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 Table of Contents  
RESEARCH ARTICLE
Year : 2017  |  Volume : 7  |  Issue : 4  |  Page : 256-259

A physiologically based model for denitrogenation kinetics


1 Medical R&D, Air Liquide Santé International, Centre de Recherche Claude-Delorme, Jouy-en-Josas, France; Department of Mechanical Engineering, Lafayette College, Easton, PA, USA
2 Medical R&D, Air Liquide Santé International, Centre de Recherche Claude-Delorme, Jouy-en-Josas, France

Date of Web Publication22-Jan-2018

Correspondence Address:
Ira Katz
Medical R&D, Air Liquide Santé International, Centre de Recherche Claude-Delorme, Jouy-en-Josas, France; Department of Mechanical Engineering, Lafayette College, Easton, PA, USA

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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/2045-9912.222449

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  Abstract 

Under normal conditions we continuously breathe 78% nitrogen (N2) such that the body tissues and fluids are saturated with dissolved N2. For normobaric medical gas administration at high concentrations, the N2 concentration must be less than that in the ambient atmosphere; therefore, nitrogen will begin to be released by the body tissues. There is a need to estimate the time needed for denitrogenation in the planning of surgical procedures. In this paper we will describe the application of a physiologically based pharmacokinetic model to denitrogenation kinetics. The results are compared to the data resulting from experiments in the literature that measured the end tidal N2 concentration while breathing 100% oxygen in the form of moderately rapid and slow compartment time constants. It is shown that the model is in general agreement with published experimental data. Correlations for denitrogenation as a function of subject weight are provided.

Keywords: physiologically based pharmacokinetic model; nitrogen; washout; medical gas administration; nitrous oxide; xenon


How to cite this article:
Katz I, Murdock J, Palgen M, Farjot G. A physiologically based model for denitrogenation kinetics. Med Gas Res 2017;7:256-9

How to cite this URL:
Katz I, Murdock J, Palgen M, Farjot G. A physiologically based model for denitrogenation kinetics. Med Gas Res [serial online] 2017 [cited 2018 Jul 21];7:256-9. Available from: http://www.medgasres.com/text.asp?2017/7/4/256/222449


  Introduction Top


Under normal conditions we continuously breathe 78% nitrogen (N2) such that the body tissues and fluids are saturated with dissolved N2. For normobaric medical gas administration at high concentrations, the N2 concentration must be less than in the ambient atmosphere; therefore, N2 will begin to be released by the body tissues. For very high concentration administration of gases such as nitrous oxide (N2O), xenon (Xe), or even oxygen (O2) the quantity of N2 out gassing can be significant. Quantification of this process can be important for at least two reasons.

First, the released N2 gas leaves the body primarily through exhalation. For the anesthetic administration of nitrous oxide or xenon to intubated and ventilated patients the exhaled nitrogen will mix with the therapeutic gases in the recirculation gas breathing circuit resulting in a decrease in therapeutic gas concentration. Thus there must be a continuous fresh supply of therapeutic gas to maintain the concentration that is especially expensive for xenon.[1] To reduce this expense a denitrogenation procedure prior to xenon administration is usually performed based on 100% O2 delivery.[1]

Second, for gases that have a greater solubility in blood than N2 there can be accumulation of gas in the bowel and other body cavities.[2],[3],[4] This is especially true for nitrous oxide that has an Ostwald solubility coefficient of 0.469 compared to 0.0148 for N2 in human whole blood (mL of gas per mL of liquid at 37°C).[5]

Thus there is a need to estimate the time needed for denitrogenation in the planning of surgical procedures. In this paper we will describe the application of a physiologically based pharmacokinetic model to denitrogenation kinetics. The results are compared to the data resulting from an elegant set of experiments by Lundin[6] that measured the end tidal N2 concentration in six adult subjects while breathing 100% O2 in the form of moderately rapid and slow compartment time constants. Furthermore, these data are the most complete set of inert gas washout from humans in the literature; thus, this comparison serves as a validation of the model. Other aspects of the denitrogenation process are also explored including the effect of subject weight and a comparison of the exhaled concentration to total body clearance.


  Materials and Methods Top


This study employs a physiologically based pharmacokinetic model developed by Lockwood[7] for anesthetic gases that has been employed within the Simbiology Toolbox of MATLAB (Mathworks, Natick, MA, USA).[8] The model considers all transport to be perfusion limited, that there is no metabolism, and all excretion is through expiration via the lung. Here we present the partition coefficients for N2 [Table 1] and a detailed explanation of the compartment consisting of the alveolar gas exchange region of the lung [Figure 1] as these are the results comparable to the published experimental data by Lundin.[6]
Table 1: Physiological data and partition coefficients used for the model

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Figure 1: Schematic of transport through the alveolar gas exchange region of the lung.
Note: QCardiac: Cardiac outpur flow rate; QShunt: fraction of cardiac output that passes by the gas exchange region; CArterial: arterial blood concentration, QMV: minute ventilation; QDS: dead space flow, CInhale: inhaled concentration; VFRC: functional residual capacity.


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[Figure 1] shows schematically how blood and gas pass through the alveoli, or gas exchange region, of the lung. On the blood side the venous blood arrives at the rate of QCardiac; a fraction QShunt (0.1 is used herein) bypasses the gas exchange region and remixes with oxygen enriched blood to obtain the full flow of QCardiac with mixed concentration CArterial. On the gas side the respiratory cycle is modeled with a simplified steady-state flow of inhaled gas at the rate of the minute ventilation (QMV) less a dead space flow (QDS) at concentration CInhale. This is mixed with the dead space flow at the concentration in the alveoli to make the flow through the gas exchange region QMV. An expression of molar exchange between blood and gas is as follows:



in which employs the blood:gas partition coefficient (PCBlood:Gas) to determine the arterial concentration and VFRC is the functional residual capacity (i.e., the gas volume in the lung).

Lundin’s data[6] are presented in the form of moderately rapid and slow compartment time constants that are calculated based on end tidal measurements in the exhaled gas, taken to be CExhale in the model. Roughly, the moderately rapid and slow time constants represent the relatively richly perfused and poorly perfused tissues as listed in [Table 1]. However, it was not possible to precisely match the model compartments with the experimental time constants. Therefore, the calculation method employed by Lundin as shown in [Figure 2] based on the exhaled concentration was used.
Figure 2: Calculation of time constants, which can be compared to [Figure 2] in the Lundin’s paper.[6]
Note: The slow time constant is found by fitting the data > 100 minutes to an exponential function (purple data) that appears linear on the semi-log plot. Results from this fit are subtracted from the original data (blue) between 10 and 60 minutes resulting in the red data. This is then fit to a second exponential to obtain the moderately rapid time constant. The data shown are for the 70 kg case. The concentration data have been normalized by the value at 10 minutes.


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  Results Top


The simulated results are first provided in terms of the moderately rapid and slow time constants as a function of weight shown in [Figure 3]. Also shown in [Figure 3] are the data from the six subjects realized from the experimental study found in the literature.[6] There is general agreement between simulated and experimental results, though the variations in experimental results are clearly not completely correlated with weight.
Figure 3: Comparison of time constants from Lundin[7] and simulated as a function of weight: the moderately fast compartment (left) and the slow compartment (right).
Note: Curve fits for the simulated data are indicated.


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The general agreement can be illustrated by considering the case with the largest difference between simulated and experimental results that occurs for the subject with a weight of 53 kg; 22 and 127 minutes and 15 and 194 minutes, for the moderately rapid and slow time constants respectively. However, these differences in time constants can still translate into reasonably accurate guidance for the exhaled concentration time series as shown in [Figure 4].
Figure 4:

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  Discussion Top


We can speculate somewhat on the experimental data as to why the results are uncorrelated with weight. It can be understood from the model that weight is not the only variable that can influence the denitrogenation kinetics. Compartment volumes that represent fat content will be unique for individuals; thus for example, if the body mass index of the subjects were known a better correlation should be possible. Other parameters such as minute ventilation, cardiac output, functional residual capacity, and dead space volume are also not known for the experimental subjects, nor varied with weight in the simulated results.

The experiments are based on end tidal concentration measurements. A relevant question that can be addressed by the model is how this parameter reflects overall corporal denitrogenation. Thus, the moles of N2 in each compartment are summed and presented in comparison to the exhaled concentration in [Figure 5]. It can be seen that denitrogenation as measured in the exhaled gas is much faster than the clearance from tissues; for the exhaled gas concentration T1/2 = 28 minutes, for the tissue moles T1/2 = 183 minutes. This divergence can be understood by noting that the exhaled concentration is closely related to blood levels, while the majority of moles of gas are stored in fat that has a much slower denitrogenation speed.
Figure 5: Comparison of tissue concentration and exhaled concentration for the 70 kg case.
Note: The T1/2 values are indicated by the dashed lines. For the exhaled gas concentration T1/2 = 28 minutes, for the tissue moles T1/2 = 183 minutes. Each time series is normalized by the value at 10 minutes.


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These results might also be relevant for decompression illness.[9] However, as there is some question on the relevance of the perfusion limited model for N2 decompression[10] and the lack of a bubble initiation model[11] in this study, for this application the results should be considered preliminary.

In conclusion, herein is presented a physiologically based model of denitrogenation kinetics that is in general agreement with published experimental data. Correlations for denitrogenation as a function of subject weight are provided.

Author contributions

IK conceived the study, created the data, and wrote the manuscript; JM and MP developed the model; and GF read the manuscript. All the authors approved the final version of the manuscript.

Conflicts of interest

None declared.

Research ethics

No ethical issues were involved in this study.

Data sharing statement

Datasets analyzed during the current study are available from the corresponding author on reasonable request.

Plagiarism check

Checked twice by iThenticate.

Peer review

Externally peer reviewed.

 
  References Top

1.
Rawat S, Dingley J. Closed-circuit xenon delivery using a standard anesthesia workstation. Anesth Analg. 2010;110:101-109.  Back to cited text no. 1
[PUBMED]    
2.
Reinelt H, Marx T, SchirmerU, Luederwald S, Topalidis P, Schmidt M. Diffusion of xenon and nitrous oxide into the bowel during mechanical ileus. Anesthesiology. 2002;96:512-513.  Back to cited text no. 2
    
3.
Reinelt H, Schirmer U, Marx T, Topalidis P, Schmidt M. Diffusion of xenon and nitrous oxide into the bowel. Anesthesiology. 2001;94:475-477; discussion 6A.  Back to cited text no. 3
[PUBMED]    
4.
Steffey EP, Johnson BH, Eger EI 2nd, Howland D Jr. Nitrous oxide: effect on accumulation rate and uptake of bowel gases. Anesth Analg. 1979;58:405-408.  Back to cited text no. 4
    
5.
Lango T, Morland T, Brubakk AO. Diffusion coefficients and solubility coefficients for gases in biological fluids and tissues: a review. Undersea Hyperb Med. 1996;23:247-272.  Back to cited text no. 5
    
6.
Lundin G. Nitrogen elimination from the tissues during oxygen breathing and its relationship to the fat: muscle ratio and the localization of bends. J Physiol. 1960;152:167-175.  Back to cited text no. 6
    
7.
Lockwood G. Theoretical context-sensitive elimination times for inhalation anaesthetics. Br J Anaesth. 2010;104:648-655.  Back to cited text no. 7
    
8.
Katz I, Palgen M, Murdock J, Martin AR, Farjot G, Caillibotte G. Gas transport during in vitro and in vivo preclinical testing of inert gas therapies. Med Gas Res. 2016;6:14-19.  Back to cited text no. 8
    
9.
Doolette DJ, Mitchell SJ. The physiological kinetics of nitrogen and the prevention of decompression sickness. Clin Pharmacokinet. 2001;40:1-14.  Back to cited text no. 9
[PUBMED]    
10.
Doolette DJ, Upton RN, Grant C. Diffusion-limited, but not perfusion-limited, compartmental models describe cerebral nitrous oxide kinetics at high and low cerebral blood flows. J Pharmacokinet Biopharm. 1998;26:649-672.  Back to cited text no. 10
[PUBMED]    
11.
Doolette DJ. Uncertainties in predicting decompression illness. SPUMS J. 2000;30:31-36.  Back to cited text no. 11
    


    Figures

  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5]
 
 
    Tables

  [Table 1]



 

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