Second Edition
`
`APPLIED
`PHARMACOKINETICS
`Principles of Therapeutic Drug Monitoring
`
`Edited by
`
`William E. Evans, Pharm.D.
`Professor of Clinical Pharmacy & Pharmaceutics
`Chairman, Department of Clinical Pharmacy
`University of Tennessee
`Center for the Health Sciences
`Memphis
`and
`Director, Pharmaceutical Division
`St. Jude Children's Research Hospital
`
`Jerome J. Schentag, Pharm.D.
`Director, Clinical Pharmacokinetics Laboratory
`Millard Fillmore Hospital
`and
`Associate Professor of Pharmaceutics and Pharmacy
`State University of New York at Buffalo
`Buffalo
`
`William J. Jusko, Ph.D.
`Frofessor of Pharmaceutics and Pharmacy
`State University of New York at Buffalo
`Buffalo
`
`Editorial Assistant
`Hayes Harrison, M.A.
`Pharmaceutical Division
`Si. Jude Children's Research Hospital
`Memphis
`
`Applied Therapeutics, Inc.
`Spokane, WA
`1986
`
`2
`Guidelines for Collection
`and Analysis
`of Pharmacokinetic Data
`
`William J. Jusko, Ph.D.
`
`Efforts in both theoretical and applied pharmacokinetics over the
`past decade have emphasized the utilization of the principles of phys(cid:173)
`iological pharmacokinetics and the use of noncompartmental
`approaches to analysis of drug disposition data. Physiological phar(cid:173)
`macokinetics involves the deployment of pharmacokinetic models and
`equations based on anatomical constructions and functions such as
`tissue masses, blood flow, organ metabolism and clearance, specific
`drug input rates and sites, and processes of partitioning, binding, and
`transport. While the complete applications of physiologic systems
`analysis may require extensive models, 1 even the simplest of phar(cid:173)
`macokinetic treatments should have a physiologic basis for interpre(cid:173)
`tation. Noncompartmental techniques in pharmacokinetics can serve
`in this regard. This term applies to curve analysis methods of data
`treatment which do not require a specific model and which yield the
`prime pharmacokinetic parameters such as systemic clearance (CL)
`and steady-state volume of distribution (V8,) which summarize the
`major elimination and distribution properties.
`This chapter is intended to provide an overview of major components
`of experimentally-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 pharma(cid:173)
`cokinetic studies. 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 de(cid:173)
`signing animal and (or) human experiments in pharmacokinetics and
`in reviewing drug disposition reports; with greater elaboration, it has
`served as a basis for a graduate course in physiological
`pharmacokinetics.
`
`9
`
`
`
`Apotex v. Novartis
`IPR2017-00854
`NOVARTIS 2041
`
`

`

`10
`
`Chapter 2: Collection and Analysis
`
`Chapter 2: Collection and Analysis
`
`11
`
`CONTEXT OF PHARMACOKINETICS
`A pharmacokinetic analysis must be made in context of, be consis(cid:173)
`tent 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 and integration of principles of
`physiology, pharmacology, biochemistry, physicochemistry, analytical
`methodology, mathematics, and statistics. Pharmacokinetics has de(cid:173)
`rived from these disciplines, and the relevant aspects of many of these
`areas must be considered in reaching any conclusions regarding a par(cid:173)
`ticular 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
`clearance. A drug disposition profile must be correlated with studies
`of structure-activity, disposition in alternative species, perfused organ
`experiments, tissue or microsomal metabolism, tissue drug residues,
`disease-state effects, and pharmacology and toxicology. For example,
`a much larger LD50 for oral doses of a drug compared with parenteral
`administration may be indicative of either poor gastrointestinal ab(cid:173)
`sorption Clow aqueous solubility?) or a substantial first-pass effect.
`Drug metabolism pathways may differ between species, but the bio(cid:173)
`transformation rate (V mox and Km) of microsomes, homogenates, or
`perfused organs can often be applied directly to whole-body disposition
`rates and often correlate between 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(cid:173)
`sons. Experienced judgment is usually required in the final interpre(cid:173)
`tation of any experimental findings and analysis.
`
`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 af(cid:173)
`fects 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:
`
`A. The dosage form should be pre-analyzed. All calculations stem
`from knowledge of the exact dose given [e.g., CL = dose/ AUC, (area
`under the plasma concentration-time curve)]. Most commercial dosage
`forms are inexact, and content uniformity should be examined. Vials
`
`or ampules of injectables typically contain some overage and require
`analysis or aliquoting for administration of a precise dose. Solid dosage
`forms are required to yield an average of the stated quantity of drug
`with limited variability, but both injectable and solid forms may be
`inaccurate for pharmacokinetic purposes. Manninen and Koriionen4
`provide an excellent example of both the variability and lack of stated
`quantity of digoxin in many commercial tablets. One product contained
`a range of 3_9% to 189% of the stated 0.25 mg dose of digoxin, while
`the most umform product, Lanoxin, exhibited 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. Poorly soluble
`drugs are 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 admin(cid:173)
`i~tration. For ease in subsequent calculations, pharmacokinetic equa(cid:173)
`tions can be used, to correct data from short-term infusion studies to
`the intercepts expected after bolus injection. The particular materials
`used in drug administration may cause loss of drug. In one of the most
`dramatic examples, MacKichan et al.5 found immediate loss of about
`50% of a dose of i.ntravenous diazepam by adsorption during passage
`through the plastic tubing of an infusion set. Inline filtration can also
`significantly reduce the potency of drugs administered intravenously
`in small doses. 6
`C. Attention to methods and sites of blood collection is needed. Ideally,
`blood sa~ples sho~ld be collected by direct venipuncture in clean glass
`t~bes without anticoagulant. Otherwise, the presence of possible ar(cid:173)
`tifacts should be tested. In the absence of any in vitro artifacts, serum
`and plasma concentrations are usually identical, and these terms are
`commonly used interchangeably. However, there are several reasons
`that they ~a~ not be identical. For example, the presence of heparin
`can result m mcreased free fatty acid concentrations causing altered
`plasma-protein binding. 7 Also, the type of blood collection tube or an(cid:173)
`ticoa~lant may be a factor.8 If protein binding is temperature depen(cid:173)
`den:, it may be. necessary to centrifuge the blood sample at 37°C to
`avoid changes m red cell-plasma distribution of some compounds.9
`The~e ~roble~s primarily pertain to weak bases such as propranolol
`and 1m1p~amme for which binding to cx1-acid glycoprotein is apprecia(cid:173)
`ble and displacement alters plasma-red cell drug distribution.
`Plasma or serum protein binding and red cell partitioning should
`be ~easured at 37°C over the expected range of plasma drug concen(cid:173)
`!rat1ons. Both _ra~e and degree of binding and uptake are theoretically
`1~portant. Th1_s m.formation may be especially needed for interpreta(cid:173)
`tion or normahzat1on of nonlinear disposition patterns.
`
`
`
`

`

`12
`
`Chapter 2: Collection and Analysis
`
`Chapter 2: Collecti.on and Analysis
`
`13
`
`Sometimes the site of blood collection and the presence of a tourni(cid:173)
`quet can alter the composition of the blood sample: serum proteins,
`calcium, and magnesium concentrations rise by 5% to 13% during ven(cid:173)
`ous stasis.10
`One of the major assumptions employed in most pharmacokinetic
`studies is that venous blood collected from one site adequately reflects
`circulating arterial blood concentrations. For practical purposes, ven(cid:173)
`ous blood samples are usually collected. The pharmacokinetic analysis
`may need to be somewhat qualified, because arterial and capillary
`blood concentrations may differ markedly from venous blood concen(cid:173)
`trations of many drugs.11 The AUC of arterial versus venous blood is
`expected to be identical for a non-clearing organ, and thus the prin(cid:173)
`cipal difference expected is in distribution volumes. Physiologically,
`organ uptake of drugs occur from the arterial blood, and clearance
`organ models are based on arterial-venous extraction principles.
`D. Serum (or blood) concentration data following intravenous in(cid:173)
`jection (bolus or infusion) provides partial characterization of drug
`disposition properties. Accurate assessment of volumes of distribution,
`distribution clearance (CL0 ), and systemic clearance (CL) can best be
`attained with intravenous washout data.
`E. Serum (or blood) concentration data following oral doses of the
`drug in solution and common dosage forms provides additional phar(cid:173)
`macokinetic parameters related to absorption and intrinsic clearance.
`The doses (or resultant serum or blood concentrations of drug) should
`be comparable to those from the intravenous dose. These data permit
`assessment of either oral clearance (CL0 • 01) or bioavailability (F), and
`of the transit time for absorption (t0 ). If relevant, other routes of
`administration should be studied. For these, the FDA guidelines for
`bioavailability studies should be consulted.12
`F. Three dosage levels (both oral and intravenous) should be admin(cid:173)
`istered to span the usual therapeutic range of the drug to permit as(cid:173)
`sessment of possible dose-dependence (nonlinearity) in absorption, dis(cid:173)
`tribution, and elimination.
`G. Urinary excretion rates of drug (as a function of time, dose and
`route of administration) should be measured to accompany the above
`studies. Urinary excretion is often a major route of drug elimination,
`and analyses permit quantitation of renal clearance (CLR). Collection
`of other excreta or body fluids (feces, bile, milk, saliva) may permit
`determination of other relevant elimination or distributional
`pathways.
`H. Many drug metabolites are either pharmacologically active or
`otherwise of pharmacokinetic interest. Phase I products such as hy(cid:173)
`droxylated or demethylated metabolites are most commonly either ac(cid:173)
`tive or toxic. 13 Their measurement will allow evaluation of AUC and
`
`transit time and perhaps permit quantitation of metabolite formation
`and disposition clearances.
`I. Multiple-dose and steady-state experiments are necessary if ther(cid:173)
`apeutic use of the drug relies on steady-state concentrations. The du(cid:173)
`ration of multiple-dosing in relation to the terminal half-life is crucial
`for ascertaining applicability to steady-state conditions. Comparative
`single- and multiple-dose studies permit further assessment of line(cid:173)
`arity and (or) allow determination of chronic or time-dependent drug
`effects such as enzyme induction, 14 unusual accumulation, 15 or drug(cid:173)
`induced alterations in disposition. For example, aminoglycoside up(cid:173)
`take into tissues is extremely slow and difficult to assess from single(cid:173)
`dose studies. Multiple-dose washout measures (Figure 2-1) led to ob(cid:173)
`servation of a slow disposition phase which was the result of tissue
`accumulation and release.16
`J. Tissue analyses add reality and specificity to drug distribution
`characteristics. Comprehensive studies in animals permit detection of
`unusual tissue affinities while generating partition coefficients (K ;)
`for individual tissues (Vi;). This can lead to complete physiologic
`models for the drug in each species studied. 1•2 Autopsy or biopsy stud-
`
`Cenlral
`
`Dose
`
`Comp1r1meen1 (
`
`Tisoue
`
`Uplake Q Compar1menl
`
`_, .
`
`Release
`
`•
`
`-
`i Renal Clearance
`
`r-
`
`.
`
`5.0
`
`I :i.
`1
`~
`E t; 1.0
`
`C
`0
`(.)
`
`C ·o ·e ~ 0.4
`C .. C,
`
`I
`I
`
`0.2
`
`E
`:3
`Qi
`en
`
`t 80 mg
`t
`Doses
`0.1 ~-!--f-~"---~--:~~--L-..........;L.::-...:.i........:.:..:1---:.1....:.::::~
`4
`12
`0
`2
`6
`8
`10
`14
`16
`20
`22
`
`Time, Days
`
`~IGURE ~-1. Pla~ma_ concentration-time profile for gentamicin disposition dur(cid:173)
`ing multipl~ dosm~ 1~ a patient showing the prolonged terminal phase caused
`by strong tissue bmdmg. These data were characterized with a two-compart(cid:173)
`ment m_odel (inset) which included prediction of drug remaining in the body
`at the time of death of the patients. Data from reference 15.
`
`
`
`

`

`14
`
`Chapter 2: Collection and Analysis
`
`Chapter 2: Collection and Analysis
`
`15
`
`ies in man may extend or complement pharmacokinetic expectations.
`This approach was found to be extremely helpful (Figure 2-2) in con(cid:173)
`firming the strong tissue binding of aminoglycosides in man which
`was anticipated on the basis of serum concentration profiles (Figure
`2-1).16
`K. Suitable drug disposition studies in patients with various dis(cid:173)
`eases and ages or given secondary drugs form the basis of clinical
`pharmacokinetics. Perturbations in organ function, blood flow, or re(cid:173)
`sponse will often alter drug disposition in a way that may warrant
`quantitative characterization. General principles may not always ap(cid:173)
`ply, and each drug needs individualized study. For example, while
`hepatic dysfunction may diminish the rate of oxidation of many drugs,
`some compounds such as oxazepam and lorazepam are predominantly
`metabolized by glucuronide conjugation, a process largely unaffected
`by liver diseases such as cirrhosis.17 Each disease state may require
`evaluation of direct effects on pharmacokinetic processes such as
`changes in renal clearance caused by kidney disease. However, indirect
`changes also require attention such as the effects on both distribution
`and clearance caused by altered plasma protein binding. 18 Finally,
`commonly encountered patient factors such as smoking habit19 and
`
`30()~
`
`CJ)
`E
`:,.-"
`
`._
`
`8 CD
`~ 200 ~
`.....
`z
`
`•• •
`•
`•
`
`•••• •
`
`~ i ,oo~
`
`0
`UJ
`
`t3
`15
`w a:
`
`CL
`
`-
`
`_._.
`• o• 0
`
`100
`
`200
`
`I
`300
`
`'
`MEASURED AMOUNT IN Tl-IE BODY, mg
`
`FIGURE 2-2. Correlation of gentamicin accumulation in the body determined
`by pharmacokinetic analysis of serum concentration data (see Figure 2-1) 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 15 and 16.
`
`obesity may cause unusual changes in drug disposition and require
`specific study and notation in patient surveys.
`L. Many questions of drug disposition can be resolved from selected,
`carefully designed studies, and alternative types of information may
`be sufficient to validate various assumptions and permit some experi(cid:173)
`mental procedures to be omitted. However, it is the investigator's ob(cid:173)
`ligation to adequately assess the literature, to avoid unwarranted as(cid:173)
`sumptions, and to satisfy the demands of experimental strategies that
`would resolve a proposed hypothesis.
`
`DRUG ASSAYS
`
`Certainty in measurement of drugs and their metabolites is a sine
`qua non in pharmacokinetics and deserves considerable attention.
`Guidelines for quality assurance in laboratory analyses have been con(cid:173)
`cisely sumITJarized by the American Chemical Society.20 It is now com(cid:173)
`monplace to report the linearity, the coefficient of variation of the
`assay at low and high drug concentrations, the minimum level of de(cid:173)
`tection, and the procedures used to assure specificity and stability,
`especially in the presence of metabolites, secondary drugs, and in spec(cid:173)
`imens from diseased patients. Microbiological assays are notoriously
`unreliable. Other antibiotics often interfere in detection of the main
`drug. Active metabolites such as the desacetyl form of some
`cephalosporins21 may be included in the measurements unless prior
`separation is made of the two active compounds. An extreme case of
`metabolite inclusion is in the use of radioisotopic tracers; total radio(cid:173)
`isotope counts generally yield total drug and metabolite activity and
`possibly the products of radiolysis. Separation of parent drug and in(cid:173)
`dividual metabolites is required for pharmacokinetic specificity. Mi(cid:173)
`crobiologic, enzymatic, and radioimmunoassays are often of uncertain
`specificity, and matrix effects may require preparation of standards
`in each patient's pretreatment plasma. Most drug companies provide
`analytical-grade samples of their drugs (and sometimes metabolites)
`to qualified investigators upon written request.
`Sample Handling. Coupled with assay reliability is concern for the
`stability of drug in biological specimens, even in the frozen state. Am(cid:173)
`picillin is unusual in that it is less stable frozen than when refriger(cid:173)
`ated. 22 Some 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. Penicillamine is unstable in the
`presence of plasma proteins, and immediate deproteination after blood
`sample collection is necessary to avoid loss of reduced penicillamine
`prior to analysis.23 Measurement of drug stability in blood will com(cid:173)
`plement the pharmacokinetic characterization of drug by revealing
`
`
`
`

`

`16
`
`Chapter 2: Collection and Analysis
`
`Chapter 2: Collectwn and Analysis
`
`L1
`
`whether hydrolysis can occur in blood or whether exposure to other
`body organs is required. Additional concerns in handling samples from
`a pharmacokinetic study include labeling and record-keeping proce(cid:173)
`dures and documentation of specimen storage conditions.
`Sample Timing. Appropriate pharmacokinetic evaluation requires
`properly timed specimens. The simplest and least ambiguous experi(cid:173)
`ment is the determination of systemic plasma clearance during con(cid:173)
`tinuous infusion at steady state:
`CL = k0
`(Eq. 2-1)
`/ C._,
`where k0 is the infusion rate and c •• is the steady-state plasma or
`serum concentration. For this equation to apply, the infusion period
`must be sufficiently long (about five terminal disposition half-lives) to
`allow steady state to be attained. Alternatively, a loading dose or
`short-term infusion may be administered to more rapidly achieve
`equilibrium. 24
`Practical and cost-effective methods are available for designing op(cid:173)
`timal sampling strategies for kinetic experiments where, such as in
`the clinic, the number of specimens is limited.25 Optimal designs
`largely depend on the likely "true" model parameter values, the struc(cid:173)
`ture of the model, and the measurement error. A sequential approach
`has been advocated with pilot studies and a sampling schedule which
`distributes time points over the major phases of drug disposition as
`the first step. Subsequent experiments can then be designed to resolve
`a specific hypothesis.
`A common and severe problem in applied pharmacokinetics is the
`inadequate or incomplete measurement of drug washout from the sys(cid:173)
`tem, either because of premature termination of sample collection or
`because of analytical limitations. The "true" terminal disposition
`phase must be examined in order for most aspects of data treatment
`and interpretation to be accurate. For example, the early distributive
`phase of aminoglycoside disposition measured by bioassay had long
`been accepted as the only phase, yet more sensitive radioimmunoas(cid:173)
`says, lengthier sample collection, and evaluation of multiple-dose
`washout revealed the slower phase of prolonged drug release from
`tissues (Figure 2-1).
`The two summary physiologic parameters in pharmacokinetics,
`namely systemic clearance and steady-state volume of distribution,
`can be most easily calculated by use of the area under the plasma
`concentration-time curve (AUC) and the area under the moment curve
`(AUMC). Both area values require extrapolation of plasma concentra(cid:173)
`tions to time infinity, and the AUMC is, in particular, prone to exag(cid:173)
`gerated error from an inaccurate terminal slope.26 If analytical or
`ethical constraints limit blood sample availability, extended saliva or
`urine collection may aid in defining the terminal disposition slope
`
`earance =
`Cl
`
`(Eq. 2-2)
`
`clearance is linear), as the sample volume is large and u:~ (if renal
`
`.
`while adding one or two other pharmacokinetic par
`analysis. Urine may be particularly useful in this r:;e~r~ to the
`·
`f
`ne concen-
`trations o ten exceed plasma values by one or more ord
`magnitude.
`ers of
`The "midpoint" (C,.v) is generally the most desirable time to collect
`blood samples to match an excretion interval in order to assess a time(cid:173)
`dependent clearance process:
`Excretion Rate Amount Excreted
`= - ----,---c=--
`-
`Cav
`AUC
`The arithmetic mean time is acceptable for slow processes, but errors
`will be incurred if the kinetic process produces rapid changes in
`plasma concentrations.27 It is common to miss an early exponential
`phase of drug disposition because of infrequent blood sampling. For a
`polynomial curve with intercepts C; and slopes >-.;, the total AUC is:
`AUC = lC;lt..;
`(Eq.2-3)
`If the _initial distributive phase is missing (area = C1 / >,.1), then the
`error mcurred in calculation of a clearance parameter (CL = dose/
`AUC) is
`
`% of CL error = 100 x (C 1 / A1) / AUC
`
`(Eq.2-4)
`
`BASIC PHYSIOLOGIC PARAMETERS
`The evolution of complete physiologic models1 and clearance con(cid:173)
`cepts applied to perfused organ systems,28•29 with the restrictions in(cid:173)
`curred by the limited in vivo visibility offered by most blood or plasma
`dru~ disposition profiles, has led to the employment of partial physi(cid:173)
`ologic models for description of pharmacokinetic data. One such model
`is shown in Figure 2-3. Its construction and use should be viewed with
`some conceptual flexibility, and this material will apply to linear pro(cid:173)
`cesses unless stated otherwise.
`Volumes. The drug in blood or plasma (Cp) is considered to be part
`of the central comp.artment (Ve). The minimum value of Ve is plasma
`volume (Vp), but, either because drug diffuses rapidly out of plasma
`
`V' the number of early time data are limited, the Ve value often exceeds
`
`p·
`. Drug which is located outside of VP or Ve is, of course, present in
`tiss~es. The ~pparent volume of the tissue compartment (VT) has two
`basic determinants: physiologic weight or volume of each tissue (V .)
`and pa~tition or distribution factors (Kp;). In analysis of plasma co~(cid:173)
`c.entrat_1on-time profiles, tissues must commonly be clustered together
`(mcludmg the clearing organs) thus:
`
`(Eq.2-5)
`
`
`
`

`

`18
`
`Chapter 2: Collection and Analysis
`
`Chapter 2: Collection and Analysis
`
`19
`
`This equation leads to definition of one of the primary pharmacoki(cid:173)
`netic parameters with a physiologic basis, volume of distribution at
`steady state (V55):
`
`v •• = V, + VT
`If plasma and tissue binding are the sole determinants of nonhomo(cid:173)
`geneous distribution of drug in the body, then one definition of v •• is
`fup V
`v .. =VP+ f
`' T
`ut
`where fup and fut are the fractions of drug unbound in plasma and
`tissue.30 Other factors may also contribute to the apparent partition
`coefficient of drugs between tissues and plasma (Table 2-1). Since, by
`definition, VP and ~Vti comprise total body weight (TBWt)
`TBWt = V., + l Vt1
`
`(Eq. 2-6)
`
`(Eq.2-7)
`
`(Eq.2-8)
`
`then the quotient of
`
`K 0 = V., / TBWt
`(Eq.2-9)
`defines the distribution coefficient (K0 ), a physicochemical and phys(cid:173)
`iological measure of the average tissue:plasma ratio of the drug
`throughout the body. Approximate values of K0 and the primary ra(cid:173)
`tionalization of the size of K0 are provided in Table 2-2 for several
`common drugs. Normalization of v •• for TBWt is thus of value for
`
`generating the K0 and for making interindividual interspecies2 com(cid:173)
`parisons of this parameter.
`One qualification of Vss is needed. Drug equilibration between
`plasma and tissue of a clearing organ is affected by blood flow (QH)
`and intrinsic clearance (CLint).31 For hepatic tissue, this yields the
`following relationship between the true partition coefficient (Kph) and
`the lower, apparent value which would be experimentally measured
`at steady state (K~tP):
`
`K = Kcxp (1 + CL;"')
`
`ph
`
`ph
`
`QH
`
`(Eq. 2-10)
`
`Distribution Clearance. The least developed and appreciated ele(cid:173)
`ment of the basic pharmacokinetic properties of drugs is the distri(cid:173)
`bution clearance (CL0 ) or intercompartmental clearance. This term
`reflects the flow or permeability property of drugs between plasma
`and tissue spaces. The simplest assumption made in constructing a
`generalized model is that distribution clearance is equal in both di(cid:173)
`rections in and out of tissues.
`Renkin has characterized distribution clearance in terms of trans(cid:173)
`capillary movement of small molecular weight substances.32 The
`model proposed is depicted in Figure 2-4. Drug transfer from blood to
`tissues is represented by flow down a cylindrical tube (Q) with perme(cid:173)
`ability (P) determined by diffusion across the capillary. Distribution
`clearance is thus defined by flow and permeability according to the
`following relationship:
`
`(Eq. 2-11)
`
`Compounds with high tissue permeability will exhibit a limiting CL0
`of Q, while those with low permeability are limited by P. These con(cid:173)
`cepts have been applied by Stec and Atkinson33 to a multicompartment
`model of procainamide and NAPA disposition and used to predict the
`extent of hemodynamic changes caused by hemodialysis. The flow or
`
`TABLE 2-1. PHYSIOLOGICAL DETERMINANTS OF DRUG PARTITION OR
`DISTRIBUTION RATIOS BETWEEN TISSUES AND PLASMA
`
`Active transport
`Donno-n ion effect
`pH differences
`Plasma protein binding
`Tissue binding
`Lipid partitioning
`
`
`
`Dpo
`I
`I
`I
`
`....
`
`!
`
`OH
`
`Div
`I
`I
`
`'
`
`\l
`
`Q
`CL0
`
`·o rn
`
`I
`I
`-.!L
`Kp I
`Vt
`C ~
`I
`I
`
`Clint
`
`I -1,.,
`I~
`I 'V
`
`I
`
`1 r
`I
`
`cvh
`
`Cvt
`
`FIGURE 2-3. Basic physiologic pharmacokinetic model for drug distribution
`and elimination. Symbols are defined in the text. The clearance organ is phar(cid:173)
`macokinetically perceived as separate from other compartment s for drugs with
`high intrinsic clearances (CL;n,) allowing characterization of the first-pass
`input.
`
`

`

`20
`
`Chapter 2: Collection and Analysis
`
`Chapter 2: Collection and Analysis
`
`21
`
`permeability coefficient can be calculated for drugs exhibiting polyex(cid:173)
`ponential disposition and is of more fundamental value than intercom(cid:173)
`partmental rate constants.
`Hepatic Clearance. The model shown in Figure 2-3 represents the
`common situation where drug must pass through a specific organ such
`as the liver or kidney for elimination. It does not apply to enzymatic
`hydrolysis in blood. This type of model reflects the dual role of blood
`flow (Q) and either biotransformation (V max, Km) or renal filtration
`(GFR) and transport (Tmnx, Tm) on removal of drug from the body and
`allows for some effects of route of administration (e.g., first-pass
`effect).
`Two types of clearing organ models are commonly used for hepatic
`TABLE 2-2. DISTRIBUTION COEFFICIENTS (Ko) FOR VARIOUS DRUGS AND PROB·
`ABLE PHYSIOLOGIC (PHYSICOCHEMICAL) CAUSE
`
`Drug
`
`Indocyanine Green
`
`Inulin
`
`Ampicillin
`
`Theophylline
`
`Antipyrine
`
`Gentamicin
`
`Tetracycline
`
`Diazepam
`
`Digoxin
`
`Ko=~
`TBWt
`
`0.06
`
`0.25
`
`0.25
`
`0.5
`
`0.6
`
`1.1
`
`1.6
`
`1.7
`
`8.0
`
`Imipramine
`
`10.0
`
`Explanation/indication
`
`Strong binding to plasma
`proteins and limited extra(cid:173)
`vascular permeability.
`Distribution limited to
`plasma and interstitial
`,fluid owing to large molecu(cid:173)
`lar weight (5,500) and lipid
`insolubility.
`Limited intracellular distri(cid:173)
`bution owing to poor lipid
`solubility (common to
`penicillins).
`
`Moderate plasma binding and
`distribution primarily into
`total body water.
`Slight plasma binding and
`fairly uniform distribution
`into total body water.
`Strong tissue binding
`(common to
`aminoglycosides).
`Strong tissue binding to cal(cid:173)
`cium in bone.
`Appreciable lipid
`partitioning.
`Strong binding to Na/K
`transport ATPase in cell
`membranes.
`Strong tissue binding
`(common to weak bases).
`
`elimination: The "Jar" or ''Venous Equilibrium" Model28 (Figure 2-5)
`and the "Tube" Model34 (Figure 2-6). Both include blood flow for sys(cid:173)
`temic drug access to the organ and, as shown in the figures, assume
`that free or unbound drug (fup) in plasma equilibrates with free drug
`in the tissue available to enzymes. The Jar Model involves the as(cid:173)
`sumption that drug in arterial blood (C 0 ) entering the clearing organ
`instantaneously equilibrates with that in the venous blood (CJ. The
`Tube Model assumes that a drug concentration gradient exists down
`the tube, with enzymes acting upon declining perfusate drug
`concentrations.
`The Jar Model yields the following relationship for hepatic clearance
`to account for the variables in the system:
`CL - QH . fup . CLuinl - Q
`QH + fup • CLuinl
`where intrinsic clearance is the ratio of V max / Km for linear biotrans(cid:173)
`formation and EH is the extraction ratio.
`The corresponding equation for CLH described by the Tube Model is
`(Eq. 2-13)
`A simulation is provided in Figure 2-7 to depict the dual effects of
`
`H -
`
`-
`
`. E
`H
`
`t!
`
`(Eq.2-12)
`
`) Q
`
`C >
`
`V
`
`Cone
`
`Distance
`
`FIGURE 2-4. Model for distribution clearance where blood flow (Q) along the
`cylindrical tube and capillary permeability (Pl are the primary determinants
`of drug loss from arterial blood (C0 ). Drug concentration in the tube will de(cid:173)
`cline monoexponentially according to distance (length) along the tube emerg(cid:173)
`ing at the venous concentration (Cvl·
`
`
`
`

`

`22
`
`Chapter 2: Collection and Analysis
`
`Chapter 2: Collectwn and Analysis
`
`23
`
`blood flow and intrinsic clearance on hepatic clearance for the two
`clearance organ models. Both models predict a lower CLH limit of fup
`· CLuint (or CLint in the absence of protein binding considerations) and
`an upper value of QH. Thus, the hepatic clearance of low clearance
`drugs is essentially equal to the product of intrinsic clearance and the
`fraction unbound in plasma.35 The maximum hepatic clearance will
`be organ blood flow. As seen by' the shape of the surfaces in Figure 2-
`7, the two models diverge somewhat in characterizing drugs with in(cid:173)
`termediate to high clearance. At the present time, it is uncertain
`which model is most generally appropriate for describing organ clear(cid:173)
`ance. The Jar Model has had most extensive use in physiological phar(cid:173)
`macokinetics.1 A spherical liver acinus model has also been proposed.36
`Radial diffusion considerations in this model produce plasma disposi(cid:173)
`tion curves of the power form C" = At·n, rather than polyexponentials,
`which can be fitted well to elimination of several drugs.
`The organ clearance models provide definitions for two types of gen(cid:173)
`eral clearance terms. Systemic clearance (CL) reflects any situation
`where