Ben-Tal, 2006

Model Status

This CellML model runs in both PCEnv and COR to recreate the published results. The units have been checked and they are balanced. Please note that this particular version of the CellML model does not correspond with any one of the four possible models from the original publication. Rather it is a combination model, made up of equations 2,7,9,10,11,12,13,16, and 20.

Model Structure

Data from several different experiments suggest that complex interactions between the respiratory system and cardiac output exist in humans. Such interactions include the synchronisation between lung ventilation rate and the heart beat, and other examples. Mathematical models to describe the mechanisms underlying these interactions are being developed with the aim of improving our understanding of these physiological phenomena.

Historically, gas exchange in the lungs has been modelled and studied at various different levels of detail. The 2005 paper by Alona Ben-Tal described here presents a hierarchy of models of increasing complexity for gas exchange in the human lungs:

  • Model A: The first model represents the lung as an inflexible, single compartment (see below);

  • Model B: The second model represents the lung as a flexible, single compartment (see below);

  • Model C: The third model represents the lung as a flexible, single compartment with gas exchange (see below); and

  • Model D: The final model represents the respiratory system as a flexible, multi-compartmental model with gas exchange and gas transport (see below).

The models developed in this paper provide a mathematical framework which is able to link together molecular scale and whole systems scale models. As an integral part of developing this framework, two commonly made assumptions have been re-examined:

  • 1) the hidden assumption that air flow through the mouth is equal to the rate of volume change in the lungs; and

  • 2) the assumption that the process of oxygen binding to hemoglobin is at near equilibrium.

Conditions under which these assumptions are valid have been studied, and the models are sufficiently flexible to be able to qualitatively explain a range of physiological observations.

The models have been described here in CellML (the raw CellML descriptions of the four different Ben-Tal 2005 models can be downloaded in various formats as described in ).

The CellML files provided below represent the 2 different versions of the aforementioned models A,B,C and D.

Schematic diagram of inflexible lung model.

Schematic diagram of flexible lung model.

Schematic diagram of flexible lung model with gas exchange.

Schematic diagram of flexible lung model with gas exchange and gas transport.

The complete original paper reference is cited below:

Simplified models for gas exchange in the human lungs, Alona Ben-Tal, 2006. Journal of Theoretical Biology , 238(2), 474-495. PubMed ID: 16038941

Full text (HTML) and PDF versions of the article are available to subscribers on the Journal of Theoretical Biology website.