(Chest. 2005;127:579-584.)
© 2005
American College of Chest Physicians
Evaluation of Capnography Using a Genetic Algorithm To Predict PaCO2*
Milo Engoren, MD, FCCP;
Michael Plewa, MD;
David O’Hara, MD and
Jeffrey A. Kline, MD
* From the Department of Anesthesiology (Dr. Engoren) and Department of Emergency Medicine (Drs. Plewa and O’Hara), St. Vincent Mercy Medical Center, Toledo, OH; and Carolinas Medical Center (Dr. Kline), Charlotte, NC.
Correspondence to: Milo Engoren, MD, FCCP, Department of Anesthesiology, St. Vincent Mercy Medical Center, 2213 Cherry St, Toledo, OH 43608; e-mail: engoren{at}pol.net
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Abstract
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Introduction: Noninvasive estimates of PaCO2 are usually done by measuring exhaled carbon dioxide at end-expiration (PetCO2). While commonly used in studies involving healthy patients, it is less useful in sicker patients. Conditions that affect the terminal dead space and hence the accuracy of PetCO2 as a surrogate for PaCO2 may also affect other components of the capnogram. A genetic algorithm is a computer technique for discovering relationships between variables. The purpose of this study was to use a genetic algorithm to improve the precision of PaCO2 prediction in comparison to PetCO2.
Methods: Inspiratory and expiratory volumes were measured and analyzed by the computerized capnogram. Data were recorded for 2 min. Within 5 min of recording the capnograms, arterial blood gases were obtained. After excluding artifact and incomplete capnograms, five of the remaining breaths from each patient were selected. A genetic algorithm, constructed in postfix notation, consisted of 1,000 chromosomes with genes randomly selected from the 11 capnographic data fields and mathematical operators. The algorithm was constructed on 400 breaths from 83 randomly selected patients (construction group) and tested on 160 breaths from the remaining 32 patients (test group).
Results: For the construction group, the bias and precision between PetCO2 and PaCO2 were 4.3 ± 4.9 mm Hg (mean ± SD). For the 160 breaths in the test group, PetCO2 predicted PaCO2 with bias and precision of 2.9 ± 4.2 mm Hg. The best chromosome found by the genetic algorithm was (10 x 5 + 5 x 5 x 5)/(10 x 10) x PetCO2 – (5 x 5 x 10 + 5 x 5)/(10 x 10) x int time + 2 x 2 x 2 x 2 + (2 x 2)/10, which reduces to 0.65 x PetCO2 – 2.75 x int time + 16.4. This produced a bias and precision of 0.9 ± 4.1 mm Hg in the construction group and 0 ± 3.7 mm Hg in the test group (p < 0.01).
Conclusions: In this study of nonintubated emergency department patients, a genetic algorithm produced an improvement in bias and precision of PaCO2 prediction.
Key Words: capnography • computer programs • end-tidal CO2 • genetic algorithms • PaCO2
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Introduction
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Adequacy of ventilation is determined by sampling of arterial blood for carbon dioxide levels (PaCO2). However, because arterial sampling is painful, and difficult in patients with poor vascular access, physicians have sought a noninvasive way to estimate PaCO2. This is most frequently done by measuring exhaled carbon dioxide at end-expiration (PetCO2). While commonly used in healthy patients to evaluate the effects of medications on ventilation, it is less useful in sicker patients.123456 One study7 in nonintubated emergency department patients found an unacceptably high bias during normal breathing that improved when PetCO2 was measured during forced expiration. Anesthesia, pulmonary emboli, COPD, and low cardiac output have been shown to worsen the ability of PetCO2 to predict PaCO2.891011 All these conditions affect not only terminal dead space, but may also affect other components of the capnogram (the visual representation of exhaled carbon dioxide as a function of time.)
A genetic algorithm is a computer technique for discovering relationships between variables; in this study, between some of the data collected by capnography and PaCO2.1213 The genetic algorithm gets its name from its similarity to genes and evolution. The types of data, such as inspiratory time (TI), PetCO2, and tidal volume, are called genes and are combined with mathematical operators, also called genes, such as multiplication, addition, and cosines, in strings called chromosomes. Each chromosome represents a formula for finding PaCO2. These chromosomes are then tested on actual patient data and measured for accuracy, the closeness to predicted PaCO2. Those chromosomes that better predict PaCO2 (are more fit) are selected for survival. Surviving chromosomes then undergo crossover, in which several genes from one chromosome are swapped with several genes from another chromosome (Table 1
). Chromosomes also undergo mutation in which one gene is changed to another gene (Table 2
). That is, TI may change to tidal volume or cosine change to sine. This new generation of chromosomes is then tested, and the process of choosing the best chromosomes, evolving, and testing is repeated until an end point is reached and the process terminated. The purpose of this study was to develop and test a genetic algorithm that used 11 variables from capnography to predict PaCO2.
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Materials and Methods
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This study was approved by the Institutional Review Board. The collection of the capnogram and arterial blood gases have been previously described.9 Briefly, patients sat in a semi-Fowler position, breathing room air for 5 min through a snorkel-like rubber mouthpiece while wearing a nose clip to occlude their nostrils to ensure that the complete inspiratory and expiratory volumes were measured and analyzed by the capnogram (CosmoPLUS!; Novametrix Medical Systems; Wallingford, CT) The capnogram was connected to a computer that digitally archived the respiratory data. Data were recorded for 2 min. Within 5 min of recording the capnograms, the anesthetized radial artery was punctured and at least 1.0 mL blood was drawn into a syringe containing lyophilized heparin lithium and analyzed immediately in a blood gas analyzer. After excluding artifact and incomplete capnograms, five consecutive breaths from each patient, with the alveolar tidal volume of each breath being within 10% of each of the other four breaths, were selected by one of the authors (J.A.K.). Patients were excluded if their PetCO2 was at least 4 mm Hg greater than PaCO2.
A genetic algorithm was constructed in postfix notation (Table 3 ) and written in Fortran (Microsoft; Redmond, WA). The genetic algorithm consisted of 1,000 chromosomes, with each chromosome containing data (the operand) and unitary and binary operators. Unitary operators (sine, cosine, logarithm, exponent [ex], and square root) perform an operation on only one data point. Binary operators (addition, subtraction, multiplication, and division) perform an operation on two data points. The data points consisted of the 11 types of data collected for each breath (phase II [PII] slope, the slope of the rapid rise portion of the capnogram; phase III [PIII] slope, the slope of the plateau portion of the capnogram; TI; expiratory time [TE]; mean expired CO2; PetCO2 – PCO2 at end-expiration, volume of exhaled CO2, inspiratory tidal volume [VI], expiratory tidal volume [VE], the PCO2 concentration at the intercept of the PII slope and the PIII slope (PintCO2), and the time from start of exhalation to the intercept of PII slope and PIII slope [int time]) (Fig 1
), along with the numbers 1, 2, 5, and 10. While numbers can be generated from the other data genes (eg, 2 = [PII slope + PII slope]/PII slope), evolution may be accelerated by seeding with numbers. Each chromosome was randomly seeded with the three types of genes with certain restrictions set by the requirements of postfix notation: the first gene must be an operand, the second gene must be an operand or unitary operator, and the last gene must be an unitary or a binary operator. While there may be an arbitrary number of unitary operators, mathematics requires that there must be one more operand than binary operator. Operators were protected to prevent mathematically illegal operations, eg, division by zero and square root of negative numbers, or computer overflow and loss of precision errors. Chromosomes that contained a protected operator were assigned a very poor fitness score to ensure their failure to propagate to the next generation.
Breaths were classified into two groups by computer randomization of patients: a construction group (of the first 400 breaths, 88 patients), in which the geometric algorithm was evolved, and a test group (of the remaining 160 breaths, 34 patients), in whom the geometric algorithm was tested for accuracy. Each chromosome was evaluated on the 400 breaths in the construction group. The absolute value of the difference between the predicted end-tidal CO2 and the measured PaCO2 was summed for each chromosome. The 20 chromosomes with the lowest values were considered the fittest chromosomes and were used to generate the next generation of chromosomes; 980 progeny formed by crossover or mutation of these 20 chromosomes, and the 20 fittest chromosomes comprised the next generation. Crossover occurred by taking a random portion of a chromosome and swapping it for a random portion of a second chromosome (Table 1). Each of the swapped sections must have one more operand than binary operator. Mutation occurred by changing any one gene to another gene of the same type (Table 2). This next generation of chromosomes was then evaluated on the same 400-breaths construction group. The process of evaluation, selection, and progeny creation was repeated until there was no improvement in fitness for 50 generations. The best chromosome from this process was then tested in the 160 breaths test group and the results presented.
Statistics
Correlation coefficients were calculated for each variable and PaCO2. Bias was calculated at the mean difference between the predicted and measured PaCO2. Precision was the SD of the differences between the predicted and measured PaCO2. Results are shown as bias ± SD (mean difference ± SD of the differences). Bland-Altman plots are shown with limits of agreement (± 2 SDs). Precision is compared with the F statistic.
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Results
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Patient characteristics are shown in Table 4
. Of the different parameters, PetCO2, PeCO2 (mean expired CO2), and PintCO2 had the best correlations with PaCO2 (Table 5
). They were also highly correlated between themselves. The genetic algorithm found that using only one of these parameters, PetCO2, and int time produced the best chromosome: (10 x 5 + 5 x 5 x 5)/(10 x 10) x PetCO2 – (5 x 5 x 10 + 5 x 5)/(10 x 10) x int time + 2 x 2 x 2 x 2 + (2 x 2)/10, which reduces to 0.65 x PetCO2 –2.75 x int time + 16.4 (with PetCO2 in millimeters of mercury Hg and int time in seconds). When evaluated on the construction group, this chromosome produced a bias and precision of 0.9 ± 4.1 mm Hg, compared to 4.3 ± 4.9 mm Hg using PetCO2 to predict PaCO2. When evaluated on the test group of 160 breaths, the genetic algorithm produced a chromosome that was statistically significantly more precise at predicting PaCO2, (bias and precision of 0 ± 3.7 mm Hg [Fig 2
] compared to bias and precision of 2.9 ± 4.2 mm Hg [Fig 3
] using PetCO2 as the predictor of PaCO2) [p < 0.01; F = 1.614; 
1 = 2 = 160].
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Figure 2. Regression plot (top) and Bland-Altman plot (bottom) with bias (—–) and lines of agreement (± 2 SDs —–) [bottom] showing relationships between measured PaCO2 and that predicted by the genetic algorithm.
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Figure 3. Regression plot (top) and Bland-Altman plot (bottom) with bias (—–) and lines of agreement (± 2 SDs —–) [bottom] showing relationships between measured PaCO2 and end-tidal CO2. Because some of the points have exactly the same values, a dot may represent one or more breaths.
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Discussion
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We found that the formula produced by the genetic algorithm nearly eliminated bias and produced a statistically significant improvement (21%) in the precision of the estimate of PaCO2. It is to be expected that PetCO2 is one of the two variables in the best chromosome. PetCO2 has long been used as a surrogate for PaCO2,1 correlates highly with PaCO2, and by itself produced precision of 4.7 mm Hg. The other predictor variable int time measures time of exhalation until the PII – PIII intercept is reached. The PII – PIII intercept occurs when the exhaled gas switches from a mixture of dead space gas and alveoli gas to alveoli gas.14 Airway obstruction will increase int time.15 While the values of int time were small (range, 0.2 to 1.5 s) and hence were a small contributor to the predicted PaCO2 value, its inclusion did improve precision by 21%.
There are several possible reasons why the precision of the genetic algorithm may have been limited. There is no known way to ensure that a genetic algorithm will reach the best solution. Limitations in programming, being trapped in local minima, or failure to run the program long enough may all produce less precise solutions. Even if programming is optimized, mutations and crossovers prevent trapping in local minima; and if the program is run sufficiently long, the program can only be as good as the data entered. If the data, other than PetCO2 or its highly correlated covariates, have no or only very limited relationship to PaCO2 (Table 5), no amount of manipulation of the data would produce a more precise formula. We were limited by having only several descriptors of the capnogram. Using other components of the capnogram may produce different algorithms and different results. Another reason is that capnograms and arterial blood gases were not truly simultaneous. While every effort was made to perform them simultaneously, or barring that, to prevent any changes in respiration, even small changes in ventilation can produce changes in PaCO2, which would lead to inaccurate predictions.
Previous studies evaluating capnography have used only the PetCO2 as a predictor of PaCO2 with mixed results. Engoren34 found it useful for adjusting mechanical ventilation, within a limited range, in both cardiac surgery and neurosurgical patients in the ICU. But other studies26 found that PetCO2 could not be reliably used to predict PaCO2. Hoffman et al6 even found that PetCO2 and PaCO2 frequently changed in opposite directions. Little study has been conducted to evaluate maneuvers or techniques that could improve the accuracy of PaCO2 prediction. Measuring PetCO2 with a forced expiration increased the precision from 5.2 to 3.9 mm Hg in nonintubated emergency department patients with respiratory distress.7 However, these results were not confirmed in surgical patients receiving one-lung anesthesia.16 While a little research has been conducted in using components other than PetCO2 of the capnogram to diagnosing disease,17 to our knowledge, no study has used these other components to predict PaCO2. Using exhaled carbon dioxide to predict PaCO2, which is a mixture of arterial carbon dioxide content from both the inspiratory (which contributes nothing to the capnogram) and expiratory portions of each breath, limits the accuracy of predicting PaCO2 because the capnogram contains no information or knowledge about carbon dioxide during inspiration or from alveoli with shunt or very low ventilation/perfusion ratio. Study is needed to determine in which patients or diseases this effect limits the precision of the capnogram in predicting PaCO2.
Genetic algorithms have been used to predict myocardial infarction in patients with chest pain, outcome of critically ill patients, and type of neurologic disorder.181920 They have several advantages over standard statistical analysis. They make no assumptions about underlying structure. For example, linear regression assumes a linear relationship between the independent and dependent variables and may fail to find nonlinear relationships. While there are techniques to linearize nonlinear variables, other than logarithmic transformations, they are not commonly employed. Furthermore, there may be a combination of two or more parameters that when combined, rather than being analyzed separately, produce a more accurate model. Analysis of these interactions is usually very limited in computerized statistical packages.
One disadvantage of using genetic algorithms is the concern for overfitting the data. As the algorithm grows and includes more and more genes, it may become increasingly accurate on the construction data, but at the cost of becoming less generalizable. We attempted to minimize overfitting by having the computer program give preference to the smaller of two chromosomes if they were equally fit at predicting outcome. Additionally, the use of two separate populations as independent construction and test groups allowed for comparison and testing for overfitting. If overfitting were present, there should be a marked worsening in precision going from the construction to the test group. The final algorithm consisting of only two variables performed equally well on the test data as it did on the construction data, which suggests that overfitting did not occur.
Another disadvantage of genetic algorithms is that there is no guarantee of the "perfect" formula being found, nor can it provide an estimate of error between the found formula and the perfect formula. This primarily arises from the large search space of possible formulas. Using as we did up to 400 genes on each chromosome, there are approximately 10552 possible chromosomes to be searched. Taking several hours, our computer examined approximately 107 chromosomes, an infinitesimally small fraction of the search universe. While the search is stochastic, driven by a fitness rule, the process consists of many random events that may create previously rejected chromosomes or get stuck in evolutionary dead ends and blind alleys. We could find no previous articles in which genetic algorithms or other forms of evolutionary computer programming were used to predict PaCO2 from the capnogram.
A limitation of this study is that it was conducted only in nonintubated emergency department patients. Further work is needed to explore its usefulness in other patients, particularly those receiving mechanical ventilation.
In conclusion, in this study of nonintubated emergency department patients, a genetic algorithm produced an improvement in bias and precision of PaCO2 prediction. Further research is needed to validate this approach and these results in other patient populations.
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Footnotes
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Abbreviations: int time = the time from start of exhalation to the intercept of phase II slope and phase III slope; PetCO2 = PCO2 at end-expiration; PII = phase II; PIII = phase III slope; PintCO2 = PCO2 concentration at the intercept of phase II slope and the phase III slope; TE = expiratory time; TI = inspiratory time; VE = expiratory tidal volume; VI = inspiratory tidal volume
None of the authors has any financial interest in any product mentioned in the manuscript.
Received for publication March 26, 2004.
Accepted for publication August 4, 2004.
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Abstract
Introduction
