Format

Choose Destination
Acta Biotheor. 2016 Jun;64(2):161-96. doi: 10.1007/s10441-016-9278-z. Epub 2016 May 21.

# Gas Exchange Models for a Flexible Insect Tracheal System.

### Author information

1
School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa.
2
DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Private Bag 3, Wits 2050, Johannesburg, South Africa.
3
School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa. shirley.abelman@wits.ac.za.
4
DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Private Bag 3, Wits 2050, Johannesburg, South Africa. shirley.abelman@wits.ac.za.
5
School of Animal, Plant and Environmental Sciences, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa.

### Abstract

In this paper two models for movement of respiratory gases in the insect trachea are presented. One model considers the tracheal system as a single flexible compartment while the other model considers the trachea as a single flexible compartment with gas exchange. This work represents an extension of Ben-Tal's work on compartmental gas exchange in human lungs and is applied to the insect tracheal system. The purpose of the work is to study nonlinear phenomena seen in the insect respiratory system. It is assumed that the flow inside the trachea is laminar, and that the air inside the chamber behaves as an ideal gas. Further, with the isothermal assumption, the expressions for the tracheal partial pressures of oxygen and carbon dioxide, rate of volume change, and the rates of change of oxygen concentration and carbon dioxide concentration are derived. The effects of some flow parameters such as diffusion capacities, reaction rates and air concentrations on net flow are studied. Numerical simulations of the tracheal flow characteristics are performed. The models developed provide a mathematical framework to further investigate gas exchange in insects.

#### KEYWORDS:

Diffusion; Discontinuous gas exchange; Hemolymph; Respiration; Spiracle

PMID:
27209375
DOI:
10.1007/s10441-016-9278-z
[Indexed for MEDLINE]