Begell House Inc.
Critical Reviewsâ„˘ in Biomedical Engineering
CRB
0278-940X
33
3
2005
Mathematical Models of Oxygen and Carbon Dioxide Storage and Transport: The Acid-Base Chemistry of Blood
209-264
10.1615/CritRevBiomedEng.v33.i3.10
S. E.
Rees
Center for Model Based Medical Decision Support Systems, Aalborg University, Denmark
S.
Andreassen
Center for Model Based Medical Decision Support Systems, Aalborg University, Denmark
This article describes a mathematical model of the acid-base chemistry of blood. The model is formulated from first principles by considering the "components" of blood and the reaction equations in the plasma and erythrocyte fractions. Equations are formulated to describe the total concentration of blood components, the physicochemical properties, and the equilibrium position of reactions. The model includes 28 equations and 12 parameters. All equations can be solved from six variables included in the model. The model uses simple mathematics, without introducing intermediate concepts or linear coefficients necessary for algebraic solution. Model equations are solved simultaneously using numerical methods. Model parameters are estimated and the model verified for plasma, fully oxygenated blood, and deoxygenated blood. Published data are used to estimate model parameters and normal conditions and to verify model simulations. The model reproduces experimental results, including addition or removal of CO2, or strong acid to plasma; CO2, strong acid or haemoglobin to blood; and the effects of deoxygenating blood. The model can also be used as the basis for models of whole body CO2 transport as illustrated in the accompanying article. As such, it is possible to simulate the effects on blood of physiological changes in ventilation or metabolism.
Mathematical Models of Oxygen and Carbon Dioxide Storage and Transport: Interstitial Fluid and Tissue Stores and Whole-Body Transport
265-298
10.1615/CritRevBiomedEng.v33.i3.20
S.
Andreassen
Center for Model Based Medical Decision Support Systems, Aalborg University, Denmark
S. E.
Rees
Center for Model Based Medical Decision Support Systems, Aalborg University, Denmark
This article describes a mathematical model of whole-body O2 and CO2 transport. The model includes representation of the acid-base chemistry of the blood, interstitial fluid, and tissues, plus transport of O2 and CO2 between compartments representing tissues, interstitial fluid, arterial and venous blood, and lungs. The model includes equations for calculation of all concentrations in the compartments, including equations describing the physicochemical properties and reaction equations of interstitial fluid and tissues. In addition, the model includes equations that describe the flow of substrate between the compartments and differential equations allowing calculation of the changes in state variables caused by the flow of substrates between the compartments. This model is designed to calculate the effects of metabolic and respiratory perturbations, such as variation in breathing pattern or production of strong acid at the tissues. The model reproduces the results of published experiments when used to simulate (1) normal conditions in the lungs, arterial and venous blood, interstitial fluid, and tissues during normal ventilation; (2) the characteristic two-exponential response to changes in minute ventilation; and (3) the relationship between arterial blood values of PCO2 and HCO3,p during inspiration of different fractions of CO2.