the uptake of anaesthetic agent is defined as the amount of vapours that is taken by the alveoli . it depends on the agent solubility , cardiac output ( co ) and alveolar to mixed venous partial pressure difference of the agent . severinghaus ( 1954 ) postulated that the uptake of nitrous oxide is inversely proportional to the square root of time ( sqrt ) . lowe and ernst gave the sqrt , which was later utilized for predicting the uptake of commonly used volatile agents . it indicates that uptake is related to patient 's weight and gradually decreases according to the sqrt . however , recent clinical observations have shown that the observed rate of isoflurane uptake differ from that predicted from the sqrt model . addition of liquid volatile agent ( ether ) into the circuit was first used by william morton in 1847 . subsequently , a series of dosage tables according to patient 's body habitus have been predicted for use during closed circuit anaesthesia . the derivations of these complex formulae and mathematical models have deterred anaesthesiologists from using low flow anaesthesia . the anaesthesiologist is more interested in attaining a desired minimum alveolar concentration ( mac ) as the parameter and not the pharmacokinetics of the agent . by studying the rate of uptake of isoflurane during our pilot cases , we modified the dosages derived from lowe and ernst equation into a simplified form of rate of liquid isoflurane injection into the circle system using low flow anaesthesia . after approval by the hospital ethics committee , 10 patients of either sex undergoing elective surgeries for 1 h to 3 h duration of anaesthesia were enrolled . patients with american society of anaesthesiologists ( asa ) physical status i , aged between 22 years and 55 years were included after informed consent . the surgeries performed were varicose vein stripping ( n=3 ) , modified mastectomies ( n=4 ) , inguinal hernia repair ( n=1 ) and superficial parotidectomy ( n=2 ) . patients with pregnancy , cardio - pulmonary pathology , any history of central nervous system disease , chronic use of psychoactive medication ; with a body mass index ( bmi ) less than 15 and greater than 30 were excluded from the study . general anaesthesia was induced with iv fentanyl 2 g / kg , propofol 1 - 2 mg / kg followed by 150 g / kg / min infusion , and vecuronium 0.1 mg / kg . bag and mask ventilation was performed for 4 min using the circle system with oxygen flows of 10 l / min ( the circle system was flushed prior to this with 100% oxygen for 5 min for de - nitrogenation ) . the circle system was closed after ascertaining the correct position of the endotracheal tube with initiation of controlled ventilation and propofol infusion was discontinued . ml / kg ideal body weight ( ibw ) h and later titrated to attain and maintain end - tidal isoflurane concentration ( et - iso ) of 1.5% ( mac 95 ) . the expiratory limb had a specialised connection with two luer lock ports , one for attachment to isoflurane infusion and the other for return of sampling gases ( 150 - 200 ml / min ) by the multigas analyzer ( datex - ohmeda s/5 , instumentarium corp , helsinki , finland ) , which was calibrated before every case . isoflurane was injected in 50 ml plastipak ( polyethylene bd ) syringe with polyethylene tubing using a syringe pump ( fresenius vial sa , france ) . the dead space of the tubing ( 2 ml ) was pre - filled with liquid isoflurane and the stated volumetric accuracy of the pump was 2% . the entire apparatus was kept at a lower level than the circle system to avoid accident spillage of liquid agent into the circuit [ figure 1 ] . ohmeda 7000 anaesthesia ventilator ( ohmeda , boc health care division , madison , wi ) with soda lime canister , corrugated rubber tubing and ascending bellows were used to provide pre - set volume ventilation . the volume of the circle system was determined individually for all the components and was 2.2 l , the volume of the connecting hose to the ventilator being 0.5 l. the amount of acceptable leak in the circuit was 50 ml / min determined during ventilation of a test lung at 30 cm peak inspiratory pressure . oxygen was used as the sole carrier gas with fresh gas flow ( fgf ) to maintain a constant circuit volume . the incision was given after 30 min of the start of the isoflurane infusion to study isoflurane uptake in un - stimulated conditions . intra - operative analgesia was maintained with fentanyl infusion of 1 g / kg / h iv . patients requiring vasopressor or cardiac medication for haemodynamic changes of or 20% of baseline values were excluded from the study . additional fentanyl ( apart from infusion ) and vecuronium boluses were given as clinically indicated . a  oxygen flow meter ; b and f  unidirectional valves ; c  inspiratory limb ; d  expiratory limb ; e  specialised connector for isoflurane infusion and return of 
 sampling gases ; g  adjustible pressure limiting valve ; h  ventilator bellows ; i  soda lime canister ; j  isoflurane infusion ; k  agent analyser ; l  computer for data recording rate of uptake and cumulative uptake of isoflurane was determined from the difference between the isoflurane administered and the system leaks ( see appendix ) . similarly , the expected rate of uptake and cumulative uptake was calculated using lowe and ernst 's sqrt model for comparison with our study . throughout the procedure bispectral ( bis ) index , non - invasive blood pressure , heart rate , haemoglobin oxygen saturation ( spo2 ) , temperature , end - tidal carbon dioxide ( et - co2 ) , inspired isoflurane ( fi - iso ) , and et - iso were recorded continuously . a computer interphased to the syringe pump and the monitor recorded the data continuously . pearson correlation coefficient was obtained between the cumulative uptake of isoflurane in the first 30 min of start of isoflurane infusion with the patients variables ; body weight , ibw , height , body surface area ( bsa ) , and ( body weight). bmi was correlated with cumulative uptake per kilogram body weight . the mean cumulative rate of uptake per kg derived from the lowe and ernst equation was compared with the observed rates at 10 min interval , from 10 min onward using repeated measured anova . the mean rate of uptake per kg per minute were averaged at 10 min intervals and also compared with that estimated from lowe and ernst equation using repeated measures anova . pearson correlation coefficient was obtained between the cumulative uptake of isoflurane in the first 30 min of start of isoflurane infusion with the patients variables ; body weight , ibw , height , body surface area ( bsa ) , and ( body weight). bmi was correlated with cumulative uptake per kilogram body weight . the mean cumulative rate of uptake per kg derived from the lowe and ernst equation was compared with the observed rates at 10 min interval , from 10 min onward using repeated measured anova . the mean rate of uptake per kg per minute were averaged at 10 min intervals and also compared with that estimated from lowe and ernst equation using repeated measures anova . patients characteristics ( six male / four female ) and anaesthesia details are given in table 1 . perioperative haemodynamics were stable in all cases with no patient requiring cardiac medication , vasopressors and/or additional doses of fentanyl or vecuronium . patient and anaesthesia details the mean fgf used was 25010 ml / min ( equal to leaks and patients oxygen consumption ) to maintain the circuit volume . after attainment of 1.5% et - iso , it was maintained between 1.4% and 1.6% . the rate of injection used did not result in liquid droplet formation in the circuit as seen by a glass window in the specialised connector . the observed cumulative uptake of isoflurane vapours by 30 min was 20.52.8 ml / kg / min . since the target et - iso ( 1.5% ) was achieved by 10 min in all the patients , we compared the predicted and the observed uptake after 10 min . observed cumulative uptake was high as compared to lowe 's equation , the difference gradually increased with time . this difference was statistically significant ( p=0.042 from 60 min onwards from the start of isoflurane infusion [ figure 2 ] . as compared to lowe 's equation the mean observed uptake per kg per min was significantly higher after initial 10 min ( p<0.05 ) . rate of observed uptake relatively stabilized after 30 - 40 min [ figure 3 ] with a mean of 0.370.47 ml / kg / min vapour requirement for keeping a mean end - tidal isoflurane concentration of 1.510.1% . there was inter - individual variability in the uptake [ figure 4 ] and it showed statistically significant correlation with ibw , wt , bsa , body weight from 30 min of start of isoflurane infusion ( p<0.05 ) [ table 2 ] . cumulative uptake kg varied inversely with bmi ( r=0.53 ) , but the relation was not statistically significant ( p>0.05 ) . cumulative rate of uptake of isoflurane ( vapour ) per kg body weight ( meansd ) . * p<0.05 ; * * p<0.01 mean rate of uptake ( sd ) of isoflurane vapour per kg actual body weight per min . also shown note the stability from 40 min onwards . * p<0.05 ; * * p<0.01 individual rates of infusion of isoflurane per kg ideal body weight per h. the different rates of infusion depict inter - individual variability for the same end tidal after functional residual capacity and circuit wash in correlation of cumulative isoflurane uptake ( at 30 min ) and measured patients variables . value in parenthesis shows the actual p value bis index was in the range of 25 - 30 and et - co2 was maintained at 32.42.1 mm hg during the study . the mean expired oxygen concentration at the end for the longest duration of surgery ( 160 min ) was 785% . we had derived isoflurane infusion rates [ figure 4 ] from our pilot cases by modification of lowe and ernst 's equation of uptake ( 1 ml of liquid isoflurane produces 205 ml vapours at 37c ) . our aim was to provide enough vapours to wash - in the circuit volume and patients functional residual capacity ( frc ) to 1.5% vapour concentration and in addition 3 unit doses ( according to sqrt principle ) within 9 min . we had decided to achieve et - iso of 1.5% within 5 - 10 min for gradual build - up of concentration , avoiding excess over pressurization and hypotensions in anaesthetized patients thus try to maintain a stable co to study uptake . though the rate of observed uptake in the initial period was lesser than predicted by the lowe 's equation , we compared uptake after 10 min ; by the time1.5% et - iso was attained in all patients . sqrt and 4-compartment models have been compared before with a lot of discrepancies with actual clinical observational studies on volatile agent uptake . changes in co with surgical stimulation were speculated as the main factor for the differences . however , even after substitution of measured co values in the formulae both models had differences between observed and calculated uptake . the same differences were observed when invasively measured fluctuating co was used to calculate and compare uptake . we tried to maintain stable haemodynamic to maintain a stable co as our fgf were near metabolic flows and did not fluctuate much . moreover when using closed - loop feedback technique to maintain constant end expired concentration , the rate of increase and consequently the uptake becomes independent of co and ventilation ; and depends on the infusion rate of the volatile agent . the other reasons to explain the difference of isoflurane requirement from the sqrt model are ; isoflurane metabolism , loss from the surgical site , body surface , anaesthetic circuitry , and absorption into soda lime . isoflurane is mainly exhaled unchanged from the body and only 0.2% of absorbed isoflurane undergoes oxidative metabolism . anaesthetic loss into the circuitry depends on the rubber / gas ( 49 ) and plastic / gas ( 58 ) partition coefficients ; however , this depot will be saturated with time and can not explain the progressive increasing in the difference of cumulative uptake . inter - individual variation is also a factor affecting uptake kinetics . on plotting the infusion requirements over time , we found that it varied for similar et - iso in different patients [ figure 4 ] . this can be due to individual differences in the factors determining uptake i.e. , co , blood / gas partition coefficient ( b / g ) . the tissue and blood solubility coefficients have been derived from tissue homogenates and vary by as much as 150% . solubility is also influenced by changes in body temperature , blood and tissue composition , genetic pre - disposition , and other unknown physiological variables . brody 's equation has been derived from a large  normal sample population under resting conditions . it does not necessary predict the output for the individual patient and might be different from the measured co in clinical situations . moreover , changes in co do not cause proportional changes in tissue perfusion to various compartments . previous comparative studies state that isoflurane uptake is overestimated and later on underestimated by sqrt model . our study shows similar results with a simpler methodology to calculate the rate of uptake . the constant difference after 30 min between the uptake curve [ figure 3 ] , imply that the difference of cumulative uptake between the observed and that from the sqrt model would gradually increase [ figure 2 ] . severinghaus had described the uptake of nitrous oxide in only 6 patients with primitive monitors . arterial to end expired gradient due to ventilation - diffusion mismatch , different exponential organ uptake time constants , inter tissue diffusion of volatile agents and regional blood flow variability may cause inaccuracy in calculating uptake . even current computer programs simulating anaesthetic uptake may not be correct because they are based on theoretical models , although they may be still useful to teach basic principles of uptake . therefore , anaesthesia techniques with low flows continue to rely on anaesthetic monitoring . nevertheless , the fact that authors have repeatedly come back to sqrt model as a benchmark suggests that it still might have some underlying validity . different studies have shown weak correlations of uptake of the agent with all patient characteristics better with body weight, bsa and actual body weight . thus , predicting anaesthetic uptake and its delivery at pre - determined rates derived from anthropometric measurements might not be accurate . we used ibw for calculating the infusion rate of isoflurane because it correlates better with lean body mass . since , this was an open labelled study the observer was not blinded . data were simultaneously being recorded intra - operatively in a computer logged on to the monitor . isoflurane uptake was based on oxygen requirement , which were derived from nomograms ( appendix ) . the decreased requirement under anaesthesia was taken care of by further decrease in fgf progressively to metabolic flows . isoflurane infusion was not connected to the inspiratory limb to avoid any accidental exposure of liquid isoflurane to patient 's airway . moreover , at the expiratory limb warm expired gases assist to maintain near body temperature and ensure vaporization . vapour loss due to system leaks and venting was evaluated based on the fgf and patient 's oxygen consumption . alveolar uptake proceeds simultaneously with wash in therefore the actual rate of uptake can not be separated from that of the system . the rate of infusion stabilized by 15 - 20 min ( 0.15 - 0.10 ml ibw / kg / h ) in all subjects and remained the same throughout . there is inter - individual variability in the pharmacokinetics of isoflurane in humans . during the initial period rate of uptake
background : the square root of time ( sqrt ) model had been used to predict the uptake of volatile agents.methods:we studied the rate of uptake of isoflurane in 10 patients using liquid isoflurane infusion through syringe pump into the closed circuit . 
 the infusion rates were titrated to maintain a constant end tidal concentration of isoflurane of 1.5% . 
 the predicted uptake values were also calculated from the square root principle and compared with the derived uptake.results:the observed rate of uptake was higher than predicted from the lowe and ernst equation ( p<0.001 ) . 
 there exists considerable inter - individual variability in uptake pharmacokinetics and it showed statistically significant correlation with ideal body weight , body weight ( p<0.01 ) , body surface area , and body weight from 30 min of start of isoflurane infusion ( p<0.05).conclusion : sqrt model is inaccurate in predicting isoflurane uptake and underestimates it during closed circuit anaesthesia .