Pharmacokinetics & Pharmacodynamics M263 Clinical Pharmacology March 30, 2011 Pharmacokinetics & Pharmacodynamics Basic Concepts Issues in Pharmacokinetics (PK) Clearance Half-lives and Residence Times Distribution Volumes Absorption & Bioavailability Measures Compartmental Modeling Pharmacodynamics (PD) Steady State Models Linking of PK & PD Mar 30, 2011 (E. Landaw) M263 Clinical Pharmacology PK/PD (E. Landaw)

M263 Clinical Pharmacology March 30, 2011 Some Resources Texts M Rowland & RN Tozer Clinical Pharmacokinetics 4th ed., Lippincott Williams & Wilkins 2011 AJ Atkinson et al. (eds). Principles of Clinical Pharmacology, Academic Press, 2nd Edition 2007 Web sites www.cc.nih.gov/training/training/principles.html www.boomer.org/pkin/ (links to PK/PD resources) Journals: Clinical Pharmacology & Therapeutics (www.ascpt.org) J. Pharmacokinetics & Pharmacodynamics PK/PD (E. Landaw)

M263 Clinical Pharmacology March 30, 2011 Basic - Definitions Pharmacokinetics (PK) – quantitative analysis of the kinetics (time course) and steady state (SS) relationships of drug “What the body does to the drug” Absorption Distribution Metabolism Excretion Elimination PK/PD (E. Landaw)

M263 Clinical Pharmacology March 30, 2011 Basic - Definitions Pharmacodynamics (PD) – quantitative analysis of relation of drug concentration at an effect site (Ce) to drug effect (E). “What the drug does to the body” Understand Dose-Effect relationships SS: Ce  measured plasma concentration Non-SS: may need to use PK to infer Ce PK/PD (E. Landaw)

M263 Clinical Pharmacology March 30, 2011 Effect Site Concentrations Concentrations Plasma, urine, tissue,… Parent and metabolites Dosing Regimen dose, frequency, route EFFECTS Rx, Toxic source: A. Atkinson PK/PD (E. Landaw)

Steady State vs. Kinetic Studies Steady state (SS) with constant IV infusion when conc. not changing with time plasma conc. CSS reflects Ctissue (usually) PK (+load) determine time until ~SS SS from Repetitive dosing (oral, IM, etc.) eventually reach constant “Profile SS” Cmax= peak ; Cmin= trough ; average CSS

Repetitive Dosing and “Profile SS” Cmax Cmin source: Rowland & Tozer

Steady State vs. Kinetic Studies Many PK/PD concepts are for SS Clearance; Volume of distribution SS PD effect for given SS conc. (time to PD SS may be longer than time to plasma SS) But some studies are kinetic e.g., single oral dose or I.V. bolus Tracer kinetic studies; PET Aim may be infer SS under rep. dosing

Linear vs Nonlinear System “Linear Pharmacokinetics” double the dose  concentration doubles AUC proportional to dose Superposition principle (example): If {I.V. bolus}  Civ(t) and {oral dose}  Coral(t) , then {both dosing together}  C(t)  Civ(t) + Coral(t) holds for small enough doses (microdoses) linearity for large doses if transport, binding, and elimination remain first order

“Nonlinear Kinetics” Example

Linear vs Nonlinear System single kinetic study + linearity  can predict response to any input, including getting to SS but for NONlinear systems: CL, V, etc. not constant; depend on CSS, Dose requires testing at different doses; models time to SS not predicted by single dose study Common nonlinearities Saturation kinetics (Michaelis-Menten) Saturable plasma protein, tissue binding Threshold effects (e.g., glucose spilling) Induction; Neuro./hormonal regulation

Importance of Experiment Design Quality & interpretation of PK/PD data depend critically on design: Dose(s), route, and form (bolus vs infusion) What to sample Plasma, urine, tissue, PET, … Total vs. unbound concentrations Parent compound, metabolites PD Effect measures What times to sample in a kinetic study Train team: record what was done, not just asked

Pharmacokinetics & Pharmacodynamics Basic Concepts Issues in Pharmacokinetics (PK) Clearance Half-lives and Residence Times Distribution Volumes Absorption & Bioavailability Measures Compartmental Modeling Pharmacodynamics (PD) Steady State Models Linking of PK & PD

Organ Clearance Clearance  Elim. flux/Cref (vol/time) Physiology: organ clearance as SS concept “E” = Single pass extraction fraction: E = Elim. flux/ input flux = (Carterial – Cvenous)/Carterial Clearance  Elim. flux/Cref (vol/time) If use Carterial as Cref , Clearance = EQ Carterial Cvenous Organ of elimination Q blood flow Elim. Flux = Q(Carterial – Cvenous) (mass/time)

Organ Clearance Clearance  Elim. flux/Cref Elimination (metabolism, transport) often function of unbound Cu (i.e., free fraction) Cu = fuC (but fu not routine measurement) Clearance = EQ high E (E>0.7), CL sensitive to Q, not fu low E (E<0.3) Q   transit time  E CL sensitive to fu, CYP induction or inhibition but SS “exposure” = fuAUC not sensitive to fu

Renal Clearance (CLR) Net CLR = (urine exc. rate)/(mid-collection C) Net Elim. flux = filtration + secretion – reabsorb. Net CLR = (urine exc. rate)/(mid-collection C) (or use 24 hour urine collection and C(t) ) Renal Filtration flux = GFR fuC GFR  CLcreat= 120 ml plasma water/minute CLR << GFR fu  significant reabsorption CLR >> GFR fu  significant secretion

Total Clearance (CLT or just CL) SS Clearances add: CL = CLR + CLH + nonrenal/nonhepatic clearance Estimating CL from single dose kinetic study i.v. Dose: CL = Dose/ ∫  C(t)dt = Dose/AUC Oral Dose: CL = FOral Dose/AUC where F = fraction of dose reaching “central pool” (plasma + tissue in rapid equilibrium with plasma) CLoral  CL/F = Oral Dose/AUC

May need to fit single exponential at end to estimate tail area to  Estimating AUC Trapezoidal rule: Fit model of data to entire C(t). e.g., C(t) = A1exp(-1t) +… + Anexp(-nt) AUC = A1/1 +… + An/n May need to fit single exponential at end to estimate tail area to  C(t) . . . . . . t

Using Profile SS to estimate AUC Profile SS after multiple repeated doses: use area under one cycle to estimate single dose AUC single dose AUC (from 0 to ) source: Rowland & Tozer

Predicting SS Concentration Constant flux infusion I (mass/time) SS plasma conc.  CSS = C() total CL = (total Elim. Flux)/Cref Here Cref is CSS Since patient at steady state, Elim. Flux = I Therefore, CSS = I / CL

Predicting SS Concentration For i.v infusion flux I: CSS = I / CL For repetitive oral dose D every T units of time, at Profile Steady State: average CSS = (FD/T) / CL . i.e. average CSS = (D/T) / CLoral where CLoral estimated from kinetic study by CLoral = Oral Dose/AUC = CL/F

Half-lives and Residence Times 1-compartment approximation for body: Drug distributes in single, well-mixed central pool 1st order elimination rate k (time-1); volume V k = CL/V V = Dose/C(0) t1/2 = 0.693/k (half-life of drug in whole body) MRT = 1/k (Mean Residence Time in body) V = total drug distribution volume = CL  MRT V logC(t) C(t) = (Dose/V)exp(-kt) . k . . t .

“Is this single exponential decay?” “What’s the half-life of this drug?”

conc. on LOG scale suggests “No!” initial t1/2 0.6 hours terminal t1/2 14 hours

Half-lives and Residence Times C(t) = A1exp(-1t) + A2exp(-2t) multi-compartment approximation for body: Drug distributes in central + peripheral pool(s) C(t) exhibits elimination and distribution kinetics 2 or more “half-lives,” but terminal half-life not always the main factor for dosing, accumulation, etc. Relative importance each half-life depends on Ai/i logC(t) C(t) = A1exp(-1t) + A2exp(-2t) V1 . . . t . . . .

Caution: Interpreting Terminal t1/2 Terminal t1/2 often related to elimination BUT NOT ALWAYS! counterexample: gentamicin CLcr 6 – 107 ml/min terminal t1/2 in all 90 hrs renal impairment affects mainly first half-life avg CSS still (D/T)/CLoral but dosing interval T to achieve desired Cmax/Cmin trickier to compute source: Rowland & Tozer Schentag et al. JAMA 238:327-9, 1977

Mean Residence Time (MRT) MRT = mean time molecule of drug resides in body before being irreversibly eliminated Assumes linear system May be useful summary measure when there are multiple half-lives Effective (overall) half-life = 0.693MRT

Mean Residence Time Estimating MRT from kinetic studies: Measure plasma concentration C(t) MRT  AUMC/AUC  ∫ tC(t)dt /AUC Equality if elimination is exclusively from central pool and no traps. Need to use a model if there is peripheral elimination. Measure total amount in body A(t) (e.g., total body scan) MRT = ∫ A(t)dt/ A(0)

Mean Residence Time 1-compartment model Multi-exponential model MRT = 1/k = V1/CL half-life = 0.693×MRT time to reach 90% SS following constant flux infusion is 2.3 MRT’s = 3.3 half-lives Multi-exponential model AUMC/AUC = w1(1/1) + … + wn(1/n) where wi  (Ai/i ) and w1 + … + wn = 1 2.3 MRT’s (i.e., 3.3 effective half-lives) is time to reach at least 84% SS

Distribution Volumes Volume of Central Pool (V1) V1 = Dose/C(0) generally need several recirculation times before well-mixed assumption holds V1 often a little larger than plasma, even with multiexponential decay (includes tissues in rapid equilibrium with plasma by time of first sampling)

C(t) = A1exp(-1t) + A2exp(-2t) multi-compartment approximation for body: Drug distributes in central + peripheral pool(s) C(t) exhibits elimination and distribution kinetics Back-extrapolated C(0) = A1 + A2 V1 = Dose/C(0) logC(t) C(t) = A1exp(-1t) + A2exp(-2t) V1 . . . t . . . .

SS Distribution Volume (VSS, VD or just V) Assume body at SS (e.g., iv infusion) A() is total amount (mass) of drug in body Define V = A() / CSS Hypothetical volume SS mass would have to occupy to yield same concentration as CSS V = CL MRT Provides insights into distribution, permeation, tissue binding, etc. back-extrapolated C(0) from terminal decay (i.e., Vextrap) may overestimate V

t1/2 depends on CL and V source: Rowland & Tozer

Absorption & Bioavailability source: A. Atkinson

Bioavailability Measures of extent and rate of absorption from admin. site to measurement site (latter usually central pool, i.e. plasma) i .v. administration is “gold standard” for complete and instantaneous absorption single oral dose: “informal” measures are: Cpeak tpeak

Bioavailability – formal measures “F” estimates extent of absorption Separate i.v. and oral studies F = (Doseiv/Doseoral) AUCoral/AUCiv fraction of administered dose reaching plasma MAT (mean absorption time) AUMCoral/AUCoral - AUMCiv/AUCiv Absorption rate constant (compart. model) Absorption flux time course (deconvolution)

Example: Rifampicin pretreatment reduces oral digoxin bioavailability

Example: Physiological PK Prediction, Scale-up , (Allometry)

Example: Compartmental Modeling Metabolism Distribution phencyclidine analogs Cho et al. Drug Metab. Dispos. 21:125-132.1993

Pharmacokinetics & Pharmacodynamics Basic Concepts Issues in Pharmacokinetics (PK) Clearance Half-lives and Residence Times Distribution Volumes Absorption & Bioavailability Measures Compartmental Modeling Pharmacodynamics (PD) Steady State Models Linking of PK & PD

Dose-Effect Relationships Drug Dose Covariates age sex body size organ function disease other drugs genes/markers PK C(t) PD Effect(s)

Dose-Effect Endpoints M263 Clinical Pharmacology March 30, 2011 Dose-Effect Endpoints Graded • Continuous scale (­dose ® ­effect) • Measured in a single biologic unit • Relates dose to intensity of effect There are 2 fundamental types of endpoints that can be used to quantify the dose-effect relationship, graded and quantal. Graded - The graded dose-effect is measured on a continuous scale and the intensity of the effect is proportional to the dose, such as measuring the change in blood pressure after administering an antihypertensive agent. Grade dose-effect relationships can be measured in a single biologic unit that is exposed to a range of doses. Therefore, a graded dose-effect study relates the dose to the intensity of the effect. Quantal - Conversely a quantal effect is an all-or-none effect such as alive or dead, asleep or awake, pain-free or in pain. Quantal dose-effect studies are performed in populations of subjects who are treated with a range of doses, and dose is related to the frequency of the all-or-none effect, such as the % of subjects who survived. Quantal • All-or-none pharmacologic effect • Population studies • Relates dose to frequency of effect source: Frank M. Balis PK/PD (E. Landaw)

M263 Clinical Pharmacology March 30, 2011 Simplest PD Model for Graded Effect (Effect  10 Drug-Receptor complex) Drug Drug-Receptor Complex This relationship between dose and effect with EPO and most other drugs is governed by the mechanism by which drugs produce their effects - by interacting with cellular macromolecules called receptors. A receptor can be any cellular macromolecule with which a drug interacts to initiate its pharmacologic effect. Proteins are the most important class of drug receptors Cellular proteins that are receptors for endogenous regulatory ligands, such as hormones, growth factors, neurotransmitters, are also the most important drug receptors. These proteins have a ligand binding domain where the drug interacts and an effector domain that propagates the message - leading to an effect. Other receptors include enzymes (acetylcholinesterase), transport proteins (Na+,K+-ATPase), structural proteins (tubulin), and nucleic acids The drug’s chemical structure is the primary determinant of the class of receptors with which the drug will interact. The intensity of the effect produced by a drug is proportional to the fraction of receptors occupied by drug and the maximal effect occurs when all receptors are occupied (receptor occupation theory). The drug-receptor interaction is reversible and conforms to the law of mass action that govern chemical reactions, assuming that 1) response to drug is directly proportional to the fraction of total receptor occupied by the drug and 2) the amount of drug bound to receptor is negligible so the concentration of free drug remains constant. The drug concentration doesn’t change during the reaction - only the proportion of free and occupied receptors changes. In the reaction scheme k1 and k2 are the proportionality constants for the formation and dissociation of the drug-receptor complex (the interaction is reversible). CLICK. At equilibrium, the reaction can also be expressed by this equation which takes the same form as the Michaelis-Menten equation where [Drug] is the concentration of free drug, maximal effect is the effect achieved when all of the receptors are occupied by drug, and KD is the dissociation rate constant for the complex. CLICK. KD is equal to k2/k1, the ratio of the proportionality constants. Ligand-binding domain k1 Effector domain k2 Receptor Effect Effect = Maximal effect • [Drug] KD + [Drug] (KD = k2/k1) source: Frank M. Balis PK/PD (E. Landaw)

Graded Dose-Effect Curve M263 Clinical Pharmacology March 30, 2011 Graded Dose-Effect Curve Maximal effect The mathematical relationship from the previous slide takes on the shape of a hyperbolic function when presented graphically. This is a dose-effect or dose-response curve. In this form of the dose-effect curve, the free drug concentration along the X-axis is a linear scale. Drug effect asymptotically approaches the maximal effect as the drug concentration increases. This is a graded dose-response relationship, because the responding system is capable of showing progressively increasing effect with increasing dose. The EC50 is the drug concentration at which the drug is half-maximally effective. If the relationship between receptor occupancy and response is linear then KD = EC50. If there is amplification between receptor occupancy and response, such as when the receptor has catalytic activity when the receptor ligand is bound, then the EC50 lies to the left of the KD. Once the dose exceeds the EC50, there is diminishing return with increasing dose. There is a smaller increment in effect with a fixed dose increment. % of Maximal Effect EC50 [Drug] source: Frank M. Balis PK/PD (E. Landaw)

Dose-Effect Parameters M263 Clinical Pharmacology March 30, 2011 Dose-Effect Parameters POTENCY: The sensitivity of an organ or tissue to the drug Graded dose-effect curves are also a good way to compare agents that produce the same effect. Drugs that produce the same effect differ in terms of potency and efficacy, which are parameters that can be assessed from the dose-response curves of the agents. Potency is a measure of the sensitivity of a target organ or tissue to the effect of the drug. It is relative term that relates the amount of one drug required to produce a desired effect compared with another agent. On a dose response curve the more potent agents are to the left (have a lower EC50 or ED50). CLICK on Potency to go to to TG vs. MP example. Efficacy is the drug property that allows the receptor-bound drug to produce its pharmacological effect. The relative efficacy of 2 drugs that elicit the same effect can be measured by comparing the maximum effects of the drugs. EFFICACY: The maximum effect source: Frank M. Balis PK/PD (E. Landaw)

Comparing Dose-Effect Curves M263 Clinical Pharmacology March 30, 2011 Comparing Dose-Effect Curves Drug A Drug B Here are the dose-effect curves of 3 drugs that produce the same effect. Drug A is more potent than Drug B. Drugs A & B are more efficacious than Drug C. Comparing the dose-response curves of drugs that produce the same pharmacological effect can also provide information about the site of action of the drugs. Drugs A and B have dose response curves with identical shapes and the same maximal level of response - the curves are parallel. This suggests that the the 2 drugs act through the same receptor. Conversely, if 2 drugs that produce the same effect have non-parallel dose-effect curves, such as Drug A and Drug C, they probably have different sites of action. If we return to the issue of potency and keeping in mind the equation (CLICK) that describes the relationship between drug effect and dose, the only way that unequal doses of 2 drugs can produce the same effect is if their dissociation constants (KD) differ. So the dissociation constant is a measure of the affinity of the drug for its receptor, just like the Michaelis-Menten constant, Km, is a measure of the affinity of a substrate for its enzyme. % of Maximal Effect Drug C Effect = Maximal effect • [Drug] KD + [Drug] [Drug] source: Frank M. Balis PK/PD (E. Landaw)

Pharmacodynamic Models M263 Clinical Pharmacology March 30, 2011 Pharmacodynamic Models Fixed effect model Linear model Log-linear model Emax model Sigmoid Emax model Effect = E0 + S•[Drug] These are the most commonly used pharmacodynamic models that relate drug concentration to effect at steady state Notice that at steady state these models are time independent. The fixed effect model is a statistical approach that quantifies the likelihood or probability that a given concentration will produce an all-or-none effect. For example, a digoxin plasma concentration of 2 ng/ml is associated with a 50% probability of developing digoxin toxicity. This is only a useful model in the clinical setting. CLICK. The linear model assumes direct proportionality between drug concentration and effect. E0 is the baseline effect with no drug present and S is the slope of the line. This is the intuitively most popular model, but it rarely applies. The most obvious limitation of the model is that it does not predict for a maximal effect. Changes in drug effect are not directly proportional to changes in the dose. CLICK. The log-linear model (I is the intercept) may be applicable over narrow dosage ranges around the EC50, but has the same limitations as the linear model at extreme doses. CLICK. The Emax and Sigmoid Emax models have the same form as the equation describing the interaction of drug and receptor, which is not a coincidence since receptor occupancy is proportional to the effect. This general equation has also been called the Hill equation (first developed to describe O2-hemoglobin interactions) and the exponent, know as the Hill constant or slope factor, determines the steepness of the curve. The Emax model is a Sigmoid Emax model with a slope of 1. Effect = I + S•Log([Drug]) Effect = EC50 + [Drug]H Emax•[Drug]H H source: Frank M. Balis PK/PD (E. Landaw)

M263 Clinical Pharmacology March 30, 2011 Sigmoid Emax PD Model Effect (%) Effect (%) H = 5 H = 2 I hope by now that you could predict the shape of the curves (concentration-effect curves) with the Sigmoid Emax model. I have plotted them using a linear and log scale for drug concentration. For this series of curves the Emax and EC50 are the same and I have varied the slope factor to illustrate the effect it on the shape of the curve. Remember an H of 1 is the Emax model. H = 1 H = 0.5 H = 0.1 EC50 EC50 [Drug] source: Frank M. Balis PK/PD (E. Landaw)

Concentration and Effect vs. Time M263 Clinical Pharmacology March 30, 2011 Concentration and Effect vs. Time Non-Steady State Central Compartment Simulation of drug concentrations in the Central, Peripheral and Effect compartments and the Effect as a percentage of Emax, based on the linked pharmacokinetic/pharmacodynamic model. Peripheral Compartment Conc./ Amount Effect [% of EMAX] Effect Effect Compartment Time source: Frank M. Balis PK/PD (E. Landaw)

Hysteresis and Proteresis Loops M263 Clinical Pharmacology March 30, 2011 Hysteresis and Proteresis Loops Intensity of Drug Effect Intensity of Drug Effect Hysteresis Loop (Counterclockwise) Proteresis Loop (Clockwise) Equilibration delay in plasma and effect site conc. Formation of active metabolite Receptor up-regulation Tolerance Receptor tachyphylaxis Under non-steady state conditions, the drug concentration at the effect site may not directly parallel the plasma concentration, and, as a result, the time course of the intensity of the drug’s effect may not parallel the time course of plasma drug concentrations. This can be evaluated by plotting the plasma drug concentration-effect data and connecting the points in time sequence. A counterclockwise or hysteresis loop (Figure 16A) could indicate a delay in equilibrium between the plasma and effect site drug concentrations, the formation of an active metabolite or the up-regulation of the drug receptor. A clockwise or proteresis loop (Figure 16B) is consistent with the development of tolerance or receptor tachyphylaxis. If properly designed, the linked pharmacokinetic/pharmacodynamic models, such as those described on the previous slides, can account for these more complex concentration-effect relationships. Plasma Drug Concentration source: Frank M. Balis PK/PD (E. Landaw)

PK/PD Applications Drug discovery/development Scaling (cell culture  animal  human) Feasible dosing, drug delivery Predict and quantify inter- & intra-patient variability Regulatory issues (FDA) Basic and Clinical Sciences Understand in vivo mechanisms Quantify PK and PD study endpoints Design of clinical studies Dosing regimens Timing of samples Identify important covariates

PK/PD Applications Therapy Pharmacogenetics/pharmacogenomics Optimal treatment strategies Individualization of therapy Clinical monitoring (PD) or predicting (PK/PD) efficacy and toxicity endpoints Pharmacogenetics/pharmacogenomics Hereditary variations in response (PK or PD) Identification of genes or loci Genome-based drug discovery Predict efficacy and potential adverse effects