ON-LINE SUPPLEMENT
VALIDATION OF BOHR DEAD SPACE MEASURED BY VOLUMETRIC
CAPNOGRAPHY
Gerardo Tusman, MD1; Fernando Suarez Sipmann, PhD2; Joao B. Borges, PhD 3; Göran
Hedenstierna, PhD3 and Stephan H. Bohm, MD4.
Volumetric capnography (VC) is an asymmetrical sigmoid curve that can be
represented by a mathematical function. Fitting an equation to clinical VC data provides
a systematic methodology to characterize VC curves and calculate properly the
parameters derived from them. We are presenting a functional approximation of the VC
curve using the acquired raw data [ref. 8]. This continuous real-valued function is
obtained by a non-linear least square curve fitting. Least squares data fitting of VC raw
data can be viewed as an optimization problem of the parameters of a proposed function
(model function). The parameters of such a model were found by a non-linear least
square curve fitting optimized by the Levenberg-Marquardt algorithm. This functional
approximation of VC curve using the Levenberg-Marquardt algorithm and calculations
of VC-derived parameters were performed with MatLab® (Mathworks, Natick, MA,
USA).
The figure 1 (suppl) show how the VC derived-parameters relevant in this paper were
calculated from this function.

Phase I is the portion of the tidal volume free of CO2 at the beginning of
expiration that belongs to the apparatus and part of the airway dead space. It was
calculated from the end of inspiration (determined by the flow signal) until the
start of CO2 elimination that coincides to the point of maximum rate of change
of the 2nd derivative (left extreme of the 3rd derivative, line B1 – figure A).

Phase II constituted the part of the tidal volume where a progressive increment
of CO2 was coming from lung units with different ventilatory and perfusion
rates. This phase extended from the point of maximum rate of change of the 2nd
derivative (B1) to the intersection of the lines of phase II and phase III (figure A).

Phase III represented the pure alveolar gas coming from the intersection of the
lines that follow the slope of phase II and III until the PETCO2 (figure A).

The airway-alveolar interface between convective and diffusive CO2 transport
within the lungs was - by convention - placed around the mid point of the line of
phase II [ref. 8]. This point was mathematically determined by the inflection
point of the whole VC curve; i.e. the point on a curve at which the curvature
changed its sign (point A).

SII was determined as the value of the 1st derivative at the inflection point (figure
A).

Angle alpha was defined by trigonometry as the angle between the regression
lines of phase II and phase III considering their intersection (figure A).

SIII was calculated as follow: first, B2 was defined like the right extreme of the
3rd derivative, from which the slope of phase III could be calculated. Secondly,
phase III data beyond the right of such line B2 until the PETCO2 value were
divided into three thirds. Thirdly, the middle third was used to calculate the SIII
because they were placed away from the interferences of the alpha angle and the
possible phase IV of the VC. This third was divided into ten equidistant points
and their individual slopes were calculated as the value of their 1st derivatives.
The mean value of such 10 slopes constituted SIII (figure B).

The VDaw was calculated as the value on the x axe at the point A (figure B).

The VTalv derived from VT minus VDaw (figure B). The product of VTalv and
respiratory rate gives alveolar ventilation (VA).

The VTCO2,br or area under the curve of the VC represented the amount of CO2
eliminated by a breath. It was calculated from the symbolic integration of the
analytic function f(t). Multiplying VTCO2,br by respiratory rate give the amount
of CO2 eliminated per minute or VCO2.

The PETCO2 is the partial pressure of CO2 at the end of expiration calculated as
the value immediately before the start of inspiration.

The PeCO2 is the mixed partial pressure of CO2 which was determined by
multiplying the fractional expired CO2 concentration by the barometric pressure
minus the water vapor pressure (figure A).

The PACO2 is the partial pressure of CO2 calculated at the midpoint of phase III ,
from the intersection of the lines that follow the slope of phase II and III until the
PETCO2 (figure A).
Figure 2 (suppl) shows correlation and Bland-Altman plots for PeCO2 and VCO2 values
obtained by volumetric capnography versus the ones calculated from MIGET.
Figure 1 (suppl): Analysis of volumetric capnograms using the functional
approximation of VC curve based on the Levenberg-Marquardt algorithm.
The dotted red line is the real curve and the continuous blue line is the function found
with the functional approximation of capnogram using the Levenberg-Marquardt
algorithm.
Figure 2 (suppl): Linear correlation and Bland-Altman plots of PeCO2 and VCO2.
Pearson’ s correlations (left plots) and Bland-Altman analysis (right plots) for PeCO2
(upper) and VCO2 (lower) values obtained by volumetric capnography (VC) versus the
ones calculated from MIGET.