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Predictive Drug Absorption Models. John Crison, Ph.D. AAPS Workshop on Evolving Science and Technology in Physical Pharmacy and Biopharmaceutics, May 13-15, 2009, Baltimore, MD. 1. Outline. Approaches to Modeling Compartmental Pharmacokinetics Reserved Length Macroscopic Mass Balance
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Predictive Drug Absorption Models John Crison, Ph.D. AAPS Workshop on Evolving Science and Technology in Physical Pharmacy and Biopharmaceutics, May 13-15, 2009, Baltimore, MD 1
Outline • Approaches to Modeling • Compartmental Pharmacokinetics • Reserved Length • Macroscopic Mass Balance • Compartmental Absorption and Transit (CAT) • Advanced Compartmental Absorption and Transit (ACAT) • Physiologically Based Pharmacokinetics (PBPK) • Supporting Predictive Models • Non-oral routes 2
Development of Drug Absorption Models(in the Pharmaceutical Industry) 1960 -1970 1980 -1990 1990 - present 3
Pharmacokinetics Wagner, J., Pharmac Ther, 12:537-562, 1981 Application of kinetics to drug therapy where Kinetics is that branch of knowledge which involves the change of one or more variables as a function of time. The purpose of pharmacokinetics is to study the time course of drug and metabolite concentrations or amounts in biological fluids, tissues and excreta, and also of pharmacological response, and to construct suitable models to interpret such data. 4
Basic Absorption and Disposition Excreted Drug excretion Drug at Absorption Site Drug in Body absorption metabolism These models use curve-fitting techniques to estimate kinetic rate constants and other parameters from time-course data for blood, tissue, or excreta; however, the curve-fitted parameters lack biological meaning. Metabolites Clinical Pharmacokinetics, Rowland and Tozer, 2nd Ed, Lea & Febiger, 1989 Wagner, J., Pharmac Ther, 12:537-562, 1981 5
Early PK Compartmental Theory One Compartment Model • F = fraction of drug available • D = dose • V = volume of distribution • = time • k = apparent elimination rate constant • CAV = average concentration (Wagner, et al, Nature, 207:1301-1302, 1965)
Multi-Compartment PK Models Over the years, multi-compartment models were developed to described more complex drug disposition scenarios (example – 2-compartment model). 2 k21 1 k12 kel Mayersohn, M. and Gibaldi, M 1971 "Mathematical Methods in Pharmacokinetics. II. "Solution of the Two Compartment Open Model," Amer. J. Pharm. Ed., 35:19-28
Pharmacokinetic Models • Applications • Since the 1960’s, classical pharmacokinetic (PK) models have been considered the standard for absorption modeling and have been widely used to study kinetic behaviors of drugs, • Both linear and nonlinear kinetics. • Measuring bioavailability and determining bioequivalence. • Modeling variability in populations. • Pharmacokinetic/Pharmacodynamic relationships.
Intestinal Reserve Length Approach Higuchi, W., et al, Drug Development and Industrial Pharmacy, 9(7): 1227-1239, 1983 • The significance of the reserve length concept is its ability to interrelate many of the factors that affect drug absorption, such as; • Physiological • Physicochemical • Dosage Form • The intestinal reserve length, RL, where L is the effective absorbing length of the intestine and L* is the length required for essentially complete absorption for a particular case, determined by experiment.
Linear Velocity, cm/min 0.25 0.50 1.00 Solubility, mg/mL 300 200 500 100 0 Bioavailability of suspensions taking into consideration particle size, solubility, membrane permeability, and intestinal flow. When RL is close to zero or negative, low bioavailability may be an issue. 50.0 5.0 Reserved Length, cm 0.5 Higuchi, W., et al, Drug Development and Industrial Pharmacy, 9(7): 1227-1239, 1983
Uses of Reserve Lengthin Drug Delivery Research • Applications: • Points out the critical in vitro physicochemical, animal and human absorption studies needed to define specific problems. • Sorts out key variables. • Sets quantitative boundaries within which optimization of oral formulations may be achieved. • Points out strategies and options in drug formulation design. • Assesses bioavailability and bioequivalence in terms of biophysical and physicochemical events. • Limitations: • Model assumes permeability is constant along intestine
Macroscopic Mass Balance (MMB) Conservation of mass in a tube Rate of mass in Rate of mass out M = mass t = time Q = flow rate Co = inlet concentration Cm = outlet concentration JW = wall flux A = wall surface area Rate of mass absorbed Sinko, et al, Pharmaceutical Research, Vol. 8, No. 8, 1991
Correlation between Fraction Absorbed and MMB, Plug Flow, Complete Radial Mixing 13
Further Extension of the Macroscopic Mass Balance Approach – Solid and Solution Phases Solid phase rate of mass in – rate of mass out – rate of mass dissolved = 0 rate of mass in – rate of mass out + rate of mass dissolved – rate of mass absorbed = 0 Soln. Phase Rate of mass in Rate of mass out Rate of mass dissolved Rate of mass absorbed Oh, et al, Pharmaceutical Research, Vol. 10, No. 2, 1993 14
Solid and Solution Phases rp = particle radius D = diffusion coefficient R = intestinal radius Q = flow rate ρ = solid density Cs = solubility CL = concentration in lumen Peff = intestinal permeability N0 = number of particles V0 = volume of water taken with dose z = axial length of tube 15
MMBA • Applications • Uses drug membrane permeability and solubility to predict fraction of drug lost from the lumen. • Includes passive and non-passive permeability. • Chemical reaction/degradation can be added. • Can include a solid phase. • Limitations • Description of drug absorption is limited to the fraction of drug loss from the lumen. 16
Dimensionless Numbers A Dimensionless Number is a quantity without physical units but is a product or ratio of quantities which have units in such a way that all the units cancel out. 17
Transport Equations for Solid and Solution Phases (Tube Model) D = diffusivity Cs = saturated concentration CL = lumen concentration rp = particle radius Q = intestinal flow rate ρ = solid density R = intestinal radiusNo = number of molecules Vo = volume of dose media 18
Quickly shows how physical chemical and formulation parameters affect absorption. griseofulvin piroxicam digoxin 20
Compartmental Absorption and Transit (CAT) Model KS Kt Kt Kt MS M1 Mn M7 MC Ka plasma MS = mass in stomach Mn = mass in small intestine compartment n MC = mass in colon t = time K = rate constant for transit, gastric emptying, and absorption 21 Yu, L, et al, Int J Pharm, 186:119-125, 1999
Enterohepatic circulation Excretion Stomach Duodenum Jejunum1 Jejunum2 Ileum1 Ileum2 Ileum3 Caecum Asc. Colon Unreleased Undissolved Dissolved Lumenal Degradation Portal Vein (losses) Gall Bladder Gut Wall Metabolism Liver Hepatic Artery Brain Systemic Circulation 2nd Compartment 3rd Compartment Adipose Muscle Skin, etc. Advanced Compartmental Absorption and Transit (ACAT) Simulation Model 22
Examples: Utility of ACAT Models to Simulate Metabolism Effects and Formulation Changes • Example 1 • Drug: cilostazol • Animal Model: beagle dogs • Model Variables: particle size and size distribution • Example 2 • Drug: Midazolam • Animal Model: humans • Model Variables: dosed w and w/o grapefruit juice, w/ and w/o cyp3A4 in gut 23
Using an ACAT Model to Predict Plasma Conc. v. Time for Cilostazol Powder Samples with Different Processing Methods and Particle Size Distributions Dosed in Fasted Beagle Dogs 0.3 – 122 mm 0.1 – 0.4 mm 0.3 – 13.7 mm Lukacova, V, Modeling Cilostazol absorption and pharmacokinetics in Beagle Dogs and design of in-vitro dissolution experiment to model the in-vivo absorption, AAPS, 2009 24
Changes to Metabolism and Addition of an Enzyme Inhibitor (grapefruit juice) w/o grapefruit juice 15mg po of midazolam was dosed w/o grapefruit juice and with grapefruit juice, and dosed with grapefruit juice but no cyp3A4 metabolism added to the model (only liver). The model was developed by fitting to iv data, enzyme distribution were taken from the literature. w/ grapefruit juice w/ grapefruit juice, but no cyp3A4 in gut Bornemann, LD, Eur J Clin Pcol, 29:91-95, 1985 25 Bolger, M, Midazolam Presentation, ODD, 2009
Compartmental Absorption and Transit Models • Applications • Can simulate drug absorption from the GI tract taking into consideration: • Gastric emptying and intestinal transit time • Changes in pH, permeability, transporters and metabolism along the intestine • Drug dissolution or modified drug release from a dosage form • Drug-drug interactions 26
Physiologically Based Pharmacokinetic (PBPK) Models • Features: • Mechanistic • Tissue anatomically correct • Structure • Volume • Composition • Blood flows • Structure is essentially the same for all mammals 27
PBPK Each compartment represents a tissue, with a specific volume, blood perfusion rate, and partition coefficient Kp(i) for each tissue, where i denotes the tissue. Three types of compartment: Blood Perfusion-limited tissue Permeability-limited tissue Tissues can have enzymes and transporters. Tissues can have intrinsic clearance. For perfusion-limited tissues, the concentration of drug in the tissue is Kp(i) * unbound concentration in plasma at all times For permeability-limited tissues, Kp(i) serves as the limiting value, but the actual tissue concentration is determined by the permeability and surface area exposed to the plasma, so time is needed to reach the concentration ratio defined by Kp(i). Physiologically Based Pharmacokinetic Modeling: Science and Applications, Eds. Reddy, Yang, Clewell, and Anderson, John Wiley & Sons, Inc., 2005 Rowland, M, et al, AAPS PharmSci, 6(1): 1-12, 2004 28
What’s Involved in PBPK • Models of individual tissues • Flows, Volumes • Global model • connections between tissues • Mechanisms • Clearance • Metabolism • Transport • Binding 29
Perfusion or Permeability Limited? PERFUSION-LIMITED: If permeability is high, then the amount of drug that partitions into the tissue will be limited by the blood flow rate (perfusion rate) through the tissue. A partition coefficient, Kp, is used to calculate the concentration of drug in the tissue at each time step. Partitioning is assumed to be instantaneous. If there are no measured values, partition coefficients can be estimated from physicochemical properties (logP, fup,fut). PERMEABILITY-LIMITED: If permeability is low, the amount of drug that partitions into the tissue will be limited by the permeability and the surface area available for permeation. A (permeability*surface) area product is used to calculate the rate of drug transfer into or out of the tissue. At early times, the tissue concentration will be less than the product of the partition coefficient, Kp, and the unbound concentration in the blood. The partition coefficient, Kp, serves to limit the extent of partitioning, while permeability limits the rate. Kp Perfusion limited Q P*A Q Permeability limited 30
Perfusion vs. Permeability Limited In this example terbinafine, an antifungal, was dosed to rats. The model predicted the data well for the 1st 4 hours using a perfusion –limited PBPK model, however over predicted beyond 4 hours. Since this drug targets and likely has higher binding to skin, the skin and reproductive organs in the PBPK model were switched to permeability limited. This approach gave a good prediction throughout the time course of the experiment. 31 Hosseini-Yeganeh, M., Antimicrob Agents Chemother, 46(7):2219-2218, 2002
Interspecies Scaling using PBPK A terbinafine PBPK model was developed using and Kp data for the rat (from previous slide). All PBPK parameters from the rat model were kept constant except for dose, tissue volumes and systemic liver clearance which were scaled for humans . Hosseini-Yeganeh, M., Antimicrob Agents Chemother, 46(7):2219-2218, 2002 32
PBPK Models • Applications • Allow prediction of concentration-time profiles of a drug in tissue and plasma prior to in vivo studies. • Make possible the extrapolation of kinetic data across dose levels, route of administration, and species. • Guide hypothesis-driven experimentation after potential drug candidates are selected. 33
Supporting Predictive Models • Numerous models, both commercial and internal, have been developed to predict: • Physico-chemical properties. • Solubility, pKa, logP, logD, diffusivity, etc. • ADMET properties • Intestinal, cell culture, and blood-brain barrier permeabilities, numerous metabolism predictions, numerous toxicity predictions (hERG, liver enzymes, mutagenicity, carcinogenicity, aquatic toxicities, etc.) • These models are extremely useful for screening NCEs with little or no bench data. 34
Non-Oral Models • Non-oral models have been published or commercialized and include: • Transdermal • Lingual, Sublingual & Buccal (oral cavity) • Ocular • Pulmonary/Nasal 35
In Summary….., “The future should involve the use of comprehensive models capable of incorporating physico-chemical data and biological information such as gastrointestinal flow, how and where drug absorption occurs, and whether and where metabolism of the drug occurs during gastrointestinal transit. Special challenges would involve the use of such models in research protocols in the optimization of drug delivery systems.” Higuchi, W, et al, Drug Devel and Ind Pharm, 9(7), 1227-1239 (1983) 37