`This material may be protected by Copyright law (Title 17 U.S. Code)
`
`
`
`702
`
`Till“. Nl{\\’ l",‘,\'(}l.;\;‘\lf}JOURNAL Oi" hiiililClNl‘l
`
`Oct. 2. 197;"
`
`h'iEDICAL if‘lTELLIGEl C .
`
`
`
`,
`ONl Mun».
`.uu
`s
`[04‘
`
`1»
`
`
`
`DRUG THERAPY
`
`Clinical Pharmaeokiueties
`
`(First of Two Parts)‘1
`
`DAVID ]. GREENBLATT, M.D.,
`JAN KOCH-WESER, MD.
`
`'flE intensity of the therapeutic and toxic effects of
`most pharmacologic agents depends on their concen-
`tration at the sites of action. The time cottrsc of this con—
`
`centration is determined by the drug dosafie schedule and
`by the metabolic fate of the drug in the body. Pharmacoki-
`netics is the quantitative study of the metabolic processes
`of drug absorption, distribtttion, biotransformation and
`elimination. The use of mathematical models to describe
`
`these processes allows predictions about drug concentra-
`tions in various parts of the body as a function of dosage,
`route of administration, and time. In view of the complex-
`ity of the human bodyand the mttltiplicityof ways in which
`it deals with foreign substances, it is not surprising that
`comprehensive pharmacokinetic analysts can be exceed-
`ingly complicated. Indeed. pharmacokineticists often use
`mathematical formulations unintelligible to most clini—
`cians. Fortunately, relativelv simple pharmacokineticcon-
`siderations are usually sufficient for quantitative guidance}
`during the clinical use of drugs.
`Knowledge of a drug’s pharmacokinetic behavior en-
`ables the clinician to choose dosage schedules that will rap-
`idly produce and constantly maintain a desired concentra—
`tion range at the sites of action. The optimal size and fre-
`quency of
`individual
`(loses administered by various
`routes, the need for and the appropriate size of loading
`doses. and the time course of accumulation in the body
`during continued administration are all functions of the
`phatmacokinetic fate of a drug. Pharntacokinetic knowl-
`edge about drugs can also guide appropriate adjustments
`of dosage schedules according to individual body size and
`composition, circulatory state, and hepaticand renal func-
`tion.
`
`Duringr recent years many sensitive analytic technics
`have been developed for the m >asurement of concentra-
`tions of drugs and drug,r metabolites in body fluids and tis-
`
`
`
`From the Clinical Pharmacology Unit, Department of Medicine, Massa-
`chusetts General Hospital, and the Centre tie Recherche Mcrrcll interna-
`tional. Strasbourg. France (address reprint requests to Dr. Greenblatt at the
`Clinical l‘harrn:_teology Unit. Massachusetts General Hospital, Boston, MA
`021M).
`
`Supported in part by grants (MH<l2379 and His-”150) from the U.S.
`PublicHealthServium
`*‘Part two will appear in the Novcmbcr6 issue.
`
`Figure 1. Schematic Diagram of the Two-Compartment Open
`Model.
`
`C, and 0;. represent drug concentrations in, and V1 and V2
`rapresent apparent volumes of central and peripheral com-
`partments. it,2 and k21 are first-order rate constants of drug
`transfer between central and peripheral compartments. It' is
`the first-order rate constant for drug elimination from the
`central compartment.
`
`TEVA1 057 '
`
`sues after the administration of therapeutic. doses. With
`thesett'clniics pharimtcokinctit'studiesofthe most impor-
`tant drugs have now been perlormed. At the same time
`the relation between concentrations in the body and in-
`tensity of phat tnacologic effects has become increasingly
`understood for many drugs.‘-'—'
`'l'hese approaches have
`contributed greatly to the effectiveness and safety of phar-
`niacotlmrapy and have made it important for practicing
`physicians to understand the basic principles of pharma-
`cokinetics.
`
`THE Two-Comparrrmmtr PHARMACOKINETIC
`MODEL
`
`Pharmacokinetic models of the human body vary great-
`ly in complexity. The simplest,
`the “one—cmnpartment
`model," assumes that drugs are instantly and homoge-
`neously distributed throughout the fluids and tissues of
`the body. Although it is of alluring simplici y, this model
`does not account accurately for the observed time course
`of the concentrations of most drugs in various parts of the 5
`body.3 In contrast, the “two—contpartment open model" i
`adequately describes the fate of many drugs in man.“l It is
`based on straightforward assumptions, and its mathemat-
`ical solutions are consistent with intuitive notions of drug
`behavior.
`'
`
`Compartments
`
`The first major assumption of the two—compartment
`model is that the body can be resolved into a central com-
`partment of small apparent volume and a peripheral com-
`partment of large ‘ apparent volume (Fig. 1). Th *:;e com-
`partments do not necessarily correspond to specific aria-
`tomic entities. They are theoretical spaces postulated to
`account for the experintent:tl‘-obsen';ttiori that drugs dis—
`tribute into various body fluids :tit‘gl tissues at different
`rates. Nevertheless, for many drugs the central compart—
`ment probably consists of the serum or blood volume to-
`gether with the extracellular .luid of highly perfused tis-
`sues such as the heart, lungs, liver, kidneys, and endocrine
`glands. Drugs distribute in a few minutes throughout this
`compartment, and equilibrium between drug:r concentra~
`
`PERlPHERAL
`COMPARTMENT
`
`CENTRAL
`COMPARTMENT
`
`kiz
`
`v
`Cl
`
`k.
`
`0055
`
`|
`
`l
`
`1
`
`TEVA1057
`
`

`

`Vol. 293 No. 14
`
`MEDICAL INTELLIGENCE — GREENB'LATT AND KOCH-WESER
`
`703
`
`[ions in the serum and in these tissues is rapidly estab-
`lished and constantly maintained. The peripheral com-
`partment is then formed by less perfused tissues, such as
`muscle, skin. 3nd body fat into which drugs enter more
`slowly. The apparent volume of the central and peripher-
`al compartments for each drug thus depends upon Lhe
`characteristics of blood flow to each component tissue. on
`the drug’s ability to enter these tissues from the circula-
`tion, and on the drug‘s affinity for them.
`
`First-Order KinetiCs
`
`The two-compartment model also specifies characteris-
`tics of drug passage into and out of the system and of
`drug transfer between the compartments within the
`system, Drugs enter the system only via the central com»
`partment and are eliminated only from the central com-
`partment. ReVersible transfer occurs between central and
`peripheral spaces, so that the peripheral compartment
`acts as a “reservoir" connected only to the central com-
`partment.
`_
`“First-order kinetics” are assumed to describe the exit of
`drugs from both compartments in the system. Under this
`assumption the rate at which a drug is removed from a
`compartment is proportional to the drug concentration
`in it. The higher the drug concentration in a compart-
`ment, the more drug leaves it in any given time; as the con-
`centration becomes smaller, the ratio of exit falls propor-
`tionately.
`In the two-compartment open model, k12 and R21 are
`first—order constants associated with drug transfer be-
`tween the two compartments (Fig. 1). The overall elim-
`ination rate constant (kc) relates the sum of all meth-
`ods of irreversible drug elimination from the central
`compartment (i.e., biotransformation by the liver, excre-
`tion by the kidney or in the feces, or exhalation via the
`lungs) to the concentration of drug in that compart—
`ment.
`‘
`When drug absorption is complete and no further drug
`enters the central compartment from outside the system,
`the concentration of drug in the central compartment (C1)
`depends upon several simultaneous and independent
`processes. The drug can leave the central space both by
`distribution to the peripheral space and by elimination.
`Since these are first-order processes, the rate at which they
`occur is directly proportional to C1, with a proportionality
`constant (rate constant) equal to the sum of k12 and kt .
`Conversely, the drug can return to the central compart—
`ment by redistribution from the peripheral space: this
`movement occurs at a rate proportional to the peripheral
`compartment concentration (C2), with a rate constant k“.
`The net rate of change of C1 is given by the sum of these
`processes:
`
`
`d5:
`
`=_ — (k12+k=)ci +k21C2
`
`(Eq_. 1).
`
`With the same reasoning, the net rate of change of C2 is:
`
`d2:
`
`(Eq' 2)'
`
`= _k21C2 + k 12C1
`
`I
`
`These two simultaneous, first-order, linear, differential
`
`equations are the mathematical basis for the two-compart-
`ment model. They are appropriately modified for differ—
`ent methods of drug administration and solved with use of
`Laplace transformations5 to yield explicit functions relat-
`ingC1 and C2 to time (t).
`
`Principles oi Pharmacokinetic Analysis
`
`The simplest method of drug administration for phar—
`macokinetic analysis is very rapid administration of a sin-
`gle dose (D) directly into the central or serum compart-
`ment. Assuming instantaneous distribution throughout
`the central compartment, the concentration there (C1) im-
`mediately after injection is equal to the dose divided by the
`volume of the central compartment. At the same time the
`drug concentration in the peripheral compartment is
`zero. Thus:
`
`at time(t) = 0, C1 = DIV1 and C2 = 0.
`
`Subject to these constraining conditions the solution of
`Equations 1 and 2 yields the following relation between C1
`and the time (t) after the end of the injection:
`
`c, =Ae—‘“+Be-lit
`
`(Eq.3).
`
`A plot of the logarithm of Cl versus time yields a curve
`with two distinct linear components (Fig. 2). The initial
`rapid fall in concentration, called the “alpha” or "distribu-
`tion" phase, mainly represents the relatively rapid process
`of drug distribution from central to peripheral compart-
`ments. The alpha or distribution half-life is defined as:
`
`t =an = 0.693
`”a
`a
`‘1
`
`(Eq.4).
`
`Once distribution is complete, the curve enters the
`relatively slow “beta" or “elimination“ phase. during
`which drug disappearance is determined mainly by irre-
`versible elimination from the central compartment. The
`slope of the curve during this phase is ,8, and its units are
`min"1 or hr”. The beta or elimination half—life is:
`
`l =an _ 0.693
`
`(Eq.5)-
`
`n+3
`
`DISTRI BUTIDN
`
`
`
` SERUMCONCENTRATION(c,)
`
`IV
`
`TIME AFTER 0055(1)
`
`Figure 2. Schematic Graph of Serum Concentrations (C1).
`Plotted on Logarithmic Scale, versus Time {1) after a Single
`Intravenous Bolus of a Drug as Predicted by the Two-Com-
`partment Open Model (See Text for Details).
`
`A
`dd“
`
`2
`
`

`

`704
`
`THE NEW ENGLAND JOURNAL OF MEDICINE
`
`Oct. 2, 1975
`
`tit-3‘ the half-life of a drug in serum after distribution
`equilibrium has been atttunetl,
`is
`the most important
`pl'larmact-ikinetic half-life. It is commonly referred to sim-
`ply as the "hall—lile.“ Each time an interval equal to time
`elapses, 50 per cent of the drug present in the body at the
`beginning of that interval is eliminated. A large value offi.
`corresponding to a short elimination half-life. indicates
`rapid elimination.
`The coefficients A and B are “intercept” terms having
`dimensions of concentration. The sum A + B is the actual
`
`t = 0 intercept of the serum concentration curve (Fig. 2),
`and B is the interceptdetermined by extrapolation of the
`beta or elimination phase of the curve to t = 0. A, B, a,
`and B are “hybrid” coefficients; each One depends upon
`a combination of ke, k2,, k”, V1, V2, and the adminis-
`tered dose (D). These hybrid coefficients are what one
`determines during pharmacokinetic studies. They are
`used to calculate the actual pharmacokinetic parameters
`as follows:
`
`
`=A+B
`ke 1+2
`a
`B
`
`k 2
`12
`
`k,. =31 —Afi_+_B_a
`ke
`A + B
`AB
`,(e — )z
`(A + B):
`k“
`
`v) = Dose
`A+B
`
`(Eq.6).
`
`(Eq.7).
`
`E
`( 11.8).
`
`(Eq.9).
`‘
`
`The calculation of V2 requires knowledge of the “total
`apparent volume of distribution" (Vd ), which is equal to
`the sum of V1 and V2. Vd is a second very important
`pharmacokinetic parameter. It may be calculated by at
`least two methods.“10 After single intravenous doses the
`“area" method provides the most useful estimate of this
`volume. The area-derived volume term accounts for ob-
`served serum concentrations on the basis of the total
`amount of drug in the body at all times after distribution
`equilibrium has been attained — that is, during the beta
`phase of the curve. 7'10 With this method,
`
`=
`
`vd (area)
`
`
`=
`D
`Dose
`Area under the serum concentration
`A + 2
`curvefromt=0tot=oo
`fl(a
`fl
`(Eq. 10).
`
`fi(
`
`)
`
`Another method of calculating V , the “steady-state"
`(ss) method, assumes that the net transfer of drug from
`central to peripheral compartment is zero. Using this
`method,
`
`
`k
`2|
`VIN”) =V,(l + k”)
`
`making
`
`V2 = Vl
`
`
`km
`1‘21
`
`(Eq.ll)-
`
`tion has been reached during continuous intravenous in-
`fusion of a drug at any unchanging rate. Under this cir-
`cumstance the above assumption is correct, and “(55)
`correctly relates the steady-state serum concentration
`to the amount of drug in the body. After single doses,
`however, Yam)
`is not useful. The necessary condition of
`no net drug transfer between compartments holds on-
`ly at that single point in time when the drug concentra-
`tion in the peripheral compartment has reached a maxi-
`mum.
`
`The total apparent volume of distribution of a drug
`provides an estimate of the extent of its distribution
`through body-fluid compartments and of its uptake by tis-
`sues. A large apparent volume of distribution implies wide
`distribution or extensive tissue uptake or both. For some
`drugs Va is many times larger than the actual volume of
`the body. so that concentrations in some tissues must be
`considerably higher than the serum concentration. Con-
`versely, a small value of Vd indicates that distribution is
`limited and tissue uptake is not extensive. The apparent
`volume of distribution of some drugs corresponds only to
`the serum or extracellular fluid volume.
`
`Clearance of a drug is the third pharmacokinetic con-
`cept of considerable importance.“ Its units are milliliters
`per minute. and it is a direct index of drug elimination
`from the central compartment. Whereas [ten depends
`upon k”, k“, and kc, clearance depends only upon kt.
`Hepatic biotransfortnation, excretion by the kidney, ex-
`halation by the lungs, and fecal excretion are the usual
`methods of drug elimination that determine clearance. It
`can be expressed as follows:
`
`Clearance =V1' k
`
`c
`
`=p.vd
`
`(area)
`
`'
`
`d (area)
`
`
`= 0.693
`['fifl
`Dose
`Area under the serum concentration
`curve fromt =0tot = on
`
`(Eq. 12)
`
`Clearance of a drug, therefore, is inversely proportional
`to its elimination‘hall—lile (twi) and directly proportional
`to the apparent volume of distribution (Vic ). For any given
`renal clearance. the greater the apparent volu me of distri—
`bution of a drug, the flatter will be the slope of its serum
`concentration curve during the elimination phase (,8), and
`the more slowly will the serum drug level fall. Conversely,
`for any given Vd , the greater the drug clearance, the
`higher will be the rate of drug elimination. Finally, for any
`given “/25, the larger V5
`the greater must be the clear-
`ance of the drug.
`When a drug is partly or entirely excreted unchanged
`from the kidney, its renal clearance can be calculated by
`division of the rate of urinary excretion of the drug (in mil-
`ligrams per minute) by the serum concentration. Alterna-
`tively, one can multiply total drug clearance by the ‘frac—
`tion of the administered dose that appears unchanged in
`the urine.
`4
`
`Example of Pharmacokinetic Analysis
`
`Vdasps useful mainly when a constant serum concentra-
`
`Application of the two-compartment open model is il—
`
`3
`
`

`

`Vol. 293 No. 14
`
`MEDICAL INTELLIGENCE — GREENBLATT AND KOCH-WESER
`
`705
`
`This analysis Yields a pharmacoltinetic profile for this
`dose of chlordiazepoxide in this subject. The elimination
`half-life of the drug (Ll-ht!) is 12 hours. Since chlordiaze—
`poxide is almost entirely metabolized by the liver, the
`clezuaiice value of 22.3 ml per minute is an index of the
`rate of hepatic metabolism of the drug. The clearance is
`considerably lower than hepatic blood flow. The two mea-
`sures of the total apparent volume of distribution. dem]
`and thm . differ only by {‘3 per cent. despite the different
`methods of calculating them .
`
`—-u
`
`REFERENCES
`
`1. Koch-Weser J : Serum drug concentrations as therapeutic guides. N
`EnglJ Med 287227—231, 1972
`2. implications of blood level assays of therapeutic agents. Clin Pharma-
`colTher 16:129‘188. 1974
`3. Riegclrnaa S. Loo JCK. Rowland M: Shortcomings in pharmacoltinet-
`it: analysis by conceiving the body to exhibit properties of a single
`compartment. J Pharm Sci 57:1 17-123. 1963
`4. Gillette J R: The importance of tissue distribution in phannncokinctic's.
`J Pharmacokinet Biopharm 1:497-5211]. 1973
`5. Benet LZ: General treatment of linear mammiilary models with elimi—
`nation from any compartment as used in pharmacokinetics. J Pharm
`Sci6l:536—541. 1972
`'
`6. Ricgelman S. Loo J, Rowland M: Concept of a volume of distribution
`and possible errors in evaluation of this parameter. J Pharm Sci 57:
`128-133. 1968
`7. Benet LZ, Ronfeld RA: Volume terms in pharmacokinetics. J Pharm
`Sci 58:639-641, 1969
`8. Gibaldi M: Effect of mode of administration on drug distribution
`in a two-compartment open system.
`J Pharm Sci 58:327-331.
`1969
`9. Gibaldi M, Nagashima R, Levy G: Relationship between drug concen-
`tration in plasma or serum and amount of drug in the body. J Pharm
`Sci 58:193-‘197, 1969
`10. Perrier D, Gibaldi M: Relationship between plasma or serum drug
`concentration and amount of drug in the body at steady state
`upon multiple
`dosing.
`J
`Pharmacol-tinet Biopharm 1:17-22,
`1973
`ll. Idem: Clearance and biologic half-life of
`hepatic metabolism.
`J
`Pharmacol
`Exp
`1974
`
`indices of
`Ther
`
`intrinsic
`191:17-24,
`
`H CHLORDlAZEPOXIDE
`o--o DESMETHYLCHLORDIAZEPOXIDE
`
`
`
`a:-
`
` __,c. = 3.1ae‘331'+1.02a—-°575'
`
`HOU/VS AFTEI? 0055
`
`
`
`
`
`SERUMCoNL‘ENTflAT/ON(pg/ml)
`
`Figure 3. Serum Concentrations of Chlordiazepoxide and of
`Its Active Metabolite. Desmethylchlordiazepoxide. after Ad-
`ministration of a 28-Mg intravenous Bolus of Chlordiazepox-
`ids Hydrochloride. Equivalent to 25 Mg of Chlordiazepoxide
`Base. to a Healthy 75-Kg Male Volunteer.
`
`lustrated by the pharmacokinedc analysis of experimental
`data shown in Figure 3. The data points were fitted to a
`biexponential function. having the form of Equation 3. by
`a computer using the least-squares technic.
`The following function was obtained by this method:
`
`c.=3.1se—m
`
`+ Lon—m
`
`>y<
`
`The actual data points and the serum concentration curve
`calculated from this function are shown in Figure 3. The
`pharmacokinetic parameters, calculated from Equations
`4 to 12, are as follows:
`
`3.3lhr“,[y§a = 0.21“—
`a
`0.0575hr“,t%5 = 12hr
`3
`it. = 0.225111"!
`it= =0.84?hr—1
`it” = 2.29m—l
`V. = 5.95liters = 0.081iters/kg
`mm“; = 23.3liters = 0.31literslkg
`V digs] = 22.0]iters = 0.291iterslkg
`Clearance = 22.3ml/min.
`
`.- Clinical Pharmacokinetics (First of Two Parts) (293:702-705.‘ 1975). p.
`05. left-hand column. line 6 should read, "The following function was ob-
`tained by this method:
`I
`
`C, =3.18<:“J 111 + 1.02e-0 0575."
`
`
`
`4
`
`

`

`HEALTH SCIENCES LIBRARY
`University of Wisconsin
`
`1305 Linden 01“., [VThéis. 53706
`
`7287
`
`Abstracts in the
`advertising
`sections
`
`
`
`
`VOLUME 293
`OCTOBER 2, 1975
`NUMBER 14
`
`
`
`Original Articles
`17a-Hydroxyprogesterone Caproate to. Pre-
`vent Premature Labor .
`. . . ...........
`
`john W.C.johmon, Kari]; Austin,
`GeargemmaSJanes, GeorgeH. Davis
`and Theodore M. King
`Thyrotropic Function after Cessation of Pro-
`longed Thyroid Suppression . . . . . , . . . . .
`Apostolos G. Vagermkis, Lewis E. Braver-man,
`FerefixmnAzizi, GaryI. Portnay
`and Sidney H. Ingbar
`..ooq-...
`Crude and Cumulative Recurrence Rates in
`Crohn’s Colitis and Ileocolitis
`
`Adrian]. Grand-sin, DavidB. Stacker.
`Bernard 8. Patter-Mack and HmryDJanmuitz
`
`675
`
`681
`
`685
`
`Physiology in Medicine
`K Brain Edema .................... . ...... . .
`Robert A. Fishman
`
`706
`
`Case Records of the
`Massachusetts General Hospital
`
`Large Jejunal Ulcer 11 Years after Hemigas-
`trectomy and Gastrojejunostomy .......
`RichardH. Marshal: and Robert E. 3.9tu
`
`712
`
`Editorials
`
`Crohn’s Disease: What Do Recurrence Rates
`Mean? .................... . ..........
`
`Teen-Age Alcoholism, Medicine, and the
`Law...... .....
`.....
`
`Special Article
`
`Impact of Nationwide'Catastrophic Health
`Insurance . . . ..na--..o.o-..n---..n.u-
`
`Planning for a Pediatric Disaster: Experience
`with 1600 Vietnamese Orphans . . . . . . . .
`S. Alex Stalwp, Mark Oscherwia, Martin S. Cohen,
`Frank Crust, Dan Broughton, Fred Stark
`andRobert Goldsmith
`
`691
`
`Medical Progress
`
`The Reliability of Clinical Methods, Data and
`judgments (Second ofTwo Parts) .......
`Lom'nM. Koran
`
`695
`
`Medical Intelligence
`
`Drug Therapy: Clinical Pharmacokinetics
`..n..-...nou-.
`(First of TwoParts) . . . . .
`David]. Greenblatt and/an Koch-Weser
`
`702
`
`i
`
`Correspondence
`Kyeim Test in Sarcoidosis ....................
`Depression of Serum InsulinbySomatostatin . . . . .
`Pancreatic Cholera and VIP ..................
`Dimethylaminoethanol Ineffective in Huntington’5
`Disease ..........
`
`Determination ofZygosity ...... . . . ........ . . .
`Test for Globus Hystericus ...................
`FrisbeeFinger(Cont.) ..... ..................
`Munchausenl'limflam
`How to Stop Duplicate Publication .............
`Another Oath for Doctors ofMedicine ~ ..........
`“lsyalty Questions” and V.A. HouseStafl .......
`Bureaucracy PutonNotice . . . ..... . ..........
`Query....................................
`BookReview .. .....
`.........
`
`Notices .........
`
`Owned, Published and °Copyrighted, 1975, by the Massachusetts Medical Society
`____________________—__________—.
`Second—Class postage paid at Boston, MA and at additional mailing office.
`Published weekly at 10 Shattuck, Boston, 021 15. Worldwide, $22.00 per year.
`NEJMAG 293(14) 675-728 (1975)
`
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