Basic pharmacokinetics Frédérique Servin APHP hôpital Bichat Paris, FRANCE
DOSE CONCENTRATION EFFECT Pharmacokinetics What the body does to the drug Pharmacodynamics What the drug does to the body Transfer to the effect site: PK or PD? Estimation of the transfer to the effect site requires a measure of effect
Pharmacokinetic steps Absorption Digestive Trans-mucosal (nasal; sub-lingual; rectal ) Distribution Elimination / transformation Metabolism Excretion in bile or urine
Absorption: first pass effect
Distribution Describes the diffusion (active or passive) of a drug in various tissues. The penetration of the drug varies with different tissues. If the drug is protein bound, only the free (active) fraction will be distributed Acid drugs are bound to plasma albumin Basic drugs are bound to a1-acid-glycoprotein BUT if the affinity for the metabolic enzyme is superior to that for the binding protein, the binding will not limit the clearance (non restrictive clearance)
Protein binding of anaesthetic agents Albumin a1 AGP binding <50% Thiopental Fentanyl Ketamine Propofol Alfentanil Pancuronium Etomidate Sufentanil Vecuronium Midazolam Remifentanil Rocuronium Flumazenil Atracurium Morphine Cisatracurium
Hepatic drug elimination The liver renders xenobiotics accessible to excretion in urine or bile water-soluble Biliary excretion Metabolism Phase 1 reactions Hydrolysis Oxidation (CYP 450) Reduction Phase 2 reactions Conjugation +++ Methylation, acetylation.
Hepatic clearance Cl H = Q H E = Q H [ [Cl i ] / [Q H + Cl i ] ] If E is close to 1, Cl H ~ Q H The clearance is flow rate dependant If E is small (low extraction), Cl i is small compared to Q H, thus [Cl i ] / [Q H + Cl i ] is close to Cl i / Q H, and Cl H ~ Q H [Cl i / Q H ] ~ Cl i The clearance is enzyme dependent, and insensitive to changes in blood flow
Hepatic clearance of anaesthetic agents Rate dependant Intermediate Enzyme dependant Propofol Midazolam Thiopental Etomidate Alfentanil Diazepam Ketamine Vecuronium Lorazepam Flumazenil Bupivacaïne Flunitrazepam Morphine Fentanyl Sufentanil lidocaïne
Hepatic metabolism of anaesthetic agents Phase 1 CP450 Phase 1 other Phase 2 Thiopental Etomidate Propofol Ketamine (Atracurium) Morphine Midazolam Flumazenil Fentanyl Sufentanil Alfentanil (Vecuronium) (Rocuronium)
Application of pharmacokinetics to clinical anaesthesia
Concentration (µg/ml) Pharmacokinetic analysis 100 10 1 0.1 C1 = A * e -a*t C2 = B * e -b*t C3 = C * e -g*t 0 10 20 30 40 50 60 Time (min) This three exponential analysis can be modified (MATHS!!!) in other forms «compartment analysis»
Pharmacokinetic model V2 CL2 V1 CL3 V3 1 - V1, V2, V3, Cl1, Cl2, Cl3 2 V1, k10, k12, k21, k13, k31 CL1 Cl1 = V1*k10 Cl2 = V1*k12 = V2*k21 V2 = V1* (k12/k21)
Compartmental models Simple ++ (max 3 cpts) Actually not much to do with reality the drug concentration drug is assumed to be uniformly equal within the compartment, with instant homogeneous distribution Mammillary model (the peripheral compartments are only connected through the central one) Elimination usually occurs only from the central compartment Advantage: they work! At least at the level of complexity adequate for clinical practice
conc 3.5 3 Bring the drug concentration in the «therapeutic» zone and keep it there as long as necessary 2.5 2 1.5 1 0.5 0 0 5 10 15 20 25 30 35 40 45 50 55 60 time (min)
The BET Bolus The target concentration is obtained by filling up the central compartment Elimination A constant rate infusion Compensates metabolism and / or excretion Transfer A gradually decreasing rate infusion Compensates the distribution to the peripheral compartments V2 V3 V1 CL2 CL3 CL1 Lauven et al A microprocessor controlled infusion scheme for midazolam to achieve constant plasma levels, Anaesthesist 31: 15-20, 1982)
BET equations Bolus: Elimination: Ct X V1 Transfer... Ct X Cl = Ct X V1 X k 10 Ct X V1(k 12 e (-k 21 t) + k 13 e (-k 31 t) ) Maintenance rate infusion is therefore: Dose = Ct X V1 (k 10 +k 12 e (-k 21 t) + k 13 e (-k 31 t) )
Building a PK model Patients or healthy volunteers Bolus dose or infusion Many blood samples (critical phases) Two stages analysis Population kinetics
Population kinetics Blood samples from all the patients are studied together (pooled approach) Significant covariates improve the statistical likelihood of the model (ex : weight, age, sex ) The influence of the covariates is considered for every parameter. Bayesian adaptation allows the estimation of individual parameters (posthoc values) Some populations (children) require specific models
Induction
Effect site concentration, fentanyl Scott, Anesthesiology 1985
Time course of action : alfentanil Scott J, Anesthesiology, 1985
Hysteresis d effet effet conc
Cl1 = V1 x k10 Cl2 = V1 x k12 = V2 x k21 Cl4 = V1 x k14 = VE x ke0; VE = e, so k14 = e, and V1 is proportional to Ke0 V2 V1 V3 CL2 CL3 ke 0 CL1 Effect site
Time to peak effect is a physiological variable independent from the model The ke0 constant associated to the pharmacokinetic model is dependent on the PK model and the time to peak effect 100.00 80.00 Female, 75 y.o., 62 kg, 59 cm propofol 70 mg, no opioid BIS Time to peak = 2.2 min Marsh model V1 = 14.1 L Ke0 = 1.11 (0.267) 60.00 40.00 20.00 Schnider s model V1 = 4.27 L Ke0 = 0.408 (0.456) 0.00 0.0 2.0 4.0
% of EEG maximum effect Opioids time to peak effect. 100 sufentanil 80 60 fentanyl 40 alfentanil 20 0 remifentanil 0 2 4 6 8 10 Minto et al, Anesthesiology 1997
Onset time time to peak effect Conc (ng/ml) 16 14 12 10 8 6 4 2 0 Minimum concentration recommanded with remifentanil (3 ng/ml) time (min) 0 10 20 30 Alfentanil Rémifentanil Sufentanil Fentanyl Lower concentration limit for endotracheal intubation
Effect site concentration, therapeutic window Propofol bolus, 2.5 mg/kg Propofol conc ( µ g/ml) 12 plasma Effect site 10 8 6 4 2 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 time (min)
Instantaneous mixing is an approximation Avram, Anesthesiology 2003
Pharmacokinetic models currently used for propofol TCI Marsh (1991) V1 = 0.228*TBW K10 = 0.119 min -1 K12 = 0.112 min -1 K13 = 0.0419 min -1 K21 = 0.055 min -1 K31 = 0.0033 min -1 Ke0 Diprifusor 0.267 Ke0 Base Primea 1.21 Azena PK Tpeak 1.6min Schnider (1998) V1 = 4.27 L V2 = 18.9 0.391*(age-53) L V3 = 238 L Cl1 = 1.89 + 0.0456*(TBW-77) 0.0681*(LBM-59) + 0.0264*(height-177) L/min -1 Cl2 = 1.29 0.024*(age 53) L/min -1 Cl3 = 0.836 L/min -1 Ke0 = 0.456
Maintenance
Concentration / effect relationship 100 90 80 probability of effect 70 60 50 E EmaxC y EC50 g Cg 40 30 20 efficiency range 10 0 EC95 EC50 20 30 40 50 60 70 80 90 100 concentration
Hypnotics Opioids Stimuli
Recovery
From maintenance to recovery Vuyk, Anesthesiology 1997
Alfentanil Vuyk, Anesthesiology Dec. 1997
Remifentanil Vuyk, Anesthesiology Dec. 1997
7 6 Propofol conc. (µg/ml) 5 4 Context sensitive half life 3 2 Decrement time 1 0 time (min)
The recovery time depends on the ratio between the maintenance concentration and the C50 for recovery 6 5 End of infusion 4 3 2 1 4 15 22 13 0 50 55 60 65 70 75 80 85 90 Time (min)
Context Sensitive Half Time Shafer SL, ASA Refresher Course, Chapter 19, 1996
Are drug models predictive? Mathematical models of drug behaviour incorporating effect site concentrations and drug interactions predict anaesthetic drug effect (e.g., loss of response to stimulation) as well as: Measured concentrations BIS AAI I am not aware of any counter examples. Slide S. Shafer
Remember Thinking in concentration is mandatory to understand a drug time course of effect and interactions Mathematics are necessary to predict drug concentration over time (thus effect) BUT pharmacokinetics is primarily proteins, enzymes, liver, kidney, blood, fluids and cells! If you understand pharmacokinetics, you will be able to understand what happens to your drug even in patients widely different from the standard population