`
`Hospira v. Genentech
`IPR2017—00805
`
`Genentech Exhibit 2011
`
`

`

`
`
`APPLIED
`
`PHARMACOKINETICS
`
`Principles of Therapeutic Drug Monitoring
`
`
`Edited by
`
`William E. Evans, Pharm.D.
`Director. Clinical Pharmacokinetics Laboratory
`and Clinical Division of Pharmacy
`St. Jude Children’s Research Hospital
`and
`Associate Professor of Clinical Pharmacy
`Department of Pharmacy Practice
`University of Tennessee
`Center for the Health Sciences
`Memphis
`
`Jerome J. Schentag, Pharm.D.
`Assistant Director, Clinical Pharmacokinetics Laboratory
`Millard Fillmore Hospital
`and
`
`Assistant Professor of Pharmaceutics and Pharmacy
`State University of New York at Buffalo
`Buffalo
`
`William J. Jusko, Ph.D.
`Director, Clinical Pharmacokinetics Laboratory
`Millard Fillmore Hospital
`and
`Professor of Pharmaceutics
`
`State University of New York at Buffalo
`Buffalo
`
`Applied Therapeutics, Inc.
`Spokane, WA
`
`ii
`
`

`

`Other publications by Applied Therapeutics, Inc:
`
`DRUG INTERACTIONS NEWSLETTER: A Clinical Perspective and
`Analysis of Current Developments, Edited by Philip D. Hansten.
`ISSN 02718707
`
`Basic Clinical Pharmacokinetics by Michaei E. Winter.
`ISBN 0-915486-04»0
`
`Applied Therapeutics: The Clinical Use of Drugs. Edited by Brian
`S. Katcher, Lloyd Yee Young. Mary Anne Koda-Kimble.
`ISBN 0-915486-05-9
`
`Copyright © 1980 by Applied Therapeutics, Inc.
`Printed in the United States of America
`
`All rights reserved. No part of this book may be reproduced. stored in a
`retrieval system. or transmitted, in any form or by any means, electronic,
`mechanical, photocopying, recording, or otherwise without prior written
`permission from the publisher.
`
`Applied Therapeutics, Inc.
`PO. Box 1903
`
`Spokane, WA 99210
`
`Library of Congress Catalog Card Number 80-53468
`ISBN 0-915486-03-2
`
`Second Printing—April 1981
`Third Printing—July 1983
`
`iii
`
`

`

`20
`
`Guidelines for Collection and
`Pharmacokinetic Analysis of
`Drug Disposition Data
`
`William J. Jusko, PhD.
`
`Many recent developments and efforts in both theoretical and ap—
`plied pharmacokinetics have emphasized the principles of physiolog»
`icaf pharmacokinetics and the use of model-independent approaches
`to analysis of drug disposition data. Physiological pharmacokinetics
`involves the deployment of pharmacokinetic models and equations
`based on anatomical constructions and functions such as tissue spaCes,
`blood flow, organ metabolism and clearance, drug input sites, and mech~
`anisms of partitioning, binding, and transport. While the complete
`application of physiologic systems analysis may require the extensive
`models proposed by Bischoff and Dedrick (1,2), even the simplest of
`pharmacokinetic treatments should have a physiologic basis for in-
`terpretation. Coupled with efforts to discern the physiologic elements
`of any set of data is the use of model-independent techniques in
`pharmacokinetics. This term applies to methods of data treatment
`and resultant parameters which either do not require a Specific model
`in the analysis or yield the physiological elements of pharmacokinetics
`such as systemic clearance (CL) or steady-state volume of distribution
`(V?) which apply regardless of the model used for calculation.
`This chapter is intended to blend the natural components of both
`approaches to applied pharmacokinetics. A summary is provided of
`the most relevant concepts, models, equations, and caveats which may
`be useful in the design, analysis, and interpretation of pharmacoki-
`netic experiments. References are provided for more complete details
`of the assumptions, derivations, and applications of these guidelines
`and relationships. This material may be helpful as a checklist in
`designing animal and human experiments in pharmacokinetics, in
`
`639
`
`

`

`640
`
`I Drug Disposition Data
`
`reviewing drug disposition reports and, in fully expanded format, has
`served as a basis for a graduate course in physiological pharmacoki-
`netics.
`
`Context of Pharmacokinetics
`
`A pharmacokinetic analysis must be made in context of, be consist-
`ent with, and explain the array of basic data regarding the properties
`and disposition characteristics of the drug.
`The tasks of model and equation selectiOn and interpretation of data
`require a fundamental appreciation of and integration of principles of
`physiology, pharmacology, biochemistry, physicochemistry, analytical
`methodology, mathematics, and statistics. Pharmacokinetics is a dis-
`tillation of many disciplines, and the relevant portions of these areas
`must be considered in reaching any conclusions regarding a particular
`set of data. The physicochemical properties of a drug such as chemical
`form (salt, ester, complex}, stability, partition coefficient, pKa, and
`molecular weight can affect drug absorption, distribution, and clear-
`ance. A drug disposition profile must be correlated with studies of
`texicity, structure-activity, disposition in alternative species, perfused
`organs, tissue or microsomal metabolism, tissue drug residues, and
`disease state effects. For example, a much larger LDso for oral doses
`of a drug compared with parenteral administration may be indicative
`of either poor gastrointestinal absorption (low aqueous solubility?) or
`a substantial first-pass effect. Drug metabolism data may be difficult
`to fully extrapolate between species, but the biotransformation rate
`(Vmax and K.) of microsomes, homogenates, or perfused organs can
`often be applied directly to whole body disposition rates in the same
`species (1—3).
`In general, the pharmacokinetic model and analysis should either
`conform to or account for the known properties and accumulated data
`related to the drug. One set of disposition data may misrepresent the
`characteristics of the drug because of any one or combination of rea—
`sons. Experienced judgment may be required to serve in the final
`interpretation and acceptance of any experimental findings and anal-
`ysis.
`
`Array of Basic Data
`
`Pharmacokinetic studies often serve to answer specific questions
`about the properties of a drug. For example, a limited experimental
`protocol can easily resolve the question of how renal impairment
`affects the systemic clearance of an antibiotic. In the total design and
`
`

`

`implementation of pharmacokinetic studies, an ideal and complete
`array of experimental data should include a number of considerations:
`
`Drug Disposition Data
`
`2‘ 641
`
`A. The dosage form should be pro-analyzed. All calculations stem
`from knowledge of the exact dose given (e.g., Clearance =
`Dosez‘AUC, where AUC is the area under the plasma concentra-
`tion versus time curve}. Most commercial dosage forms are inex-
`act. Vials or ampules of injectables typically contain some ov-
`erage and require analysis or aliquoting for administration of
`a precise dose. Solid dosage forms are required to yield an av-
`erage of the stated quantity of drug with limited variability, but
`both may be inaccurate for pharmacokinetic purposes. Manni-
`nen and Koriionen {4) provided an excellent example of both
`the variability and lack of stated quantity of digoxin in many
`commercial tablets of this product. One product contained a
`range of 39 to 189% of the stated 0.25 mg dose of digoxin, while
`the most uniform product, Lanoxinfl (Burroughs-Wellcome}, ex-
`hibited a range of about 95 to 106% for one batch of drug. To
`evaluate the potential uncertainty of the dOSe of drug used in
`disposition studies, it may be necessary to collect and analyze
`replicate doses of the product used. Low dose and poorly soluble
`drugs may be most susceptible to erratic formulation.
`B. Accuracy in administration of the dose should be confirmed. All
`doses should be timed exactly for starting time and duration of
`administration. Pharmacokinetic equations are available to cor-
`rect data from short-term infusion studies to the intercepts ex-
`pected after bolus injection for ease in subsequent calculations.
`The duration of multiple-dosing in relation to the terminal half—
`life is crucial for ascertaining whether steady-state conditions
`obtain. Materials used in drug administration may cause loss of
`drug. As one of the most dramatic examples, MacKichan et al
`{5) found immediate loss of about 50% of a dose of intravenous
`
`diazepam by adsorption during passage through the plastic tub-
`ing of an infusion set.
`C. AttentiOn to methods and sites of blood collection is needed.
`
`Blood samples shOuld either be collected by direct venipuncture
`in clean glass tubes without anticoagulant and centrifuged
`while maintained at 37°C or assessment of possible artifacts
`from alternative procedures should be made. Maintenance of a
`heparin trap can result in increased free fatty acid concentra-
`tions in blood causing altered'drug-protein binding {6). The type
`of plastic, commercial tube, or anticoagulant may be a factor
`
`

`

`642
`
`1’ Drug Disposition Data
`
`{7). Changes in temperature may alter red cell distribution of
`some compounds (8). These problems primarily pertain to weak
`bases such as propranolol and imipramine where plasma protein
`binding is extensive and displacement alters plasma-red cell
`drug distribution (7). Platelets accumulate marked concentra-
`tions of pyroxamidin which can be released during blood clot-
`ting, producing a 5—fold increase in plasma concentrations of
`this 00mpound (9).
`One of the major assumptions employed in most pharmaco-
`kinetic studies is that venous blood collected from one site ad-
`
`equately reflects circulating arterial blood concentrations. For
`practical purposes. most drug disposition studies use venous
`blood samples. This may require that the pharmacokinetic anal-
`ysis be somewhat qualified. Arterial and capillary blood concen-
`trations may differ markedly from venous blood concentrations
`of many drugs (10). The AUC of arterial versus venous blood is
`expected to be identical for a non-clearing organ and thus the
`principal difference expected is in distribution volumes. Phys-
`iologically, organ uptake of drugs occurs, of course, from the
`arterial blood. The clearance models described subsequently are
`based on arterial-venous extraction.
`
`D. Plasma (or blood) concentration data following intravenous in-
`jection provide partial characterization of drug disposition prop-
`erties. Accurate assessment of volumes of distribution, distri-
`
`bution clearance (CID), and systemic clearance (01,) can only be
`attained with intravenous washout data. The kinetic relation-
`
`ships will be presented in greater detail in a later section. Three
`dosage levels should be administered to span the usual thera-
`peutic range of the drug to permit assessment of possible dose-
`dependence (nonlinearity).
`Plasma (or blood) concentration data following oral doses of the
`drug in solution add additional pharmacokinetic parameters
`related to absorption and intrinsic clearance. The doses (or re-
`sultant plasma or blood concentrations of drug) should be com-
`parable to those from the intravenous doses. These data permit
`assessment of linearity of either oral clearance (Clam) or avail-
`ability {FF*), and the minimum transit time for absorption
`(-5,). If relevant, additional study of other dosage forms and
`routes of administration should be made. For these, the FDA
`guidelines for bioavailability studies should be consulted (11).
`Plasma protein binding and red cell partitioning should be
`measured over the expected range of plasma drug concentra-
`tions. Both rate and degree of binding and uptake are important.
`
`

`

`Drug Diaposition Data
`
`f 643
`
`5-"O
`
`1.0
`
`,ug/ml
`SERUMGENTAMICJN(XJNCENTRATION.
`
`
`
`0
`
`2
`
`4
`
`6
`
`8
`
`12
`i0
`T? ME . days
`
`14
`
`f6
`
`18
`
`20
`
`22
`
`FIGURE 1. Plasma concentration versus time profile for gentamicin disposi-
`tion during multiple dosing in a patient showing the prolonged terminal
`phase caused by strong tissue binding. This type of data was characterized
`with a two-compartment model (insertJ which included predictiori of drug
`remaining in body at time of death of patients. Data from Reference 14.
`
`These data should be obtained at 37°C. This information may
`be needed for interpretation or normalization of clearances and
`nonlinear disposition patterns.
`G. Urinary excretion rates of drug {as a function of time, dose and
`route of administration} should be measured to accompany the
`above studies. This is often a major route of drug elimination
`and analyses permit quantitation of renal clearance (CIR). Ad»
`ditional analyses of other excreta or body fluids (feces, milk, bile,
`saliva) if feasible and relevant may permit determination of
`other elimination or distribution clearances.
`
`H. Many drug metabolites are either pharmacologically active or
`otherwise of pharmacokinetic interest. Oxidation products such
`as hydroxylated or demethylated metabolites are most com-
`monly either active or t0xic (12). Their measurement will allow
`evaluation of AUC and transit time and perhaps permit quan-
`titation of metabolite formation and disposition clearances.
`I. Multiple-dose and steady-state experiments are necessary if this
`is the mode of therapeutic use of the drug. Comparative single-
`
`

`

`644 I Drug Disposition Data
`
`300
`
`cu
`
`E
`
`§
`“IJ 200
`l—
`a
`._
`
`g
`
`D 100
`E
`o
`—
`D
`a
`
`-'
`
`I'-
`
`.
`
`'
`
`.'
`
`I
`
`"
`.I'
`
`u
`
`..
`
`..
`I
`
`.-
`ll-
`I
`
`0 Io
`100
`200
`300
`
`MEASURED AMOUNT IN THE BODY, mg
`
`FIGURE 2. Correlation of gentamicin accumulation in the body determined
`by pharmacokinetic analysis of serum concentration data (see Figure I} and
`by direct analysis of body tissues obtained at autopsy from the same patients
`who were evaluated pharmacokinetically prior to death. Dotted line indicates
`perfect correlation. Data from References 14 and 15.
`
`and multiple-dose studies may permit further assessment of
`linearity andfor allow determination of chronic drug effects such
`as enzyme induction {13), unuSual accumulation (14), or self-
`induced alterations in disposition. For example, aminoglycoside
`uptake into tissues is extremely slow and was difficult to assess
`from single-dose studies. Multiple-dose washout measurements
`(Figure 1} led to observation of a slow disposition phase which
`was the result of tissue accumulation (14).
`
`J. Body tissue analyses add reality and specificity to drug distri-
`bution characteristics. Comprehensive studies in animals per-
`mit detection of unusual tissue affinity while generating parti-
`tion coefficients (Kw) for individual tissues (Vti). This can lead
`to complete physiologic models for the drug in each species
`studied (1,2). Autopsy or biopsy studies in man may extend or
`complement pharmacokinetic expectations. This approach was
`found to be extremely helpful (see Figure 2) in confirming the
`
`

`

`Drug Disposition Data I 645
`
`strong tissue binding of aminoglycosides in man which was
`anticipated on the basis of serum concentration profiles {Figure
`1, Ref. 15).
`K. Comparable or partial drug disposition studies in patients with
`various diseases form the basis of clinical pharmacokinetics.
`Perturbations in organ function, blood flow, or response will often
`alter drug disposition which may warrant quantitative charac-
`terization. General principles may not always apply and each
`drug needs individualized study. For example, while hepatic
`dysfunction may diminish the rate of oxidation of many drugs
`such as most benzodiazepines, some compounds such as loraze-
`parn are predominantly metabolized by glucuronide formation,
`a process largely unaffected by liver diseases such as cirrhosis
`(16). Each disease state may require evaluation of direct effects
`on pharmacokinetic processes such as changes in renal drug
`clearance caused by renal disease. However, indirect changes
`also require attention, such as the effects on both distribution
`and clearance caused by altered plasma protein binding (17).
`
`This list is meant to be comprehensive. Many drug disposition ques-
`tions may be resolved from selected, limited studies and alternative
`types of information may permit some experimental procedures to be
`omitted and validate various assumptions. However, it is the inves-
`tigator's obligation to adequately assess the literature, to make no
`unwarranted assumptions, and to satisfy the demands of rigorous and
`precise experimentation.
`
`Drug Assays
`
`There are several common concerns in the employment of various
`drug analysis techniques. Certainty in measurement of drugs or me-
`tabolites is a major sine qua non in pharmacokinetics and deserves
`considerable attention. 'Ib start, it is obvious that the assay method
`must be specific, sufficiently sensitive, and precise for the intended
`range of drug concentrations, especially in the presence of metabolites,
`secondary drugs, and in the occurrence of a disease state. Microbiol-
`ogical assays are notoriously unreliable in many of these regards.
`Other antibiotics often interfere in detection of the main drug. Active
`metabolites such as the desacetyl form of some cephalosporins (18)
`may be included in the measurements unless prior separation is made
`of the two active compounds. Limited microbiological sensitivity ini-
`tially prevented adequate characterization of gentamicin in single-
`dose studies (14). An extreme case of metabolite inclusion is in use of
`
`

`

`646 I Drug Disposition Data
`
`radioisotopic tracers; total radioisotope counts generally yield total
`drug and metabolite activity and provide minimal pharmacokinetic
`data. Separation of parent drug and individual metabolites is required
`for pharmacokinetic specificity. Microbiologic, enzymatic, and ra-
`dioimmunoassays may require preparation of standards in each pa-
`tient’s blank plasma for accurate pharmacokinetic data.
`Coupled with assay reliability is concern for the stability of drug in
`biological specimens, even in the frozen state. An unusual case is
`ampicillin which is less stable frozen than when refrigerated (19).
`Same drug esters such as hetacillin (a prodrug of ampicillin}, continue
`hydrolyzing in blood and during the bioassay, and imprudent handling
`of the blood specimens can confound the true disposition profiles of
`both prodrug and drug (20). Measurement of drug stability in blood
`will complement the pharmacokinetic profiling of a drug in discerning
`whether drug clearance can occur directly from blood or whether
`exposure to other body organs is required.
`
`Sample Timing
`
`Appropriate pharmacokinetic evaluation requires properly timed
`specimens. The simplest and least ambiguous experiment is the de-
`termination of systemic plasma clearance at steady-state:
`
`CI_ = k,th
`
`{Eq. 1)
`
`where k0 is the infusion rate and Cf is the steady-state plasma con-
`centration. For this equation to apply, the infusion period must be
`sufficiently long to allow steady-state to be attained.
`“
`A specific cempartmental type of analysis requires multiple blood
`samples to be collected during each phase of drug disposition. More
`frequent samples are needed for more rapid exponential phases. A
`pilot study or other preliminary data is usually necessary to aid in
`design of more extensive studies.
`A common and severe problem in applied pharmacokinetics is the
`inadequate or incomplete measurement of drug washout from the
`system. This is often caused either by premature termination of sam-
`ple collection or by analytical limitations. The ‘true’ terminal dispo-
`sition phase must be examined in order for most aspects of the phar-
`macokinetic treatment and interpretation to be accurate. For example,
`the early distributive phase of aminoglycoside disposition had long
`been acoepted as the only phase, yet more sensitive radioimmunoas-
`says, lengthier studies, and evaluation of multiple-dose washout re-
`vealed the slower phase of prolonged drug release from tissues (see
`Figure 1).
`
`

`

`Drug Disposition Data l 647
`
`The two principal model-independent, physiologic parameters in
`pharmacokinetics, systemic clearance and steady-state volume of dis-
`tribution, are calculated by use of the area under the plasma concen-
`tration versus time curve {AUG} and the area under the moment curve
`
`{AUMC}. Both area values require extrapolation of plasma concentra-
`tions to time infinity, and the AUMC is, in particular, prone to error
`from an inaccurate terminal slope. If analytical or ethical constraints
`limit blood sample collection and assays, saliva concentration moni-
`toring and extended urine collection may aid in defining the terminal
`disposition slope while adding One or two other pharmacokinetic pa-
`rameters to the analysis.
`The “midpoint” {6] is generally the most desirable time to collect
`blood samples to match an excretion interval to assess a time-depend-
`ent clearance process:
`
`Clearance :
`
`Excretion Rate A Amount Excreted
`6
`"
`AUC
`
`(Eq. 2)
`
`The arithmetic mean time is acceptable for slow processes but errors
`will be incurred if the kinetic process produces rapid changes in
`plasma concentrations. The mean transit time (t) of the excretion
`interval provides a true time at which the blood sample should be
`collected to yield an accurate C and time-average clearance (21,22) for
`exponential processes:
`
`‘2
`AUMC = AUG-t = 6-?
`
`(Eq. 3)
`
`This requires foreknowledge of the shape of the plasma concentration
`versus time curve over the excretion interval in order to estimate the
`
`time of occurrence of t. Curve-fitting may permit this to be done
`retrospectively.
`It is common that an early exponential phase of drug disposition is
`missed because of infrequent blood sampling. For a polynomial curve
`with intercepts, Ci, and slopes, ii, the total AUC is:
`
`AUC = Eton.)
`
`[Eq. 4)
`
`If the initial distributive phase is missing (Clan, then the error
`incurred in calculation of a clearance parameter (Clearance =
`DoseiAUC) is:
`
`% of Cl Error = 100 x (engrave
`
`{Eq. 5)
`
`Different degrees of error will be produced in the values of the volumes
`of distribution and distribution clearance as can be discerned by anal-
`ogous inspection of later equations.
`
`

`

`648 3 Drug Disposition Data
`
`Basic Physiologic Models
`
`The evolution of complete physiologic models (1—3) and clearance
`concepts applied to perfused organ systems (23,24) with the restric~
`tions incurred by the limited visibility of most blood or plasma drug
`disposition profiles has led to the employment of partial physiologic
`models for description of pharmacokinetic data. One such model
`is
`shown in Figure 3. Its construction and use should be viewed with
`some conceptual flexibility. The concepts described in this section will
`apply to linear or first-order processes unless otherwise stated.
`Volumes. The drug in blood or plasma (0,) is considered to be part
`of the central compartment (Vcl. The minimum value of Vc is plasma
`volume (Vp), but because drug either diffuses rapidly out of plasma or
`the number of early time data are limited, a Vt larger than plasma
`volume is frequently observed.
`Drug which is located outside of VP or Vc is, of course, present in
`tissues. The apparent volume of the tissue compartment {VT} has two
`basic determinants: physiologic weight or volume of each tissue (Va)
`and partitionfdistribution factors (K3,). In analysis of plasma concen-
`tration versus time profiles, tissues must commonly be merged to-
`gether (including the clearing organs); thus:
`
`v, = Bug-v“)
`
`(Eq. 5)
`
`This leads to definition of one of the primary model-independent,
`physiologic parameters, volume of distribution at steady-state {V’g‘}:
`
`V3” = V: + VT
`
`(Eq. 7)
`
`Q C
`
`1D
`
`I
`——'—"
`KP '
`1
`l
`
`I
`.'
`I V,
`
`:
`
`Cw
`
`
`
`Clint
`
`FIGURE 3. Basic physiologic pharmacokinetic model for drug distribution
`and elimination. Symbols are defined in the text. The clearance organ is
`pharmacokinetically perceived as separate from other compartments for drugs
`with high intrinsic clearances (Clml allowing characterization of the first-pass
`input. Low clearance drugs may not exhibit separate distribution and clear-
`ance properties for the clearance organ (see Figure 1].
`
`

`

`PHYSIOLOGICAL DETERMINANTS OF DRUG PARTITION OR
`TABLE 1.
`DISTRIBUTION RATIOS BETWEEN TISSUES AND PLASMA
`
`Drug Disposition Data f 649
`
`Active Transport
`Donnan Ion Effect
`
`pH Differences
`Plasma Protein Binding
`Tissue Binding
`Lipid Partitioning
`
`If plasma (fup) and tissue (fut) binding are the sole determinants of
`nmhomogeneous distribution of drug in the body, then one definition
`of V3” is:
`
`f
`vg=vp+f—"lol
`“P
`
`(Eq.8}
`
`as proposed by Gillette (25} where fu is the fraction of drug unbound,
`and V‘ is the volume or the weight of all tissues except plasma. Other
`factors may also contribute to the partition coefficient of drugs be-
`tween tissues and plasma (Table 1}. Since by definition VP and Vt
`comprise total body weight (TBWt):
`
`then the quotient of:
`
`TBWt = vp + v‘
`
`KD = Vg‘ITBWt
`
`{Eq. 9)
`
`[Eq. 10)
`
`defines the distribution coefficient (KD), a physicochemicab’physiolog‘ical
`measure of the average partitiOn coefficient of the drug throughout
`the body. Approximate values of KD and the primary rationalization
`of the size of KD are provided in Table 2 for various oommon drugs.
`One qualification of V3“ is needed. Drug equilibration between
`plasma and tissue of a clearing organ also encompasses the blood flow
`(QR) and intrinsic clearance (Clint) (26). For hepatic tissue this yields
`the following relationship between the true partition coefficient (Km)
`and the apparent value which would be measured at steady-state
`(K‘gh):
`
`KW =K‘;,;[1+
`
`
`Clm
`QH
`
`(Eq. 11)
`
`Distribution Clearance. The least developed and appreciated ele-
`ment of the basic pharmacokinetic properties of drugs is the distri-
`bution clearance (CID) or intercompartmental clearance. This term
`reflects the flowftransfer property of drugs, repreSenting movement in
`
`

`

`650 I Drug Disposition Data
`
`TABLE 2. DISTRIBUTION COEFFICIENTS (Kn) FOR VARIOUS DRUGS
`AND PROBABLE PHYSIOLOGIcfPHYSICOCHEMICAL CAUSE
`
`Drug
`
`lndocyanine Green
`
`K ...
`_ L6”
`TBWI
`n
`
`0.06
`
`lnulin
`
`0.25
`
`Ampicillin
`
`0.25
`
`Theophylline
`
`Antipyrine
`
`Gentamicin
`
`Tetracycline
`
`Diazepam
`
`Digoxin
`
`0.5
`
`0.6
`
`1.1
`
`1.6
`
`1.7
`
`8.0
`
`Imipramine
`
`10.0
`
`Explanationflndicntion
`
`Strong binding to plasma
`proteins and limited
`extravascular
`
`permeability.
`Limited distribution into
`plasrna and interstitial
`fluid owing to large
`molecular weight (5500}
`and lack of lipid
`solubility.
`Limited intracellular
`distribution owing to
`poor lipid solubility.
`Distribution primarily into
`total body water.
`Fairly equal distribution
`into total body water.
`Strong tissue binding
`common to
`
`aminoglycosides.
`Strong tissue binding to
`calcium in bone.
`
`Appreciable lipid
`partitioning.
`Strong binding to Na ‘fK'
`Transport ATPase in cell
`membranes.
`
`Strong tissue binding
`common to many basic
`amines.
`
`and out of physiological spaces. The simplest assumption made in
`constructing a generalized model
`is that distribution clearance is
`equal in both directions; that is, clearance in equals clearance Out of
`tissues.
`Renkin has characterized distribution clearance in terms of trans-
`
`capillary movement of small molecular weight substances (27). The
`model he proposed is depicted in Figure 4. Drug transfer from blood
`
`

`

`Drug Disposition Data
`
`1 651
`
`to tissues is represented by flow down a cylindrical tube (Q) with
`permeability (P) determined by diffusion across the capillary. Distri-
`bution clearance is thus defined by flow and permeability according to
`the relationship:
`
`01., = Q(1—e"”°)
`
`(Eq. 12)
`
`Compounds with high tissue permeability will exhibit a limiting ClD
`of Q:
`
`lim 01D = Q
`Pan-rm
`
`while those with low permeability are limited by P:
`
`lim Cln = P
`P—II-O
`
`(Eq. 12a)
`
`(Eq. 12b)
`
`One of the determinants of the capillary permeability of drug is mo-
`lecular weight, as indicated in Table 3 (28). This description of distri-
`bution clearance, while based on capillary transfer, demonstrates its
`physiological and physicachemical basis. Other processes may be rate-
`limiting for specific drugs where the tissue barriers are cell mem-
`branes rather than blood vessel walls (29).
`
`0
`
`G
`
`c. 9— v
`
`P
`
`cu
`
`Cone
`
`Distance
`
`FIGURE 4. Model for distribution clearance where blood flow (Q) along the
`cylindrical tube and capillary permeability (P) are the primary determinants
`of drug loss from arterial blood (0). Drug concentration in the tube will
`decline monoexponentially according to distance (length) along the tube
`emerging at the venous concentration (0,).
`
`

`

`652 1’ Drug Disposition Data
`
`TABLE 3.
`
`PERMEABILITY 0F MUSCLE CAPILLARIES TO WATER-
`SOLUBLE MOLECULES
`
`Radius of
`Equivaient
`Sphere {A}
`
`1.6
`3.6
`4.4
`5.6
`
`15.2
`19
`31
`
`Diffusion Coefficient
`In waterl D
`Across
`(cmafseci
`Capillary, P
`x 105
`{cm3fsec. 100g)
`3.20
`3.7
`1.95
`1.83
`0.91
`0.64
`0.74
`0.35
`0.56
`0.24
`
`0.21
`0.15
`0.094
`0.085
`
`0.036
`0.005
`0.001
`(0.001
`
`Molecular
`Weight
`18
`60
`180
`342
`594
`
`5.500
`17,000
`69,000
`69.000
`
`Water
`Urea
`Glucose
`Sucrose
`Raffinose
`
`Inulin
`Myoglobin
`Hemoglobin
`Serum Albumin
`
`From Reference 28.
`
`The CID can be perceived as a model-independent, physiologic pa-
`rameter when summed for all distribution processes:
`dlil
`
`(Eq.13)
`
`CID = Clm + Cl
`
`+ .... + cud,
`
`Thus, apparent three-compartment (Cldl2,Cld,3} distribution can be
`blended with two~compartment ClDby combining Clm and Clm values
`for the former model. In this context, CID becomes the total transcap-
`illary distribution clearance (30) with cardiac output as the limiting
`value (Q).
`Organ Clearance. The model shown in Figure 3 represents the
`common situation where drug must pass through a specific organ such
`as the liver or kidney in order for elimination to be effected. It does
`not apply in a situation such as enzymatic hydrolysis of the drug
`occurring in the blood. This type of model allows characterization of
`the dual role of blood flow (Q) and either biotransformation (VW, Km)
`or renal filtration (GFR) and transport (Tum, Tm) on removal of drug
`from the body and permits accurate representation of the effects of
`route of administration (e.g., first-pass effects) on drug disposition.
`Two types of clearing organ models have been proposed for hepatic
`elimination: the "Jar" Model (1—3.23) (Figure 5) and the “Tube” Model
`(31,32) (Figure 6). Both include blood flow for systemic drug access to
`the organ and, as shown in the figures, currently assume that free or
`unbound drug (C3 in plasma equilibrates with free drug in the tissue
`
`

`

`
`
`Con:
`
`Di 5 lance
`
`FIGURE 5. The "well-stirred” or “jar” model for hepatic uptake and metabo-
`lism {Vwi’Kml of drug where instantaneous venous and hepatic equilibration
`of unbound (Cr) drug is assumed. Inflow and outflow (Q) are assumed to be
`identical.
`
`
`
`Distance
`
`FIGURE 6. The "tube" or "parallel tube" model for hepatic uptake and me-
`tabolism (meKml of drug where venous concentrations (CV) decline monoex-
`ponentially as flow {Q} carries drug past homogenously distributed sites of
`biotransfonnation. The log-mean concentration (C) in the tube is indicated.
`
`653
`
`

`

`654 1" Drug Dispoaition Data
`
`available to enzymes (33,34). The Jar Model involves the assumption
`that drug in arterial blood {Ca} entering the clearing organ instants»
`neously equilibrates with the venous bleed drug concentration (CV).
`The Tube Model assumes that a drug concentration gradient exists
`down the tube with enzymes acting upon declining drug concentra-
`tions in the microenvironment.
`
`The Jar Model yields the following relationship for hepatic clear-
`ance to account for the variables in the system:
`
`=
`"'I' 2
`Q“ - a -CI
`
`01H Q—L—ufl+ fur 01m
`
`‘
`on ER
`
`(Eq.14}
`
`where intrinsic clearance is the ratio of Van“me for a linear biotrans-
`formatioa and ER is the Extraction Ratio. Wilkinson and Shand (24)
`
`have depicted the various theoretical relationships among the deter-
`minants of ClH (Figure 7].
`The corresponding equation for ClH described by the Tube Model is:
`
`01,, = QHuHe—rup-cmu) : Qflosa
`
`(Eq. 15)
`
`Pang and Rowland (35a) have compared the two hepatic models in
`int
`terms of the effects of QH and Cl on 01,.I and ER. Both models predict
`a lower limit of:
`
`and upper value of:
`
`lim ClH = fun-Cl...“
`CIR—I‘- 0
`
`lim Cl” = QH
`
`Clrbx‘
`
`(Eq. 15a)
`
`[Eq. 15b)
`
`Thus the hepatic clearance of low clearance drugs is essentially equal
`to the product of intrinsic clearance and the fraction unbound in
`plasma (33). The maximum hepatic clearance will be organ blood flow.
`The two models diverge somewhat in characterizing intermediate
`clearance drugs. At the present time, it is uncertain which model is
`most generally appropriate for describing organ clearance. The Jar
`Model has had most extensive use in physiological pharmacokinetics
`(1—3).
`
`The organ clearance models provide definitions for two types of
`general clearance terms. Systemic clearance (CL) reflects any situation
`where drug is administered without its initially passing through the
`clearing organ. Intravenous, intramuscular, buccal, and subcutaneous
`injection of drugs yields plaSma concentration versus time data gov—
`erned by systemic clearance, e.g.:
`
`

`

`2.
`
`5
`
`2.0
`
`LE;
`
`IO
`
`ER
`
`LO
`0.9
`
`0.8
`
`0.?
`
`0.6
`0.5
`
`0.4
`/,/—e——r— 0'3
`E 0-5
`u, f 0-2
`1:
`0|
`0
`
`0
`
`0.5
`
`1.0
`
`I.5
`
`2.0
`
`2.5
`
`LIVER BLOOD FLOW. LITERJ’MIN
`
`LO
`