Dash, Bassingthwaighte, 2004

Model Structure

As blood flows through capillaries the affinity of the protein hemoglobin (Hb) for oxygen (O2) and carbon dioxide (CO2) changes. This affinity is dependent on the relative concentrations of oxygen and carbon dioxide, on the temperature and on the pH of the blood. For example as blood flows through metabolically active tissues it becomes warmer, its pH decreases (the blood becomes more acidic), and the rising partial pressure of CO2 (PCO2) all act to reduce the affinity of Hb for O2. Combined, this causes the Hb in the blood to release O2 into the respiring tissue. In contrast, for blood flowing through the lungs, the reduced temperature, rise in pH (the blood becomes more alkaline), and the loss of CO2 all in crease the affinity of Hb for O2. Together, the conditions in the lung and the respiring tissues maximise the delivery of O2 from the alveolar air to the tissues.

The literature contains several examples of mathematical models which have been developed to describe the dissociation of HbO2 under different physiological conditions. In the model presented here, Ranjan Dash and James Bassingthwaighte formulate equations to describe the O2 and CO2 saturation of Hb in red blood cells. They suggest this relatively simple model can be adopted to to simultaneously analyse the transport and exchange of O2 and CO2 in the alveoli-blood and blood-tissue exchange systems. This paper is cited below:

Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2, pH, 2,3-DPG and temperature levels, Ranjan K. Dash and James B. Bassingthwaighte, 2004, Annals of Biomedical Engineering , 32, 1676-1693. (A PDF version of the article is available to journal subscribers on the Annals of Biomedical Engineering website.) PubMed ID: 15682524

It should be noted that this particular CellML description of the Dash-Bassingthwaighte model is a reduced version of the complete model. A complete translation of the model into CellML was attempted but the model was underconstrained due to circular arguments.