טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentGendel Sergey
SubjectDiffusion of Fine Particles in lung Alveoli
DepartmentDepartment of Applied Mathematics
Supervisor Professor Emeritus Shimon Haber


Abstract

Lungs are built from 20-23 binary bifurcations of airways. The most peripheral generations of airways are covered with alveoli, which are outcroppings of the respiratory bronchioles, and the primary sites of gas exchange with the blood. Alveoli appear starting from bifurcation 16, and their number increases downward the lung tree.

 During the breathing process different particles are inhaled, a fact that can be used as efficient tool for drug delivery. At the same time, the lungs are constantly exposed to air borne pathogens and dust particles that can cause serious illness.

Until lately,  it has been widely accepted that gravitational settling and deposition of fine particles deep inside the lung can reasonably be predicted, assuming that  a simple Poiseuille flow can represent the flow field inside the acinus, ignoring completely the complexity of the flow that exists inside the alveoli.

Another, more complex, model was proposed by Haber et al  (2000).

According to this model the alveolus may be approximated geometrically by a spherical cap attached at its rim to the alveolar duct. Use of this geometry promises that the flow structure inside the alveolus is likely to present a more faithful portrayal of real events than in previous, simpler, models. Using Haber’s model of the alveolus unit, the velocity field in lung alveolus induced by shear flow and by alveolus expansion and contraction was solved.

In the present work, relying on this solution, we built the differential model describing transport phenomena of fine particles

 (less then 1.3μm ), moving in the foregoing alveolar flow field and simultaneously subjected to a gravity field. The resulting model is governed by three-dimensional convection-diffusion equation which we solved numerically.

A monodispersed bolus is introduced at a given location and its temporal distribution is calculated assuming that a particle that reaches the alveolar wall is also deposited.

We used the numerical solution to investigate the influence of some parameters, like as: particle diameter, alveolus location along the acinar tree, the initial location of the particles and gravity (to some extent),  specifically the role of diffusion on the deposition of inhaled particles in the pulmonary acinus.