Application Of Mathematical Models Of Pulmonary Gas Exchange In Oral And Maxillofacial Surgery

Late postoperative arterial hypoxaemia is common after major surgery,and may contribute to cardiovascular,cerebral or wound complications. Thisstudy investigates the time course of hypoxaemia following operation of oraland maxillofacial surgery, and estimates parameters of mathematical modes ofpulmonary.gas exchange to describe hypoxaemia.Following uncomplicated major surgery, patients may develop arterialhupocaemia (SAO2<92%). Early postoperative atertial hypoxaemia(EPAH)occurs during the first few hours after surgery and may be related to the typeand duration of anaesthesia, type of surgical inervention and to patientage .EPAH presents in 41-55% of patients after different types of surgicalintervention. For the first few hours after surgery patients reside in the postanaesthesia care unit ,where routine continuous monitoring of artetialoxygenation, using pulse oximetry, enables early recognition and relevanttreatment of hypoxaemia.Late postoperative arterial hypoxaemia (LPAH) occurs in 41-50% ofpatients after major major abdominl or thoracic surgery during the secondpostoperative night, with 38-50%of these patients having episodes of suddenoxygen desaturation below 85% . During this phase the patient has returned tothe surgical ward where continuous monitoring of oxygen saturation is lessroutine and as a consequence the decision to provide supplementary oxygen ismore difficult. LPAH is therefore a potential threat to the patient ,and if leftuntreated poor post-operative oxygenation may contribute to cardiovascular,cerebral or wound complications.Determining clinical parameters to describe a patient's risk of hypoxaemiacould aid in deciding whether to provide supplementary oxygen in the latepostoperative phase. Arterial oxygen saturatin changes rapidly in cases ofLAPH , meaning that measutements of SAO2 taken on single occasions mingtnot be sufficient to describe a patien's risk of hypoxaemia. In cases of LAPH, amore detailed description of oxygenation problems is neededMathematical models of the lung eitg two parameters are sufficient todescribe the variation in SAO2 with changing inspired oxygen fraction(FIO2).These models include pulmonary shunt (shunt) and either alveolarresistance to oxygen diffusion , or asymmetry of ventilation-perfusion(V/Q).These models have been shown to fit the data form patients studied followingsurgical intervention ,where abnormalities of oxygen diffusion or V/Q mismatchwere associated with large reductions of SAO2 for very small changes in inspiredoxygen, suggesting that these patients were at increased risk of hypoxaemia.This study investigates the presence of hyoxaemia in both the early and latephases following operation of oral and maxillofacial surgery,and subsequentlyestimates parameters describing hypoxaemia in both these phases.Twenty-two patients scheduled for surgery in oral and maxillofacial partwere in cluded in the study. In all cases patients were ASA Ⅰ–Ⅱ, with meanage 30 years and weight 62.5 kg. Anaesthesia was uneventful usingthiomebumal, fentabyl (Janssen Pharmaceutica n.v.,Beerse,Belgium),vecuronium (Organon Thknika,Skovlunde,Denmark)..Intraoperative monitoringincluded electrocardiography, capnography ,pulse oximetry and invasive bloodpressure through an arterial catheter.Measurements were taken preoperatively, and then 2,8 and 48 h aftersurgery. One patient withdrew from the study after the 2 h measurement with afurther two patients withdrawing after the 8 h meansurement. On each occasion(preoperatively, 2,8 and 48 h ) F1O2 was increased from 0.21to 1.00 in 5 to 8steps in order to achieve oxygen saturations in the range 90-100%. At each step5 min was allowed for equilibration at the new F1O2 level.The patients were breathing through a face mask with a three-way valveseparating inspired and expired air. A number of measurements were made oneach occasion and at each F1O2 level. At each F1O2 level ,we mensured minuteventilation using a valume meter, respiratory frequency recorded by acapnograph (average over 3min),F1O2, FEO2 (expired oxygen fraction), andarterial oxygen saturation measured by pulse oximetry (SpO2)..At both 2and 8 hpostoperatively arterial oxygen saturation (SAO2)was measured from arterialblood samples at each F1O2 level. Preoperatively and 48 h postoperativelyoxygen saturation, measured using pulse oximetry, was supplemented by asingle arterial blood sample ,which was used to calibrate the pulse oximeter. Thefollowing procedure was used: For each patient a single graph of SpO2 wasconstructed for the data collected preoperatively,2,8and 48 hpostoperatively.This curve was used to calibrate the pulse oximetry readingstaken preoperatively and 48 h after surgery. Calibration was performed byadjusting the pulse oximetry readings using a linear regressionfit to the SPO2,SAO2 data. The mean correlation correlation coefficient of the linear regressionfit across all patients was r2=0.97 (range 0.91-0.99). In all cases blood sampleswere analused to obtain measurements of acid-base status, blood gases andconcentrations of haemogolobina (pH, PaO2, PaCO2 , BE, Hb , HbMet andHbCO).Preoperatively, 2 h, 8 h and 48 h after surgery the oxygen consumption(VO2) was determined at F1O2=0.21 by collecting expired gases in a Douglasbag and measuring the minute volume and mixed expired oxygen fraction.The conditions in the pre-, per-and postoperative periods were stable. In allcases at least one arterial blood gas was taken, and acid-base status measured. Inaddition, FECO2 was measured continuously throughout the experiment, andremained relatively constant during variation of F1O2. All patients werenormothermic Hence, apart from 2,3-diphosphglucerate (2,3-DPG) allparameters necessary to describe the oxygen-dissociation curve (ODC) wereavailable. Preopreatively a normal value of 2,.3-DPG was assumed. Tow andeight hours after surgery 2,3-DPG was estimated from 4-6 blood gasmeasurements. Forty-eight hours after surgery 2,3-DPGwas assumed to be thesame as the value estimated eight hours after surgery.Anatomical dead space was assumed to be 150 ml, and the volume of theface mask was measured as 50 ml, giving a total dead space of 200 ml. It wasnot possible to measure cardiac output in these patients and a value of 51/minwas assumed in all cases. It has been shown previously that changes in themodel parameters due to variations in cardiac output are not clinically relevant,as a variation of cardiac output of 40% causes a change in the estimate of shuntfrom 10% to 12% and a negligible variation in the estimated Rdiff.These measurements were inserted into the equations of tow mathematicalmodels of oxygen transport. These models include parameters describing gasexchange. Abnormalities of gas exchange are described by variation in thevalues of pulmonary shunt (shunt) and alveolar oxygen diffusionresistance(Rdiff). These abnormalities are described by variation in the values ofpulmonary shunt (shunt)and asymmetry of ventilation and perfusion (fA2). FA2is the fraction of ventilation to an alveolar compartment that is perfused by 90%of the non-shunted blood flow. Model parameters were estimated on each of thefour occasions so as to fit the measured SAO2 and PaO2 using the weighted leastsquares method, as follows: Initial values of "shunt" and either "Rdiff" or "fA2"were assumed;subsequently the equations were used to predict values of SAO2and PaO2 over a range of F1O2. The least squared distance between predicted andmeasured SAO2 and PaO2 values (residual sum of squares (RSS)) was thenminimzed by varying "shunt" and either "Rdiff" or "fA2" until the best fit of themodels to the measured data was found.Measurement errors of 0.2% for SAO2 and 0.6% for PaO2 wereassumed.P-values are obtained form a two-sided t-test.Informed written and oral consent was obtained in all cases.The results were that or the patient group as a whole oxygenation wasimpaired after surgery. When this is described using single measurements ofarterial oxygen saturation at FIO2=0.21, SAO2 was significantly reduced frompreoperative values of 97.5±0.96%(mean±SD) to 94.3%±2.17% (mean±)(P<0.001). However, when the inspired oxygen fraction is varied and themeasured arterial oxygen saturation (SAO2) is plotted against the end-tidaloxygen fraction (FEO2), a more detailed description of oxygenation is possible.This is illustrated for one patient preoperatively (crosses) and 8 h after surgery(circles), along with curves fitted to the data using the single-compartmenttwo-parameter shunt/Rdiff model of oxygen transport (Fig.1) (solid line) and thetwo-compartment two-parameter shunt/fA2 model of oxygen transport (dashedline). These two models provide an almost identical fit to the data, and thedashed and solid lines are difficult to distinguish. Note how the curve is shiftedto the right after surgery, meaning that desaturation of arterial blood occurs athigher values of FEO2. data from one patient measured 8 h after surgery aregiven.Table above gives values of model parameters (shunt/Rdiff and shunt/fA2) when the models are fitted to all 22 patients. The mean values of shuntwas gived.Rdiff and fA2 and P-values obtained from a two-sidedt-test for all patientson each of the four occasions. Prior to surgery the mean values were shunt=1.2± 2.5%(upper normal range7.8%);Rdiff=1.7 ± 2.4(upper normal range6.7kPa/(l/min)and fA2=0.7± 0.11(lower normal rang0.6). As a group thepatients had significantly increased values of shunt and Rdiff significantlydecreased values of fA2following surgery. Values of shunt, Rdiff and fA2remained significantly changed both 2 h and 8 h after surgery. Forty-eight hoursafter surgery Rdiff and fA2 were still significantly changed whilst shunt was nolonger significantly higher than normal. The two models provided an almostidentical fit to the patient data with a linear regression fit to the RSS giving acorrelation coefficient of r2=0.9995. Fig. 5a and 5b illustrate the time course ofvariation in Rdiff and fA2 preoperatively and 2,8 and 48 h after surgery. Eighthours after surgery 4 patients had increased values of Rdiff and decreasedvalues of fA2. Forty-eight hours after surgery two of these patients still hadsignificantly different values of these parameters compared to the preoperativesituation. Fig. Above illustrates measured arterial oxygen saturation plotted(SAO2) preoperatively and 2,8,and 48 h after surgery for the two patients withincreased Rdiff or decreased fA2 48 h after surgery . Curves illustrate the fit ofthe two different models of oxygen transportto these data, i.e. shunt/Rdiff(solidlines) and shunt/fA2 (dashed lines). Model predicted values of FEO2 atSAO2=92%,are shown on each of the plots;these values illustrate the right shiftin the FEO2/SAO2 curve following surgery in these two patients. These changes inoxygenation are present 48 hours after surgery when the patients are in thesurgical ward without monitoring or oxygen treatment and may place them atincreased risk of hypoxaemia.This study investigated twenty-two patients on four occasions: prior to andthen 2,8 and 48 h after operation of oral and mxillofacial part. On each of theseoccasions data have been collected describing oxygenation at varuing inspiredoxygen fractions. As assessed by single measyrements of SAO2 at FIO2=0.21,hypoxaemia (SAO2<92%) was present in two patients 48h after this low risksurgical intervention. Single measurements of SAO2, however, may not beenough to describe the individual patients risk of hypoxaemia, since theoxygenation level in patients with late postoperative hypoxaemia is rapidlychanging.It has been shown previously that the shape and position of the FEO2/SAO2curve is affected by disorders in pulmonary gas exchange. Figs. show plots ofthe FEO2/SAO2 data for the patients with oxygenation problems. The curves areshifted to the right following surgery, such that desaturation of arterial bloodoccurs at higher values of FEO2, and the patients are at a greater risk ofhypoxaemia.These data enable a more complete description of the oxygenation problemthan values of arterial oxygen saturation measured at single inspired oxygenfraction. In particular they enable estimation of the parameters of mathematicalmodels of oxygen transport . i.e. pulmonary shunt, alveolar/lung capillaryoxygen diffusion resistance (Rdiff), and asymmetry of ventilation and perfusion(V/Q). It has been shown previously that simulations performed using thesetwo-parameter models can produce FEO2/SAO2 curves which are both verticallyand laterally displaced. The vertical displacement (downward shift) beingexplained by increases in shunt, and the lateral displacement (right shift)explained by either increased Rdiff or decreased V/Q. This is not possible usinga single-parameter shunt only model. In a previous study the two-parametershunt Rdiff model was shown to give a significantly better fit to the data of 9postoperative cardiac patients than the single-parameter "effective shunt"model,even after accounting for the difference of degrees of freedom between the twomodels.Values of shunt/Rdiff and shunt/fA2 have been obtained for each patient oneach of the four occasions and are given in Table For the group as a wholevalues of shunt and Rdiff were significantly increased and values of fA2 weresignificantly decteased 2 and 8 h after surgery Forty-eight hours after surgerythe increase in Rdiff and decreased in fA2remained significant, with shuntreturning to normal For two patients shunt, Rdiff and fA2 remained abnomal48 h after surgery. In these patients, the right shift in the FEO2/SAO2 curves seenfollowing surgery is explained by high values of Rdiff or low values of fA2, notshunt. Where the FEO2/SAO2 curves are shifted to the right,.small changes inFEO2 result in dramatic reductions in SAO2. Small changes in FEO2, caused byirregular breathing patterns and a right-shift of the FEO2/SAO2 curve areconsistent with the episodes of severe arterial hypoxaemia seen in the latepostoperative phase. Further studies on larger patient guoups are required toinvestigate whether abnormal values of model parameters are correlated withearly and late postoperative hypoxaemia.For all patients the model gave a reasonable fit to the data. This isillustrated where measured data and model simulated curves are given forthree patients. in addition the two models provided an almost identical fit to thedata .When estimating values of shunt, Rdiff and FA2 anatomical dead spacewas assumed to be 150 ml and cardiac output was assumed equal to 5l/min.Previously we have shown that the estimates of shunt and Rdiff are insensitiveto fairly large variations in cardiac output with a variation of 40% causing achange in shunt of only 2% and a negligible variation in Rdiff. Estimation ofshunt is, however, sensitive to errors in the measurement of SAO2 a deviation of0.01 changing shunt by up to 12%). In this study the arterial oxygen saturationwas measured preoperatively and 48 h after surgery using pulse oximetry withthese measurements being supplemented by arterial blood samples, and SPO2values calibrated as described in the methods section.This paper has described postoperative hypoxaemia using two differentphysiological models including pulmonary shunt and either a resistance toalveolar oxygen diffusion or an asymmetry of ventilantion and perfusion.Postoperative hypoxaemia is usually attributed to atelectasis cause by the effectsof anaesthesia and surgery. Complex experimental studies using multiple inertgases as tracers . have associated postoperative atelectasis, as assessed by CTscans, with abnormal shunt and ventilation-perfusion asymmetry. Theventilation-perfusion model may thesefore be a more appropriate physiologicaldescription of the data presented here. The true pathophysiological nature of theoxygenation problem cannot be obtained from this simple experimentalprocedure, and the striking similarity of the fit of these models to data seen hereand elsewhere means that either can be used to describe the severity of theoxygenation problem. Both models describe a drop in oxygen pressure from themouth (FEO2) to blood leaving the lung capillaries (PCO2). The Rdiff parameterdescribes this oxygen pressure drop across the alveolar-lung capillary membrane,whereas the fA2 parameter describes the oxygen pressure drop using lungcompartments with different oxygen pressure (PCO2(1), PCO2(2)).The methods presented here for estimation of shunt, Rdiff and fA2 can bemade with equipment routinely available in departments of anaesthesia andintensive care medician. Experiments of this type could be performed quicklysince oxygen equilibrates 2-3 min after perturbation. Studies including 4measurement points, where arterial blood oxygen saturation is measured usingpulse oximetry, can therefore be performed in 10-15 min. This technique mightthen be used as a clinical tool for assessing postoperative hypoxaemia.This paper has described oxygenation in twenty-two patients preoperatively,2,8 and 48 h after surgery. For two of these patients oxygenation problems weresuch that supplementary, oxygen was still required 48h after surgery. Twodifferent mathematical models of oxygen transport was fitted to these dataincluding parameters describing pulmonary shunt (shunt) and either resistance tooxygen diffusion (Rdiff) or asymmetry of ventilation and perfusion (fA2). Highvalues of Rdiff or low values of fA2 describe yeh apparent right shift in theFEO2/SAO2 curve seen in patients with oxygenation problems. Either Rdiff orfA2 may therefore serve as a useful quantitative index to assess and monitorhypoxawmia in these patients.