# The S Factor--a New Derived Hemodynamic Oxygenation Parameter--a Useful Tool for Simplified Mathematical Modeling of Global Problems of Oxygen Transport.

## Publication/Presentation Date

1-1-1997

## Abstract

We describe a new derived hemodynamic oxygenation parameter, the S factor (S). The factor is based on oxygen delivery and oxygen consumption and can range from -3 to 1. It allows simplified mathematical modeling of clinical problems of oxygen transport and can be applied to many clinical situations. A new hemodynamic oxygenation parameter, the S factor (S), is introduced as an aid to mathematical modeling. It is defined as follows: [formula: see text] (DO2 = oxygen delivery, VO2 = oxygen consumption) S can theoretically vary from -3 (DO2 = VO2) to +1 (VO2 = 0). When DO2/VO2 = 4 (ie. OER = 0.25), S = 0. An S < 0 implies utilization of reserve oxygen transport capacity. An S > 0 implies increased oxygen delivery in relation to oxygen consumption (ie. "shunted oxygen delivery"). By algebraic manipulation and substitution of the components of DO2 into Equation 1: DO2 = Q x Ca x 10 DO2 = Q [(Hb)(Sat)(1.36) + PaO2(.0031)] 10 (2) the following equations can be derived: [formula: see text] [formula: see text] Ca - Cv (Ca = arterial content, Cv = venous content) can be determined by substituting components of oxygen consumption: VO2 = Q (Ca - Cv) x 10 (5) into equation 1 and solving for Ca - Cv. [formula: see text] Equation 6 can be simplified to: [formula: see text] A previously defined relationship between mixed venous PO2 (PvO2) and DO2/VO2 (where calculated P50 is 26.6 +/- 1.0) can be used to modify S in a clinically relevant manner. PvO2 = 5.44D O2/VO2 + 18.16 (8) The relationship between S and PvO2 can be defined by substituting Equation 4 into Equation 1 and solving for PvO2 PvO2 = [21.76/(1-S)] + 18.16 (9) As an example, at a PvO2 of 28 torr (anaerobic threshold), S = -1.2. The relationship between PvO2 and S is shown in Figure 1. S, which can also be defined as 1-4(VO2/DO2) or 1-4(OER), is a useful tool for mathematical modeling of global problems of oxygen transport because the previously derived equations with the S value allow the components of oxygen transport to be interrelated in a clinically relevant manner. Additional advantages of using S in mathematical modeling are: 1. Conceptually it 'fits' in that in regards to the sign (+ or -), as a -S implies utilization of reserve oxygen transport capacity and a +S implies wasted or excess oxygen delivery (shunted). 2. These concepts are easily quantified using the S factor. 3. It 'spreads out' the difference between values for parameters (OER or S) integrating components of oxygen transport, ie. in the 'normal state' regarding oxygen transport, OER = 0.25 and S = 0. At the anaerobic threshold (PvO2 = 28 torr), OER = 0.55 and S = -1.2. Thus, the change in OER from 'normal state' to anaerobic threshold is 0.3 (0.55-0.25) and the change in S is 1.2. This represents a four-fold increase. Four examples of mathematical modeling of global problems of oxygen transport using the S factor are described below.

## Volume

411

## First Page

149

## Last Page

155

## ISSN

0065-2598

## Published In/Presented At

Farrell, K., & Wasser, T. (1997). The S factor--a new derived hemodynamic oxygenation parameter--a useful tool for simplified mathematical modeling of global problems of oxygen transport. *Advances In Experimental Medicine And Biology*, *411*149-155.

## Disciplines

Medical Sciences | Medicine and Health Sciences

## PubMedID

9269423

## Department(s)

Department of Medicine, Department of Medicine Faculty

## Document Type

Book Chapter