PKPD Exam 5

Linear PK

• Dose & concentration independent

• PK parameters do not change with dose

• Drug concentration and AUC increases proportionally to dose

Nonlinear PK

• Handling of drug is not first order

• Subject to capacity limited or dose dependent biological procsses

Linear PK Measures

• Exposure (AUC, Cmax, CP,) vs. dose → increase proportionally

• PK parameters (CL, V, Vss, T1/2, F) vs. dose → remain constant

• PK parameters vs. time → remain constant

• Dose normalized Cp ( Cp / dose) → should be superimposed

Nonlinear PK Measures

• Exposure (AUC, Cmax, CP,) vs. dose → increase disproportionately

• PK parameters (CL, V, Vss, T1/2, F) vs. dose → increases or decreases

ADME Saturability

• Dissolution → concentration has upper limit, no matter how much more is added concentration remains the same

• Metabolism → rate of enzyme metabolism approaches upper limit as substrate conc. increases

• Transport → Rate of transport has upper limit

• Plasma protein binding → protein binding is limited by available binding sites

Nonlinear Absorption

• More than proportional → saturable efflux transporters

• Less than proportional → saturable active absorption

Michaelis-Menten Elimination

• Low Cp → Approximation to first order (rate of elim. = -km * Cp)

• Cp = Km → mixed first and zero (rate of elim. = - Vm / 2)

• High Cp → Approximation to zero order (rate of elim/ = -Vm)

Semi-Log Plot that displays Saturable Metabolism

• Km can be estimated when rate changes from zero to first order

• Curve starts at zero order → maximum rate regardless of concentration

• Once drops below Km → first order kinetics

Dose Dependent Clearance

• As Cp(dose) increases → Clearance decreases

  • thus, Kel decreases and T1/2 increases

• INITIALLY → increasing Cp increases elimination rate and clearance

  • saturation then slows this down

Average Concentration at Steady State

• Steady state → rate of administration = rate of elimination

• CP average can increase exponentially with increase dosing rate

  • should titrate dose changes due to small changes causing huge effects

• Increasing dosing rate (DR) not only more than proportionally increases steady state conc. but also increases time required to reach 90% steady state

Nonlinear Renal Clearance

• tubular secretion → saturable

  • renal clearance decreases (less drug put into urine and cleared)

• tubular reabsorption → saturable

  • renal clearance increases (less drug reabsorbed into blood and excreted through urine)

Plasma Protein Binding Saturability

• As Cp (dose increases) → Fu increases

  • Thus V increases (big V, not small V)

• Clearance can increase or not change (depends on ER)

  • High ER → Cl ~ Q (no change)

  • Low ER → Cl = Fu* Clint (will increase)

Why is Oral dose limited for Biologics?

• Low bioavailability

  • low permeability due to large size

  • lack of lipophilicity

  • rapid enzymatic inactivation or degradation

Pulmonary Biologics

• Pros

  • Ease of administration, presence of large surface area, high vascularity, bypass first pass metabolism

• Cons

  • Lung proteases, immune cell degradation, local side effects, MW limitations

SC & IM Injections Biologics

• Cons

  • decreased F (site degradation / limited uptake into circulation)

  • Limited volume of fluid per injection

• SC and IM routes only feasible for high potent drugs

Biologic Half Lives

• Increase in MW increases T1/2

  • less renal clearance

  • resides more in lymph

• Charge

  • Isoelectric point → pH net charge is zero

  • Higher isoelectric point at 7.4 pH will mean it is a positive charged molecular → more binding to proteins that can degrade it

• FcRN

  • higher dose can saturate FcRn

Biologics Distribution

• Most have small Vd due to limited volume of extracellular space and mobility

Glycosylation

• Sugar on AB

• Increasing Sialic Acid → decrease Clearance

  • prevent binding of AB to liver receptors to be metabolized

TMDD for mAb’s

• TMDD → target mediated drug disposition

• lower dose = faster clearance

  • low dose = all bound by metabolizing enzyme

  • high dose = saturates enzyme, lasts longer

• dosing

  • low dose → higher clearance

  • high dose → FcRn saturation

ADCC & ADCP

• bind to antibody coated cells and can destroy them

• FCgamma helps clear proteins

Basic Tenets of Pharmacodynamics

• Capacity-limitation → law of mass action and small quantity of targets leads to capacity limitations in most responses

• Turnover & homeostasis → diseases and drugs both interfere with homeostasis in the body resulting from natural turnover of biological substances

Receptor Binding of Prednisolone

• increasing drug increases bound drug

• However, after Kd, the binding starts to hit a plateau

Clark’s Occupancy Theory

• First model to account for quantitative behavior of a receptor mediated process

• Pharmaceutical effect is directly proportional to the number of receptors bound

• “Corpora non agunt nisi fixata” → substances do not act unless bound

  • Paul Ehrlich

How to find Slope (m)

• Slope = m

  • Slopes of E vs. Log C plots are often linear

• m = (Emax * gamma) / 4

S Slope

• S slope = delta QT / delta Cp

• Female population has a steeper S slope meaning more sensitive to changes in Cp and bigger QT effects

Estimating Parameters of Sigmoid Emax Models

• When the highest measured of effect intensity was less than 95% of Emax, than Emax and EC50 were poorly estimated

Equation of Life

• Function = capacity * substrate / 1/affinity + substrate

• Derived from law of mass action

Simple Direct Effects

• Examples

  • ACE activity, platelet aggregation, muscle activity, EKG, lymphocyte activity

Duration of Effect

• Td (duration of effect) will increase with:

  • larger dose

  • longer T1/2

Expected PK/PD Graphs

• PK → Linear decrease of concentration over time

• PD → decrease in response over time, increasing dose increases duration, highest doses hit plateau

Biological Turnover Rates from Fast to Slow

• Electrical signalIn

• Neurotransmitters

• Chemical signals

• hormones

• mRNA

• Proteins

• Cells

• tissues

• organs

• Human

Indirect Response Models

• Model 1 → inhibits Kin

• Model 2 → inhibits Kout

• Model 3 → stimulates Kin

• Model 4 → stimulates Kout

Rosiglitazone Model 4

• Rosiglitazone stimulates insulin transporters (making more sensitive) and therefore stimulated Kout of blood glucose (model 4)

SGLT2 Inhibitors

• inhibit Kout of urine reabsorption (model 2)

• therefore more glucose is excreted through urine

DPP4 Inhibitors and GLP1

• GLP1 exerts main effect by stimulate insulin release from pancreas

  • GLP1 is broken down by DPP4 enzymes

• GLP1 also exerts effects by slowing gastric emptying, reducing food intake

Population PK

• Study of variability in drug concentrations across individuals in target population

• Focuses on interindividual variability

  • supports dose optimization in real world settings

Covariates

• Factors affecting PK / PD

  • disease

  • age

  • diet / nutrition

  • weight

  • genetics

  • etc..

Covariate Model

• Quantitative relationship between parameter values and covariates

Statistical Model

• Variability of parameter values across populations of patients

  • between subject variability

  • Residual unexplained variability

Structural Model

• Defines shape of curve

  • 1 compartment, 2 compartment models

  • Mean PK parameter values (Cl, V, F)

Interindividual Variability

• How each individual deviates from the population mean

Residual Variability

• Variance from each individual from their own mean predicted curve

Sources of Residual Variability

• Measurement Error (observed data)

  • Assay variability

  • Investigator, patient

• Measurement Error (time)

  • Investigator, patient

• PKPD Model

  • inappropriate or incomplete model

  • intraindividual variability

  • data errors

Population PK Parameters

• Include:

  • Mean parameter values

  • quantitative relationships between parameter values and covariates

  • Variability of parameter values across populations