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Background: New gas therapies using inert gases such as xenon and argon are being studied, which would require chronically administered repeating doses. The pharmacokinetics of this type of administration has not been addressed in the literature. Methods: A physiologically based pharmacokinetics (PBPK) model for humans, pigs, mice, and rats has been developed to investigate the unique aspects of the chronic administration of inert gas therapies. The absorption, distribution, metabolism and excretion (ADME) models are as follows: absorption in all compartments is assumed to be perfusion limited, no metabolism of the gases occurs, and excretion is only the reverse process of absorption through the lungs and exhaled. Results: The model has shown that there can be a residual dose, equivalent to constant administration, for chronic repeated dosing of xenon in humans. However, this is not necessarily the case for small animals used in pre-clinical studies. Conclusions: The use of standard pharmacokinetics parameters such as area under the curve would be more appropriate to assess the delivered dose of chronic gas administration than the gas concentration in the delivery system that is typically reported in the scientific literature because species and gas differences can result in very different delivered doses. Keywords: Pharmacokinetics,Xenon,Argon,Human,Pig,Rat Introduction the PK analysis of gaseous anesthetics [5, 6]. Filser, Bolt Gases with proven or exploratory medical use include and their colleagues have presented an impressive series oxygen, hydrogen, carbon monoxide, carbon dioxide, of papers on the application of PK in the context of the hydrogen sulfide, nitric oxide, nitrous oxide, xenon, environmental toxicology of gas pollutants [7–12]. argon, helium and other noble gases [1–4]. In general, In recent years evidence has been accumulating to in- the relatively fast wash-in and wash-out of gases, and dicate that certain inert or noble gases, existing as their application only for acute treatment (with the mono-atomic gases with low chemical reactivity, never- exception of oxygen), has made pharmacokinetic (PK) theless express biological activity. Numerous in vitro analysis of secondary importance such that it has not and in vivo experiments have demonstrated intriguing been a focus of research or regulation. However, there biological effects for xenon, argon and helium, with are notable exceptions. Lockwood and his colleagues neuro- and organo-protective properties as the most have developed experimental techniques and models for clinically promising [4, 13]. Extensive research has fur- ther revealed some of the underlying mechanisms and include competitive antagonism at the NMDA/AMPA * Correspondence: ira.katz@airliquide.com Medical R&D, Air Liquide Santé International, Centre de Recherche receptor [14], anti-apoptotic properties (inhibition of Paris-Saclay, 1, chemin de la Porte des Loges, BP126 - 78354 Jouy en Josas, mitochondrial cytochrome c release) [15], activation of France pro-survival signaling pathways (increased expression Department of Mechanical Engineering, Lafayette College, Easton, PA 18042, USA © 2015 Katz et al. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http:// creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Katz et al. Medical Gas Research (2015) 5:8 Page 2 of 10 of Bcl-2/Bcl-xL, inhibition of Bax) [16], MAPK regulation Dead space gas bypass (p38, ERK ) [17, 18] and potassium ion channels activa- 1/2 tion (K , TREK-1) [19, 20]. The preclinical models ATP suggest potential clinical benefit in indications such as Inhaled traumatic brain injury, ischemic or hemorrhagic stroke, minute perinatal hypoxic-ischemic brain injury, coronary artery volume Lung bypass graft surgery, organ protection during transplant- ation, chronic pain, and addiction [13, 21–23]. Any clinical benefit, however, would require chronic (or repetitive) administration of inert gases, in contrast to the currently accepted acute, single administration for the induction Pulmonary shunt blood bypass and maintenance of general anesthesia (e.g. xenon). From a PK standpoint there are several issues that arise Brain concerning the development and future application of the chronic administration of inert gases. For these reasons Richly perfused tissue we have developed a computational physiological based pharmacokinetic (PBPK) model for inert gases primarily Liver based on the model of Lockwood [5]. The model was used to investigate chronic administration of the noble gases Poorly perfused tissue xenon and argon in terms of empirically determined physiological PK parameters (i.e., partition coefficients), species comparisons, and intersubject variability. These is- Muscle sues will inevitably be important in moving from animal models to clinical testing, toxicological testing, the devel- Richly perfused fat opment of delivery devices, and the regulatory purview of gas treatments. One particular aspect of methodology ad- Poorly perfused fat dressed herein is the definition of the dose itself. We use PK variables to define the dose at the site of action, Fig. 1 Schematic of the pharmacokinetic model, compartments and whereas, the dose of a gas treatment is typically given as gas species flows. The model does not consider the lung tissue per the concentration of the inhaled gas. se (except as part of the richly perfused tissue compartment), but the gas volume within it Methods A pharmacokinetic model principally following the one time scale that would include several breaths (minutes) described by Lockwood [5] was developed using the not during a breath (seconds). Morphological complexity Simbiology Toolkit of MATLAB (Mathworks, United of the respiratory tract is accounted for by including a States). Simbiology provides a graphical environment component of dead space; that is gas that never reaches and programming tools to model, simulate, and analyze the alveolar gas exchange region of the lung, is considered PK applications. Specifically in this case, it allows for as a gas bypass of 32.5 % of minute volume (i.e., 162.5 ml simplified development, programming and debugging, of of dead space and 500 ml tidal volume). The exhaled gas the PK model including the numerical solver of the compartment consists of 90 % alveolar gas and 10 % resulting system of differential equations. inhaled gas to account for the complex mixing inherent in The model is described by the schematic shown in Fig. 1 real respiration. In terms of pulmonary circulation, 10 % and the data listed in Table 1. Regarding Fig. 1, it can be of the cardiac output was shunted past the lung without discerned that gas therapy starts in the lung. The model gas exchange. Thus the equation for transfer from the al- does not consider the lung tissue per se (except as part of veolar gas to the arterial (oxygenated) blood in the lung is the richly perfused tissue compartment), but the gas vol- ðÞ 0:9 AV C þðÞ CO C inhaled venous ume within it. The extreme complexity of the lung and C ¼ 0:9 arterial lung 0:9AV CO þ the dynamics of respiration [24–27] are greatly simplified PC blood:gas following Lockwood in that the model does not take into þ 0:1 C venous account the oscillatory nature of inhalation and exhalation ð1Þ or details of ventilatory distribution. Thus the ventilatory input is the minute volume, inspired tidal volume multi- where AV is the alveolar ventilation (the inhaled tidal plied by the respiratory rate in breaths per minute. volume less the dead space times the respiratory rate), Changes in minute volume can be modeled, but only at a C is the inhaled concentration, C is the inhaled venous Arterial supply Venous return Katz et al. Medical Gas Research (2015) 5:8 Page 3 of 10 Table 1 Physiological data and partition coefficients used for C in mol/L is related to the percentage by volume, inhaled the model %gas (equivalent to the molar percentage), by the perfect Parameter Mouse Rat Pig Human gas law. (Adult Male) P %gas Body Weight (kg) 0.025 0.25 25 70 total C ¼ inhaled ð2Þ -1 RT 100 Minute Ventilation (l.min ) 0.385 0.18 3.6 7.5 -1 Alveolar Ventilation (l.min ) 0.025 0.117 2.34 4.875 − 1 − 1 where R = 8 314.4621 Pa. L. mol . K is the universal -1 Cardiac Output (l.min ) 0.017 0.083 2.060 6.0 perfect gas constant, the temperature considered at am- Perfusion per compartment (as a fraction of Cardiac Output) bient is T = 298K and the total pressure is assumed to be Fat (Richly perfused) 0.09 0.09 0.1747 0.04 P = 1 atm = 1.01325 × 10 Pa. total Fat (Poorly perfused) NA NA NA 0.01 The cardiac output is apportioned to the tissue com- Liver 0.25 0.25 0.3052 0.26 partments. All exchange is based on the perfusion lim- ited model that assumes the tissue and venous blood are Richly perfused tissue 0.415 0.484 0.1829 0.3303 in equilibrium based on the partition coefficient for each Poorly perfused tissue NA NA 0.0553 0.01 compartment using Equation 3. Muscle 0.15 0.15 0.2523 0.24 Brain 0.095 0.026 0.0296 0.093 tissue C ¼ venous ð3Þ Volumes (fraction of Body Weight) PC tissue:blood Arterial blood 0.0110 0.0167 0.018 0.0209 Venous blood 0.0331 0.050 0.042 0.0545 where C is the concentration in the tissue for the tissue compartment, and PC is the partition coefficient Lung blood 0.0049 0.0074 NA 0.00245 tissue:blood for that tissue compartment and blood. The consequence Fat (Richly perfused) 0.10 0.07 0.3 0.09 of this assumption is that all exchanges between gas and Fat (Poorly perfused) NA NA NA 0.09 blood, as well as blood and tissue compartments, are as- Liver 0.055 0.04 0.0294 0.06 sumed to occur instantaneously. The resulting differential Richly perfused tissue 0.0454 0.0497 0.0697 0.0624 equation for the tissue compartment is Poorly perfused tissue NA NA 0.1269 0.24 tissue Q C − Muscle 0.66 0.676 0.4 0.44 arterial tissue dC PC tissue:blood tissue ¼ ð4Þ Brain 0.0046 0.0003 0.004 0.0176 dt V tissue Partition coefficients for Xenon where Q and V are the perfusion and volume for tissue tissue Blood:gas 0.207 0.207 0.11 0.14 the compartment, respectively, and C is the concen- arterial Fat:blood 6.2802 6.2802 11.8182 9.287 tration in the arterial blood supplying the compartment. Liver:blood 0.7246 0.7246 1.3636 1.071 One difference between our model and the Lockwood Richly perfused tissue:blood 0.6951 0.7229 1.3774 1.071 model follows from the definition of compartments; Poorly perfused tissue:blood 0.7246 0.7246 1.3636 1.071 within Simbiology compartments must be defined in terms of volume, whereas Lockwood’s compartments are Muscle:blood 0.7246 0.7246 1.3636 1.071 is in terms of mass [5]. Thus, assumed density values Brain:blood 1.1233 1.015 1.1233 1.123 were used to derive the compartment volume fractions Partition coefficients for Argon listed in Table 1. Other differences include the definition Blood:gas 0.037 0.037 0.037 0.037 of organ compartments such as the brain from the richly Fat:blood 4.1622 4.1622 4.1622 4.162 perfused tissue compartment for some of our simula- Liver:blood 0.7539 0.7539 0.7539 0.754 tions as shown in Fig. 1. The numerical solution of the model, a system of Richly perfused tissue:blood 1.0663 1.0323 1.0506 1.028 differential equations, was accomplished within Matlab Poorly perfused tissue:blood 0.9987 0.9987 0.9987 0.999 using the “ode15s” code; a quasi-constant step size im- Muscle:blood 0.7205 0.7205 0.7205 0.720 plementation in terms of backward differences of the Brain:blood 0.6747 0.6747 0.6747 0.675 Klopfenstein-Shampine family of numerical differenti- ation formulas [28, 29]. This method was efficient and stable, as no simulations took more than a minute on a concentration of the gas in the venous blood, CO is the computer workstation. A maximum step size of 0.5 s cardiac output, and PC is the partition coefficient was used for numerical purposes, though we emphasize blood:gas between the gas phase and in solution in the blood. that the model results cannot be applied to this time Katz et al. Medical Gas Research (2015) 5:8 Page 4 of 10 resolution. A convergence test based the parameter area assessed by using scaling of compartment volumes, venti- under the curve (AUC, to be explained below) resulted in latory parameters, and cardiac output and their distribu- a value within 0.01 % of the value for a time step of 0.1 s. tions based on size, gender and age. For example, the The physiological data for humans in Lockwood were percentage of fat as a function of body weight and gender extrapolated to pigs and rats based on data from several is on average 13.5 % for men and 26.5 % for women [39]. references [5, 12, 30–32]. The resulting parameters are It was assumed that the relative amounts of highly and compiled in Table 1. Note that detailed data such as a poorly perfused fat and their perfusion were the same as breakdown between rich and poorly perfused fat were the base human model [5]. Adaptations for arterial blood not found for the other species. volume [40], cardiac output [41], and ventilatory parame- Another key physical/chemical parameter is the spe- ters [42] were made based on correlations found in the cific partition coefficients for each gas in each compart- literature. ment for each species. These data are not complete in the literature, thus requiring extrapolation from correla- Results tions from known data for other gases; for example, Validation is an important step in the use of any model. compartment:blood partition coefficients were deter- Unfortunately; in vivo measurements of noble gas con- mined from known fat:blood values using the linear centration are difficult; and therefore, quite rare. The correlations for organs described by Fiserova-Bergerova first comparison performed used data calculated by and Diaz [33]. We developed linear correlations for the Lockwood [5] for xenon uptake as shown in Fig. 2. This vessel rich and vessel poor tissue compartment by mak- is a validation of the parameters, system of equations, ing similar correlations using the data for six anesthetic and solution techniques employed. The second valid- gases analyzed in Lockwood [5]. For argon Ostwald solu- ation comparison (shown in Fig. 3) was made from bility coefficients are available for blood, 0.037 [34], and in vivo measurements of xenon concentration in arterial for olive oil, 0.154 [35]. The solubility coefficient is and mixed venous blood using gas chromatography- equivalent to the partition coefficient if one of the com- mass spectrometry of the head space gas over samples partments are in the gas phase [36]; in our model this is taken during the wash-in of xenon into eight pigs [43]. the case for the lung compartment. Furthermore, due For this comparison compartment volumes are esti- to the scarcity of data, solubility in olive oil is used in mated because the weight of each pig was not available. lieu of fat [37]. The relevant fat:blood partition coeffi- Pharmacokinetic results for exposure of 50 % xenon cient for argon is found by the ratio of (olive oil:gas)/ for one hour to an adult male, a pig and a rat are given (blood:gas), or 4.162. in Table 2. Similar results are also given for 50 % argon The dose of a gas treatment is typically given as the for one hour in the human model. concentration (molar, by volume, or by parts) of the Graphically, the results of a one hour exposure to inhaled gas, to the point that it is rare to find the use of xenon are given in Fig. 4a in terms of arterial blood con- classic PK parameters to assess the dose. Research based centration and xenon concentration in the two fat com- on inhaled dose as concentration of administered gas partments that have different perfusion rates. The very does not take into account complex physiological differ- different timing of absorption rates is evident between ences between species. Thus we use variables such as the compartments. These differences are also apparent C the peak concentration for a particular compart- in the example of chronic, or repeated, dosing shown in max ment, t , the time necessary to reduce the concentra- Fig. 4b. In this case the one-hour exposure to 50 % 1/2 tion from C by half, and AUC or the area under the xenon is repeated once per day for 10 days. Note that max curve, the integral of concentration through time that the peak concentration and the residual concentration, reflects the total exposure of the compartment to inter- the concentration just before the next exposure, are rising pret the inhaled dose concentrations [38]. These data in the fat compartment over the three days shown in the are derived (e.g., using numerical integration for AUC) figure. There are no apparent differences each day in the from the discrete concentration data calculated at each arterial blood concentration. However, in Fig. 4c residual time step for each compartment. t , the time neces- concentrations for arterial blood and poorly perfused fat max sary to reach C , is generally at the end of administra- are shown using different scales, where it is clear that the max tion. However, due to a fast rise followed by slower residual concentration in both compartments increases uptake in fat, t is calculated as four times the expo- for about 5 days before reaching a plateau. max nential time constant estimated from the elimination In Fig. 5 are shown the plots of arterial blood concen- time, t . tration during exposure to 50 % xenon in the adult hu- 1/2 The physiological parameters for each species are given man male, rat (the mouse, not shown for clarity, is close in Table 1. The human is based on a 70 kg adult male as to the rat) and pig models. The human and pig are simi- described by Lockwood [5]. Intersubject variability can be lar while the concentration in the rat is almost double. Katz et al. Medical Gas Research (2015) 5:8 Page 5 of 10 Lockwood Model 0 50 100 150 200 250 300 350 400 Time (Min) Fig. 2 Comparison of xenon uptake in humans calculated using the current model to numerical data published by Lockwood [5]. This comparison between models is a validation of parameters and coding 0.0035 0.003 0.0025 0.002 Nalos values - arterial 0.0015 Nalos values - venous Model values - arterial 0.001 Model values - venous 0.0005 020 40 60 80 100 120 140 Time (min) Fig. 3 Comparison of xenon uptake in pigs calculated using the current model to experimental data published by Nalos et al. [43]. The Pearson regression coefficient r calculated in Excel (Microsoft, United States) for the models compared to the experimental data are 0.7923 and 0.9616 for the arterial and venous blood compartments, respectively Xe Uptake (g) Xenon concentration (mol/L) Katz et al. Medical Gas Research (2015) 5:8 Page 6 of 10 Table 2 Pharmacokinetic results for a 60 min exposure to 50 % in Fig. 6 in the form of arterial blood concentrations as a xenon or argon mixture with oxygen function of time. Note, that the equivalent delivered Gas AUC C t t doses of 50 % for one hour result in very different phar- max ½ max (mol.min/l) (mol/l) (min) (min) macokinetic doses (e.g., see the AUC for the brain for Species these two cases in Table 2: 0.173 for xenon and 0.029 for Compartment argon). Xenon Human An example of the effect of intersubject variability on Blood (venous) 1.31E-01 2.54E-03 3.64 42.0 pharmacokinetics of gases is shown in Fig. 7. We note Blood (arterial) 1.61E-01 2.78E-03 0.21 2.4 that in general, Cmax is determined by the partition co- Liver 1.64E-01 2.98E-03 2.87 33.1 efficients, such that there is very little intersubject vari- Muscle 1.10E-01 2.73E-03 15.83 182.7 ability for this parameter. However, the kinetics are a Fat (Richly perfused) 1.66E-01 5.46E-03 29.12 336.1 function of the relative volume distribution between the compartments. Thus, there is significant variation in t 1/2 Fat (Poorly perfused) 4.41E-02 1.49E-03 30.42 351.1 as a function of weight as shown in this plot of for adult Richly perfused tissue 1.64E-01 2.94E-03 2.40 27.6 males who have received a 50 % exposure to xenon for Poorly perfused tissue 1.58E-03 5.23E-04 29.44 339.8 one hour. Brain 1.73E-01 3.12E-03 2.52 29.1 Xenon Pig Discussion Blood (venous) 8.63E-02 1.77E-03 4.62 53.3 A pharmacokinetic model has been presented for the Blood (arterial) 1.26E-01 2.16E-03 0.19 2.2 chronic administration with repeated dosing of inert, noble gases (xenon and argon) to humans, pigs and rats. Liver 1.67E-01 2.95E-03 1.59 18.4 The absorption, distribution, metabolism and excretion Muscle 1.03E-01 2.61E-03 16.91 195.2 (ADME) modeled are very simple; absorption in all com- Fat 1.64E-01 5.37E-03 28.98 334.5 partments is assumed to be perfusion limited, the gases Richly perfused tissue 1.54E-01 2.97E-03 5.31 61.3 are not metabolized, and excretion is only by the reverse Poorly perfused tissue 8.42E-02 2.30E-03 20.40 235.4 process of absorption through the lungs and exhaled. Brain 1.37E-01 2.43E-03 1.79 20.7 The model was validated by comparison to published data; to xenon uptake data in humans from a different Xenon Rat model [5] and from experimental measurements of Blood (venous) 9.84E-01 3.41E-03 0.31 3.6 xenon blood concentrations during wash-in to pigs [43]. Blood (arterial) 1.20E + 00 4.05E-03 0.05 0.6 Both comparisons (Figs. 2 and 3) show that the current Liver 8.66E-01 2.93E-03 0.35 4.1 model can accurately determine the rate of disposition Muscle 2.46E-01 1.14E-03 2.29 26.4 of the gas in the body. We note that this accuracy is Fat 1.52E + 00 7.15E-03 2.39 27.6 achieved in spite of the fact that the model does not ac- count for mixing or circulation in the arterial blood Richly perfused tissue 8.74E-01 2.94E-03 0.26 3.0 compartment. Brain 1.22E + 00 4.11E-03 0.09 1.0 Based on the example of a one-hour administration of Argon Human xenon per day, the key physiological results show that Blood (venous) 3.74E-02 7.02E-04 2.71 31.3 fat acts as a reservoir for gas storage, such that there is a Blood (arterial) 4.41E-02 7.49E-04 0.18 2.1 residual dose that is equivalent to a continuous expos- Liver 3.21E-02 5.64E-04 1.89 21.8 ure. The residual dose, the concentration just before the Muscle 2.37E-02 5.26E-04 11.25 129.9 re-administration, is at a relatively low level (equivalent to breathing 0.01 % xenon gas composition) but this is Fat (Richly perfused) 4.18E-02 1.30E-03 26.55 306.4 still about a thousand times greater than ambient expos- Fat (Poorly perfused) 1.19E-02 3.93E-04 29.48 340.3 -6 ure (8.7x10 % of xenon in the atmosphere) in humans. Richly perfused tissue 4.36E-02 7.70E-04 2.07 23.9 It is important for preclinical testing that the clearance Poorly perfused tissue 4.35E-03 1.42E-04 28.93 333.8 is much faster in small animals (about 10 times faster, Brain 2.90E-02 5.05E-04 1.46 16.8 see t for rats in Table 2) such that there is essentially 1/2 no residual dose between exposures for the same Also note that the timing is almost ten times faster in chronic application example presented for humans in the rat than in the larger species as reflected in the data Fig. 4b and c. Thus, preclinical studies with small ani- given in Table 2. mals might not indicate benefits or the negative effects Results from simulations of one-hour exposures to associated with these therapies that occur after adminis- 50 % xenon and argon in the human model are shown tration of the gas. However, preclinical studies could be Katz et al. Medical Gas Research (2015) 5:8 Page 7 of 10 0.006 Blood (arterial) 0.005 Fat (richly perfused) 0.004 Fat (poorly perfused) 0.003 0.002 0.001 0 102030405060 Time (min) 3.0E-03 Arterial Blood Poorly perfused fat 2.5E-03 2.0E-03 1.5E-03 1.0E-03 5.0E-04 0.0E+00 01 23 Time (days) 6.0E-04 2.5E-07 5.0E-04 2.0E-07 4.0E-04 1.5E-07 3.0E-04 1.0E-07 Poorly perfused fat 2.0E-04 Arterial blood 5.0E-08 1.0E-04 0.0E+00 0.0E+00 02 468 10 12 Time (days) Fig. 4 a. Arterial blood, richly and poorly perfused fat xenon concentrations after a single administration for 1 hr of 50 % xenon to a male adult human. b. Poorly perfused fat xenon concentration after the repeated administration of the same dose once per day. c. Residual xenon concentration just before the next administration for 10 days. The residual dose is at a relatively low level (equivalent to breathing 0.01 % xenon gas composition) but this is still about a thousand times greater than ambient exposure Fat Residual Concentration (mol/L) Concentration (mol/L) Concentration (mol/L) Arterial Blood Residual Concentration (mol/L) Katz et al. Medical Gas Research (2015) 5:8 Page 8 of 10 0.005 0.004 0.003 0.002 Human 0.001 Pig Rat Time (min) Fig. 5 Comparison of arterial blood xenon concentration after a single administration of 1 hr of 50 % xenon for a small animal (rat), a large animal, (pig), and a male adult human designed to include a residual dose to mimic the effect delivered to the patient, in this example 50 % xenon for of gas storage in fatty tissue that occurs for humans. one hour, will be different at the site of action for each Note that argon differs from xenon in that the residual species. Changes in concentration can readily be imple- dose is not important because the baseline atmospheric mented using Equation 2, including hyperbaric condi- concentration is 1 %. tions. The most important and direct effect of changes Another important aspect of interspecies variability is in concentration are proportional changes in saturation the different tissue solubility for each gas among animal concentrations. species as indicated by the partition coefficients listed in To expand on the point of characterizing experiments Table 1 and the arterial blood concentration plots shown with the true dose (i.e., the AUC at the site of action) in Fig. 5. Furthermore, these differences are expressed in the gas delivery system must be considered. Due to the the differences in dose for each species in each compart- physics related to filling the dead volume or leaks in the ment listed in Table 2. The key message is that the dose delivery system it is virtually impossible to immediately 0.003 Xenon 0.002 Argon 0.001 0 102030405060 Time (min) Fig. 6 Variation of uptake with gas type; comparison of arterial blood concentration after a single administration of 1 hr of 50 % xenon or argon to a male adult human Concentration (mol/L) Concentration (mol/L) Katz et al. Medical Gas Research (2015) 5:8 Page 9 of 10 -10 -20 -30 50 60 70 80 90 100 110 120 Weight (kg) Fig. 7 An example of intersubject variability; the variation of t for the brain compartment for administration of xenon as a function of weight 1/2 for adult males. The variation is expressed as a percentage of the value for a 70 kg individual apply the inhaled dose as has been modeled herein. Certainly, more experimental data of pharmacokinetics Thus the wash-in of gas into animal boxes [44] and with pharmacodynamics are needed for the development ventilators [45] should be taken into account to deter- of optimized gas therapies. mine the true AUC and is the subject of future work for our team. Conclusions The measure of intersubject variability in this ADME An ADME PBPK model has been developed to investi- PBPK model only accounts for physiological parameters, gate the unique aspects of the chronic administration of it does not take into account pharmacological variations noble gas therapies. The model has shown that there that are also known to occur due to age and gender can be a residual dose, equivalent to constant adminis- (e.g., for xenon anesthesia [46]). tration, for chronic repeated dosing of xenon in humans. There are several aspects of the model that can be However, this is not necessarily the case for small ani- improved. The basic, steady state model for respiration mals used in pre-clinical studies. The use of standard PK can be improved to better account for the complex dis- parameters such as AUC would be more appropriate to tribution of gas concentration that exists in real lungs assess the delivered dose than the gas concentration in (for example oxygen [27] and nitric oxide [47] uptake the delivery system that is typically cited. have been examined in the literature). There may be exceptions to the perfusion limited assumption used in Abbreviations the model. For example, studies in volunteers have ADME: Absorption, distribution, metabolism and excretion; AUC: Area under the shown non-uniform distributions of xenon in blood as curve; Bax: Bcl-2-associated X protein; Bcl-2/Bcl-xL: B-cell lymphoma 2/ B-cell lymphoma-extra large; ERK : Extracellular-signal-regulated kinases 1/2; 1/2 a function of hemocrit [48] and in the brain [49] using MAPK: Mitogen-activated protein kinase; NMDA/AMPA: N-methyl-D-aspartate, computed tomography imaging. Another study in sheep /α-Amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid; p38: p38 is in fact p38 [50] has shown that a PK model with direct diffusion MAPK and means Mitogen-Activated Protein Kinase; PK: Pharmacokinetics; PB: Physiological Based; TREK-1: TWIK-1 related K+ channel-1. between brain regions was better for fitting the experi- mental data for the absorption of helium. In principle, Competing interests the model can readily be extended to other gases where The authors declare that they have no competing interests. metabolism does not occur or is insignificant, krypton, neon, helium, nitrous oxide, and nitrogen; the last use of Authors’ contributions the model would be to investigate the di-nitrogenation IK conceived of the study, analyzed the results and drafted the manuscript; process that is necessary to optimize the delivery of gases JM developed the model and read the manuscript; MP further developed the model, ran the simulations and organized the data, and read the using recirculating systems [45]. However, all the neces- manuscript; JP helped draft and edit the manuscript; and GC helped to sary partition coefficients are not readily available in the conceive the study and read the manuscript. All authors read and approved literature for all compartments, animal species, and gases. the final manuscript. 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Medical Gas Research – Springer Journals
Published: May 29, 2015
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