`
`Boume and Dlttert
`
`plot can be generated for an entire dosing regimen in a very short time. The next example
`illustrates such a calculation.
`
`EXAMPLE. The following microcomputer program, written in BASIC, will solve Eq. (56) with
`an added loading dose for any time during a repetitive dosing regimen.
`
`Program Listing 1
`
`10 TEXT : HOH£
`
`20 VTA8 10: PRINT "MULTIPLE DOSE - PLASMA CONCENTRATION"
`100 VTAB 15: PRINT "NEW PATIENT"
`
`110 PRINT : PRINT "ENTER ELIMINATION HALF-LIFE IN HOURS" : INPUT T
`120 KEL • 0.69 IT
`
`130 PRINT : PRINT "ENTER ABSORPTION KALF-LIFE IN HOURS" : I.NPUT T
`140 KA• 0.69 / T
`
`150 PRINT: PRINT "ENTER VOLUME OF DISTRIBUTION AS FRACTION OF
`BODY WEIGHT": INPUT T
`160 PRINT
`PRINT "ENTER PATIENT WEIGHT IN KG":
`170 VO • T * TT
`200 PRINT
`PRINT "NEW DOSE OR REGIMEN"
`210 PRINT
`PRINT "ENTER FRACTI ON OF DOSE ABSORBED":
`INPU°F
`220 PRINT
`!?RI NT "ENTER LOADING DOSE IN HG" : INPUT TT
`230 LO• T • TT
`240 PRINT
`PRINT "ENTER MAINTENANCE DOSE IN HG": INPUT TT
`250 MD • T * TT
`260 PRINT
`
`INPUT TT
`
`T
`
`PRINT "ENTER DOSI NG I NTERVAL":
`
`INPUT T
`
`270 TAU• T
`
`280 PRINT
`: PRINT "ENTER TIM£ INTERVAL BETWEEN POINTS": INPUT T
`290 STP • T
`
`300 PRINT
`310 PRINT
`
`PRINT "NEW TIME POINT"
`PRINT "ENTER NUMBER OF MAINTENANCE DOSES GIVEN":
`
`INPUT T
`
`320 N • T
`!?RINT : PRINT "PU.SHA CONCENTRATION AFTER"
`400
`
`410 PRINT N;" MA I NTENANCE DOSES"
`420 PRINT : PRINT .. TIME (HR)", "CONCE.NTRATION (KG/LI•: PRINT
`
`430 FOR TIM£• 0 TO TAU STEP STP
`440 El • 0 : IF (l -
`EXP (KA• TAUi ) • 0 THEN GOTO 460
`
`450 El
`
`•
`
`(LO• EXP
`
`( - N •KA• TAU) +HD* (1 -
`
`EXP ( - N * KA
`
`EXP ( - KA• TAUi)) • EXP ( - KA• TIN£)
`/
`• TAUi )
`( l -
`EXP (KEL • TAUi) • 0 THEN GOTO 480
`460 E2 • 0 : IF ( 1 -
`470 E2 •(LO• EXP ( - N • KEL * TAU) +HD• (1 -
`EXP I - N *
`-
`KEL • TAU) I
`EXP
`I - KEL • TAU) I) • EXP ( - KEL •
`/
`TIM£ )
`
`(1 -
`
`FRESENIUS EXHIBIT 1012
`Page 100 of 293
`
`
`
`116
`
`Boume and Dtttert
`
`EXAMPLE. Calculate CP at quarler-hourly intervals for the first 24 hr of the kanamycin dosing
`regimen described in the first example in this subsection. The entry data are as follows:
`
`= 2.3 hr
`Half-life for elimination
`= 0.2 hr
`Half-life for absorption
`Fracrion of body weight equal to volume of distribution = 0.27
`= 74 kg
`Subject weight
`= 1.0
`Fraction of the dose absorbed
`= 800 mg
`Loading dose (D0)
`= 800 mg
`Mainlenance dose (do)
`= 6 hr
`Dosing interval (T)
`= 0.25 hr
`Tune interval
`= 0- 4
`Number of maintenance doses (n)
`
`The results of the calculation are shown in Fig. 15. Nole that Cm .. and Cm,n are identical with
`the values calculated in the aforemen•ioned example.
`
`C . Dosage Regimen Adjustment In Renal Failure
`
`The influence of impaired renal or liver function on lhe rate of elimination of a drug was
`mentioned previously, and a method for predicling the half-life of kanamycin in palients with
`varying degrees of renal impairment was described earlier (see Sec. VI). If patients with i.m-
`
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`
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`Time (hOurs)
`
`15
`
`18
`
`21
`
`24
`
`0
`
`3
`
`6
`
`9
`
`Fig. 15 Plot of kanamycin plasma concentrations (circles) versus time following multiple IM injections,
`calculated with Eq. (56).
`
`FRESENIUS EXHIBIT 1012
`Page 101 of 293
`
`
`
`Phcrmacoklnetfcs
`
`117
`
`paired renal function are given a normal-dosing regimen of kanamycin, they will soon build
`up toxic plasma concentrations of the drug. However, they can be dosed safely and effectively
`by adjusting the dosing regimen in accordance with the predicted elimination half-life. Dosing
`regimen adjustment involves changing the dose or the dosing interval.
`
`Alteration of the Dosing Interval
`The kanamycin package insert recommends that a dose of 7.5 mg/kg be administered every
`three half-lives, and that for patients with impaired renal function, the half-life in hours can
`be estimated by multiplying the serum creatinine level (mg/100 ml) by 3 (see also Sec. VI).
`Thus the dosing interval for a renal patient should be nine times serum creatinine level (mg/
`100 ml).
`
`EXAMPLE. A patient (74 kg) bas a serum creatinine level of 6 mg/100 ml (elimination half(cid:173)
`life ... 18 hr); therefore, the dosing regimen would be 7.5 mg/kg IM every 54 hr. Figure 16
`shows the results of this dosing regimen in terms of the plasma concentrations of kanamycin
`produced in the renal patient (solid line) and a normal patient (dashed line). In both cases, the
`C,...~ values are below the MTC of 35 µ g/ml, but the C..,,. values fall below the MEC of 10
`µ g/ml (Sec. IX.A).
`For the normal patient, the time during which the plasma concentrations are below 10 µ g/
`ml is only about 4 hr for each dosing interval; but for the renal patient, this time extends to
`about 18 hr. This gives the renal patient inadequate therapy for long time periods and can
`foster the development of strains of bacteria that are resistant to kanamycin.
`
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`20
`
`40
`
`60
`80
`Time (hours)
`
`100
`
`120
`
`140
`
`Fig. 16 Plot of kanamycin plasma concentration versus time following multiple IM injections i.n a
`normal patient (dashed line) and a renal patient (solid line), calculated with Eq. (56) and T = 9 X serum
`creatinine level (mg/100 ml) (altered-dosing interval approach).
`
`FRESENIUS EXHIBIT 1012
`Page 102 of 293
`
`
`
`118
`
`Boume and Dlttert
`
`Alteration of the Dose
`In a previous example the "maintenance dose every half-life" regimen was proposed for kana(cid:173)
`mycin because it maintained plasma concentrations between the MTC and MEC. The same
`regimen could be employed for IM injections of kanamycin in renal patients, but the logistical
`problems that arise in the clinic when the maintenance doses must be given at odd time intervals
`(e.g., 18 hr) make this regimen somewhat impractical. It would be much better if the maintenance
`doses could be administered at the same time other medication is given (i.e., every 4, 8, or 12 hr).
`The same loading dose (in milligrams per kilogram) can be given to all patients regardless
`of their renal function because the loading dose is determined by the volume of distribution
`(or body weight) and not by the rate of elimination. However, if a normal-dosing interval is
`used, the amount of drug eliminated over one interval (T) will be much less for a patient with
`renal failure than for a patient with normal renal function . As a result, the maintenance doses
`must be reduced to replace only that amount of drug lost during the preceding dosing interval.
`EXAMPLE. The dosing regimen recommended for normal adults in the kanamycin package
`insert is 7.5 mg/kg every 12 hr. The insert also states that the half-life of kanamycin in a
`normal adult is about 4 hr. What should the 12-hr maintenance dose be for the individual in
`the previous example?
`For a person whose half-life is 18 hr (ke1 = 0 .0385 hr- 1
`), the amount remaining at the end
`of a 12-hr- dosing interval is
`Ao
`k.11
`l
`og A = 2.30
`
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`
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`
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`
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`
`20
`
`40
`
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`60
`Time (hours)
`
`100
`
`120
`
`140
`
`Fig. 17 Plot of kanamycin plasma concentration versus time following mu.ltiple IM injections in a
`normal patient (dashed line) and a patient with renal impairment (solid line) calculated with Eq. (56) and
`maintenance dose = amount lost over each 12-br- dosing interval (altered dose approach).
`
`I •
`I •
`..
`..
`-
`-
`0-+----~-----------,-----.----...---~
`
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`
`FRESENIUS EXHIBIT 1012
`Page 103 of 293
`
`
`
`Pharmocoklnetlcs
`
`7.5
`log-=
`A
`
`0.0385 X 12
`2.30
`
`A = 4.72 mg/kg
`
`119
`
`The amount lost over the 12-hr interval is
`
`7.5 mg/kg - 4.72 mg/kg = 2.78 mg/kg
`Therefore, the maintenance dose= 2.78 mg/kg every 12 hr. The loading dose (same as normal)
`= 7.5 mg/kg.
`The results of this dosing regimen in terms of plasma concentrations are shown as a solid
`line in Fig. 17. The dashed line in Fig. 17 shows the plasma concentrations that would be
`produced in a normal patient on a normal-dosing regimen (7.5 mg/kg every 12 hr). Figure 17
`shows that the administration of 2.8 mg/kg maintenance doses every 12 hr to the aforemen(cid:173)
`tioned renal patient is a convenient dosing regimen that produces C""" plasma levels above the
`MEC and Cmu plasma levels below the MTC.
`
`REFERENCES
`
`4.
`
`1. R. E. Notari, Biopharmacewics and Clinical Pharmacokineucs: An Introduction, 4th Ed., Marcel
`Dekker, New York, 1987.
`2. M. Gibaldi and D. Perrier. Pharmacokinetics, 2nd Ed., Marcel Dekker, New York, 1982.
`J. G. Wagner, Fundamentals of Clinical Pharmacokilletics. Drug lntelligence Publications, Hamilton.
`3.
`IL, 1975.
`J . G. Wagner, Biopharmacewics and Relevant Pharmacokinetics, Drug Intelligence Publications,
`Hamilton, lL, 1971.
`S. G. A. Portmann, Pharmacokinetics, in Current Concepts in the Pharmaceutical Sciences: Biophar(cid:173)
`maceuticals (J. Swarbrick, ed.), Lea & Febiger, Philadelphia, 1970.
`6. W. J. Westlake, The design and analysis of comparative blood-level trials, in Current Concepts in
`the Pharmaceutical Sciences: Dosage Form Design and Bioavailability (J. Swarbrick, ed.), Lea &
`Febiger, Philadelphia, 1973.
`
`FRESENIUS EXHIBIT 1012
`Page 104 of 293
`
`
`
`5
`
`The Effect of Route of Administration and
`Distribution on Drug Action
`
`Svein tale and Leslie Z. Benet
`University of California, San Francisco, California
`
`I. THE DOSE-EFFICACY SCHEME
`
`When a health practitioner administers (or ' ' inputs ") a dose of drug to a patient, usually the
`ultimate goal is solely directed to the usefulness of the drug under abnormal conditions. That
`is, the drug must be efficacious and must be delivered to its site of action in an individual
`experiencing a particular physiological anomaly or pathological state. Pharmaceutical scientists,
`on the other hand, concentrate their attention to solving problems inherent in drug delivery to
`deliver the optimal dose to the site(s) of action.
`The general pathway a drug takes from residence in a dosage form until its clinical utility
`is depicted in Fig. 1. ldeaHy, the drug should be placed directly at the site of action, as
`illustrated by the stippled arrow in Fig. 1, to maximize the effect and minimize side effects
`relating to unwanted responses at sites other than the target tissue. However. delivery directly
`to the site of action is more often than not, impractical or not possible. Instead, we have to
`settle for the most convenient routes of delivery. This is illustrated by the solid arrows in Fig.
`1. That is, the drug is placed directly in the vascular systems or in close proximity to some
`biological membrane through which the drug can traverse to reach body fluids or the vascular
`system. The delivery system is generally designed to release the drug in a manner that is
`conducive to this passage through the membrane. Previous chapters have discussed how drug
`delivery systems may be optimized in terms of dissolution in the fluids surrounding the
`membrane to allow the desired rate of passage through the membrane. Subsequent chapters
`will deal with specific drug delivery systems and their optimization. Once the drug has passed
`through the membrane and into the blood stream adjacent 10 the site of absorption, a general
`distribution of the drug will take place throughout the biological system. As pointed 01,1t in
`Chapter 3, the degree of dilution (referred to as the apparent volume of distribution) will dictate
`the initial concentration of drug in the general circulation, as sampled from a peripheral vein.
`Usually, the dose of the drug administered to the patient was chosen to give sufficiently high
`
`155
`
`FRESENIUS EXHIBIT 1012
`Page 105 of 293
`
`
`
`156
`
`tale and Benet
`
`OISTAIBUTION
`
`INPUT
`
`Drug in Blood
`at Site of
`Administration
`
`El
`
`.,,.-0-Ee...,,.-si-re_d........_)
`(
`,
`"""'
`.
`
`~
`
`~U-nw_a_n-ted_a_nd_
`
`Toxic Effects
`
`Fig. 1 A schematic representation of the dose-efficacy relationship for a drug.
`
`blood levels so that an adequate quantity of the drug would reach the site of action. The rate
`of input needed to achieve adequate levels of the drug at the site of action is influenced not
`only by the distribution and general elimination in the body, but may also be modified by the
`loss processes that are unique to a specific route of administration. This chapter will deal
`primarily with the distribution and loss processes that result uniquely from the physiological
`parameters inherent in the use of a particular route of administration.
`Unfortunately, no drug is yet so specific that it interacts with only the target site in the
`target tissue, and will not give rise to hyperclinical activity. Too much drug at the wrong place
`or too high a concentration at the right place may result in unwanted or toxic effects. Thus the
`practitioner must determine the usefulness of any dose of a drug from a particular drug delivery
`system by balancing the efficacy achieved from the clinical effect against the toxic reactions
`observed.
`Most drug delivery systems achieve the required drug levels at the site of action as a result
`of attaining adequate blood levels in the general circulation (see Fig. 1, solid arrows). This
`process is followed because of the ease with which present drug delivery systems can "input"
`drugs into the general circulation and the inherent difficulties in delivering the drug selectively
`to a relatively inaccessible site (e.g., pituitary gland). In addition, for many compounds, the
`exact site of action is still unknown. However, when the site of drug action is sufficiently
`defined, Fig. 1 illustrates the advantage of delivering the drug directly to the site of action. By
`direct administration to the active site, a lower dose could be used to achieve the clinical effect
`because the drug no longer is diluted or eliminated en route. As a result, drug concentrations
`at unwanted sites of action could be kept to a minimum; in addition, clinically effective levels
`at the site of action might be attained much more rapidly, since the process of distribution
`throughout the entire body could be avoided. One should not forget that, in addition to the
`obvious clinical advantage of direct administration, there is also an economical one. By deliv(cid:173)
`ering the drug to the site of action, the amount of drug needed is much smaller than by more
`traditional delivery methods. This is particularly important for many of the newer recombinant
`
`FRESENIUS EXHIBIT 1012
`Page 106 of 293
`
`
`
`Effect of Administration Route and Distribution
`
`157
`
`compounds that can be very expensive. Much work is currently being carried out in an attempt
`to achieve such a selectiveness as that described in Fig. l.
`
`11. PHYSIOLOGICAL CONSIDERATIONS FOR THE VARIOUS
`ROUTES AND PATHWAYS OF DRUG INPUT
`A. DNg Input at or Close to the Site of Action
`
`Figure 2 illustrates a number of sites where drug delivery systems have historically been used
`to input drug directly to its site of action [1,2). Various classic dosage forms were developed
`to take advantage of these input sites: eye, ear, and nose drops; inhalation, oral, topical, and
`vaginal aerosols; topical solutions, creams, and ointments; and rectal solutions, enemas, and
`suppositories. Each of the sites for local drug administration requires specific formulation to
`allow the drug to remain at the site of application for a sufficient length of time to allow the
`drug to penetrate through the particular membrane(s) so that it can reach the actual site of
`action adjacent to the site of application. For example, some ophthalmic preparations may be
`given to elicit a superficial anti-infective effect, such as treatment of an inflammation of the
`conjuctiva. Thus, only topical effects are desired, and there is no need for the drug to penetrate
`into the eyeball. Formulation of such products would be quite different than formulation of a
`drug delivery system for which the drug must be absorbed into the interior of the eye to produce
`
`sampleable
`blood
`ment
`
`sublin1ual
`
`1///...,i.---rectal
`
`vaginal
`
`Ag. 2 Various routes and pathways by which a drug may be "input" inco cbe body. The position of
`one lung is distorted to emphasize that the lungs are in an excellent position for cleansing the blood. The
`diagram is especially useful in explai.ning the first-pass effect following oral dosing, for which drug
`absorbed from the small intestine or stomach must first pass through the liver and, therefore, is subject
`to metabolism or biliary excretion before reaching the sampleable blood. (From Ref. 2.)
`
`FRESENIUS EXHIBIT 1012
`Page 107 of 293
`
`
`
`158
`
`tale and Benet
`
`a response, such as miotics, mydriatics, anti-inflammatory drugs that act in the anterior segment
`of the eye, and, occasionally, drugs for treatment of infections. A detailed description of the
`factors involved in the development of such ophthalmic preparations. as well as the particular
`physiological characteristics of the eye. will be presented in Chapter 15. Similar types of design
`problems arise for many of the other sites that are traditionally treated by direct local appli(cid:173)
`cation. One of the most difficult problems facing the formulator is that the behavior of the
`diseased tissue may be different from that for healthy individuals, and it may also change over
`the course of treatment. For example, diseased skin is often more permeable than healthy skin;
`therefore, the drug may disappear faster from the site of administration than desired, and the
`effect wiU be less than expected. Should the formulation be designed to accommodate this
`phenomenon, one must be mindful of the fact that as the pathological condition improves. the
`absorption may also change.
`Although the classic dosage forms mentioned earlier can be used to put drug directly into
`the site of action, many of them have a degree of " messiness'' that prevents good patient
`acceptance and adherence. Not only is there an initial psychological barrier that must be over(cid:173)
`come, but the general public ha.c; an aversion to taking drugs by routes other than oral. There
`is. in addition, a general dislike for sticky creams, drippy drops, greasy ointments, and the
`like. Over the last two decades much work has been directed toward developing more accept(cid:173)
`able delivery systems than the traditional ones. Emphasis has been placed on long-acting drug
`delivery systems that may be more convenient, since they would only require self-administra(cid:173)
`tion once a week or possibly at even longer intervals.
`A large number of new devices have been developed, and new ones are constantly being
`investigated. Plastic disks for placement in the eye (similar to a contact lens) that slowly release
`drug into the humoral fluid; drug-impregnated plastic rings or loops that when placed in the
`uterus will release controlled amounts of contraceptive agents; bioadhesive tablets or disks that
`can be placed buccally, nasally. or vaginally for local release; hydrogels for slow release in
`the eye are examples of such new delivery systems that input drug directly to the site of action.
`In a more ambitious move, many groups have also embarked on site-specific delivery to
`less accessible sites than those given in Fig. 2. Although numerous experimental systems have
`been designed, few have reached the clinical stage. The simplest and most direct method when
`a specific target organ can be located is cannulation ( direct access port). A catheter is placed
`in an appropriate artery or vein. If a vein is used, the catheter has to reach the organ, o r
`otherwise the drug will be flowing away from the target tissue, be diluted with blood from the
`rest of the body, and be not different than a systematic intravenous administration. Catheters
`can also be placed in the peritoneum, the bladder, and in the cerebrospinal fluid. A drug can
`now be administered directly into the desired tissues at a rate that can be well controlled.
`Although catheter delivery is a direct method, it is limited in that it is essentially restricted to
`inpatient use. Use of implants in the desired tissue, or a drug carrier (e.g., liposomes, nano(cid:173)
`particles, and such) that will either home in on the desired tissue by specific receptors, or
`release their content at the desired site by an external stimulus (e.g., magnetic fields, light,
`current), are drug systems currently being explored for target-specific delivery.
`Although the method of direct delivery is a very attractive one, it also has its regulatory
`problems. Benet [1) has noted that assessing the bioavailability of this system can create dif(cid:173)
`ficulties because the manufacturer may not be able to devise a control procedure that can
`measure drug concentration at the site of action. For example, the extent and rate of availability
`of an orally administered drug can easily be assessed by measuring blood levels, whereas for
`a drug input into a site of action, significant blood levels would indicate distribution away
`from that site. Frequently, significant blood levels of a drug that is administered at a site of
`action (such as a topical preparation, an eye drop, a nasal insufflation, or an antibiotic that acts
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`on intestinal flora) indicate either a poor drug delivery system or substantial overdosing. For
`this class of drug delivery systems, clinical efficacy necessarily has to serve as the best meas(cid:173)
`urement of drug availability and dosage form efficacy.
`
`a. Drug Input Into the Systemic Circulation
`The overwhelming majority of existing drugs are, however, given by general routes; that is,
`by routes that do not deliver the drug directly to the site of action. These modes of drug input
`rely on a passive delivery of drug through distribution by the vascular system. The most
`commonly accepted method is oral administration. As will be discussed later, oral administra(cid:173)
`tion is not ideal, as one needs to be concerned about whether the drug can be destroyed in the
`stomach, in the gastrointestinal fluid, in its passage through the gut wall, through the liver, or
`simply not be absorbed in time before it is expelled from the gastrointestinal tract. Several
`alternative routes of delivery are being used or are being developed to diminish these potential
`losses. The advantages and problems inherent in the individual routes of administration will
`now be discussed.
`
`Parenteral Administration: lntravascular
`Of the routes of input depicted in Fig. 2, intravenous (IV) administration yields one of the
`fastest and most complete drug availabilities. However, intra-arterial injections might be em(cid:173)
`ployed when an even faster and more complete input of drug to a particular organ is desired.
`By administering the drug through an artery, the total drug delivered will enter the organ or
`tissue to which the artery flows. Intravenously administered drug will first be diluted in the
`venous system as the venous blood is pooled in the superior and inferior vena cava. It then
`enters the heart, and is subsequently pumped to the lung before it can enter the arterial system
`and reach the target organ(s). In addition, the fraction of the drug reaching a desired site is
`dependent on the fraction of the arterial blood flow reaching that site. Additional drug can
`reach the target tissue only by being recirculated from the other organs. In comparison with
`intra-arterial administration, IV administration reaches the target slower, and initially at a lower
`concentration. Although intra-arterial injections appear superior, they are infrequently used
`because they are considered much more dangerous than IV administration. Intra-arterial ad(cid:173)
`ministration has been associated with patient discomfort, bleeding, and thrombosis.
`In addition to the dilution factor resulting from mixing with larger volumes of blood after
`intravenous administration, one also needs to consider the possibility of temporary or permanent
`loss of drug during its passage through the lung. The position of the lungs in Fig. 2 has been
`distorted to emphasize the point that the lungs are in an excellent strategic position for cleansing
`the blood, since all of the blood passes through the lungs several times a minute. Apart from
`their respiratory function and the removal of carbon dioxide from the pulmonary c irculation,
`the lungs serve other important cleansing mechanisms, such as filtering emboli and circulating
`leukocytes, as well as excretion of volatile substances. The lungs also have metabolic capacity
`(3) and may serve as a metabolic site for certain drugs (4) or as an excretory route for com(cid:173)
`pounds with a high vapor pressure. The lungs can also act as a good temporary storage site
`for a number of drugs, especially basic compounds, by partitioning of the drug into lipid tissues,
`as well as serving a filtering function for particulate matter that may be given by IV injection.
`Accumulation of lipophilic compounds and filtering of any compounds in solid form cal) be
`viewed as a temporary clearing or dilution of the drug, as it will eventually leac h back into
`the vascular system. Thus the lung serves as a dampening or clearing device, that is not present
`following intra-arterial injection. Drugs given by the IV route may, therefore, not necessarily
`be completely available to the site of action, since a certain fraction of the drug could be
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`eliminated by the lung before entering into the general circulation (5). This might be called a
`"lung first-pass effect."
`The foregoing concepts may be visualized by referring to Fig. 3. In this figure one can
`readily see the difference between intra-arterial and intravenous administration of drugs. Let
`us assume that compartment n is the target tissue. Administration into any vein (i.e., into any
`of the efferent arrows on the left-band side of the figure) would lead the drug to the heart and,
`from there, to the lung. Drug that enters the lung can leave by only one of two routes, as
`illustrated in Fig. 4: by the blood that leaves the lung, or by being eliminated. The result is
`that there is a competition between the two routes for the drug, and the greater the ability of
`the lung to eliminate the drug in comparison with the pulmonary blood flow, the more dru~
`will be extracted. If we assume that the pulmonary blood flow is Q, and that the intrins, ...
`elimination clearance of the organ is CL,.,. and no plasma protein binding occurs (Cu = c •• ,),
`then the extraction ratio can be expressed as
`
`(1)
`
`In perfusion models, as depicted in Fig. 3, it is assumed that distribution into and out of the
`organ is perfusion rate-limited such that drug in the organ is in equilibrium with drug concen(cid:173)
`tration in the emergent blood (6). The intrinsic clearance of an organ is different from the
`value we normally think of as the clearance of the organ. The clearance of the organ is defined·
`as the rate of loss in relation to the incoming concentration, whereas the intrinsic clearance is
`defined as the rate of loss in relation to the organ concentration (or exiting concentration). In
`addition, it is also clear that. of the drug that escapes elimination in the lung, only a small
`fraction goes to compartment n. the rest is distributed to other organs. Drugs that enter these
`organs will be exposed to elimination in these organs and must necessarily recirculate through
`the heart and lungs before they again have the opportunity to reach compartment n.
`
`Parenteral Administration: Depot
`The other parenteral routes depicted in Fig. 2, intramuscular (IM) and subcutaneous (SC)
`injections, may also be considered in terms of Fig. 3. Drug absorbed from the IM and SC sites
`into the venous blood will return to the heart and pass through the lungs before being distributed
`to the rest of the body. However, there will be an initial lag between the time when the drug
`is injected and when it enters the circulation. Thus, the kinetics for drugs administered by these
`parenteral routes would be expected to show a decreased rate of availability and may also
`show a decreased extent of availability in comparison with intravenous administration, if loss
`processes take place at the site of injection. For example, we could consider that drug is now
`injected directly into compartment m in Fig. 3 and that this compartment is the muscle. The
`rate at which the drug leaves the muscle will depend primarily on blood flow in relation to
`the size (apparent volume of distribution) of the organ.
`Evans and co-workers (7) measured resting human muscle blood flow through the gluteus
`maximus, vastus lateralis, and deltoid muscles. Deltoid muscle blood flow was significantly
`greater than gluteus muscle blood flow, with vastus being intermediate. Because the two sites
`most commonly used for IM injections are the deltoid and the gluteus muscles, we might
`expect to see differences in rates of drug absorption following injection to these sites. Lidocaine
`is one drug that has been investigated for its effect in response to the site of injection [8,9).
`Deltoid injection gave higher peak levels than lateral thigh injection which, in turn, gave higher
`levels than gluteal injection. Schwartz et al. (9) demonstrated that therapeutic plasma levels
`for a particular lidocaine dose were reached only when the deltoid injection site was used.
`Evans et al. (7) concluded, ''This demonstrates that the site of injection can influence the
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`Compartment 1
`Lung
`
`-
`CL1
`•
`
`Right
`Heart
`
`Left
`Heart
`
`~ Compartment 2
`
`Mesen1enc Tissues -
`
`•
`
`•
`
`'.
`
`•
`
`,
`
`•
`
`•
`
`,
`
`--
`
`-
`,
`
`-
`
`-
`
`-
`-
`
`-
`
`2
`
`CL
`,.
`-
`-
`-
`C½
`,
`
`~
`
`-
`,,
`-
`-
`
`Compartment 3
`Liver
`
`Compartment m
`
`CL
`m
`
`Compartment m+1
`
`~
`
`Compartment n
`
`Fig. 3 The body depicted as a physiological perfusion model. Compartment m must be considered as
`a summation of the individual tissues that metabolize the drug and compartment m + 1 through n as
`noneliminating tissues.
`
`Cu - tu B .cout
`
`Ag. 4 Flow model of an eliminating organ. The drug enters the body by the organ blood flow, CL,.
`and is immediately mixed in the organ. The drug leaves the organ by either being eliminated (CI...,Cu)
`or by the exiting blood flow.
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`plasma level achieved and that the deltoid muscle should be used to achieve therapeutic blood
`levels as rapidly as possible.'• Likewise, if a sustained or a prolonged release is desired, this
`would more readily be achieved by injection into a lower blood flow muscle, such as the
`gluteus.
`Loss processes may also account for a decrease in the extent of availability following an
`IM injection. This can be visualized by assuming that the dose is injected into compartment
`m, which, as depicted in Fig. 3, is capable of eliminating the drug. As shown i.n Fig. 4, the
`drug can leave the tissue only by one of two routes, either by the blood leaving the organ, or
`by being eliminated by metabolism i.n the muscle. In addition, the drug that leaves the site of
`administration will also be sub