1. 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, (E. Landaw)
M263 Clinical Pharmacology
PK/PD (E. Landaw)

2. 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
(links to PK/PD resources)
Journals:
Clinical Pharmacology & Therapeutics (
J. Pharmacokinetics & Pharmacodynamics
PK/PD (E. Landaw)

3. 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)

4. 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)

5. 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)

6. 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

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

8. 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

9. 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

10. “Nonlinear Kinetics” Example

11. 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

12. 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

13. 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

14. 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)

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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 .

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

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

25. 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 . . . .

26. 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

27. 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

28. 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)

29. 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

30. 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)

31. 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 . . . .

32. 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

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

34. Absorption & Bioavailability
source: A. Atkinson

35. 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

36. 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)

37. Example: Rifampicin pretreatment reduces oral digoxin bioavailability

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

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

40. 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

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

42. 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)

43. 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)

44. 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)

45. 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)

46. 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)

47. 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)

48. 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)

49. 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)

50. 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)

51. 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

52. 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