Applications of the single path convection diffusion model of the human respiratory system
Abstract
The volume based CO$\sb2$ washout curve, or capnogram, can yield large amounts of anatomical and physiological information. The Single Path Model (SPM) consists of the convection-diffusion equation with a source term applied to a symmetric anatomic model of the airways. The numerical SPM, using a finite volume method, can generate capnograms and intra-airway gas concentration profiles for a variety of simulated breathing conditions. We have incorporated four effective diffusivities into the numerical SPM. By hypothesizing that the acinus is designed to minimize longitudinal diffusive resistance, we found two optimal acinar total airway cross sectional area-distance functions, A(x). For resting breathing and molecular diffusivity, A(x) increases as the square root of x, while for maximal ventilation and Taylor diffusion A(x) is exponential in x. Several pediatric SPMs were developed which yield normalized slope and dead space data in agreement with experimental measurements on children. A totally noninvasive method of cardiac output and mixed venous P$\rm\sb{CO2}$ recovery was described. Using a subject's normalized phase III P$\rm\sb{CO2}$ slope (NS) vs. tidal volume data, a factor $\beta$ is found which matches the subject's acinar airway dimensions to the SPM. The SPM can then simulate the subject's breathing using the same tidal volume, frequency, and $\beta$, and compare the numerically generated $\rm\dot V\sb{CO2}$ and NS with the subject's actual values. From this comparison process, cardiac output and mixed venous P$\rm\sb{CO2}$ were recovered within 15% and 10% of experimentally measured values, respectively. Multiple breath and single breath N$\sb2$-O$\sb2$ washout curves were modeled with the SPM. It was shown that the source term plays an important role in steady state multiple breath N$\sb2$ body tissue degassing. The unsteady state single breath N$\sb2$-O$\sb2$ test may require a modified source term to account for degassing of the tissues and/or N$\sb2$ gas trapped behind collapsed airways during the initial exhalation to reserve volume. ^
Subject Area
Biology, Animal Physiology|Engineering, Biomedical|Biophysics, General
Recommended Citation
Joseph Daren Neff,
"Applications of the single path convection diffusion model of the human respiratory system"
(January 1, 1996).
Dissertations available from ProQuest.
Paper AAI9636189.
http://repository.upenn.edu/dissertations/AAI9636189