Predictive validity of a novel non-invasive estimation of effective shunt fraction in critically ill patients

Background Accurate measurement of pulmonary oxygenation is important for classification of disease severity and quantification of outcomes in clinical studies. Currently, tension-based methods such as P/F ratio are in widespread use, but are known to be less accurate than content-based methods. However, content-based methods require invasive measurements or sophisticated equipment that are rarely used in clinical practice. We devised two new methods to infer shunt fraction from a single arterial blood gas sample: (1) a non-invasive effective shunt (ES) fraction calculated using a rearrangement of the indirect Fick equation, standard constants, and a procedural inversion of the relationship between content and tension and (2) inferred values from a database of outputs from an integrated mathematical model of gas exchange (DB). We compared the predictive validity—the accuracy of predictions of PaO2 following changes in FIO2—of each measure in a retrospective database of 78,159 arterial blood gas (ABG) results from critically ill patients. Results In a formal test set comprising 9,635 pairs of ABGs, the median absolute error (MAE) values for the four measures were as follows: alveolar-arterial difference, 7.30 kPa; PaO2/FIO2 ratio, 2.41 kPa; DB, 2.13 kPa; and ES, 1.88 kPa. ES performed significantly better than other measures (p < 10-10 in all comparisons). Further exploration of the DB method demonstrated that obtaining two blood gas measurements at different FIO2 provides a more precise description of pulmonary oxygenation. Conclusions Effective shunt can be calculated using a computationally efficient procedure using routinely collected arterial blood gas data and has better predictive validity than other analytic methods. For practical assessment of oxygenation in clinical research, ES should be used in preference to other indices. ES can be calculated at http://baillielab.net/es. Electronic supplementary material The online version of this article (10.1186/s40635-019-0262-1) contains supplementary material, which is available to authorized users.


=̇2.
(1) The model performs in the blood (using Equation 4 and Equation 5) an analogous calculation to that performed in the alveolar space (using Equation 2 and Equation 3) by the alveolar gas equation.
For simplicity and computational speed, we used a three compartment (deadspace, shunt fraction and a single exchanging lung compartment) steady-state model. Dead space is the volume of each tidal volume breath that does not reach parts of the lung participating in gas exchange; shunt fraction as the analogous, but hypothetical, fraction of blood that passes through the lungs without participating in gas exchange. Alveolar ventilation is determined by respiratory rate, tidal volume and dead-space, lung perfusion by cardiac output and shunt fraction -all determined by the user.

Inter-conversion between whole blood content and partial pressures
We employed the formulae of Dash and Bassingthwaighte [3], with minor correction and modifications, and their analytical or numeric inversions as appropriate.
Whole blood content of oxygen and carbon dioxide were expressed as functions of their respective partial pressures, erythrocyte pH and the P 50 (oxygen) of haemoglobin. Unfortunately, the equations for whole blood content are not amenable to analytical inversion. We obtain numeric solutions using root-finding algorithms.
The Henderson-Hasselbalch equation describes the relationship between pH, acid and salt and can be applied to the bicarbonate buffer system that operates in mammalian blood (Equation 8).
The van Slyke equation describes the carbon dioxide equilibration curve of blood in vitro. Simultaneous solution of the van Slyke and the Henderson-Hasselbalch equations allows for estimation of acid-base state where only one of bicarbonate concentration, partial pressure of carbon dioxide or pH is known. We made use of user-determined base excess, in fully saturated blood, and applied the van

Diffusion limitation
We modelled diffusion limitation of oxygen in the gas exchanging lung compartment by taking the initial conditions of blood entering the lungs as those of mixed-venous blood. Using a method similar in nature to that of Wagner & West [2], a set of differential equations describing alveolar gas and pulmonary capillary blood were obtained and solved numerically. In contrast with the method of Wagner and West, we allowed alveolar gas composition to vary with time (as gases are exchanged with the blood) and made the simplifying assumption that the rate of reaction of carbon dioxide (as a whole) with blood is instantaneous. The complex interaction of carbon dioxide and blood was not modelled and for this reason diffusion limitation of carbon dioxide transfer is not discussed further.
Equation 9 and Equation 10 represent metabolic consumption of oxygen and production of carbon dioxide as functions of mixed-venous oxygen and carbon dioxide concentration. We solve this set of simultaneous equations (Figure 2), using numerous inter-conversions between whole blood content and partial pressure, each time an input value changes.

Heterogeneity Index
In order to model various degrees of heterogeneity across the pulmonary vascular bed in matching of ventilation to perfusion, we defined a heterogeneity index. This value is a dimensionless number defining the standard deviation of a log normal distribution describing V:Q across a multicompartment lung, analogous to the "logSD" values derived from experimental data in the multiple inert gas elimination technique (MIGET). [5] The following values are expected in normal subjects: 0.4-0.6; moderate disease: around 1.0; and severe disease: 1.5-2.5. [5] Abbreviations Symbols are constructed in three parts: a primary symbol and a two part subscript.
The primary symbol describers what quantity the symbol is in relation to; the secondary part, where it is in relation to and the tertiary part, what substance.  These variables represent the modifiable inputs that the user is able to adjust in this on-line model and their default values when the user initially enters the web site.