An anatomically based mathematical model of the human lungs, applied to gas mixing and water vapour and heat transport
Restricted Item. Print thesis available in the University of Auckland Library or available through Inter-Library Loan. This thesis has focused on developing an anatomically-based model of the human
lungs, initially to be used for modelling transport problems.
An algorithm is presented for generating three-dimensional conducting airway
models into anatomically-based host volumes. The algorithm uses a bifurcating
distributive method to generate a three-dimensional tree that fills an anatomically
based pleural cavity. Branching, length, and diameter ratios from the generated model
are consistent with experimental results, and the mean branch angles are consistent
with a theoretical 'ideal' angle. The proportion and number of branches in each of the
five model lobes are similar to those from the literature.
A lumped parameter model for respiratory airway gas mixing is developed,
based on results from gas mixing in a multi-branching model. Development of
a computationally small respiratory airway model for coupling to the asymmetric
conducting airway model is necessary to ensure that solution of transport equations in
the coupled model are feasible. The lumped parameter model is calibrated using gas
mixing results from an anatomically-based multi-branching respiratory airway model,
over a wide range of simulation conditions and model sizes. The lumped parameter
model is in the form of regression equations that are used to predict transitional
bronchiole concentrations throughout expiration, based on inspiratory parameters that
are particular to each coupled lumped parameter model.
The lumped parameter respiratory airway model is coupled with the asymmetric
conducting airway model to simulate gas mixing in the entire lung system. Results
from full lung gas mixing show the importance of respiratory airway asymmetry and
incomplete mixing, conducting airway asymmetry, blood gas exchange, and airway
mechanics, on generation of a sloping alveolar plateau in phase I11 of the washout
curve. Respiratory airway asymmetry and incomplete mixing is shown to have the
greatest contribution to S, (the slope of the alveolar plateau normalised by the mean
expired gas concentration) in the first breaths of multiple washin tests. Conducting
airway asymmetry is shown to increase S, in a manner consistent with the literature,
even when flow is distributed uniformly throughout the model. Blood gas exchange
moderates the S, curve such that the plot of S, against breath number approaches
a plateau after approximately 18 breaths. Airway mechanics are represented in this
study by idealised pleural pressure gradients. The pleural pressure gradients are
shown to have a complex effect on S,. This study highlights the import contribution
made by each of these factors to generation of S, over multiple breaths.
A model of water and heat exchange in the asymmetric conducting airway model
is developed for investigating penetration of the airways by unconditioned gas, and
for investigating airway drying. The water and heat transfer model incorporates
radial layers of airway surface liquid, sub-mucosa/tissue, and a surrounding capillary
bed. Additional layers can be included in the model to simulate an endotracheal tube
and associated condensation. Unlike other models in the literature, the respiratory
transfer model presented in this study uses power law curves to describe the velocity,
temperature, and concentration across an airway. The model therefore solves coupled
transport and transfer equations both axially and radially. The transfer of water vapour
or heat is governed by the concentration and temperature gradients at the interface
between the surface liquid and the air in the lumen: empirically derived transfer
coefficients are not used to predict heat and mass transfer in this model.
Comparison of results from the water and heat transfer model with experimental
results shows that the model presented in this study produces airway temperatures
close to experimental measurements for ventilation up to 60 L .rnin-' with an
inspired temperature of 30.3"C. For combined higher ventilation rates and lower
temperatures the model does not sustain sufficient wall cooling during inspiration.
The model simulates temperatures down an endotracheal tube that are close in value
to experimental temperatures. Airway drying in the model is shown to be dependent
on the rate of replenishment of the airway surface liquid by the surrounding tissue.