AIMS

The aim of this project is to develop a comprehensive simulation tool for the study of inhaled therapies. Objectives for the simulation are therefore to track the progress of the drug delivered from an inhaler device in whatever form that may take (particle or aerosol) through the entire respiratory system. In particular an accurate prediction of the distribution of the drug within the lung would enable targeted drug delivery depending on the desired purpose of the drug i.e. whether the action of the drug is to take place on a local or systemic level. 

The proposed model for the respiratory system is a compartmental model of the whole system with different mathematical models used to illuminate the characteristics of individual compartments. The emphasis is on the integration of 3-D computational fluid dynamics (CFD) in realistic geometries with the complete systemic model. The delivery device components together with the respiratory system are divided into the compartments shown below. 

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The delivery device together with the upper respiratory tract, and tracheo-bronchial tree are modelled using 3-dimensional CFD flow analysis, while the drug uptake and clearance are modelled using a lumped-parameter pharmacokinetic approach 
 

SEGMENTATION OF AIRWAYS FROM MEDICAL IMAGES

The accurate anatomical representation of the complex 3-dimensional geometry of the upper respiratory tract and the tracheo-bronchial tree are to be determined from medical images. The extraction (the 'segmentation') of this geometry is developed by the University of Mainz and described briefly below. 

Of current imaging modalities, high resolution CT (HRCT) provides 2D images with maximum spatial resolution, and are especially suited to the measurement of airway diameters and lung density. They are frequently performed as inspiratory/expiratory pairs, and they provide static information at different levels of respiration. 

Segmentation of airways and airspaces from soft tissue on the basis of CT data sets is quite straightforward due to the high-density differences between the air-filled lumen and the surrounding tissue. Since the density differences are high, the lung is generally referred to as a high-contrast organ. Obviously, simple thresholding techniques can be used to segment the trachea, which is surrounded by high density soft-tissue. However, at the main bronchi the density difference between the air-filled lumen and the delicate bronchial walls is much smaller. Since selective segmentation of the airways must be obtained it is necessary to differentiate air-filled alveolar spaces surrounding the bronchial walls and the lung tissue at the same time. This requires dedicated post-processing software, as reliance on mere thresholding is inadequate. Such techniques will prevent 'leaking' from the airways into the alveolar space. Consequently semi-automatic segmentation software, called SegoMeTex, has been written especially customised for the bronchial tree.  

Three different methods were developed: 

•3D Seeding for segmentation of the trachea 
•2D Bronchus finder to counteract partial volume effects caused by the slice thickness 
•2D peripheral airway finder to counteract partial volume effects occurring within the individual slice

Merging of  these three methods has produced an effective hybrid system. The 3D-algorithm starts from a seed point which is set manually. From there it detects the air-filled lumen of the trachea and the central bronchi by the use of a density threshold. Additional  texture analysis features are introduced to prevent “leaking out” of the segmented volume e.g. into emphysematous lung. This part of the hybrid algorithm detects the trachea and main bronchi with high specificity. The results of the seeding-algorithm provides starting points for the 2D airway finder. It is able to detect airways that lie in the plane of the slice. Substitution of missing details of the trachea and the central airways is also possible (see illustration below). The results of the 2D airway finder are monitored by a protocol to prevent “leaking”. In order to counteract spatial volume effects, the 2D peripheral airway finder module has been implemented to find very small bronchi (approx. 2 mm). It uses template matching evaluated by a fuzzy-logic. 

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The improvement of each of the three methods on segmentation results can be seen in the animation below: 

Click here for animation

Click here for information on hyperpolarise 3 He imaging for validation.

MODELLING, 3D FLOW ANALYSIS AND DEPOSITION

3D models of the upper respiratory tract and tracheo-bronchial tree

The compartmental model together with the 3D models of the airways are being developed by the University of Sheffield with the use of CFX5.4 and SIMULINK from MathWorks.

Detailed geometrical information for flow analysis is highly desirable for a number of reasons. While idealised geometries have been used extensively in flow studies of various parts of the respiratory tract, their strength lies in understanding the underlying mechanisms of transport and mixing in the respiratory tract. Realistic geometries however allow a more thorough analysis of actual flow patterns and corresponding deposition in a geometry that is highly variable from subject to subject. In addition to this, simulation of flow can be carried out for different lung pathologies that will clearly affect  the geometry and mechanical properties of the respiratory tract in many different ways. 

A volume mesh is generated from the results of the segmentation in the following way: 

• Bitmaps stacks containing the results of the segmentation algorithms are read into MATLAB
• An isosurface is created around the segmented regions of the bitmaps 
• The isosurface consisting of tessellating triangles is imported into a 3rd party software in the form of nodal coordinates and connectivity. CFX is currently modifying the import functions to enable import of the surface mesh directly into CFX.5.4. 
• Boundary nodes are picked within ANSYS and the volume mesh generated from the triangular elements making up the surface. 
• The volume mesh and information about the boundary nodes are imported into CFX5.4. 

This reconstructed geometry can be rendered in a number of ways for visualisation purposes as shown in the animations below. The 3D reconstruction and mesh generation can be carried out for individual patients. 

The animation below shows the reconstruction of the oro-nasal cavity. Note that the CT scans were taken at end inspiration during breath hold. As a result the larynx closes and the resulting isosurface creates two separate structures. The oral cavity is not visible in this example due to the fact that the subject’s tongue may be touching the roof of the oral cavity.

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The animation below shows an example of a reconstructed tracheo-bronchial tree down to the 5th generation 

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Steady flow analysis is carried out in the tracheo-bronchial geometry shown above. A velocity boundary condition is set at the inlet, and pressure boundary conditions (of atmospheric pressure) are set at the outlets. The figures below  show the result of a simulation for which the inlet velocity (at the top of the trachea) is set to 0.05ms^-1. The k-ε turbulence model within CFX5.4 is used to calculate turbulent flow. Isosurfaces of equal fluid velocity are shown in the figure on the left while pressure drop is shown on the right. The deep blue shows surfaces with lowest velocity and the red shows surfaces with the highest velocity. The pressure drop down the tree can be seen to occur as expected. It may appear curious that the fluid velocity is greater in the lower branches. This is simply a consequence of the fact that each vessel from one bifurcation point to the next tapers significantly.  The method of visualisation used here enables one to see the different values of core flow. An important observation can be made here that in many senses is intuitive but is encouraging to see borne out by the flow analysis: the cross-sectional area of the right main bronchus (on the left of the figure below) and of the branches orginating from the right main bronchus are slightly greater than those of the left main bronchus (on the right of the figure below) resulting in a larger proportion of the flow being directed down the right lung. The consequences of asymmetry in the airways are clearly demonstrated in this realistic asymmetric geometry; in reality it is indeed the right lung that is known to be larger and receive greater ventilation. 

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An example of simulated expiratory flow  below shows results for such a simulation with the pressure at the opening of the trachea set to atmospheric and fluid velocity boundary conditions at each ending set to 0.05 ms-1. Again a k-ε turbulence model is used to carry out the flow analysis. The velocity at each ending need not be identical. Indeed in the final compartmental model this 3D component will be coupled to the peripheral airways compartment resulting in different pressures at these boundaries. 

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While the boundary conditions used here are not realistic, integration of this model into the compartmental framework will take into account boundary conditions at the interfaces with other compartments and therefore more realistic pressures here. 

The results for a transient flow analysis can be seen in the animation below. Here the velocity at the top of the trachea varies sinusoidally as a function of time, with peak inspiratory velocity of 0.5 ms^-1 and peak expiratory velocity of -0.5 ms^-1 over a period of 4 seconds. The animation shows massless particles in the resulting transient flow field. 

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Device models

Several types of delivery devices and spacers or holding chambers will be considered, ranging from ventilator delivered nitric oxide through to pressurised metered dose and dry powder inhalers from Aventis Pharma. The following section concentrates on flow and particle deposition analysis in the E-haler - a multi-capsule, unit-dose, dry powder inhaler from Aventis Pharma. The CAD representation is provided by Aventis Pharma and the flow analysis has been carried out at CFX.

There are a number of issues in the fluid-dynamic performance of delivery devices which manufacturers face. These include:

• flow rate/pressure drop characteristics
• residence time distribution
• particle trajectories
• deposition and impaction

The CFD models which are being employed and developed within COPHIT provide detailed information to the designer on the flow behaviour within the devices. The CFX-5 software is used for the flow simulations.

Figure 1 shows the original CAD model of the Aventis Pharma E-haler, whilst Figure 2 shows the surface mesh created in CFX-5. CFX-5 uses mixed-element meshes which can comprise tetrahedra, hexahedra, pyramids and prisms. Inflation of the elements adjacent to the walls of a device allows accurate solution of the flow in the boundary layers.

Figure 1 CAD model of AventisPharma Ehaler		Figure 2 CFX-5 Surface Mesh

In Figure 3, streamlines coloured by the local flow speed reveal the complex flow patterns within the device. The flow is driven by the difference in pressure between the air inlets and the mouthpiece, which can be made to vary with time to replicate real inhalation profiles.

Figure 3 Streamlines Coloured by the Local Flow Speed

Figures 4.1 to 4.4 are plots of the trajectories of typical drug particles of different sizes. Smaller particles are seen to follow the air flow more closely than larger ones, which due to their inertia, tend to spiral out towards the outer wall of the device.

Figure 4.1 Tracks for 0.1 micron Particles		Figure 4.2 Tracks for 0.3 micron Particles
Figure 4.3 Tracks for 1.0 micron Particles		Figure 4.4 Tracks for 2.0 micron Particles

Link to image of all four figures

Pharmacokinetic models for drug uptake and clearance

Good pharmacokinetic models of drug uptake are needed to calculate the concentration of drug in the blood after it has passed through the lung and the subsequent clearance from the body. Pursuit of a satisfactory biokinetics model (at the University of Shefffield) to describe the uptake of drugs at the alveolar membrane and via the oral and infused route  has resulted in the formulation of a simplistic, but robust three-compartment model. This is designed to be the simplest system that can accommodate the parameters of pharmaceutical profiles required for medical approval (eg. FDA). These are shown below: 
 

 
The pharmacokinetic model is depicted below:

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•  A first order description of reaction processes based on Ficks law has been employed. 
• The simplicity of the model ensures that all relevant rate constants can be uniquely determined.
• Data has been collected on some well characterised pharmaceuticals (eg. Iloprost) in order to test and validate the model. It has demonstrated satisfactory description of pharmacokinetic data (ie. generally to within 10% - see table...)

 
 Pharmaceutical data from ….       Grant et al. Drugs 43(6);889-924  1992 
 

• The limitations of this biokinetic model need to be established, and this is being pursued by monitoring its ability to cope with an increasingly wide selection of pharmaceuticals. 
• The model has been constructed in Simulink to comply with the wider programming requirements of COPHIT. 
• Systemic biokinetics and alveolar exchange: 
• The model  has demonstrated satisfactory description of systemic biokinetics.  Attention must now be focused on drug transfer across the alveolar membrane since this is the primary feed to the systemic biokinetic model. 

VALIDATION

The 3D simulations for flow analysis of the gas and particle/droplet deposition in the flow field will need to be validated before the software can be used with confidence. 3 main validation routes are considered and described below: 

Hyperpolarised Helium-3 Magnetic Resonance Imaging

The use of hyperpolarised noble gases with Magnetic Resonance Imaging (MRI) is a recent approach to the imaging of ventilation. The University of Mainz is responsible for leading this area of validation.

In contrast to conventional (proton-based) MRI techniques, a gas is used as a “contrast agent”, which can be directly visualised, thus revealing the airways in a more direct manner rather than relying on indirect effects (oxygen in blood or differences in tissue). Normally, the density of gases is too low to produce a detectable signal. This drawback is overcome by artificially increasing the amount of polarisation per unit volume (hyper-polarisation) using an optical pumping technique. 

For the specific purposes of ventilation imaging, 3 He provides a number of advantages over 129 Xe. The polarisation is higher, and the gyromagnetic ratio of 3 He is approximately three times that of 129 Xe, yielding a signal-strength that is almost an order of magnitude higher [5]. The lack of anaesthetic effects of 3 He has made patient studies easier to expedite. The main disadvantage of 3 He is its limited availability compared to the natural abundance of 129 Xe. 

Another unique aspect of gas imaging is the ability to image dynamic ventilatory function directly. With the appropriate fast imaging sequences, cine image reconstruction can show continuous visualisation of the respiratory cycle, including inspiration, distribution of 3 He within the alveolar space, and expiration. Distribution analysis of normal and abnormal ventilated regions and corresponding time constants becomes feasible. An example of such images are shown below. 

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The figure above shows a time series of images acquired following inhalation of a 286 ml bolus of hyperpolarised helium gas by a healthy volunteer. These images are projections, in which anatomical detail is blurred compared to slice-selective morphological scans. 

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3 He MRI is an attractive new imaging modality. It is ideally suited to the visualisation of pulmonary ventilation and to the provision of quantitative data on ventilation defects and the time course of the ventilation of different alveolar regions. The application of dynamic imaging is particularly promising as a means to expand radiological methods to the distribution analysis of ventilation. In COPHIT, hyperpolarised MRI of 3 He gas will be used as a means of providing static and dynamic images of gas inhalation. It will provide information from normal volunteers and from patients with a variety of lung diseases, which will help to validate the predictions of the lung model. 

Concentration measurements in the airways

INO Therapeutics is at the centre of developments in nitric oxide delivery. They have introduced Pulmonox and Pulmonix-mini, which are automatically controlled nitric oxide dosing units for use with ventilated patients. In addition to this they are able to place catheters - that measure the concentration of nitric oxide - at different sites in the tracheo-bronchial tree for both spontaneously breathing and ventilated subjects. The concentration measurements will also be used for validation of the 3D flow models for inhaled gas such as helium and nitric oxide. The protocols are shown shematically in the diagrams below:

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Gamma Scintigraphy

The validation of particle deposition models within the 3D models of the airways is to be carried out by comparing the results with gamma scintigraphy images of the lungs. Aventis will lead this investigation in which the aerosol or dry powder is labelled with a radio-isotope (e.g. Te 99m) and then inhaled using one of the delivery devices. The lungs will then imaged using a gamma camera and the deposition of the actual medication consequently analysed.

The flow field and particle trajectories within the Aventis E-haler can be seen here.