal, sphenoid, ethmoid and maxilla, contain hollow air-filled spaces, i.e. the sinuses. Under and lateral to each of the turbinates are passages called the inferior, middle (and superior) meatus. The nasal sinuses open into these spaces. The olfactory mucosa is situated in the roof of the nasal cavity, with correspondence to the brain. A prerequisite for an odour sensation is that molecules can be brought in direct contact with the olfactory receptor cells in this area. Approximately 2-3 cm from the nares is the narrowest portion of the entire airway, the nasal valve, with a cross-sectional area of about 30-60 mm2 on each side. The nasal valve is the narrowest and most resistive portion of the whole airway. To fulfil the continuity criterion by the nasal valve, since the cross-section area decreases, the fluid flow velocity increases, i.e. the average velocity is inversely proportioned to the cross sectional area. After passing through this narrow region, the airflow enters the nasal cavity, where the cross sectional area increases considerably. According to Proctor & Andersen (1982), the direction of the airflow undergoes a bend of nearly 90○ at this juncture. The bilateral airstreams increase in velocity as they join in the nasopharynx, which is the upper part of the throat, where another change in direction occurs.

In addition to the sense of smell, the nose acts as a filter, a humidifier and a heat exchanger. The air is moistened, filtered and warmed during inspiration, and during expiration, heat and moisture are conserved as the warm,

1 Corresponding author. Phone: +47 35575190, Fax: +47 35575001, E-mail: marit.kleven@hit.no2 Telemark University College (HiT-TF) and Telemark R&D Centre (Tel-Tek), Porsgrunn, Norway3 CMA, University of Oslo, Oslo, Norway4 SimSurgery AS, Oslo, Norway5 Interventional Centre at Rikshospitalet, Oslo, Norway6 Norwegian Computing Center, Oslo, Norway7 OptiNose AS, Oslo, Norway

moist air now passes the cooler turbinates of the nose. The air passages are largely dependent upon these defence mechanisms for protection against the hostility of the environment.

Of major significance for effective cleansing and conditioning of the air is the disruption of laminar flow patterns of respiratory air which brings about its intimate mucosal contact and mixing. The break up of a stable insulating boundary layer of air enables rapid warming and moistening of inspiratory air together with removal of particulates and soluble vapours to take place. According to Cole (1993), there are several features of inspiratory airflow and of the upper-airway passages themselves that disrupt laminar flow. Respiratory flow is repeatedly accelerating, then decelerating, and then reversing again. It changes direction through 180° between the anterior nares and the pharynx and flows through a lumen of varying shape and cross-sectional dimension, most marked by narrowing at the nasal valve. All these features impose disturbances on the flow pattern of the inspiratory air stream.

Major factors that influence removal of particulates from the airflow and their depth of penetration into the air passages include particle size, velocity, shape, density, hygroscopicity, turbulence of the airflow, and configuration of the air passages (Proctor & Andersen (1982) and Cole (1993)). The fate of a particle in the air passage will be influenced by the dimensions of the tube through which it passes and the nature of airflow in that passage. The characteristics of airflow of importance are the linear velocity, bends in the passage, and the degree of turbulence of flow. Gravity and inertia of a particle are forces involved in the likelihood of deposition. The effect of gravity will, in proportion to the particle’s mass, influence its tendency toward sedimentation downward. Inertia forces will affect the fate of a particle in proportion both to its mass and the velocity of the stream in which it is suspended. This force is of special importance in relation to bends in the airflow caused either by turbulent flow or by a change in direction of the air passage (Proctor & Andersen (1982)).

Motivation

Nasal delivery is considered for an increasing number of existing and new drugs and vaccines. Nowadays, most drugs are being administered by the oral route or by injection, and vaccines are mainly injected. As Djupesland et al. (2004) refers, the first-pass-effect, degradation in the stomach and intestines and adverse intestinal effects related to oral administrations as well as the costs, safety issues, pain, and logistical and waste problems associated with needle injections, are all factors that call forth an interest for a nasal delivery route. The easy access to the highly vascularized nasal mucosa rich in immunologically active dendritic cells and organized lymphatic tissues makes the nose especially attractive. However, in spite of the importance of the narrow flow passages in the nose, they offer many challenges for efficient nasal delivery of drugs and vaccines. Current nasal delivery devices, like spray pumps and pipettes, have major disadvantages and there is a considerable potential for improvement.

The Norwegian company OptiNose AS is developing a novel concept that challenges traditional delivery systems. During respiration acts, such as forceful blowing through the mouth, the soft palate moves backward and upward closing off the main portion of the nasopharynx from its communication with the main pharyngeal airway (Proctor & Andersen (1982)), i.e. closes off the nasal cavity completely. The bi-directional nasal delivery concept takes advantage of this closing off during oral exhalation. Forceful blowing into a delivery device triggers release of liquid or powder particles into the airflow, which enters one nostril via a sealing nozzle, passes throughout the communication posterior to the nasal septum, and exits through the other nasal passage. The opposite directed airflow in the exit nostril will cause particles to be deposited on the posterior surface of the nasal structures. Users simply blow through a lower mouthpiece which causes drugs in either liquid or powder form to be delivered beyond the nasal valve to the target sites in the posterior two thirds of the nose. Small particles not deposited in the exit passage escape to the atmosphere, or may be collected by a filter. The patented bi-directional delivery system improves drug and vaccine distribution to the nasal mucous membrane while at the same time preventing lung deposition. In a study of 16 healthy subjects using 99mTc-labeled nebulized particles with a mean particle size of 3,5 µm, Djupesland et al. (2004) reports that bi-directional delivery resulted in no or minimal lung deposition, i.e. 0,8±2,0%, whereas significant fractions were deposited in the lungs in all 16 subjects, mean 22,3±8,1%, following conventional nasal inhalation. New guidance from the U.S. Food and Drug Administration (FDA) emphasises the importance of limiting the fraction of small particles, i.e. <5-10 µm, able to bypass the nose. Since the bi-directional nasal airflow is completely separated from the oral cavity and lower airways, it is possible to adjust e.g. particle size and airflow, permitting optimized distribution in the nasal mucosa, even to the posterior regions of the nasal structures. That the bi-directional delivery provides a positive pressure expanding narrow segments of the nasal passages indicates an improved distribution of delivered particles, too. By the nasal valve, the sealing nozzle itself expands the passage. An improved, and more precise,

deposition pattern, potentially improves the immune response of the drug, and increases the reproducibility. This indicates a potential drug dose reduction.

The flow of particles and droplets in gases has a wide application in industrial processes, and models based on Computational Fluid Dynamics (CFD) are often used to study such problems. Since CFD is a very useful tool when analyzing process equipment, it seems reasonable also to use this tool in the study of nasal aerodynamics. The objective of this article is to show how CFD can be applied as a tool to visualize and demonstrate the basic features of this technique and how it can be used to further optimize design and function of novel delivery devices based on the bi-directional concept. CFD computations can increase the efficiency of device development and reduce the need for expensive and time consuming laboratory experiments.

The only published study on CFD simulations of bi-directional nasal delivery (Kleven et al. (2004) refers to promising experimental studies performed, to validate the simulations. In the present paper, comparison between CFD simulations and human studies with radiolabeled particles are presented. Thorough validation against physical experiments is essential for the reliability and value of the CFD computations.

METHODS

Surface grid generation

To be able to perform successful CFD calculations on the nose, construction of a proper surface grid of the nasal cavity is mandatory. The first step of the modelling process was to acquire a high resolution CT-scan, i.e. Computer Tomography. This was executed by The National Hospital in Norway. One of the authors was imaged in a CT scanner, generating 109 slices of the nasal geometry with 1 mm between each slice. Prior to further processing, these data were segmented, that is, each voxel in the data was given a unique label indicating whether it belongs to the airway or not. This is a classical problem in image processing, and many possible methods exist. We used a Markov Random field based method, see Derin & Elliott (1987), as these produce particularly smooth interfaces between the different groups of voxels, see Figure 1 for an example.

Figure 1: The surface of the nasal cavity is identified as part of the segmentation process.

The next step in the process was to produce from the segmented image data, a surface triangular mesh that modelled the surface of the nasal cavity. The mesh was later used as input to the volume grid generator and was to comply with a set of constraints and quality measures dictated by the grid generator and the CFD software. These measures can be divided in two categories; geometric quality and mesh quality. We wanted on the one hand a mesh that closely modelled the geometry of the surface of the nasal cavity and on the other hand a mesh configuration that gave high quality volume grids of the cavity itself. To summarize, the most important requirements were that the mesh:

• Closely approximated the underlying geometry.• Had the correct topology and was a closed surface without singularities and self intersections. • Was geometrically smooth whenever the underlying model was smooth.• Had well shaped triangles, i.e. triangles should not be too far from equilateral.

• Had a suitable number of triangles due to the efficiency of the CFD software.

• Had triangle density proportional to the local thickness of the geometry.

These requirements will be explained in more detail in the following. Our overall strategy was to first generate an initial mesh directly from the segmented image. This mesh was typically unsuitable for the grid generation step, with far too many triangles, topological and geometric artefacts and suboptimal mesh structure. We therefore took a number of steps such as decimation, smoothing, refinement and mesh optimization to enhance its quality. Due to the often competing requirements, the nature of the enhancement process was iterative, see Figure 2 for an illustration.

Figure 2: Overview of the surface grid generation process.

Our first step was to employ the Marching Cubes (MC) algorithm of Lorensen & Cline (1987), which in this setting can be seen as to extract the surface of the segmented voxels in a consistent and efficient manner. We experienced that the Generalized Marching Cubes algorithm used in AMIRA produced non-manifold meshes, requiring tedious manual fixing. However, the original Marching Cubes algorithm did not suffer from the same problems and was found better in the present context. The resulting mesh revealed artefacts such as topological holes stemming from inaccuracies in the segmented data. One of the requirements to the mesh was that it had the correct topology and was a closed surface without singularities and self intersections. We found it convenient in this situation to go back to the 3D image and remove the artefacts in the images before generating an updated mesh with the MC algorithm. After that, the mesh was pruned for irrelevant parts and holes where filled by manually editing the mesh. Figure 3 illustrates the initial mesh generated with the marching cubes algorithm. Here, we can see the placement of the device in the left nostril.

Figure 3: An initial mesh generated with the marching cubes algorithm.

Having successfully obtained a surface mesh with the right topology we could begin enhancing the geometry of the model.

The next step was to smooth the initial mesh, getting rid of the jagged geometry visible in Figure 3. One important requirement during the surface mesh production was that the mesh should be geometrically smooth whenever the underlying model was smooth. We used variants of Laplacian Smoothing, see Taubin (1995), as it is a straightforward and common smoothing method. It is based on mesh topology alone and thus does not respect the local geometry of the mesh very well, especially where neighbouring triangles differ significantly in size. A more sophisticated method is presented in Desbrun et al. (1999), where the intrinsic geometry of the surface is taken into account, giving a better geometric smoothing. We also found a rather effective smoothing

method that we called barycentre smoothing as it amounts to moving each vertex to the average of the positions of its mesh neighbours, i.e.

∑=

=in

jij

ii v

nv

1

1

(1)

The first two methods where typically iterated until we got a visually pleasing mesh. The barycentre method on the other hand is very effective with one or two steps sufficient. A side effect that we learned to appreciate was that it also improved triangle shape significantly with many triangles being smoothed to be nearly equilateral. All of the smoothing methods mentioned had the tendency to shrink the volume enclosed by the surface. We countered this problem with a common workaround: scaling the vertex positions such that the volume remained the same after each smoothing step.

The next step was to reduce the number of triangles down to a size that was manageable for the grid generator, typically 100 000 triangles. Mesh decimation algorithms such as the one in Garland & Heckbert (1997) are typically based on a primitive mesh decimation operator such as the half edge collapse; a vertex is removed by identifying it with a neighbouring vertex, reducing the number of vertices by one and the number of triangles with at least two. In addition a norm measuring the quality of the mesh is used. Based on this, a standard greedy strategy can be employed, where one in each step perform the decimation operation that reduce the geometric quality the least. In other words, we reduce the size of the mesh while keeping the most significant geometric information. In addition a set of constraints can be built in, such that e.g. operations that produce badly shaped triangles are not allowed. In principle we could have used the criterions listed in the section above to guide the decimation process, but we found that it was not necessary to maintain high mesh quality during the decimation process. We thus employed the algorithm described in Garland & Heckbert (1997), where the most important optimization criterion is geometric approximation quality. The other quality criterions were taken into account at a later stage. We reduced the number of triangles from more than a million to around 75 000 which amounted to 75% of our triangle budget. This gave us good enough approximations while leaving enough room for later refinement if necessary.

The next step was to improve the triangle shapes and distribution. One could think of this as the problem of redistributing the triangles so that they obtained better shape, while still representing the same geometry. The input mesh to the grid generator must have nicely shaped triangles; ideally all triangles should be equilateral. Skewness measures how far a triangle is from being equilateral and is formally defined as the ratio

( )M

AMSkewness t−

= , (2)

where At is the area of the triangle, and M is the area of an equilateral triangle with vertices on the circumcirle of the triangle, see Figure 4 for illustration.

Figure 4: Skewness measures how far a triangle is from being equilateral.

An equilateral triangle thus has skewness 0 while a maximum degenerated triangle has skewness 1. Our objective was to minimize the overall skewness and avoid triangles with skewness above 0.75.

The methods we used to optimize over skewness fall into two categories, optimizing over either vertex positions or vertex connectivity. We found the Laplacian Smoothing type of techniques described above particularly effective. The reason for the effectiveness was that these methods are based on averaging the geometry and thus the resulting mesh stays close to the geometry of the initial mesh. One step of barycentre smoothing was very effective in that respect. The other type of method we used was based on keeping the vertices of the mesh fixed while optimizing the vertex connectivity. The basic operation in the former type of method is the edge flip illustrated in Figure 5.

Figure 5: Edge flips improve the overall skewness of the triangle mesh.

We used the greedy local optimization (LOP) technique (Lawson (1972) and Dyn et al. (2001)), with the cost for a triangle amounted to an exponential function of its skewness s, on the form

pi Csc = , (3)

with C = 10 and p = 5. This ensured that triangles with high skewness were punished hard. The cost function in the LOP algorithm was the sum of this expression over all triangles. We also tested more advanced optimization techniques, but concluded that the simple LOP algorithm was equally effective and produced meshes with few skew triangles. If there where still triangles with high skewness we improved their quality manually. See Figure6 for an example of mesh optimization with respect to skewness.

Figure 6: Part of the mesh before and after swapping with the LOP algorithm.

The grid generation process produces volumetric grids with element size proportional to the size of the surface triangles. In fact, a surface triangle in the input mesh ends up as a facet of a tetrahedron in the volumetric mesh. Therefore it is of vital importance that the density of the surface triangles is adapted to the thickness of the geometry. In other words, the size of the surface triangles is required to be proportional to the thickness of the geometry, with small triangles in thin regions.

Thickness of the geometry could be defined in different ways. We define the thickness in a point on the surface to be the interior distance to other parts of the surface. In practice, we estimated the local thickness at a triangle by measuring the distance to the nearest surface triangle in the normal direction. Due to the instable nature of these calculations, we employed a median filter to obtain consistent thickness values throughout the mesh. We found the results of this method satisfactory and sufficient for our purposes. Defining also the size of a triangle to be the length of its longest edge, we required the triangle size to be a factor 5 of the local thickness. We allowed in other words the volume to be at approximately five elements thick. In practice we adapted the local triangle density by adaptively refining the mesh in thin areas, splitting edges in two and dividing the triangles in smaller triangles. Special care had to be taken for triangles neighbouring triangles that were meeting the thickness criterion, see Figure 7. We repeated the following steps until our thickness criterion was met:

1. Associate thickness with each triangle.2. Split triangles with too high triangle size.3. Optimize the split triangles with respect to triangle shape.

Figure 7: Adaptively splitting triangles in thin regions.

After the above steps we would have a final surface mesh that met all our requirements with respect to geometric- and surface mesh quality. The final step was to divide the mesh into logical partitions each consisting of a set of connected triangles that would model inlet/outlet or other areas of special interest. We assigned each triangle to one unique partition and used this as part of the mesh description. The nature of the inlet/outlet partitions allowed us to use a simple region growing algorithm based on surface normals. We subsequently edited the partitions manually to obtain visually smooth partitions, see Figure 8 for example.

Figure 8: Creating visually smooth partitions was our final step.

The final surface mesh is shown in Figure 9.

Figure 9: The final mesh modelling the surface nasal cavity.

Volume grid generation

Figure 9 shows the final grid modelling the surface nasal cavity. By use of the default algorithm included in Tgrid, i.e. the highly automated Delaunay method (Tgrid 3 User’s Guide (1997)), tetrahedrons in the nasal cavity volume were generated. The cell quality was tested in Tgrid, to ensure a proper grid for the simulations. This

was done by investigating the degree of skewness, this time based on comparison of the cell’s shape to an equilateral cell of equivalent volume. Again, the skewness range is between zero and one, where zero skewness is optimal and a skewness of one indicates a degenerate cell. The following Figure 10 shows images from the volume grid in Fluent.

Figure 10: Images from Fluent showing the grid. Upper left side: grid seen from below, upper right side: the same image showing details from the nostrils’ faces, including the medication tube in the left nostril. Lower left side: Frontal grid view, lower right side: Grid seen from behind.

CFD simulations in Fluent

The grid developed throughout the described process was imported into the commercial CFD code Fluent. This code provides comprehensive modelling capabilities for a wide range of fluid flow problems, where a useful group of models are the multiphase flow models. According to Fluent User’s Guide (2003), there are currently two approaches to the numerical calculation of multiphase flows; Euler-Lagrange approach and Euler-Euler approach. In this work, i.e. an analysis of a gas-particle flow, the discrete phase model (DPM) is used. This model follows the Euler-Lagrange approach. The gas phase is treated as a continuum by solving the Navier-Stokes equations, i.e. the conservation equations. In addition, the DPM performs Lagrangian trajectory calculations for the dispersed phase, i.e. the particles, including coupling with the continuous phase. In modelling, particles include both solid particles and droplets.

The fate of a particle in the air passage will be influenced by the dimensions of the space through which it passes and the nature of the airflow in that passage. The characteristics of airflow of importance are the velocity of the stream, bends in the passage, and the degree of turbulence of the flow. Other factors that influence the deposition and absorption of the medicaments from a nasal spray include particle size, particle size distribution, shape and density (Proctor & Andersen (1982) and Cole (1993)). The angle of the spray nozzle piece in the nasal vestibule and particle velocity from the nozzle also contributes (Cheng et al. (2001)).

The flow in the nose is, however, neither turbulent nor laminar, but lies in the transitional regime (Cole (1993)). Modelling a flow in the transitional regime is seen as a difficult task. Since the turbulence affects the distribution and uptake of medications in the nasal cavity in a positive manner, it was decided to simulate the airflow as a

laminar flow in this study. This would rather under-estimate the degree of deposition than the opposite, if deviating from the real deposition pattern. The difference in particles entering and exiting the nares, is assumed to be the amount of particles that deposit in the nasal cavity. The full distribution of particle sizes in a nasal spray was not considered. It was assumed that the density of the particles is equal to that of water. This is reasonable, because most nasal medications are diluted with water. It is furthermore assumed that the particles are spherical, which for droplets is a quite good assumption. The particles were released on the face of the left nostril medication unit. The simulations were carried out with reasonable values for high and low air flows and different particle sizes.

Below, the conservation equations for mass and momentum for laminar flow are presented. The equation for conservation of mass for the continuous phase, can be written as

( ) 0=∂∂+

∂∂

ii

uxt

ρρ(4)

The right-hand-side of Eq. (4), i.e. the source term, is set to zero, since there is assumed no mass added to the continuous phase from the dispersed second phase, e.g. due to vaporization of liquid droplets. Conservation of momentum in the ith direction in a non-accelerating reference frame is described by

( ) ( ) iij

ij

iji

j

i Fgxx

puu

xt

u++

∂∂

+∂∂−=

∂∂+

∂∂ ρ

τρρ

(5)

The last term on the right-hand-side of Eq. (5), Fi, represents the contributions from the dispersed phase. The stress tensor τij is given by

ijl

l

i

j

j

iij x

u

x

u

x

u δµµτ∂∂

−

∂∂

+∂∂

=3

2(6)

The gas phase is treated as a continuum by use of the above equations, while the dispersed phase is solved by performing trajectory calculations. In this work, it is assumed steady state for the continuum, therefore, the transient terms in Eqs. (4) and (5) can be neglected.

The equation describing the velocity of an individual particle can be found by executing a force balance, i.e. Newton’s 2nd law, for one particle;

( ) ( ) ( )ρρρ −+−−= ppppDpp VguuuuAC

dt

umd

2

1

(7)The first term on the right-hand-side of Eq. (7) represents the drag force, and the next terms represent the gravity force. In addition, we could have added other forces, like the lift force, virtual mass force and Basset force. During the simulations, only the drag force is included in the model. The gravity force will depend on the position of the head, and since it usually is not well-defined how a person is positioned when using the medication device, this force was neglected. Additionaly, while testing the model, it was seen that the gravity force only was important for large particles. This way or the other, the gravity is easy to include in the model, if this is wanted. The other forces are also easy to include, but not of importance in this study. Integrating Eq. (7) with respect to time yields the particle velocity. The time is the time from particle release. The position of the particle is calculated from

pp u

dt

xd

= (8)

Fluent allows the use of either a segregated or coupled solver as the numerical method. In both cases, the CFD code will solve the governing equations for the conservation of mass and momentum, and, when appropriate, for other scalars such as turbulence. Using either method, a control-volume-based technique is used. First, one divides the domain into discrete volumes using a computational grid. See Figure 9 and Figure 10 for illustration of the grid. The governing equations, described above, are then integrated to produce a system of algebraic equations for the dependent variables in every computational cell, such as velocities and pressure.

In this work, the equation system is solved by the segregated solver. By this approach, the equations for the conservation of mass and momentum are solved sequentially, i.e. segregated from one another. Several iterations of the solution loop, is then required to meet a converged solution. The fluid properties are first updated by an initialized solution, before the momentum equations are solved using current values for pressure and face mass

fluxes, in order to update the velocity field. A pressure correction equation is then solved to obtain the necessary corrections to the pressure and velocity fields and the face mass fluxes such that continuity is satisfied. Where appropriate, equations for scalars such as turbulence, energy, species, and radiation are solved using the previously updated values of the other variables. When inter phase coupling is to be included, the source term, Fi, in the appropriate continuous phase momentum equation is updated with the discrete phase trajectory calculations. For relatively small particle size and low mass flow, the coupling between the two phases is weak. Then, we can exclude the inter phase coupling, in order to increase the speed of the calculation. Finally, a check for convergence of the equation set is made, and iterations stop when the convergence criteria is fulfilled. Otherwise, the fluid properties are updated, based on the current solution, and the steps are continued until the convergence criteria is met.

Verification of CFD simulations

Essential for the CFD computations is thorough validation of the results. Without comparison against physical experiments, the simulations are of limited value. For this purpose, two series of measurements are used in this work. The two measurement series give the fractions by-passing the bi-directional nasal passage and exiting through the other nostril before being trapped in an exit filter. The fractions of drug were found by use of gamma-scintigraphy with 99mTc-labeled nebulized particles.

The first serie of measurements was done with a Pari LC Plus nebulizer (Pari, GmbH, Starnberg, Germany) powered by the Pari Boy 038 Compressor. The mass median aerodynamic diameter (MMAD) is 3.5 µm, with a mass fraction of 68% below 5 µm. Bi-directional administration was performed by 20 sec of nebulizing through a tight fitting nozzle introduced approximately 1 cm into the right nostril. The air flow through the nasal passages was constantly of 6 l/min. An exit filter was attached to the exit nostril with an anatomic adaptor designed to avoid distortion of the nasal valve. In Djupesland et al. (2004), this information is more thoroughly described. In this paper, it is also described how the net counts from the gamma camera system are raw counts that must be corrected for the effect of attenuation of the photons originating from the inner surface of the nose. An estimate for the correction factor for the lateal nose counts, was determined to be 1.85. Before calculating the relative distribution of radioactivity, the raw counts were multiplied by this number. Three subjects underwent the present described procedure for bi-directional delivery, with a filter in the exit nostril, and nebulizing by use of the Pari LC plus nebulizer.

The second serie of measurements was performed in the same way as the first in seven subjects, using the Pari Sole nebulizer (Pari, GmbH, Starnberg, Germany) producing a mean particle size of 10 micron. The mass fraction above 5 µm, is for this system approximately 70-80 %.

Analysis of nasal dimensions for the subjects involved in the experiments were done by use of acoustic rhinometry (Rhin 2100, Rhino Metrics AS, Lynge, Denmark), see Djupesland et al. (2004) for more details.

RESULTS AND DISCUSSION

CFD simulations

A typical result from the simulations of the bi-directional flow pattern in Fluent is shown in Figure 11, where the nose geometry is included and a number of particles are released on the face of the left nostril medication unit. The figure shows the path of particles from the introduction into the left nostril and to the back of the nasal cavity, where the particles turn and follow the air stream out of the right nostril. The darker lines show cross-sections of the nasal cavity. The particle traces are coloured by the particle residence time. The colour scale in all the simulation results goes from red representing high values, to blue representing low values.

Figure 11: Flow of particles in the nasal cavity with 6 l/min air and a uniform particle size of 3.5 µm. The darker lines show the cross-sections.

From Figure 11, it is seen that the number of particles in the left nostril is considerably higher than in the right nostril. The difference in particles entering and exiting the nostrils is assumed to be the amount of particles that deposit in the nasal cavity. In this particular simulation, 54.6% of the particles by-passes the bi-directional nasal passage.

We can also focus on the cross-sections of the nasal cavity, illustrated by the darker lines in Figure 11, and study the gas velocity distribution with the air flow of 6 l/min.

Figure 12: The velocity distribution in the cross-sections of the nasal cavity with an air flow of 6 l/min.

Figure 12 shows that the air velocity is highest where the airway passage is the narrowest, i.e. where the air flow turns around the nasal septum, and by the nasal valve in the exit nostril. Due to the placement of the medication device, and hence an expanding of the nasal valve, in the left nostril, the same air velocity increment is not seen around the nasal valve on this side.

We can also pick one of the cross-sections of the nasal cavity, illustrated by the darker lines in Figure 11, and study the velocity distribution from an orthogonally view. Figure 13 shows that the air velocity is highest in the exiting nasal passage, however, the mass flow of air in the two nasal passages is equal.

Figure 13: The velocity distribution in one of the cross-sections of the nasal cavity with a 6 l/min air flow.

Kleven et al. (2004) concluded that the particle deposition rates increased with both increased air velocity and increased particle size, seen in simulations carried out by the procedure described. In this paper, we will only focus on simulations with a 6 l/min air flow, since this is the air flow in both measurement series we are using for the comparison analysis.

Figure 14 though, is showing an equal number of larger particles, i.e. 10 µm, being released on the face of the left nostril medication unit, compared to the 3.5 µm particles being released in Figure 11.

Figure 14: Flow of particles in the nasal cavity with 6 l/min air and a uniform particle size of 10 µm. The darker lines show the cross-sections.

Figure 14 shows that when increasing the particle size, but keeping the air velocity constant, less particles follow the air stream around the nasal septum and out the right nostril. This is due to inertia forces. In this simulation, where the uniform particle size is set to 10 µm, 30.8% of the particles by-passes the bi-directional nasal passage, compared to 54.6% for 3.5 µm sized particles.

Experimental results

In the first serie of measurements, with the Pari LC Plus nebulizer producing a mean particle size of 3.5 µm, and three subjects, the fractions deposited in the filter after exhalation were 28.8%, 23.9%, and 58%. The first two subjects have small nasal dimensions, whereas the last subject has a large nasal dimension. Summarizing these deposition data, result in a mean value of drug captured in the exit filter of 36.9±18.4%. The results from the measurement series are given as means±standard deviation.

In the second serie of measurements, where seven subjects were nebulized by the Pari Sole nebulizer producing a mean particle size of 10 µm, the fractions deposited in the exit filter were 25%, 14.4%, 28.5%, 13.6%, 28.9%,

19%, and 24.8%, resulting in a mean value of 22±7.5%. In this serie, two different concentrations (doses of radioactivity) were used, but this should not influence the percentage deposition rate results.

Comparison of simulations and experimental results

Comparison of the simulations with gamma-scintigraphic studies is promising. Results from Fluent simulations show that for particles with a uniform size of 3.5 µm, the exit flow of particles is 54.6% of the total flow entering the left nostril. The corresponding gamma-scintigrapic result is 36.9±18.4%. Correspondingly, the exit flow of particles with a uniform size of 10 µm is 30.8% of the total flow entering the nose. Here, the gamma-scintigraphic result is 22±7.5%. For direct comparison against the Fluent simulation, the subject that was CT-scanned for this model had, respectively, 23.9% and 19%, in the gamma-study. Hence, the Fluent simulations underestimate the deposition of particles in the nasal cavity.

Certainly, the errors are quite large, both for 3.5 µm and 10 µm sized particles, and even larger when comparison of the data coupled to the person that was scanned for the model. Still, considering physiological phenomena, such as the nasal cycle, causing each side of the nose alternatively to congest and decongest every 3-7 h (Jones (2001)), this is seen as a promising result. It is furthermore important to remember, that models like the one implemented in Fluent, does not simulate the mucus lining, cilia, or different epithelial surfaces, nor replicate the changes in the nasal airway due to the already mentioned nasal cycle. As Zwarth & Guilmette (2001) refers, particle deposition is observed to be dependent on the individual being studied, and the large intersubject variation observed is believed to be due to the anatomical complexity of the nasal airway.

There are also other obvious explanations to the deviations. These sources of errors can be divided into two main groups; the errors related to the Fluent model, and those related to the physical gamma-scintigraphy results. Starting with the last type of errors, the estimated attenuation factor used in the radioactivity counts is probably too high, and hence overestimate the measured particle deposition rate in the nasal cavity. This explanation arises due to the relatively large fraction of particles deposited in the anterior part of the nose just posterior to the nasal valve. This region is mainly positioned outside the bony structure of the nose providing less attenuation of the radioactivity. Minor decrements in the attenuation factor, results in radically higher exit filter deposition rates, i.e. reduced deposition in the nose.

Since the nebulizers used in the gamma-scintigraphy studies have typical particle size distributions, contrary to the equally sized particles used in the Fluent simulations, the simulation results can never be the same as the results from the measurement series. As been shown in the present paper, and in earlier work (Kleven et al. (2004)), the deposition rate in the nasal cavity increases as the particle size increases, i.e. the degree of particles exiting the nostril decreases. In proportion to the comparison against a method based on counting radioactive elements, the assumption of equally sized particles in the Fluent simulations, is even more wrong. In the particle size distributed gamma-measurements, one large particle will count as many, since it is the counting of radioactive elements per mass we find. In Fluent each and every particle counts the same. It will be interesting to see the effect of running the simulations with the exact same particle size distributions as in the gamma-scintigraphic study in the future, instead of assuming uniform particles.

Another error related to the Fluent model, has to do with the assumption of laminar flow. As described earlier in this paper, the flow in the nose will vary between the laminar and turbulent regimes. In areas where turbulence occurs, more particles will be deposited. Analyzing the flow pattern more thoroughly, e.g. testing different turbulence models included in Fluent, will be done in the future. Perhaps the use of a turbulence model will improve the results further.

CONCLUSIONS AND FURTHER WORK

This work shows that by starting with a CT-scan in hospital, one can establish a nasal geometry surface mesh, a volume mesh, and then run simulations on the nasal cavity, yielding trustworthy simulation results, due to promising validation results. It is thus possible, that CFD computations can increase the efficiency of device development and reduce the need for expensive and time consuming laboratory experiments and clinical trials. More validation against physical experiments will, however, be of importance.

The mean nasal attenuation factor for the radioactivity deposited in the nose may be too high because a relatively large fraction of the particles will be deposited in the anterior segment of the nose just posterior to the nasal valve. This region is mainly positioned outside the bony structure of the nose providing less attenuation of the radioactivity. Further studies on regional nasal attenuation factors could improve the quality of the data.

Improvements of the Fluent model and the grid used will be important, too. For instance, it might be that grid size refinement will be necessary. Analyzing the need for use of turbulence models, and introducing the particle size distributions in the simulations, are two obvious areas of improvement. Due to differences in nasal structures from person to person, it will be interesting to establish geometrical grids for several noses, to see the effects of anatomical differences.

NOMENCLATURE

A Projected area of particle [m2]At Area of a triangle of the grid [m2]ci Cost for a triangle amounted to an exponential function of its skewness sCD Drag coefficientFi Source term [kg/(m2⋅s2)]g Gravity [m/s2]mp Particle mass [kg]M Area of the equilateral triangle with vertices on the circumcirle of the triangle At [m2]ni Number of vertices in geometryp Pressure [Pa]s Skewness of a cellt Time [s]u Velocity of the gas phase [m/s]up Particle velocity [m/s]vi Vertex no. iVp Volume of particle [m3]xp Particle position [m]µ Viscosity of the gas phase [kg/(m⋅s)]ρ Density of the gas phase [kg/m3]ρp Particle density [kg/m3]τij The stress tensor [Pa]

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