Mathematical Modeling/Problem Solving in Global Oxygen Transport

A simplified approach to mathematical modeling/problem solving in global oxygen transport is presented. In addition to standard oxygen transport formulae, it uses the S-Factor and a mathematical relationship relating SvO₂ to the ratio DO₂/VO₂. This method allows the determination or specification of SvO₂, PvO₂, P₅₀, and systemic shunting in the context of this simplified approach. Heretofore this has not been possible. With this approach, essentially all clinical problems in global oxygen transport can be dealt with. This is illustrated by the broad scope of the five problems presented.

Key Words: mathematical modeling, oxygen transport, mixed venous oxygen saturation, systemic shunting

Abbreviations: Ca, oxygen content of arterial blood (volumes %), Cv, oxygen content of mixed venous blood (volumes %), Cc, oxygen content of pulmonary capillary blood (volumes %), Ca – Cv, oxygen extraction (volumes %), OER, oxygen extraction ratio, PAO₂, pulmonary alveolar oxygen tension (torr), P_atm, atmospheric pressure (torr), P_H2O, water vapor pressure (torr), PaO₂, oxygen tension of arterial blood (torr), PaCO₂, partial pressure of CO₂ in arterial blood (torr), PvO₂, oxygen tension of mixed venous blood (torr), P₅₀, oxygen tension at 50% saturation of hemoglobin, SaO₂, oxygen saturation of arterial blood (%), SvO₂, oxygen saturation of mixed venous blood (%), DO₂, oxygen delivery (ml/min/m²), VO₂, oxygen consumption (ml/min/m²), Q, cardiac output (L/min/m²), Q_s, ‘shunted’ flow [systemic] (L/min/m²), Q_Spul, ‘shunted’ pulmonary blood flow (L/min/m²), Hb, hemoglobin concentration (gms.%), URO₂TC, utilization of reserve oxygen transport capacity (%), S, S-Factor, FiO₂, fraction of inspired oxygen, RQ, respiratory quotient