The incentive of these pharmacokinetic DiY blogs was to give colleagues that have an interest in pharmacokinetics and pharmacodynamics a relative simple tool to use published pk/pd models and make simulations that can be used to deepen the understanding of the tools like TCI that we use in daily practice to perform anaesthesia. We have used the Euler approximation in a spreadsheet and demonstrated that small steps of 5 seconds could be sufficiently closely matched to the exponential equations and graphs that represent the evolution of drug concentrations in a patient. This was possible for bolus, infusion and target controlled infusion in a deterministic way, in other words: based on calculations that are simple and valid for all drugs simulations.

For me these spreadsheets are valuable despite the fact that I have developed Tivatrainer(X) that uses analytical equations and is in theory more accurate. For a quick simulation to verify an idea or concept I still use the spreadsheet approach because it will allow the use of any model not just compartimental. The principle of a spreadsheet is that in every row a small linear step of a complex process is performed while the input comes from another previously calculate row or cell. This is not sufficient for effect compartment control as this requires a forward looking algorithme: run the pump on maximum speed untill after stopping the blood and effect site concentration equilibrate to the required target without over or undershoot of the effect compartment concentration. Steve Shafer proposed a calibration dose in his book on IV anesthesia: give a bolus, look at the peak effect: this is where blood and effect equilibrate and note the overshoot of the blood concentration. Because pharmacokinetics are assumed to be linear(2 x dose -> 2 x concentration) you can work out the required bolus for a given effect. TCI systems use infusions not bolusses so this approach will not work. But the calibration concept is usable for the proposed heuristic solution. In the spreadsheet there is an 'EffectCalibrate' sheet. Infusion is given at a maximum rate specified in the 'data' sheet. After 100 seconds the infusion is stopped and the maximum effect site concentration(this is the equilibrium between effect and blood) is stored also in the 'data' sheet. These calculations in the 'EffectCalibrate' sheet can be done with or without opioid pk. An interval of 1 second is used in the 'EffectCalibrate' sheet to minimise the inaccuracy that is caused by the the Euler technique of stepwise change. For Propofol this 1 second is acceptable but for other drugs running the infusion at maximum speed for 1 second too short or too long will create a too big deviation and the stepsize possibly should be decreased. Then the peakeffect is used to calculate the time the maximum infusion has to run to achieve the required calculation using the calculation:

\(Time_{MaxInfuse}= (Target / PeakEffect * 100 -1\)) sec

With some if statements this calculation is activated only when there is an increase in target. For the remaining, effect TCI and blood TCI is similar appart from a decrease in the target, then the infusion is stopped until the effect concentration equals the target. This works suprisingly well when super imposed on the existing TCI calculations.

You may notice a small undershoot in the second target increase. This is because opposite to the linear Pk for boluses this is not valid for infusions. Nevertheless this heuristic model serves our purpose well. When compared with a TivatrainerX simulation the total amopunt given by the spreadsheet after 91.6 minutes was 858 mg versus 856 mg predicted by Tivatrainer.

Now the induction scenario, presented in the previous DiY blogs can be worked out for effect compartment control: the TCI device uses the Eleveld model *with* opioid but the patient receives the opioid only after 5, 10 or 15 minutes. So for that period the pharmacokinetics of the propofol in the patient do not match the used pharmacokinetics in the TCI system. In blog DiY3 this is worked out for (effect compartment) concentration and BIS using blood control TCI, in this spreadsheet it is worked out for effect target controlled infusion.

How it works:

-after setting the target in Effect_TCI check the opioid tickbox in effect_TCI.(set it to 'true' in excel) This will automatically also set the opioid pk in EffecCalibrate sheet to true and in the data sheet the maximum effect site concentration after 100 minutes running maximum infusion rate is stored(7.20745 µg/ml)

Based on the above equation the duration of the infusion running on max for the target is calculated.

The infusion rates produced by this simulation[column G] are now copied and the formula *results*** (**or *values* excel) are pasted into the induction sheet[column F]. See blog DiY3 for a more detailed instruction. All the spreadsheets use 5 second intervals. For the effect compartment control an adaptation is built in to adjust the last step otherwise the maximum infusion rate could run 5 seconds too long or too short.

Therefore you will have to copy the step in the *sec* column (column C) to the *sec* [column C] in the induction sheet. Again paste the formula *results* (*values* in excel]

If you check all the rows in the *opioid*[column D](= use opioid Pk) the the effect compartment concentration should nicely match the target. For our scenario uncheck the rows in the* opioid*[column D] for the respective period of time : 5, 10 or 15 minutes and for each step copy the concentration, effect site concetration and Bis to a column for graphing. Again paste formula *results* (*values* in excel)

There is a considerable undershoot in the blood concentration AND effect site concentration due to the fact that mainly the clearance of propofol is higher than the ETCI systems calculates. However in the effect : the BIS, this is smoothed out. It has been said in the previous blog: these are simulations based on extrapolated data. In reality the effects maybe or maybe not noticable, but if you notice differences these simulations may help to understand the origin of the differences. If you select a little bit higher target for induction and a bit lower once the opioid has been started you may (in theory) adjust for the effect for the later start of the opioid but as more factors determin how adequate your anesthesia is (Pd interaction with other drugs, surgical stimulus, hemodynamic changes) adjusting the target based on these simulation is possibly a control overshoot.

The biggest advantage of the Eleveld model is that clinicians do not have to worry about the validity of the model for different patients. You can use it for old, young, and obese patients with no need to 'patch' the input. Using TCI then resembles more the inhalational technique. The question is if the availability and implementation of two different models, with and without opioid really contributes to the ease of applying intravenous anesthesia and if it would not be better to leave the (model) adaptation to the titration skills of the anaesthesiologist. Cardiac output changes the uptake of inhalational agents. Opioids (and other drugs and intraoperative events) change the cardiac output so for that only, adjustments of the vaporiser settings are required and anaesthesiologist are familiar with doing so: it is part of their professional skills. Are we not witnessing another example of theoretic reasoning being forced into practice without observed or demonstrated clinical benefits while facing again the confusion that it wil generate? It is up to you to answer this.

Happy thinking!

Again like has been said in previous blogs: If you use this material than please disclose the source as an appreciation of my work:**Frank Engbers at Eurosiva**

Please use the box below for comments and questions. Messages can be sent anonymously.

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]]> In part 1 I have explained how a relative simple spreadsheet can produce the concentration of an intravenous drug dose with given pharmacokinetic parameters that describe a 2 or 3 compartment model. In part 2, target controlled infusion(TCI) for blood control has been introduced together with a method to use two pharmcokinetic models in one simulation: the Eleveld model with and without opioid.

In this episode I add the effect compartment and the Emax model for the BIS, available in this relative new Eleveld population Pk/Pd model, the first 'universal' model for propofol. The principles on which the spreadsheets are built are similar for other drugs. So you could use these spreadsheets with a bit of parameter alteration for Lidocaine, Remifentanil, Sufentanil or whatever other drug that can be modelled with compartimental kinetics. In part 1 I have explained how you can verify your simulations with the original study data by what I called the overlaying technique. If your simulation does not fit then remember it could be the original study that is erronous. Some time ago I discovered a study that fitted a double effect compartment for propofol. For various reasons I considered this finding interesting, specially from a brain-fysiology point of view: after a forced receptor based hypnosis(first effect) the brain slowly 'settles' in the new situation(second effect) because stimulation of the brain is reduced. But I could not synchronise(overlay) my spreadsheet simulation with the graphs in the paper. I asked our mathematical whiz kid Eric Olofsen for help(again) and he discovered an error in the formulas that where used in the description of the model. This explained the discrepancy.

Let's dig in the spreadsheets that I developped for part 3. I have centralised the data that are used in the other sheets in a separate sheet called data. Patient data, Pk/Pd parameters, dilution , maximum pumprate etc are stored there. The effect compartment and related BIS is now implemented in the spreadsheets. Tricky part is the age dependent delay in the BIS. This is solved by making a lookup table from time and BIS and then selecting a time and BIS with the apropriate age dependent delay and putting that in the current time row. The simulations in part 2 of the blog considered two clinical scenarios:

- Eleveld model with opioid: starting induction in TCI mode without opioid and adding the oipoid after 5, 10 or 15 minutes
- Eleveld model no opioid: using TCI for sedation but start an opoid after 45, 60 and 75 minutes

Now with the implementation of the effect compartment and the related BIS we can workout what will happen with the effect in these scenarios. Let us again go trough the steps required to make these graphs

- In the TCI sheet set the <
*target[column B]*> and set <*opioid[Column D]*>*on*(*true*in excel) in all rows - <
*Inf(mg/hr)[Column F]*> now holds the infusions that are calculated to obtain and maintain the required target, using the pk set with the opioid - copy these infusion rates and
- paste them as formula results or values(excel) in the induction sheet on <
*Inf(mg/hr)[Column F]*>**Do not paste them directly because then you will paste the formulas in the cells, not the displayed values.**

**In numbers you can only select the pasting format in the edit menu at the top, in excel right mouse click can be used.** - If the <
*opioid[Column D]*>rows are selected (*true*in excel) then the concentrations must be equal to the concentrations in the TCI sheet. When deselecting <*opioid[Column D]*>rows (set*false*in excel) the non opioid pharmacokinetics are used in that row. Do that in all the rows for the period when no opioid was used. - Finaly copy the results(values in excel) from each simulation to a place where they can be used for graphing. In my spreadsheet example I used column Q to AB plus the time in minutes [Column J] for the x axis.

For the other scenario: starting with TCI with no opioid and then administer opoid during a sedation you will need to do the oposite: TCI with no opioid, copy to the sedation sheet and switch on the opioid kinetics where apropriate.

Now to the results:

The magnitude of decrease in the bloodconcetration does not differ too much between 5, 10 and 15 min delay in the start of the opioid: ~15%. For the effect site concentration and the BIS the differences are more marked, although I doubt that this will clinicaly be noticable in particular looking at the minimal influence on the Bis in the 5 and 10 minutes delay in opioid administration.

What about the sedation scenario?

For the sedation scenario the smoothing out of the change in blood concentration by the effect compartment and BIS is remarkable. You may notice the change in BIS in practice since you now know it could be the effect of the opioid. Like I said before the effect of an opoid on the Bis in the Eleveld model is binary: it is there or not and is not dose or opioid type dependent. Most likely there is a relationship with the opioid concentration but even the large population studied is not large enough to reveal this and the available BIS data in the Eleveld study were rather limited. Maybe, maybe big data analysis may produce an answer in the future if the battle on the models has stopped and the same model is used for all the anaesthesia procedures.

You may notice that the simulations will predict a rather slow increase in the effect when using blood control TCI. In practice you will probably not wait for 10 minutes to see the BIS going down to 50(at least not in a healthy patient). But with the spreadsheets presented you can simulate other dosage schemes. The TCI sheet can handle changes up and down in the target concentration.The differences between patients,obese, peadiatric etc, can also be simulated with the spreadsheet.

I intended to stop the DiY blog here but after a holiday-long thinking I worked out a spreadheet that will approach effect compartment control. Effect compartment control needs a much more complicated algorithm as it has to look in the future to work out an infusion so that the effect compartment will achieve the target concentration as fast as possible without overshoot. In the last DiY pharmacokinetics blog I will show you this method and see how it influences the induction scenario, that we used above.

Considering the effect concentration, the Eleveld model without opioid is remarkable similar to the old Marsh model (for the default patient of 80 kg, 40 yr, 170cm at least). However Hernán Boveri from Buenes Aires has the experience that the Eleveld model *with* opioid performs better in clinical practice, specially when using a titrating technique during induction to effect. Maybe I can convince him to reveal this in a future blog.

If you use these simulations for education or any other purpose appart than solely for your own understanding than I hope you will reveal the source of your material as an appreciation of the work that has been put in: **Frank Engbers at Eurosiva.**

Happy simulating!

Please use the box below for anonymous comments and questions.

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]]>The concept of the effect site was first described

]]>Last week I was at the dentist needing a minor procedure that involved having a local anaesthetic. As the I was sitting in the dental chair receiving the injection and experiencing the numbness spreading, I was thinking about the effect site.

The concept of the effect site was first described by Holford and Sheiner [1] and adopted more recently to explain the observed delay or time differential between a given drug concentration in the whole blood or plasma and its observed effect at that time on the patient. The evolution of this relationship was used to explain changes of intensity of drug effect in relation to increasing or decreasing drug concentrations. In essence, the effect site was conceptualised as a PkPd link model.

In intravenous pharmacology of the recent past, describing the effect site has been a common feature in pharmacokinetic and pharmacodynamic modelling, mainly to demonstrate that some drugs have faster and some slower effect site equilibration characteristics. The lidocaine injection that I received seemed to have had a fairly quick onset, as the drilling began soon after and I had to pause my reflections for a moment.

Later, during my walk home, I continued to think about the effect site and how the scientific and clinical community is currently dealing with it, in particular when it comes to TCI (Target Controlled Infusion).

First up are the PkPd modellers. These are individuals who believe that a drug effect can be described with mathematical models, just as the blood concentration, characterised with coefficients and thus describing the time course of the drug effect more accurately and improving our knowledge in drug dosing [2]. When using the effect site as a control parameter in a TCI algorithm became available, most doctors thought it to be a progress over simple blood controlled TCI because it looked more scientific and complicated, so it must be good. But were we overthinking it, was the concept convincing and robust, did it work in clinical practice? Let's pause here for a moment and move on to the next group, the medical device and pump manufacturers.

The success of TCI was partially due to the clever implementation of a pharmacokinetic model and its algorithm to run an infusion device with a level of ease and simplicity not seen before. But with all computer-based devices, like our personal computers, they occasionally need an upgrade. This was done by the pump manufacturers pretty much as they liked and felt good with it, including new models, various versions of the same model and of course, effect site control. Like all technological advances, it was seen as a selling point not be missed in a competitive market. Whether it made sense was a lesser concern.

Now let's focus for a moment how the effects site is established. If you read through the publications that are mostly cited and referenced to provide the details of effect-site calculations, you come across two consistent features. One is the methodology of the Emax model, a probability of how likely a blood concentration predicts a drug effect, assuming this drug effect is either binary or linear. The second refers to the measurement of drug effect, usually a processed parameter of the electroencephalogram, mostly the BIS, occasionally other fringe versions of a processed EEG. The problem with the latter is that their validity to represent drug effect in a linear and unequivocal fashion is highly uncertain. In fact, there are plenty of recent papers dealing with the rather complex nature of general anaesthetics on brain function [3].

A typical example of how relating incremental drug effect to EEG becomes quite bizarre, are the PkPd models for opioids, especially remifentanil [4]. As opioids have little to no effect on the electroencephalogram at a dose range usually applied in anaesthesia, the effect modelling utilised the delta pattern in the EEG which you get when about three times as much opioids are administered that are required. It is difficult to imagine how this relates in any way to the anti-nociceptive effect opioids are usually used for. Therefore, I have yet to be convinced how this effect-site modelling for remifentanil TCI would assist in clinical practice.

I am now nearly back home but decided to walk a small detour in the woods to refresh my mind a bit further on the effect-site (there is still some lidocaine effect left in my jaw). I remind myself about a study where effect-site parameters were linked to observed clinical effect only and not to EEG measures [5]. Not surprisingly, the ke0 values, usually obtained to describe the link model, in this study differed from EEG-derived studies. Clinical observations may actually be more valuable than using sophisticated measures after all.

But what is the real issue with the effect site? I am thinking this through again while reflecting on a recent publication from Thomas Schnider [6] where he reports a retrospective observation from his own hospital. The paper is headlined as 'The drug titration paradox'. He observed in a large retrospective data set on TCI and BIS data that during maintenance of anaesthesia there seems to be a discrepancy between the target effect site concentrations and BIS values in the sense that often increases of effect site targets go along with, paradoxically, an increase in BIS readings. Analysing the data and putting them in a publication [6], he concludes that the link of dose and observed effect is not necessarily linear and may indeed not linked at all by the rules that we know.

Now while this scientific contribution has generated some discussion and other quick-fire letters and editorials [7], we have to be cautious in not throwing out the child with the bath water. First, the conclusions drawn have been made on data generated by using the Schnider Pk/Pd model from which we know litte on predictive performance during maintenance, particularly when used in effect site control. Secondly, and maybe more important, BIS as a wholesale measure of anaesthetic effect is almost certainly overstated. Unfortunately, is has become almost the default for clinical studies that inform developments in TCI. The complexity of the patients response to anaesthesia in general and certain anaesthetic drugs in particular as well as the limited capture of this version of the processed EEG makes it a pretty poor sensor candidate to reflect the effect site [8]. Its most relevant shortcoming, as mentioned already, is the lack of linearity in the scale relating to effect. This makes small and subtle changes to the drug concentration, as often done in TCI titration, very difficult to capture in a precise and consistent pattern. We deserve better effect site measures. Maybe machine learning algorithms can help here [9]. A recent publication from Taiwan has even shown that a ML model /neural network assisted administration of propofol can outperform that of the recently suggested Eleveld model in predicting the state of anaesthesia as reflected in BIS [10].

What Thomas Schnider's contribution has undoubtedly shown us that clinicians, as well as researchers, should continue to reflect on the clinical utility of TCI and measure its performance. To safeguard this groundbreaking technology for the future, we need to apply a healthy scepticism when judging new models and applications and always demand clinical plausibility.

It takes a long time for academic consensus to settle and years to conduct and publish studies, and even longer for an overwhelming weight of evidence to emerge. Don't get me wrong, the effect site exists. We can observe hysteresis every time we give an anaesthetic. And dose matters. There might even be specific measures and rules to describe this phenomenon for induction and, yet differently, maintenance of anaesthesia. But let's face it, we haven't found it yet.

Meanwhile I arrived at home and the local anaesthetic had completely worn off.

References:

[1] Holford NH and Sheiner LB. Understanding the dose-effect relationship: clinical application of pharmacokinetic-pharmacodynamic models. Clin Pharmacokinet 1981;6:429-53.

doi: 10.2165/00003088-198106060-00002.

[2] Coppens M, Van Limmen JG, Schnider TW et al. Study of the time course of the clinical effect of propofol compared with the time course of the predicted effect0-site concentration: performance of three pharmacokinetic-pharmacodynamic models. Br J Anaesth 2010;104:452-8.

[3] Brown EN, Pavone KJ and Naranjo M. Multimodal general anesthesia: theory and practice. Anesth Analg 2018;127:1246-58.

[4] Minto CF, Schnider TW, Egan T, et al. Influence of age and gender on the pharmacokinetics and pharmacodynamics of remifentanil. 1. Model development. Anaesthesiology 1997;86:10-23.

[5] Thomson AJ, Nimmo AF, Engbers FH and Glen JB. A novel techniques determine an 'apparent ke0' value for use with the Marsh pharmacokinetic model for propofol. Anaesthesia 2014;69:420-8.

[6] Schnider TW, Minto CF and Filipovic M. The Drug Titration Paradox: Correlation of more drug with less effect in clinical data. Clin Pharmacol Therapeut 2021;110:401-8.

[7] Egan TD. The drug titration paradox: something obvious finally understood. British Journal of Anaesthesia, 128 (6): 900e902 (2022).

[8] Pullon RM, Warnaby CE, Sleigh JW. Propofol-induced Unresponsiveness Is Associated with a Brain Network Phase Transition. Anaesthesiology 2022; 136:420–33.

[9] Abel JH, Badgeley MA, Meschede-Krasa B, et al. Machine learning of EEG spectra classifies unconsciousness during GABAergic anesthesia.PLoS ONE 16(5): e0246165.

[10] Lee HC, Ryu HG, Chung EJ, et al. Prediction of bispectral index during target-controlled infusion of propofol and remifentanil. Anaesthesiology 2018;128:492-501.

]]>In the pharmacokineticsDiY part 1 the numerical approach of pharmacokinetic calculations was explained. Using relative simple formulas implemented in a spreadsheet the concentrations of a drug could be calculated following variable drug input protocols. The Eleveld model for propofol was used. This was not without a reason. Douglas Eleveld and co-authors analyzed the data from numerous other studies, collected in the open Target Controlled In fusion(TCI) initiative, to develop a pharmacokinetic and pharmacodynamic model for broad application in anaesthesia and sedation.

Their work is a milestone in the development of Pk/Pd models that will improve the clinical usability of Target Controlled Infusion systems and the understanding and interpretation of the observed effect related to these models. Until recently most of the implemented models in Target Controlled Infusion systems were limited in usability and hampered by unverified extrapolation of data from studies that were not intended to deliver robust, population models for TCI. So a model for an 'average' patient could be unreliable or even be proven wrong for a paediatric or obese patient. But appart from an elaborated relation with antropometric properties, age, weight etc, they also found a dependency of the *pharmacokinetic *model with the co-administration of opioids. The influence of an opioid on the pharmacokinetics of propofol has been studied before and one of the possible explanations is that the influence of opioids on the heart rate and thereby the cardiac output could change the clearance of propofol by decreasing the liver flow. Antropometric properties, age,weight,length, gender usually do not change during an application of TCI but whether or not, and the point in time an opioid is administerd may vary in clinical situations.

The influence of the opioid on the pharmacokinetics of propofol is a small example of the complexity of the anaesthetic state that is the resultant of anaesthetic drugs, surgical stimuli and responses of the patient who has its own internal regulation and homeostasis processes for the most part intact because the patient is alive. Observation as the titration paradox are in my opinion not surprising and only prove that we do not understand the full complexity of this state.

With the spreadsheet presented in this blog the effect of an opioid on the pharmacokinetics can be switched on or off. The effect on the pharmacokinetics of propofol is binary, it is present or it is not. So the amount of opioid does not influence the effect(at least not in the model). In part 1 it was shown that the time interval of 5 seconds was more than enough to deliver a highly accurate simulations in comparison with TivatrainerX that uses an analytical('exact') calculation. Again the results of the simulation are verified with the overlay approach as explained in part 1. If we look at the differences between the pharmacokinetic set with and without opioid we see that the clearance decreases together with the size of the 3th compartment. In timeconstants: k10,k31 and k13. Using the offset function in a spreadsheet the correct values are selected dependent on the tickbox (Numbers) or TRUE/FALSE (excel) value in the 'opioid' column[D].

In order to simulate a real live scenario also a TCI simulation is added. This is done in the sheet called TCI. Calculation is based on the same principles of the Euler approximation for the Pk model: the infusion to achieve and maintain a specific concentration is a loading infusion amount: target * V1. Subtracted from this amount is the amount already present and subsequently in following steps drug is replaced that is lost from the central compartment with an equal amount by infusion. Negative drug input is impossible and there is a limitation of the maximum rate a pump can deliver(this can be adjusted).These constraints are implemented with simple If.. Else statements. If the input is negative it is zero, if the input is larger than the infusion pump can deliver then the input equals this maximum. The verification of the implemention of the pharmcokinetics with opioid has been done similar to the verification of the pharmacokinetics in part 1. For verification of the TCI sheet a target scheme was compared with TivatrainerX. Differences are neglectible and the total amount predicted by TivatrainerX: 14.1 ml was comparable to the total amount of the numerical appraoch: 14.07 ml.

It will be very unlikely that pumpmanufacturers will allow a possible change between the two Pk Eleveld models: with or without opioid, during a TCI application, but with the spreadsheet some different scenarios can be investigated:

- You select Eleveld
**+ opioid**because opioid is intended to be given for incision but induction is without opioid. In the figure below this situation is simulated when the opioid is given 5, 10 and 15 minutes after induction. The simulation is achieved by setting the target to 3.5 µgr/ml in the TCI sheet[B] and selecting opioid (or setting True in excel) for all the timesteps[D]. Then copy the data in the pump rate column[G] and paste the results in the pump rate column of the induction sheet[F]. Make sure that you not simply paste the cells, but that you paste the**results(numbers) or values(excel)**. Now you can select the period that no opioid was given by deselecting the cells in the opioid column[D]. Then copy the resulting concentrations as**results(numbers) or values(excel)**to a place in the spreadsheets where you can use them for graphing.

The following observations can be made:

- Because the central volume is not changed by the opioid the loading dose to achieve the target is the same with or without opioid. Thereafter the clearance of the patient(no opioid) is higher than predicted by the model(+opioid) therefore the concentration will drop roughly by 15%. the changes in the 3th compartment hardly play a role so early in the pk of the model.

- You are performing a sedation with TCI, target 2.5 µg/ml, using the Eleveld model with no opioid. At a certain moment some opioid is needed to control a painfull stimulus for examle. In the spreadsheet a sheet is added called sedation for working with this scenario. Steps to perform are similar to the first scenario.

These simulations are obviously over-simplifications of real clinical scenarios. One of the limitations is that the opioid influence is not modelled dependent on the amount of opioid or potency of the opioid. Also they do not show the pharmacodynamic interaction of propofol and the various opioids. So adjustments of dosing solely based on these simulations is probably unwise. But they may help in understanding observations made in clinical practice and thereby help us with the task of titrating the anaesthetic drugs.

And still an aspect of the Eleveld paper is still untouched: The pharmacodynamics, involving the effect compartment, effect compartment control and the relation to the Bispectral Index. In the next blog I will use the spreadsheet appraoch to try to shine some light on these items.

For now: download the spreadsheets and play around with them and if you have questions, want to debate or add comments: use the form below the blog.

]]>This blog is about pharmacokinetics: Do It Yourself. Only a bit of knowledge of using spreadsheets is required.

If you read publications on pharmacokinetics you will have noticed that the model parameters are usually presented in two different notations: clearances V1,V2,V3,Cl,Cl2,Cl3 and time-constants(V1,k10,k21,k12,k13,k31). For a 3 compartment open model these 6 parameters describe the state of the model. To my knowledge the 2 and 3 compartment models with elimination from the central compartment are currently the only models used in modern infusion pumps that are capable of Target Controlled Infusion.

For the clearance annotation the parameters consist of the volumes of the compartments V1, V2, V3 and the clearances (vol/time) to the outside: central clearance Cl and inter-compartmental clearances Cl2 and Cl3 often called Q2 and Q3.

For the time constant annotation, it is the volume of the central compartment V1 and the time constants in-between de compartments k12 , k21, k13, k31 (/time) and to the outside k10(/time) that describe the model.

The two annotations are interchangeable by using simple formulas (see table 1). Having said that, when population parameters are connected to the model parameters, the interpretation of specially V1 becomes tricky. I have tried to explain this in the addendum of:

Engbers, F. H. M. & Dahan, A. Anomalies in target‐controlled infusion: an analysis after 20 years of clinical use.Anaesthesia73, 619–630 (2018).

Solving the pharmacokinetic equations for a 3 compartment model can be done analytical. With that approach the concentration can be calculated at any point in time given that the state of the model is unchanged. The state of the model changes when there is a change in input, for example a bolus or a change of infusion, or when one of the parameters changes because it is connected to an external parameter like an opioid on board or no opioid, which is the case in the Eleveld model. The latter state change has not been used in commercial TCI systems. It is unlikely that this will ever be incorporated because it will increase the complexity of the Target Controlled Infusion system and hence make it more error prone.

The concentration can also be calculated using a relative simple numerical approximation of the equations. The exponential curves basically are cut into small steps that are assumed to be horizontal and linear. The smaller the steps the higher the accuracy. This is known as the Euler technique, named after and invented by the famous mathematician from the 18th century. For pharmacokinetic calculations a step size of 5 second gives sufficiently accurate outcomes, but you can try for yourself with the downloadable spreadsheet.

We are going to use the time-constant notation for simplicity.

The model is based on the amounts present in the compartments. A certain amount in mg is going into the model as input. A bolus(B) is considered to immediate being added to the model, for an infusion we will calculate the dose in the step change that we use to evolve the model: in our case 5 second. In fact the infusion is split up to small boluses(Inf) as long as the infusion runs. We transfer the infusion from mg/hr to mg/sec and we only have to multiply that with the step size in seconds to know what is going in, in each step.

From that Amount(A1) during 1 second A1 x k12 will go to the second compartment to create an amount there:A2. Similar for the third compartment A1 x k13 will build the amount A3, and drug is also cleared: A1 x k10. But the central compartment is not only losing drug: drug will come back from the other compartments: from the second: A2 x k21 and from the third A3 x k31.

So the amount change in the central compartment over a period of T seconds is what goes in minus what leaves the central compartment:

this change must be added to the amount already present, which is stored in the cell above the current one.

For the second compartment the change is similar: what goes in minus what goes out:

and for the third compartment:

These changes again have to be added to the amount already present in the respective compartments. The central concentration can be derived by dividing A1 by the known volume of V1 and adjusting for the units difference between input(mg) and required concentration(mcg).

The final challenge is the calculation of the 6 parameters in the two Eleveld models and putting everything in a spreadsheet. I have used the worked out calculation I use in Tivatrainer(X). The outcome of these calculations have been checked with the author of the models: Douglas Eleveld, as there was a typo in the initial publication. All parameters are calculated independently therefore they look a bit weird and complicated, even more than in the original paper. This was necessary as Tivatrainer could only parse(translate) the individual Pk parameter values.

We can use the equations in table 1 to transfer the results of the calculations that are annotated as clearances to the time-constant annotation.

In this first part I have built a spreadsheet to do the calculations with the Eleveld model without opioids. There are two versions, one Numbers for macOS and an Excel version. The operation of these spreadsheet is simple and based on the typical copy/paste functionality of the spreadsheets. A typo is easy made so the spreadsheets had to be verified on correctness.

I have used TivatrainerX that runs on iPhone and the new MacBooks with M1 and M2 processor. I have made a screenshot and put that into the Numbers spreadsheet application and set it to the background. The data from the spreadsheet are fed into a 2d scatter chart that has been overlayed over the screenshot. By resizing that chart with dragging, the axes are fitted to the axes of the TivatrainerX screenshot. I needed a shift of one pixel otherwise the red line would be fully covered. The blue line is from the spreadsheet simulation, the red one from TivatrainerX. You may notice that the predicted peak concentration of tivatrainer is a bit lower than the concentration in the spreadsheet. This is not an error. In the TivatrainerX app the graph is drawn from the point where the bolus is given to one second after that moment. TivatrainerX uses the analytical calculation of the concentration so this is merely a consequence of the way the concentrations are displayed.

From the bolus and infusion comparison it is clear that the 5 second interval is accurate enough for the purpose of this excersise.

By the way, this overlaying technique is also very useful for verifying the data during the review of publications, specially when no detailed concentration data are supplied. More than once I discovered errors both in the representation of data from the study as well as in the conceptual setup of a study, using this simple technique.

Engbers F. Is unconsciousness simply the reverse of consciousness? Anaesthesia. 2018 Jan;73(1):6-9. doi: 10.1111/anae.14121. Epub 2017 Oct 23. PMID: 29057452.

Non-mac users can accomplish the same with exporting screenshots to Adobe photoshop or Adobe illustrator or similar software. You will have to transfer the screenshot to PNG format as this will allow you to set the required transparency. For not-so-familiar-with-spreadsheet-colleagues, I have made a small video to explain how to operate the spreadsheet. It is based on the powerful copy and paste function of spreadsheets. In the following blog I will add the Eleveld model with opioid. In that spreadsheet it will be possible to change the model in every 5 second epoch. So we can study the prediction of starting with no opioid and adding opioid later. If there is enough interest I will thereafter incorporate the effect compartment and the related pharmacodynamic effect. We can even go one step further and build complex models with transient compartments like is done in this paper:

Masui, K. et al. Early phase pharmacokinetics but not pharmacodynamics are influenced by propofol infusion rate. Anesthesiology111, 805–817 (2009).

For now it is sufficient to know that without using elaborate software it is possible to accurately calculate concentrations of IV drugs. The numerical approach can be used to make advanced models, check existing models or extrapolate models to answer ‘what if’ questions. If you measure the weight of a fluid as the output of your pump you can even use it to verify that your TCI system works correct. I will publish this technique in a separate paper. Please use the comment box below for questions, criticism or a simple thumbs up for keeping us going. If you use your email address to do that, we will send you a mail when the next part is published. Stay tuned!

My name is Stefan Schraag. Since 2008 I have been chairing the Board of EuroSIVA, a handpicked selection of experts in the field of clinical pharmacology, research and monitoring. Together, we have achieved to establish a team of expertise in many areas of intravenous anaesthesia and target-controlled infusion (TCI). Over the years, this team has devoted time and energy in building and delivering top-class teaching and education through scientific conferences, interactive workshops, clever advisory tools and a variety of publications.

All of us have seen people, ideas and concepts coming and going. Maybe the longevity of engaging in TIVA and TCI over now 25 years, has given EuroSIVA the expertise and reputation that remains core to what we do but also retained our healthy scepticism to judge upcoming trends and innovations.

However, all of us grow older and some have already jumped over the fence of retirement. Nonetheless, all members of the Board have retained their expertise and are engaging in a variety of scientific and commercial activities related to TIVA that you might be interested in.

Over the coming weeks we will let you know what each of us are doing and publish a personal profile of each Board member in this blog. Maybe you find something that interests you and want to follow up with us.

Let’s start with me.

I am a cardio-thoracic Consultant Anaesthetist in a large tertiary University-affiliated hospital in the West of Scotland. Also approaching the retirement age, I have recently dropped my cardiac and critical care on-call commitment after so many years which now feels like a new lease of life. I have also reduced my clinical hours slightly to lead in the design and roll-out of a new and comprehensive Anaesthesia Information Management System (AIMS) for our hospital, a project that started two years ago and is just over the finish line now. The highlight was that we could successfully connect all of out TCI pump stacks to the main system, a feature that we were long waiting for. The downside is, however, that it is never easy and straighforward to work with a big medical device cooperation.

I was always interested in data science. Over the last three years I had the opportunity to mentor a PhD student from the local University of Strathclyde’s Computer and Information Department. Together we set up a data science hub and developed risk analysis tools and prediction models for cardiac surgery based on modern machine learning algorithms. The results clearly show that traditional risk scores, like the Euroscore, are no longer fit for purpose. Our data driven models could for example predict postoperative complications, such as delirium or acute kidney injury with high predictive accuracy.

Another project that keeps me busy is the development of a patient-controlled sedation system for patients undergoing procedures. This system is based on a propofol TCI system and has been first developed by fellow Board members Gavin Kenny and Nick Sutcliffe here in Glasgow. The initial clinical studies that were based on a prototype device and date back to the early 2000’s, are now supplemented by studies in larger cohorts of patients with a commercial partner in China and include a feedback function to increase safety. It is expected that the results of these studies, that have just finished, will further enhance the algorithm of the commercial product that is expected to be launched next year.

So this should be enough for now, thank you for your interest in EuroSIVA.

]]>Using my prerogative as webmaster I open this blog to inform you on the purpose and features of the blog.

In the Eurosiva-blog the individual board members will write what keeps them busy or what they think is interesting for IV and not so IV enthusiast colleagues. We plan to update this post at least every 4 weeks. Topics could be news from the meetings, from the different projects, a comment on an article and so on. We may also invite non board members to post in our blog. Before publishing, the post will be read and aproved by at least one co-board member.

We also added the possibility to comment on the blog. We will respect your privacy and will not share your email address, but if you want you can log in anonymously. We will however remove comments that are inappropriate or otherwise not supportive for an open discussion.

The Eurosiva does not have a commercial connection with any of the companies involved in IV anaesthesia, neither pump manufacturers, depth of anaesthesia monitoring, pharmaceutical companies or other. Individual board members may have such connections but these connections will be disclosed in their individual blogs.

As an example, here is my personal 'hot topic' list: I am preparing a post on how to use a simple spreadsheet for doing pharmacokinetic calculations. I will make a spreadsheet that will show what happens when the two Eleveld models for propofol(with and without opioid) are used when the opioid is added later so the model theoretically has to change after an induction with no opoid on board and after the opioid is given for incision. My guess is that the impact will not be that big from a pharmacokinetic point of view, but it will be interesting to see. You may also be interested in the efforts to make the Tivatrainer platform-independent so it will run on iOS, android, macOS, Linux and windows. The search for an appropriate model for Remimazolam for TCI and to implement in Tivatrainer is another thing that keeps me busy together with the extension of Tivatrainer to incorporate the concentrations of drug metabolites:for example for ketamine, lidocaine. For the first months I think my blogs topics are covered.

Happy reading!

Frank Engbers

Secretary and webmaster Eurosiva

Disclosure: Owner of Gutta, the company responsible for the creation of Tivatrainer and LabelSyringe.

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