![Direct versus Indirect Link Models
• Also known as Biophase distribution model
• To model the time lag between the plasma concentration in
the central compartment and response.
[D] plasma = [D] at site
• This could be due to multiple mechanisms: delayed
distribution to organs, active metabolite formation etc
• Direct Link: When there is no lag
• Indirect link: When there is time lag
• An additional effect compartment is built into the model to
minimize the time-lag between the concentration and effect
20-02-2020 40](https://image.slidesharecdn.com/pkpdseminar-210209064643/85/PKPD-seminar-40-320.jpg)
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PKPD seminar
- 1. Introduction to PK-PD Modeling Seminar by, Pooja SG Final Year PG Resident 20-02-2020 1
- 2. Outline of the Seminar • Definitions • Pharmacokinetic modeling • Pharmacodynamic modeling • Population PK-PD modeling • Software for PK-PD modeling • Role of PK-PD modeling in drug development 20-02-2020 2
- 3. Pharmacokinetics • Describes the concentration-time course of the drug in the body after administration of a certain dose of the drug. • What the body does to the drug - ADME 20-02-2020 3
- 4. Pharmacodynamics • Describes the intensity of drug effect in relation to the concentration • What the drug does to the body 20-02-2020 4
- 5. Modeling • Description of a biological process by which one can predict one variable from another by using mathematical and statistical principles 20-02-2020 5
- 6. What is PK-PD modeling? • PK PD modeling combines both these (PK, PD) approaches and tries to establish models in order to describe effect – time course directly. 20-02-2020 6
- 7. What is PK PD modeling? 20-02-2020 7
- 8. Rationale for PK-PD modeling Administered dose of the drug Resulting concentration in the measurable compartment of body Intensity of the effects caused by the attained concentrations PK & PD determine the relationship between: Rational use of drugs and design of regimens 20-02-2020 8
- 9. Rationale for PK-PD modeling Examples • From single dosing to multiple dosing regimen • From intravenous to oral route Extrapolation of data (PK/PD data) 20-02-2020 9
- 10. Components of PK PD modeling PK Model PD Model Integration of PK and PD model 20-02-2020 10
- 12. PK Parameters Primary Parameters Clearance (CL) and Volume of distribution (Vd) Secondary Parameter Half life (t1/2) 20-02-2020 12
- 13. Broad Categories of PK Models 1. Compartmental models 2. Non compartmental models 3. Physiologically based PK models (PB PK models) 20-02-2020 13
- 14. Compartmental models Most frequently preferred: ✓Provide continuous conc. - time profile in the body that can be related to continuous effect – time profile 20-02-2020 14
- 15. Assumptions for compartmental concept • Human body is made of compartments. These compartments are not anatomical, physiological but hypothetical. • Each compartment is well stirred instantaneously so that drug is distributed uniformly throughout the compartment. • Elimination occurs only from central compartment. 20-02-2020 15
- 18. Cp vs Time Log Cp vs Time Cp: Plasma Concentration 20-02-2020 18
- 21. Cp vs Time Log Cp vs Time Cp: Plasma Concentration 20-02-2020 21
- 22. Allotment of compartments • Central compartment – blood, extracellular space, well perfused organs like liver, kidney, heart, lungs • Peripheral compartment – poorly perfused organs like fat, bones, skin • Brain ➢ Lipophilic drugs – central ➢ Hydrophilic drugs – peripheral 20-02-2020 22
- 23. Non Compartmental Models • Also known as model-independent • Do not rely on any assumptions When to go for it? • When the distinction between one, two or multi compartment model is not clear • Insufficient no. of samples from each subject so that characterization of model becomes difficult e.g. neonates, animals (as no. of samples will be less due to concerns of blood loss) 20-02-2020 23
- 24. Non Compartmental Models • PK parameters are derived from AUC Reason: • Of all the PK parameters, AUC is most insensitive for change in compartment models. 20-02-2020 24
- 25. Non Compartmental Models Parameters calculated • AUMC (area under the first moment curve) Area under concentration times time versus time curve • MRT (mean residence time) = AUMC/AUC • Kel = 1/MRT • Clearance (CL) = Dose / AUC • Vol. of dist. in steady state (Vss) = CL x MRT = (Dose x MRT)/AUC 20-02-2020 25
- 26. Physiology Based PK modeling 20-02-2020 26 Jones H, Rowland-Yeo K. Basic concepts in physiologically based pharmacokinetic modeling in drug discovery and development. CPT Pharmacometrics Syst Pharmacol. 2013 Aug 14;2:e63
- 28. Factors to be considered while selecting a PD model • Drug used • Nature of the response • Degree of linearity in the effect concentration curve • Potential for achieving maximal effect 20-02-2020 28
- 29. Broad Categories of PD Models PD models for steady state conditions 1. Fixed effect model or quantal effect model 2. Linear model 3. Log linear model 4. Emax model 5. Sigmoid Emax model PD models for non steady state conditions 1. Direct vs Indirect link models 2. Direct vs Indirect response models 3. Soft vs hard link models 4. Time invariant vs time variant models 20-02-2020 29
- 30. PD models for steady state conditions 20-02-2020 30 Meibohm B, Derendorf H. Basic concepts of pharmacokinetic/pharmacodynamic (PK/PD) modeling. Int J Clin Pharmacol Ther. 1997 Oct;35(10):401-13.
- 31. Fixed Effect (quantal effect) Model • It relates drug concentration with the statistical likelihood of a predefined, fixed effect to be present or absent • Eg: Ototoxicity occurs when gentamicin therapy exceeds the levels of 4 μg/mL E=ototoxicity when C > Cthreshold(4 μg/mL) • Given the variability in the population, the threshold conc varies among individuals 20-02-2020 31
- 32. Fixed Effect Model • Then, this model can predict • If the conc is > 4 μg/mL, 50% probability to observe ototoxicity • If the conc is > 7 μg/mL, 90% probability to observe ototoxicity • This model can only be used as approximation of dose- response relationships • They may not be useful for prediction of complete effect- time profiles 20-02-2020 32
- 33. Linear Effect Model • Model assumes that conc. is directly proportional to drug effect e.g. Salivary flow rate and plasma concentration of pilocarpine infusion • Most intuitive model • Generally used for IV infusions Mathematical Expression of Model E = m x C + E0 (E0: Baseline effect, m:proportionality factor (slope), C: Concentration of drug) 20-02-2020 33 m
- 34. Log-linear Model • Applicable when the conc- effect curve is hyperbolic • Log conc-effect relationship is roughly linear in the range of 20 to 80% Mathematical Expression of Model E = m * log C + b (m and b are the slope and intercept in a plot of Effect E vs Log C) 20-02-2020 34
- 35. Emax Model • Falls in line with the receptor theory • Takes into account the intrinsic activity and potency of drug (Emax: Maximim effect possible, E50: Concentration causing 50% effect) (Emax refers to intrinsic activity of drug, E50 to its potency) • This model can describe complex concentration effect relationships 20-02-2020 35 Mathematical Expression of Model Receptor occupancy theory
- 36. Emax Model Concentration-effect relationship from Emax model 20-02-2020 36
- 37. Sigmoidal Emax model • Extension of the Emax model • It describes for many drugs that appear to be S shaped rather than hyperbolic as described by more simple Emax model. • Excellent model for combining data across doses • Allows accurate estimation of differences between doses Mathematical Expression of Model (n is the slope factor, that determines the shape of the curve, larger the n, steeper is the linear phase of Log-conc-effect curve) n is an exponent describing the number of drug molecules that combine with each receptor molecule. 20-02-2020 37
- 39. PD models for non steady state conditions 20-02-2020 39
- 40. Direct versus Indirect Link Models • Also known as Biophase distribution model • To model the time lag between the plasma concentration in the central compartment and response. [D] plasma = [D] at site • This could be due to multiple mechanisms: delayed distribution to organs, active metabolite formation etc • Direct Link: When there is no lag • Indirect link: When there is time lag • An additional effect compartment is built into the model to minimize the time-lag between the concentration and effect 20-02-2020 40
- 41. Indirect Link Direct Link This model has been used to characterize Pk-PD of several drugs whose concentrations could not be corelated with effect. Eg: midazolam, pancuronium, alprazolam 20-02-2020 41
- 42. Direct versus Indirect Response Models • Used when there is a lag time for development of a response even after drug reaches the target site • Direct response – Observed effect of the drug is directly mediated by its interaction with response structures (receptors / targets) • Indirect response – mechanism of action of drug mediated through other pathways like gene expression • Mechanism: time required for inhibition or stimulation of synthesis, processes etc. eg: effect of glucocorticoids, warfarin 20-02-2020 42
- 43. Direct versus Indirect Response Models Indirect response model for the effect of fluticasone propionate on the number of lymphocytes in blood 20-02-2020 43
- 44. Soft versus Hard Link Soft Link • Both PK and PD data are used to determine link Hard Link • PK data with additional information from in vitro studies are used • PD is not used 20-02-2020 44
- 45. Time Variant versus Invariant The previously discussed PK/PD models all assume that • Only the measured concentration and observed effects undergo time dependent changes • But the involved PD parameters e.g Emax and E50 are constant over time. • Thus, these models are time invariant 20-02-2020 45
- 46. Time-variant Models Counter/Anti clock-wise hysteresis in effect versus conc loop: • Same drug concentration produces two different magnitudes of pharmacological effects measured effect increases with time (Sensitization) • Small effect at a given drug concentration; however, after some time has passed the same drug concentration gives rise to a greater measured effect than expected 20-02-2020 46
- 47. Time-Variant Models Counter/Anti clock-wise hysteresis: 20-02-2020 47 • Mechanisms: delayed uptake into active site, active metabolites, upregulation etc • Eg: Fall in standing SBP by ISDN is greater at declining phase
- 48. Time-variant Models Clock-wise hysteresis loop in effect vs conc: • Same drug concentration produces two different magnitudes of pharmacological effects measured effect decreases with time (Tolerance) • Greater effect at a given drug concentration; however, after some time has passed the same drug concentration gives rise to a smaller measured effect than expected 20-02-2020 48
- 49. Time-variant Models Clock-wise hysteresis: 20-02-2020 49 • Mechanisms: active antagonistic metabolites, receptor down regulation, negative feedback etc • Eg: natriuretic response of furosemide, opioids
- 50. Population PK-PD modeling The non-linear mixed-effects modeling software (NONMEM) introduced by Sheiner and Beal is one of the most commonly used programs for population analysis. 20-02-2020 50 Purpose: Characterization of interindividual variations in PK/PD parameters This includes the search for covariates which contribute to interindividual variability, affecting PK/PD relationship. Eg: weight, age, renal function & disease status The detection and quantification of covariate effects, their influence on the dosage regimen design.
- 51. Software for PK-PD modeling • WinNonLin • GastroPlusR • P-Pharm • PH/EDSIM • MEDICI – PK • Pmetrics • NONMEM 20-02-2020 51
- 52. Role of PK-PD modeling in Drug Development • Allows successful extrapolation of preclinical results to predict effective and toxic drug concentrations • Helps in selection of appropriate doses for subsequent phases • Helps to study inter-individual differences • Helps in dose adjustments in special populations • Makes drug development more rational and efficient 20-02-2020 52
- 53. Case study PK/PD Analysis to Identify Reason for Study Failure • An example of Direct Link/Response Model KG Kowalski, S Olson, AE Remmers and MM Hutmacher, Modeling and Simulation to Support Dose Selection and Clinical Development of SC-75416, a Selective Cox-2 Inhibitor for the Treatment of Acute and Chronic Pain, Clinical Pharmacology & Therapeutics, Vol83, 857-866, 2008 20-02-2020 53
- 54. Background • A selective COX-2 Inhibitor- SC-75416 • Preclinical and PK from Healthy volunteers suggested 60 mg SC-75416 would provide pain relief (PR) similar to 50 mg rofecoxib (Vioxx) • In a dose-ranging study for pain relief in post-surgical dental patients: • Single oral dose of placebo, 3, 10, and 60 mg SC-75416 CAPSULES were compared with 50 mg rofecoxib • 10 and 60 mg doses were better than placebo, but did not achieve PR comparable to 50 mg rofecoxib • Drop out rate was higher in SC-75416 groups than rofecoxib 20-02-2020 54
- 55. Phase I (Healthy Volunteer study) 2 Individual (gray lines) and median (K) SC-75416 plasma concentrations–time profiles over 6 h following a single 60 mg oral dose of SC-75416 administered as an oral solution in healthy volunteers (N ¼ 30) and in capsule form in post- surgical dental patients (N ¼ 50). 20-02-2020 55
- 56. • A PK/PD model was developed to predict how a 60 mg oral solution dose may have performed in the post-oral surgery pain study • These models predicted that a dosage form with a PK profile similar to the 60 mg oral solution would have had Pain response comparable to 50 mg rofecoxib. 20-02-2020 56
- 57. • Moreover, extrapolations suggested that higher doses could achieve clinically superior pain response relative to 50 mg rofecoxib or other non-steroidal anti-inflammatory drugs (NSAIDs). • This hypothesis encouraged the team to consider an acute pain development strategy, with the high dose providing efficacy differentiation from the other products. 20-02-2020 57
- 58. • Results from a Subsequent Clinical Study Comparing Oral Solution SC-75416 and Ibuprofen 400 mg Rafecoxib was withdrawn by the time they conducted the next study 20-02-2020 58
- 59. 20-02-2020 59 Modeling results used to • Identify reason for trial failure • Predict outcome for new formulation • Facilitate dose selection
- 60. 20-02-2020 60 In another example, In an oncology development program, • The relationships between pharmacokinetic and safety/efficacy were investigated in a phase I study conducted in patients. • PK-PD model was developed and analyzed for various dose-range • These results helped to skip phase II and were used to design the pivotal phase III study • Saved 12-18 months of development time Reigner BG, Williams PE, Patel IH, Steimer JL, Peck C, van Brummelen P. An evaluation of the integration of pharmacokinetic and pharmacodynamic principles in clinical drug development. Experience within Hoffmann La Roche. Clin Pharmacokinet. 1997 Aug;33(2):142-52.
- 61. Thank you ☺ 20-02-2020 62