1521-009X/42/11/1890–1905$25.00 http://dx.doi.org/10.1124/dmd.114.059121DRUG METABOLISM AND DISPOSITION Drug Metab Dispos 42:1890–1905, November 2014Copyright ª 2014 by The American Society for Pharmacology and Experimental Therapeutics

Special Section on DMPK of Therapeutic Proteins—Minireview

Pharmacokinetic Modeling of the Subcutaneous Absorption ofTherapeutic Proteins

Leonid Kagan

Department of Pharmaceutics, Ernest Mario School of Pharmacy, Rutgers, State University of New Jersey, Piscataway, New Jersey

Received May 15, 2014; accepted August 13, 2014

ABSTRACT

Subcutaneous injection is an important route of administration fortherapeutic proteins that provides several advantages over othermodes of parenteral delivery. Despite extensive clinical use, theexact mechanism underlying subcutaneous absorption of proteinsis not completely understood, and the accuracy of prediction ofabsorption of biotherapeutics in humans remains unsatisfactory.This review summarizes a variety of models that have beendeveloped for describing the pharmacokinetics of therapeutic

proteins administered by subcutaneous injection, including single-and dual-pathway absorption models. Modeling of the lymphaticuptake and redistribution, absorption of monoclonal antibodies andinsulin, and population analysis of protein absorption are discussed.The review also addresses interspecies modeling and prediction ofabsorption in humans, highlights important factors affecting the ab-sorption processes, and suggests approaches for future develop-ment of mechanism-based absorption models.

Introduction

Biotherapeutics denotes a rapidly growing class of drugs with morethan 200 biopharmaceuticals already approved, including vaccines,hormones, cytokines, and monoclonal antibodies (mAbs) (Walsh, 2010;Janowitz, 2011; Reichert, 2012). Several hundred new products areunder development, such as a variety of mAbs, Fc-fusion proteins,antibody-drug conjugates, and alternative protein scaffolds (Beck et al.,2010; Dostalek et al., 2013). Parenteral administration is a major limitationfor treatment with biotherapeutics. The subcutaneous route may be advan-tageous over intravenous or intramuscular administration, especially forimproving patients’ convenience and reducing treatment costs (McDonaldet al., 2010; Dychter et al., 2012; Richter et al., 2012). Subcutaneousinjection has been used clinically for decades for administration of drugssuch as insulin, erythropoietin, and growth hormone. Several mAbs andFc-fusion proteins are currently approved for subcutaneous administration,and the interest in subcutaneous delivery of other antibody-based treat-ments is growing (Misbah et al., 2009; Aue et al., 2010; Bittner et al.,2012; Bittner and Schmidt, 2012; Davies et al., 2014; Tobinai, 2014).However, variable and incomplete bioavailability is a major concern forsubcutaneous delivery, and the mechanisms of subcutaneous absorptionof protein therapeutics are not fully understood and require further in-vestigation. Furthermore, current methods for predicting absorption ofbiotherapeutics in humans are inadequate (McDonald et al., 2010;

Richter et al., 2012). Pharmacokinetics of protein therapeutics is oftennonlinear, and extensive mathematical modeling may be required forresolving complexities associated with their absorption and disposition.This review summarizes a variety of existing models for describing

the pharmacokinetics of therapeutic proteins administered by subcu-taneous injection, highlights important factors affecting the absorptionprocess, and suggests approaches for future development of mechanism-based absorption models.

Background

Subcutaneous injection delivers drugs into the hypodermis, theinterstitial space located below the dermis. The structure and phys-iology of the interstitial space have been reviewed extensively (Porterand Charman, 2000; Swartz, 2001; Lin, 2009; Richter et al., 2012).Briefly, collagen, glycosaminoglycans, and elastin are the main structuralunits of the interstitium that provide strength and elasticity whilemaintaining the volume of the matrix. The extracellular matrix hasan overall negative charge, and transport of macromolecules throughthe interstitium is likely dependent on their physical and electrostaticinteraction with the components of the matrix. It has been suggestedthat the interstitial transport is the rate-limiting step in absorption ofmacromolecules (Porter and Charman, 2000; Swartz, 2001). Aftersubcutaneous injection, protein therapeutics can reach the systemiccirculation through blood and lymphatic capillaries. Blood capillar-ies of the subcutaneous space are continuous in nature, characterizedby tight interendothelial junctions and an uninterrupted basementmembrane, which provides a selective barrier for molecular permeation.Lymphatic capillaries are built from a single layer of overlappingendothelial cells, the basement membrane is incomplete, and the

Part of this work was previously presented at the following workshop: Kagan L(2013) Pharmacokinetic modeling of subcutaneous absorption. 2nd BioTx ADMEWorkshop. ADME of Protein Therapeutics: Science and Application; 2013 Aug 11–13; Buffalo, NY.

dx.doi.org/10.1124/dmd.114.059121.

ABBREVIATIONS: AUC, area under the plasma (or serum) concentration-time curve; F, absolute bioavailability; FcRn, Fc receptor of neonates;IFN, interferon; mAbs, monoclonal antibodies; NPH, neutral protamine Hagedorn; PEG, pegylated.

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tight junctions are absent (Swartz, 2001). The structure of thelymphatic system allows for unidirectional flow; and the lymph isformed as the interstitial fluid enters the lymphatic capillaries,driven by the gradient in the hydrostatic and osmotic pressure.The role of the lymphatic system in subcutaneous absorption oftherapeutic proteins and particulate formulations has been investigatedin several species (Porter et al., 2001; McLennan et al., 2005b;Gershkovich et al., 2007; Wang et al., 2012).Factors affecting the absorption of biotherapeutics after subcutaneous

injection can be divided into species, subject, and drug dependent.Differences in skin morphology, such as presence of panniculuscarnosus muscle in lower species and the greater mobility of skin inscruff animals, may contribute to the lack of correlation between thebioavailability of biotherapeutics in animals and humans (McDonaldet al., 2010; Richter et al., 2012). Differences in binding affinitybetween Fc receptor of neonates (FcRn) and IgG among species maycomplicate interspecies modeling of subcutaneous absorption of mAbs(Ober et al., 2001). Although pig skin is similar to human skin, the rateof subcutaneous absorption of several mAbs was 2- to 5-fold greater inminipigs as compared with humans (Zheng et al., 2012). The bio-availability of mAbs in humans is often overestimated based onnonhuman primate data (Richter et al., 2012). The structure of thesubcutaneous tissue in animals and humans varies depending on theanatomic location in the body, which may result in different absorptionbehavior and increase the pharmacokinetic variability (Beshyah et al.,1991; Macdougall et al., 1991; Ter Braak et al., 1996; Kota et al., 2007;Kagan et al., 2012). In humans, hypodermis thickness increases withbody weight, decreases with age, and depends on gender (Gibney et al.,2010). For example, the distance between the skin and the gluteal musclewas 1.6 cm in normal women (body mass index 18.5–24.9 kg/m2) ascompared with 3.6 cm in obese women (body mass index 30–40 kg/m2)(Shah et al., 2014). Other factors controlling the rate and the extent ofabsorption include the molecular size of the drug, formulation excipients,restraint status or anesthesia, and application of heat or pressure (Porterand Charman, 2000; Porter et al., 2001; McLennan et al., 2005b). Forexample, the rate of the thoracic lymph flow was higher in freely movinganimals as compared with anesthetized ones (Lindena et al., 1986), andthe rate of absorption of soluble insulin was positively correlated with thesubcutaneous blood flow (Vora et al., 1992).

Modeling of the Subcutaneous Absorption of TherapeuticsProteins

Pharmacokinetic and pharmacodynamic relationships for therapeu-tic proteins tend to be more complex than for small molecule drugs.High-affinity binding to pharmacologic targets (soluble and tissuebound) often leads to nonlinear distribution and elimination patterns,which are dependent on the drug dose and the underlying dynamicsof the target. The biodisposition of mAbs is affected by multiplebinding interactions specific to the particular drug (through the Fabregion) or drug class (through the Fc region). Noncompartmentalmethods of analysis, including calculation of the bioavailability andinterspecies scaling, can be unreliable for biotherapeutics due to dose-dependent pharmacokinetics and slow equilibration between the plasmaand the sites of elimination (which violates the underlying assumptionsof this approach). Therefore, advanced mechanism-based pharmacokinetic/pharmacodynamic models may be required for describing absorption,biodisposition, and efficacy in preclinical and clinical studies.Significant progress has been made in understanding the complex-

ities of the systemic pharmacokinetics of protein therapeutics in recentyears. Target-mediated (or receptor-mediated) drug disposition modelsare often applied to mechanistically describe the systemic disposition

of biotherapeutics (Levy, 1994; Mager and Jusko, 2001). Binding ofmAbs to FcRn and the role of this interaction in protecting mAbs fromdegradation and extending their biologic half-life is well established(Ghetie et al., 1996; Junghans and Anderson, 1996), and an endosomalrecycling model was proposed to describe this phenomenon (Hansenand Balthasar, 2003).This review is focused on the absorption component of the phar-

macokinetic models developed for therapeutic proteins. In the majorityof the discussed studies, modeling of systemic disposition was sup-ported by data obtained after intravenous administration of compounds.It should be noted that the selection of the systemic structural model(especially in the case of nonlinear disposition) might have a substantialimpact on the fit of the absorption phase of pharmacokinetic profiles.Analysis of such interactions and their impact on the selection ofappropriate absorption models is beyond the scope of this review. Tofacilitate the discussion, equations describing the systemic dispositionwere replaced by a (6 disposition) term. For the purposes of thisreview, absorption models were divided into single- and dual-pathwaycategories. The later was subdivided into empirical models (based onstudies measuring plasma/serum concentrations only) and mechanisticmodels describing the plasma pharmacokinetic profiles and the amountof drugs in the lymph simultaneously. Absorption models for mAbs andinsulin are reviewed separately.

Single-Pathway Subcutaneous Absorption Models

Although subcutaneous absorption of therapeutic proteins is controlledby multiple factors, a rate-limiting step in the absorption pathway (suchas transport through the interstitium, penetration of blood capillaries, orlymph flow rate) may limit our ability to identify these complexities. Thesimplest structural model being evaluated to describe the subcutaneousabsorption includes a first-order absorption rate constant (ka) and abioavailability term (F) (Fig. 1A). This model has been successfullyapplied for describing the subcutaneous pharmacokinetics of manyproteins—such as human interferon a2b (IFN-a2b) in healthy humanvolunteers (Radwanski et al., 1987) and recombinant human growthhormone in rhesus monkeys (Sun et al., 1999). Selection of this simplemodel is often dictated by limited data (e.g., single-dose level or sparsesampling during the absorption phase). The number the model pa-rameters can be further reduced by estimating the apparent volume ofdistribution (Vd/F) and clearance (CL/F) terms if the intravenousadministration is not evaluated and a priori knowledge of the systemic

Fig. 1. General schematic of the subcutaneous absorption models for therapeuticproteins. (A and B) Single-pathway model. (C) Empirical dual-pathway model.Systemic disposition can be described by different models depending on the drugand, for simplicity, is shown as a single gray compartment. Optional rates andcompartments are shown with dashed lines. Selected studies that used model C arelisted in Table 1. SC - subcutaneous space; F, systemic bioavailability; Frc, fractionof the bioavailable dose absorbed via the first-order pathway; ka, first-orderabsorption rate constants; t, duration of the zero-order absorption; Tlag, a lag time forthe first-order absorption; Vmax and Km, parameters for a Michaelis-Menten kinetics.

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bioavailability is unavailable. Absorption rate-limited elimination (flip-flop kinetics) should be considered in this case, and physiologic in-terpretation of the modeling results may be problematic. When the ratesof absorption and elimination appear similar, the corresponding rateconstants can be constrained to be equal. This approach was applied todescribe the time-course of IFN-a2a and pegylated (PEG)-IFN-a2aconcentrations after subcutanous administration of a range of doses (3–18 MIU) to healthy volunteers (Nieforth et al., 1996) and PEG-IFN-b1a(0.3–3.0 MIU/kg) to cynomolgus monkeys (Mager et al., 2005).A Michaelis-Menten model (Vmax and Km) can be implemented if

saturation of the absorption kinetics with increasing dose level areobserved. This mechanism was used to describe the absorption ofrecombinant human growth hormone in chronic dialysis patients andhealthy subjects (Klitgaard et al., 2009) and to support dose selectionfor exenatide in clinical studies (Fineman et al., 2007). Carrier-mediated transport or precipitation at the injection site are commonlypostulated; however, the nature of this saturable absorption forproteins is generally unknown.A model with a single transit compartment between the injection site

and the central compartment of the systemic disposition model wasproposed to describe a distinct delay in subcutaneous absorption ofsome proteins (Fig. 1B) (Mager and Jusko, 2002; Mager et al., 2003;Segrave et al., 2004). The transit compartment was sometimes attributedto the lymphatic system, although no direct assessment of the lymphaticcomponent was performed. Parameterization of the model includes thebioavailability (F) and two first-order rate constants (ka1 and ka2), whichcannot be uniquely identified.Biotherapeutics often exhibit nonlinear subcutaneous absorption,

and dose-dependent parameters are commonly used to facilitate modelfitting. Although this approach may be appropriate in fit-for-purposescenarios, it provides little insight into the mechanisms of absorptionfor a specific drug, which is essential for accurate assessment of thebioavailability, optimizing delivery, and predicting absorption inhumans, including the effects of population covariates. For example,a dose-dependent absorption rate constant (ka2, increasing with thedose level) was required for describing the absorption of leukemiainhibitory factor administered to sheep (Segrave et al., 2004).Evaluation of other absorption models, such as zero-order and a com-bination of the first-order and zero-order, did not provide satisfactoryresults. Dose-dependent bioavailability (increasing with the dose level)combined with target-mediated systemic disposition was used to cap-ture the pharmacokinetics of IFN-b1a in cynomolgus monkeys (Mageret al., 2003). Saturation of the injection site-specific metabolism washypothesized to be the source of this phenomenon; however, in-corporation of the Michaelis-Menten mechanism did not improve thefit (Mager et al., 2003).

Empirical Dual-Pathways Subcutaneous Absorption Models

The existence of two absorption pathways (through the blood andlymph capillaries) for large molecules after injection into the in-terstitial space has been recognized for many years. Deconvolutionanalysis of plasma concentration-time profiles after subcutaneous ad-ministration frequently demonstrated several absorption phases fortherapeutic proteins (Radwanski et al., 1998; Ramakrishnan et al.,2004). A model with two parallel absorption processes was suggested,although a direct assessment of the contribution of the lymphaticsystem was not performed experimentally. A general schematic of themodel is shown in Fig. 1C, and several variations of this model havebeen used to describe the absorption of proteins in animals andhumans (Table 1). The model uses a combination of a zero- and first-order processes originating from the subcutaneous space and leading

to the central distribution compartment. The zero-order process is lim-ited in duration from the time of injection to time t, and is usually de-scribed as absorption through the blood capillaries. The first-order process(ka) is usually attributed to lymphatic absorption that occurs after a delay(Tlag). The fractions delivered by the first- and zero-order processes aremodeled as parameters Frc and (1-Frc). In a general form the resultinginput function can be represented by the following equation:

Input ¼ F × Dose × ð12FrcÞt

× Qðt2 tÞþ

þka × F × Dose × Frc × e2ka×ðt2TlagÞ × Qðt2 TlagÞð1Þ

where F is the absolute bioavailability, and Q(x) is the step functionthat equals to 1 for x . 0 and 0 otherwise. To further delay theabsorption, a single transit compartment is sometimes added to eitherone of the two pathways with sequential first-order uptake into thecentral compartment (ka2 or ka3, dashed-line compartments in Fig. 1C)(Bocci et al., 1986; Radwanski et al., 1998). To reduce the numberof the estimated parameters, Tlag and t are often constrained to beequal to each other (Table 1). However, this assumption essentiallytransforms the model into a sequential two-phase absorption, whichlimits its physiologic interpretation. It should be noted that by fixingthe fraction absorbed of one of the processes to zero the model couldbe reduced to a single-pathway model (which can be useful for modelevaluation).This model was suggested to capture the pharmacokinetics of re-

combinant human IFN-a2 after subcutaneous injection to rabbits (Bocciet al., 1986). The systemic disposition was described using threecompartments and linear elimination. Separate sets of parameters wereestimated for IFN-a2 given alone or in combination with absorptionmodifiers (albumin and hyaluronidase). Individual pharmacokineticprofiles of interleukin-10 in healthy humans after intravenous andsubcutaneous dosing were described by a similar model (Radwanskiet al., 1998). A single transit compartment with a first-order ratetransfer to the systemic circulation (ka2) was added to the linear pathwayto further delay the absorption. The mean duration of the zero-orderabsorption (t) was estimated as 0.47 6 0.52 hour (mean 6 S.D.), andthe Tlag for the first-order absorption was 0.23 6 0.52 hour, whichallowed for two processes to occur simultaneously. Similar to the single-pathway models, dose-specific parameters (bioavailability and first-orderabsorption rate constant) have been used to account for nonlinearities inthe absorption process (Ramakrishnan et al., 2003, 2004).A wide range of values was reported for the parameters for various

proteins in different species (Table 1). Although this model was originallyproposed to mechanistically describe protein absorption, limited in-ferences of physiologic relevance of the estimated parameters couldbe drawn at this time. For example, the fraction of the bioavailabledose absorbed through the zero-order pathway varied from 5 to 88%,and the estimated duration of the zero-order process in humansranged from 0.47 to 60 hours.

Mechanistic Dual-Pathway Subcutaneous Absorption Models(Models of Lymphatic Absorption)

Following an early work that found a direct linear correlationbetween the molecular weight of compounds and the percentage of thesubcutaneous dose recovered in peripheral lymph (Supersaxo et al.,1990), other investigators evaluated the contribution of the lymphaticpathway to the subcutaneous bioavailability of protein drugs in asheep model. These studies provided most of the data for developmentof the lymphatic absorption models (McLennan et al., 2003, 2005a,2006; Kota et al., 2007). The first generation of this model included

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two pathways connecting the injection site and the central distributioncompartment in non–lymph-cannulated animals. In contrast to empiricaldual-pathway models, the absorption was modeled through simulta-neous analysis of the plasma (or serum) pharmacokinetic profiles incontrol (noncannulated) and lymph-cannulated animals and the time-course of the drug recovery in the lymph of lymph-cannulated animals.This direct experimental assessment of the lymphatic component(although technically challenging) results in more meaningful pa-rameter estimates as compared with empirical dual-pathway absorptionmodels. In lymph-cannulated animals, only blood vessels deliver thedrug to the central compartment, and the drug transported through thelymphatics is continuously collected.Two variations of this general concept were developed to capture

the pharmacokinetics of different proteins in the sheep model (Fig. 2),and two ways to parameterize the model were reported: 1) using therate constants and 2) using the fraction terms. The correspondingparameters can be interconverted as follows:

F ¼ kblood þ klymphkblood þ klymph þ kloss

ð2Þ

Flymph ¼ klymphkblood þ klymph

ð3Þ

Fblood ¼ kbloodkblood þ klymph

ð4Þ

where kblood, klymph, and kloss are the first-order rate constants foruptake by blood and lymph capillaries, and degradation, F is theabsolute bioavailability, and Fblood and Flymph represent the fraction ofbioavailable drug absorbed by the corresponding pathway.Recombinant methionyl human leptin was administered subcuta-

neously (0.15 mg/kg) into the interdigital space of the hind leg tocontrol (non–lymph-cannulated) and lymph-cannulated (efferentpopliteal duct) sheep (McLennan et al., 2003). The cumulative

TABLE1

Studies

that

used

acombinatio

nof

zero-andfirst-orderkineticsto

describe

subcutaneous

absorptio

nof

therapeutic

proteins

Model

schematic

isshow

nin

Fig.1C

.

Drug

Species/Population

Durationof

the

Zero-Order

Absorption

Percentageof

Bioavailable

DoseAbsorbedby

Zero-Order

Process

RateCon

stantforthe

First-O

rder

Absorption

Bioavailability

Systemic

Dispo

sitio

nMod

elReference

Anakinra

Rat

2h

Not

reported

0.39

h21

100%

2CM

with

linearelim

ination

Liu

etal.,2011

Erythropoietin

Rat

13.5

h68

0.146h2

159%

2CM

with

linearandMM

elim

ination

Woo

etal.,2006

Erythropoietin

Cynom

olgus

monkey

10h

350.044–

0.053h2

1dose

dependent

27–100%

dose

dependent

2CM

with

MM

elim

ination

Ram

akrishnanet

al.,2003

Erythropoietin

Health

yhumans

44–60

hdose

dependent

880.022h2

10.3884

+0.0002495•Dose

1CM

with

MM

elim

ination

Ram

akrishnanet

al.,2004

Erythropoietin

Health

yhumans

0.38–1.39

ddose

dependent

79.1

0.7day2

1Not

reported

1CM

with

MM

elim

ination

Krzyzanskiet

al.,2005

Filg

rastim

Health

yhumans

6.6h

58.6

0.403h2

169.1%

TMDD

Wiczlinget

al.,2009

IL-10a

Health

yhumans

0.47

h5

k a1=0.16

h21with

Tlag=23

hk a

2=0.61

h21

42%

2CM

with

linearelim

ination

Radwanskiet

al.,1998

IFN-a2b

Rabbit

1h

Not

reported

0.1h2

1Tlag=3.4h

Not

reported

3CM

with

linearelim

ination

Bocci

etal.,1986

IFN-a2b

Hum

anpatients

2.5h

240.18

h21

Not

reported

1CM

with

linearelim

ination

Chatelutet

al.,1999

Parathyroid

horm

one

Rat

5min

70.018min

21

Not

modeled

Hom

eostasismodel

for

endogenous

horm

one

Abraham

etal.,2009

1CM,2C

M,3C

M,one-,two-,three-compartmentmodel;IL,interleukin;

MM,Michaelis-M

enten;

TMDD,target-m

ediateddrug

disposition.

aAnadditio

naltransitcompartmentforthefirst-orderprocess.

bModel

parameterschangedby

presence

ofalbumin

orhyaluronidase.

Fig. 2. Schematic of the first-generation mechanistic dual-pathway subcutaneous(SC) absorption models. (A) Model without a lymph compartment was used forleptin (McLennan et al., 2003) and darbepoetin (McLennan et al., 2006) in sheep.(B) Model with a separate lymph compartment was used for erythropoietin(McLennan et al., 2005a) and darbepoetin (Kota et al., 2007) in sheep. The model isfitted simultaneously to the plasma (or serum) pharmacokinetic profiles in control(noncannulated) and lymph-cannulated animals and to the cumulative recovery inperipheral or central lymph of lymph-cannulated animals. Systemic disposition canbe described by different models depending on the drug and, for simplicity, is shownas a single gray compartment. Here, kblood, klymph, and kloss are the first-order rateconstants for uptake by the blood and lymph capillaries, and degradation; kinput is thefirst-order rate constant for drug transfer from the lymph to the central compartment(model B only).

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amount of leptin in the peripheral lymph was 34.4 6 9.7% of thedose, and the area under the plasma concentration-time curve(AUC) in the lymph-cannulated group was 38% of the AUC of thenoncannulated group. Systemic pharmacokinetics were describedusing a two-compartment model with linear elimination (based on0.1 mg/kg i.v. dose), and the corresponding disposition param-eters were fixed for analysis of subcutaneous groups. Absorptionwas modeled as two first-order processes originating from theinjection space (kblood and klymph) (Fig. 2A). Individual animaldata were described using the following equations:

dSC

dt¼ 2ka × SC ð5Þ

For the control group:

dCnoncan

dt¼ ka × SC × F

Vc6 disposition ð6Þ

For the lymph-cannulated group:

dCcan

dt¼ ka × SC × F × ð12FlymphÞ

Vc6 disposition ð7Þ

dL

dt¼ ka × SC × Fabs × Flymph ð8Þ

where SC is amount of the drug at the injection site, C is theconcentration in the central compartment (with the volume of Vc), andL is the amount of the drug in the lymph of the cannulated group. Theabsorption rate constant (ka = kblood + klymph) was allowed to varybetween lymph-cannulated and control animals.The model was also applied to describe the absorption of

darbepoetin, a hyperglycosylated analog of recombinant human eryth-ropoietin a, in sheep after subcutaneous administration of 2 mg/kg (atthe interdigital space of hind leg) to control and peripheral lymph-cannulated animals (McLennan et al., 2006). Mean data from allgroups were fitted simultaneously, and the absorption parameters wereshared between subcutaneous groups; however, a separate eliminationrate constant was estimated for the intravenous and each of thesubcutaneous groups.A model with a separate lymphatic compartment (Fig. 2B) was used

to describe the absorption of recombinant human erythropoietin a aftersubcutaneous injection to sheep (McLennan et al., 2005a). Nonlinearityin systemic disposition (10–1000 IU/kg i.v. dose) was describedusing a combination of a linear and Michaelis-Menten eliminationmechanisms. A single subcutaneous dose (400 IU/kg, interdigitalspace of hind leg) was administered to control, peripheral lymph-cannulated (popliteal duct), and central lymph-cannulated (thoracicduct) animals. Mean data from all groups were fitted simultaneously,and all parameters were estimated with good precision. The rates ofabsorption through the blood capillaries and the rate of presystemicdegradation were described using the first-order rate constants (kbloodand kloss). The rate of lymphatic uptake (klymph) was shared betweenall groups; however, a lag time parameter (0.52 hour) was estimatedto account for a delay in erythropoietin appearance in the centrallymph. It is unclear whether the lag time was included for the SCcontrol group. Another first-order rate constant was estimated todescribe the drug transfer from the lymph compartment to the centralcompartment (kinput) (Fig. 2B):

dSC

dt¼ 2ðkblood þ klymph þ klossÞ × SC ð9Þ

For the control group:

dCnoncan

dt¼ kblood × SC

Vcþ kinput × L

Vc6 disposition ð10Þ

dLnoncandt

¼ klymph × SC2 kinput × L ð11Þ

For the lymph-cannulated group:

dCcan

dt¼ kblood × SC

Vc6 disposition ð12Þ

dLcandt

¼ klymph × SC ð13Þ

A similar absorption model structure was used to describe thepharmacokinetics of darbepoetin in another study that comparedlymphatic uptake from different anatomic locations (Kota et al.,2007). Central lymph was collected in all cannulated groups.Parameters for the systemic disposition were shared among all groups.The absorption model for the injection at the interdigital spacefollowed the model for erythropoietin (eqs. 9–13; Fig. 2B).Absorption from the abdominal injection site followed a biphasicpattern that was captured by two first-order inputs for both lymph andblood pathways. Specific equations used by the investigators were notprovided, and it is unclear whether the second rate constant was addedto or replaced the first rate constant after the lag time. The presystemicdegradation rate constant (kloss) was constrained to be equal betweennoncannulated and lymph-cannulated groups.A common limitation of the previously discussed lymphatic ab-

sorption models is the inability to account for redistribution of sys-temically available protein to the lymphatic system. The drug collected inthe lymphatic fluid after subcutaneous injection comes from two sources:1) drug entering the lymphatics at the site of injection and 2) systemicallyavailable drug that extravasated and was drained from the tissues by thelymphatic system (Fig. 3A) (Kagan et al., 2007). The role of thelymphatic system in the recovery of macromolecules from the interstitialspace in tissues and return to the systemic circulation is well established.Several decades ago, this mechanism was incorporated into the phys-iologically based models describing the pharmacokinetics of antibodiesand antibody fragments (Covell et al., 1986; Jain and Baxter, 1988;Baxter et al., 1994, 1995). Quantitative information on the lymphaticrecovery of macromolecules after redistribution of the systemicallyavailable drug is limited. Collection of the lymph after the in-travenous administration of compounds can be used to obtain suchdata. For example, plasma and central lymph concentration-timeprofiles after intravenous administration of tumor necrosis factor,IFN-b, IFN-a2, and interleukin-2 to rabbits (Bocci et al., 1987,1988a,b, 1990) and PEG40-erythropoietin to a dog (Wang et al.,2012) have been reported. The recovery of IFN-a2a in peripherallymph was 0.001–0.003% of the intravenous dose in sheep (Supersaxoet al., 1988). Similar concentrations of erythropoietin were found in theplasma and thoracic lymph 1.5 hours after intravenous injection to rats(Kagan et al., 2007). Up to 20% of the dose of a radiolabeled peptide([3H]MRL-1) was recovered in thoracic lymph over 3 days afterintravenous injection to dogs (Zou et al., 2013), and 44% of trastuzumabintravenous dose was collected over 30 hours in the thoracic lymph ofrats (Dahlberg et al., 2014).Collectively, these works indicate that redistribution of the sys-

temically available drug to the lymph can be significant, so including

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this pathway(s) into the pharmacokinetic model is important. A failureto account for this phenomenon might result in an overestimation of thelymphatic absorption, especially if central lymph is collected and thetotal collection period spans a long time. Comparable concentrationsmeasured in the plasma and thoracic lymph after subcutaneous ad-ministration of several proteins to rats was attributed to the redistributionphenomenon, and including this pathway into the absorption model wassuggested (Kagan et al., 2007); however, the estimation of the cor-responding parameters was not performed. Recently, Dahlberg et al.(2014) extensively evaluated the pharmacokinetics of trastuzumab usingintravenous and subcutaneous (hind leg above the ankle) delivery tolymph-cannulated and control rats. A significant amount of trastuzumabwas recovered in the lymph after both modes of administration, anda mechanistic model that included two lymphatic systems was proposed(Fig. 3B). The posterior lymphatic system drained one part of the body,including the injection site, and the amount of trastuzumab in the centrallymph was measured (lymph-cannulated group). The anterior lymphaticsystem drained the rest of the body. Each lymphatic system wasrepresented by two sequential compartments (peripheral and centrallymph). The systemic disposition of trastuzumab was described by thecentral and peripheral compartments, and the drug was allowed toredistribute from these compartments into the lymphatics by first-orderprocesses (k36, k34, k24, k26). The absorption part of the model includedfirst-order uptake into the posterior peripheral lymph compartment (k14)

and Michaelis-Menten transport into the central compartment (Vmax andKm) (see also section on mAbs absorption models). All other processeswere modeled as first-order kinetics. Because of the large number ofparameters, the rate constants associated with two lymphatic systemswere shared (k45 = k67, k36 = k34, k24 = k26, k52 = k72). A populationanalysis was performed, and it provided a good description of the dataand satisfactory estimation of the structural parameters. However, largestandard errors were reported for the between-subject variability terms(Dahlberg et al., 2014). Simulations using the model indicated that onaverage each trastuzumab molecule recirculated 4 to 5 times through thelymphatic systems before being eliminated. These results emphasize theimportance of including a redistribution mechanism into models ofsubcutaneous absorption for therapeutic proteins; otherwise, therelative contribution of the lymphatic system to the subcutaneousbioavailability of proteins can be overestimated. It is anticipatedthat the role of redistribution mechanism would be more significantfor larger proteins (such as mAbs) as compared with smallerproteins and peptides.

Insulin Absorption Models

Insulin was the first purified protein drug to become available forhuman use. Since its discovery in the early 1920s, multiple forms ofinsulin and insulin analogs with varying absorption and action profileshave become available. The therapeutic utility of insulin has beenexpanded by modifying the protein sequence (recombinant DNAtechnology) and altering the association and release properties of theformulation (using zinc, protamine, other excipients, and pH mod-ifications) (Beals et al., 2013). Multiple factors have been shown toaffect insulin absorption, including physiologic variables (such astemperature, exercise, and site and depth of injection) and product-dependent factors (type of insulin, concentration, and volume ofinjection), as reviewed by Hoffman and Ziv (1997), Nucci and Cobelli(2000), Charman et al. (2001), and Wong et al. (2008).An important intrinsic property of the insulin molecule that governs

absorption is the ability for self-association. Most studies have as-sumed that only insulin monomers and dimers are small enough to beeffectively absorbed, and the absorption delay was attributed to thetime required for the hexamers to dissociate. However, experimentswith nondissociating cobalt insulin have shown that it is absorbed inthe form of hexamers, although the rate of absorption was slower ascompared with the absorption of dimers (Brange et al., 1990). Inaddition, lymph collection experiments in sheep suggest that insulin ispartly absorbed in the form of hexamers (Charman et al., 2001).Simple compartmental models were used in early studies to describe

insulin pharmacokinetics. For example, Kobayashi et al. (1983) used asingle first-order rate constant to describe absorption after continuoussubcutaneous infusion and subcutaneous bolus injection (Fig. 1A).Two transit compartments (injection site and interstitium) and twofirst-order rate constants (Fig. 1B) were used to characterize ultralenteinsulin absorption in diabetic patients (Puckett and Lightfoot, 1995)and in a population study in healthy volunteers (Potocka et al., 2011).A combination of zero- and first-order kinetics was selected in a ratstudy (Fig. 1C) (Gopalakrishnan et al., 2005).Other investigators proposed noncompartmental approaches for

describing the absorption of different insulins. Berger and Rodbard(1989) used a two-parameter logistic equation to describe the absorptionof four types of insulin (regular, neutral protamine Hagedorn [NPH],lente, and ultralente):

A%ðtÞ ¼ 1002100 × ts

ðT50Þs þ tsð14Þ

Fig. 3. (A) General schematic of the subcutaneous (SC) absorption that includesredistribution of the systemically available proteins from the tissues to the lymphaticsystem, as proposed by Kagan et al. (2007). (B) Schematic of the model that wasused to describe the plasma and lymph data after introvenous (IV) and subcutaneousadministration of trastuzumab to rats (Dahlberg et al., 2014). Compartments and rateconstants are described in the text.

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where A% is the percentage of injected insulin remaining at theabsorption site, t is time after injection, s is the steepness parameter,and T50 is the time interval to permit 50% of the dose to be absorbed(T50 was expressed as a linear function of the dose). Mosekilde et al.(1989) used three coupled partial differential equations to describeprocesses that were assumed to govern the absorption of soluble insulin:diffusion of free insulin, transformation between hexamers and dimers,binding of the dimers in the subcutaneous tissue, and absorption ofinsulin dimers. Degradation at the injection site was considered in-significant. Equations were solved numerically by dividing the sub-cutaneous layer into 20 rings, centered around the injection site.The model was modified and extended to describe absorption of

monomeric insulin analogs (Trajanoski et al., 1993) and glargineinsulin (Tarin et al., 2005). Later, this model was incorporated into aninteractive educational diabetes simulator to support clinical decisions(Lehmann et al., 2009). Although this model provides a more phys-iologic description of the processes at the injection site (as comparedwith conventional compartmental models), relatively complex mathe-matics and intensive computation requirement might preclude itsapplication for future pharmacokinetic and pharmacodynamic analyses.Wong et al. (2008) proposed a unifying model for six different

insulins based on ordinary differential equations to simplify computa-tion (Fig. 4). It was assumed that absorption of all types of insulinoccurs through a common dimeric/monomeric compartment (Xdim). Theentire dose of monomeric insulin was assumed to be injected into thedimeric/monomeric compartment. For regular insulin, the dose wasdistributed between the dimeric and hexameric compartments (Xh), andhexamers dissociated into dimers by a first-order process. The NPH,lente, and ultralente insulin models were similar to the model of regularinsulin with an additional crystalline (C) state compartment. The NPHand lente insulin shared a common hexameric state with regular insulin,whereas ultralente insulin had a separate hexameric state with slowerdissociation (Xh,ulen). For glargine insulin, separate precipitation (Pgla)and hexameric (Xh,gla) compartments were included, and the dissolutionrate was dose dependent. The effect of the volume of injection wasmodeled by a rate of diffusive loss (kd) (assuming a spherical depot).The delivery of insulin from the injection site into the systemiccirculation occurred through a single transit compartment (Xint, inter-stitium), and loss in this compartment was included (kdi). Taken together,the model was able to describe the absorption kinetics for six differentinsulin types, including the concentration dependency for regular insulinand dose dependency for glargine insulin (Wong et al., 2008).

Mechanistic Models for Subcutaneous Absorption of MonoclonalAntibodies

Monoclonal antibodies are a distinct group of protein therapeuticswith common structure and a high molecular weight that use antibody-specific mechanisms (i.e., binding to FcRn) to reduce degradation.Therefore, it can be hypothesized that different mAbs (and Fc-fusionproteins) may exhibit similar absorption patterns. Several studies haveshown that binding to FcRn is an important determinant of sub-cutaneous absorption of mAbs. Wang et al. (2008) reported that thesubcutaneous bioavailability of 7E3 IgG1 was 3-fold higher in wild-type mice compared with FcRn-deficient animals. Antibody variantswith enhanced binding affinity to FcRn at pH 6.0 and 7.4 showedincreased and decreased bioavailability in mice, respectively (Denget al., 2010, 2012). In contrast, no definitive effect of altering FcRnaffinity on subcutaneous absorption was found for a series of IgG4variants in cynomolgus monkeys (Datta-Mannan et al., 2012).A series of studies by our group has systematically investigated

multiple factors that influence the absorption of rituximab in rodents

(Kagan et al., 2012, 2014; Kagan and Mager, 2013). Specifically, thefollowing factors were evaluated: 1) the role of the anatomic locationof the subcutaneous injection site (back, abdomen, and the dorsal sideof the foot), 2) the volume of the injection, 3) dose level, 4) binding toFcRn; 5) diffusion through the extracellular matrix, and 6) the rate ofdrug delivery. Rodents do not express human CD20 antigen, so rituximabpharmacokinetics are not affected by the antigen-antibody binding inthese species, thus facilitating the analysis of the absorption kinetics. Theanatomic site of injection had a major impact on the rate and the extent ofsubcutaneous absorption of rituximab in mice and rats, which isconsistent with other studies (Beshyah et al., 1991; Macdougall et al.,1991; Jensen et al., 1994; Ter Braak et al., 1996; Kota et al., 2007).Interestingly, injection-site differences were not observed for golimumabin humans (Xu et al., 2010a). An inverse correlation was found betweenthe dose level (1–40 mg/kg) and the subcutaneous bioavailability ofrituximab in mice and rats (Kagan et al., 2012, 2014).Modeling was used to distinguish between the two proposed

mechanisms of dose-dependent absorption of rituximab: 1) FcRn-mediated protection from degradation at the injection site, and 2)FcRn-mediated transcytosis from the interstitial space to the blood.FcRn-mediated transport of IgG across cells has been demonstrated invitro (Dickinson et al., 1999; Antohe et al., 2001). Only the model thatincorporated binding of rituximab to a receptor (presumably FcRn) asa part of the absorption pathway was able to capture the observeddose-dependent bioavailability of rituximab (Kagan et al., 2012). Thefinal absorption model included three competing processes at theabsorption site: degradation of free rituximab (kSCdeg), absorption of freerituximab (presumably through the lymphatics, ka1), and absorption ofbound rituximab (presumably through FcRn-mediated transcytosis,ka2) (Fig. 5A). The binding process was assumed to occur rapidly atthe absorption site (ABS) and was characterized by the equilibriumdissociation constant (KSC

D ), and the amount of binding sites was heldconstant (RSC

tot ). The following differential equations defined theabsorption model:

Fig. 4. Schematic of the unifying model of the subcutaneous absorption of differentinsulins (modified from Wong et al., 2008). Absorption of all types of insulin occursthrough a common dimeric/monomeric compartment (Xdim). Short dashed arrowsrepresent the distribution of the insulin dose for different types of insulin. Solidarrows represent first-order rate processes. Long dash arrows represent the diffusionloss of insulin at the absorption site (kd). C, crystalline insulin; P, precipitatedinsulin; Xh, hexameric insulin; Xint, interstitial space; Xplasma, plasma space.

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dAinj

dt¼ 2kinj × Ainj ð15Þ

dABStotdt

¼ kinj × Ainj 2 ðkSCdeg 1 ka1Þ × ABSfree 2 ka2 × ðABStot 2ABSfreeÞð16Þ

ABSfree ¼ 0:5 ×h�ABStot 2RSC

tot 2KSCD

�

þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ABStot 2RSC

tot 2KSCD

�2 þ 4 × KSCD × ABStot

q ið17Þ

dC

dt¼ ka1 ×

ABSfreeVc

þ ka2 ×ðABStot 2ABSfreeÞ

Vc6 disposition ð18Þ

where C is the antibody concentration in the central compartment,ABSfree is free rituximab at the absorption site, and (ABStot 2 ABSfree)is bound rituximab at the absorption site. Interestingly, the majority ofmodel parameters were shared between the back and the abdomeninjection sites (with the exception of the rate of absorption for freedrug ka1, which was attributed to the differences in the subcutaneousspace structure between two anatomic locations). A separate injectionsite compartment (Ainj) was included to account for a delay in theabsorption observed in rats; this compartment was not required fordescribing the mouse data.To further investigate the role of FcRn in the subcutaneous ab-

sorption of mAbs, rituximab was coadministered subcutaneously witha large amount of nonspecific IgG (500 mg/kg). The observed de-crease in bioavailability was attributed to the saturation of FcRn-binding, and the model provided a good prediction of the experimentalresults for different rituximab dose levels and injection sites based onparameters estimated for rituximab given alone (Kagan and Mager,2013). For simplicity, the same affinity to FcRn was assumed forrituximab and IgG, and the amount of endogenous IgG at the ab-sorption site was considered negligible. In addition, the model cap-tured the pharmacokinetic profiles after coadministration of rituximabwith subcutaneous hyaluronidase, which resulted in an increase inbioavailability, using parameters estimated for rituximab given alone,with the exception of the absorption rate constant for the free drug(Kagan and Mager, 2013). This result was in agreement with the modeof action of hyaluronidase (i.e., disruption of glycosaminoglycanmatrix) (Bookbinder et al., 2006; Frost, 2007).The model was applied for description of rituximab pharmacoki-

netics after intravenous and subcutaneous administration to mice.

Several model parameters were shared between species, but otherswere scaled with body weight (see Interspecies Modeling ofSubcutaneous Absorption for Protein Therapeutics) (Kagan et al.,2014). Simulations were used to help visualize the competition amongthe two absorption pathways and degradation kinetics (Kagan andMager, 2013; Kagan et al., 2014). For rituximab given alone, receptor-mediated transport accounted for absorption of approximately 57, 22,and 9% of the dose for 1, 10, and 40 mg/kg dose levels (subcutaneousinjection at the back to rats); this pathway was almost completelyabrogated by coadministration with a large amount of nonspecific IgG(Kagan and Mager, 2013).This mechanistic model was useful for evaluating the relative

contribution of two pathways to subcutaneous bioavailability of rituximab(Kagan and Mager, 2013), and may be further applied for investigatingthe role of system- and drug-dependent parameters on the rate and extentof absorption of mAbs. For example, Fig. 6 shows that 10-fold differencein the binding affinity or the receptor expression level may havea significant effect on subcutaneous bioavailability of rituximab.Dahlberg et al. (2014) used a combination of the first-order

lymphatic uptake and Michaelis-Menten uptake by blood capillaries intheir model of trastuzumab absorption in rats (Fig. 3B). A range ofintravenous doses (0.02–2.0 mg/kg) and a single subcutaneous dose(2 mg/kg) were evaluated in non–lymph-cannulated and lymph-cannulated animals (see Mechanistic Dual-Pathway SubcutaneousAbsorption Models). The estimated bioavailability of trastuzumab was85.5%, which is similar to the extent of absorption reported forrituximab (70% at 1 mg/kg dose level in rats) (Kagan and Mager, 2013).The lymphatic pathway and the saturable uptake through bloodcapillaries accounted for 53.1 and 32.4% of the absorbed dose. TheMichaelis-Menten kinetics were superior to the first-order kinetics indescribing the absorption, and the estimated Km value suggested thatthis process was considerably saturated by the administered dose. TheMichaelis-Menten kinetics as implemented in this study were similar tothe receptor-mediated absorption mechanism of rituximab (as describedbefore) (Kagan et al., 2012). A comparison of the Michaelis-Menten andreceptor-binding models for describing the systemic disposition of drugshas been reported (Gibiansky et al., 2008; Yan et al., 2010).The pharmacokinetics of anti-amyloid-b wild type and Fc-variant

(I235A.H435A) mIgG2a was evaluated after a single intravenous andsubcutaneous dose (5 mg/kg) in SCID mice (Deng et al., 2012). Thebioavailability for the wild-type and Fc-variant antibody, lackingbinding affinity to FcRn at pH 6.0 and 7.4, was 76.3 and 41.8%. Amodification of the endosomal recycling model (previously used fordescribing the systemic disposition of mAbs by Hansen and Balthasar,

Fig. 5. (A) Schematic of the pharmacokineticmodel used to describe the subcutaneous (SC)absorption of rituximab in mice and rats (modifiedfrom Kagan et al., 2012, 2014; Kagan and Mager,2013). Optional compartment is shown with dashedline. (B) Schematic of the pharmacokinetic modelwith two endosomal spaces used to describe thesubcutaneous absorption of wild-type and Fc-variant mIgG2a in SCID mice (Deng et al., 2012).Compartments and rate constants are described inthe text. DR, drug-receptor complex; Rfree, freereceptor.

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2003) was developed and included two separate endosomal compart-ments for the skin and the rest of the body (Fig. 5B). Absorption ofmAbs was described by a combination of the first-order absorption(F•ka) attributed to the lymphatic uptake and a first-order uptake fromthe skin to the endosomal compartment (ke). The systemic dispositionmodel was parameterized as described before (Hansen and Balthasar,2003). Antibodies entered both endosomal spaces with a first-orderrate constant (kup), where they could rapidly bind to the FcRn (withaffinity KD). Total concentration of the FcRn was set to be the samefor both endosomal compartments [RT1(nonskin) = RT2(skin)];however, it is unclear whether the relative sizes of the endosomalspaces (whole body versus injection site/skin) was included. Freeantibodies were degraded with a first-order process (kdeg), and bound

antibodies returned to the vascular space with a first-order process(kret, which was constrained to be equal to kup). The unbound fractionof IgG in the endosomal compartments was calculated (nonskin fu1,skin fu2). The competition between the exogenous test antibodies andendogenous murine IgG for FcRn binding was not considered due tothe low endogenous IgG concentration in SCID mice. Fractionunbound (fu) for Fc-variant antibody was set to 1. The model was ableto simultaneously capture the data for both the wild-type and the Fc-variant mAbs (Deng et al., 2012).Zhao et al. (2013) proposed a physiologic model of subcutaneous

absorption of mAbs based on the structural tissue model developed byGarg and Balthasar (2007) for mAbs disposition. The majority ofmodel parameters were fixed to previously published values. Lymphatictransit time and lymphatic elimination rate constant were estimatedusing the pharmacokinetic profiles of omalizumab in humans. Based onthe sensitivity analysis, these investigators suggested that the lymphaticflow rate and lymphatic drug elimination constant were the mostinfluential to bioavailability. However, it was mentioned that the extentof lymphatic elimination of mAbs remains unknown. Analysis of datafor other mAbs administered by the subcutaneous route can be po-tentially used to further evaluate this model.

Population Modeling of Absorption and Covariate Analysis forProtein Therapeutics

Extravascular dosing commonly results in a greater variability ascompared with intravenous administration. Quantification of the var-iability, in addition to the estimation of the structural parameters, isimportant in clinical settings for better understanding of the dosingrequirements for an individual patient. At the same time, populationvariability may hamper identifiability of the structural parameters forcomplex mechanism-based models. Blood sampling during theabsorption phase is often limited in clinical trials; and nonlineardisposition, frequently exhibited by protein therapeutics, may furtherobscure the absorption behavior. These factors may lead to over-simplification of the absorption component of the pharmacokineticmodel. For example, between-subject variability is often omitted for theabsorption rate and bioavailability parameters. Covariate analysis israrely reported for absorption parameters; however, several studies haveidentified body size, age, and population characteristics as factors thatmay affect the rate of absorption (Agoram et al., 2007; Potocka et al.,2011; Naik et al., 2013).Table 2 summarizes selected studies that used population modeling

approach for therapeutic proteins. For example, the pharmacokineticsof pegylated erythropoietin, peginesatide (a 40-kDa PEG-peptide),filgrastim, and darbepoetin alfa were well described using a first-orderabsorption rate constant and a bioavailability term (Fig. 1A) (Jolling et al.,2005; Agoram et al., 2007; Krzyzanski et al., 2010; Naik et al., 2013).Chatelut et al. (1999) used a dual-pathway absorption model (withsequential zero-order and first-order absorption) (Fig. 1C) in populationpharmacokinetic analysis of IFN-a2b after a single subcutaneous injectionin patients with chronic hepatitis C infection. All absorption parameterswere estimated with good precision, except for the absolute bioavailability(because of lacking intravenous data). Covariate analysis for absorptionparameters was not performed, and the between-subject variability forthese parameters was 33–40% (CV%). Saturable carrier-mediated mem-brane transport and precipitation with subsequent dissolution werediscussed as potential reasons for complex absorption behavior. Otherevaluated absorption models included zero-order or first-order only (withor without a lag time), and a combination of zero- and first-order pro-cesses occurring simultaneously. Models combining zero- and first-orderabsorption kinetics were reported for other proteins (Table 2).

Fig. 6. The effect of a change in the expression level of the receptor and the bindingaffinity on the subcutaneous bioavailability of mAbs. Simulation was performedusing the model developed for rituximab injected subcutaneously at the back of rats(Kagan et al., 2012); the model schematic is shown in Fig. 5A. Reported values ofKD and Rtot were changed 10-fold from the reported values, and all the otherparameters were kept constant. The column in the middle (relative values of 1 for KD

and Rtot) represent (A) the experimentally obtained bioavailability of 69% for 1 mg/kgand (B) 18% for 40 mg/kg dose.

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A population model-based meta-analysis described the pharmaco-kinetics of recombinant human erythropoietin after intravenous andsubcutaneous administration using data from 16 trials (Olsson-Gisleskog et al., 2007). Deconvolution analysis revealed complexabsorption behavior, with a relatively dose-proportional first phase andmore than dose-proportional second phase. The systemic dispositionmodel included central and peripheral compartments and a combina-tion of linear and saturable elimination. The best fit was obtained witha model that included two absorption mechanisms. The fasterabsorption phase was described as a sequential zero-order input intothe depot compartment (with duration of 0.725 hour), followed by afirst-order absorption into the central compartment. The slowerabsorption phase started after a delay (2.72 hours) and was describedas a zero-order input directly into the central compartment (withduration of 37.8 hours). The fraction absorbed through the firstpathway was 81 and 60% for dose levels smaller than or greater than300 IU/kg, respectively. The absolute bioavailability was described bya hyperbolic function based on the dose level. The model successfullycaptured data from all studies, but the underlying mechanism forcomplex absorption remained unclear (Olsson-Gisleskog et al., 2007).A recent review summarized a large number of human population

pharmacokinetic studies for mAbs (given mostly by the intravenousroute) (Dirks and Meibohm, 2010). Two-compartment model withlinear elimination or a combination of linear and nonlinear clearanceswas usually used for mAbs. Body size was a commonly identifiedcovariate for the volume of distribution and clearance. This reviewfocuses on studies that performed population analysis for mAbs andFc-fusion proteins given by the subcutaneous route (Table 3). First-order kinetics were selected for describing the absorption process aftersubcutaneous injection in all reviewed studies. Several studiesreported evaluating zero-order kinetics or a combination of zero-and first-order processes. The absorption was generally slow, with theabsorption rate constant ranging from 0.12 to 1.2 day21. The between-subject variability associated with the absorption rate constant wasusually high or not estimated because of the limited data during theabsorption phase. The absorption rate constant was found to decreasewith age for canakinumab, denosumab, and AMG317, and theexponent on the centered covariate was from 20.319 to 20.72. Adecrease of the lymph flow with age was suggested before asa mechanism of this behavior (Agoram et al., 2007).In the majority of studies, covariate analysis for the absorption rate

constant was not reported for mAbs. A high shrinkage for the estimateof ka precluded further evaluation of covariate effects on this pa-rameter in several studies. Trials that evaluated intravenous admin-istration estimated the absolute bioavailability, which ranged from 7 to74%. For canakinumab, the bioavailability depended on the drugproduct (59–74%) (Chakraborty et al., 2012, 2013). The estimation ofbetween-subject variability and the evaluation of covariates wasgenerally not performed for the bioavailability parameter. Because ofthe lack of intravenous data, the apparent values for the clearance andthe volume of distribution (CL/F and V/F) were estimated in severalworks, and body weight was frequently found to be a significantcovariate. Therefore, dependence of the bioavailability on body weightand other covariates cannot be ruled out at this time.

Interspecies Modeling of Subcutaneous Absorption for ProteinTherapeutics

The ability to predict pharmacokinetic and pharmacodynamic prop-erties of drug candidates in humans based on preclinical data isessential for improving the success rate and predictability of drugdevelopment. In addition, development of approaches for sharing and

scaling of parameters among species may provide an efficient way forintegrative analysis of data from different species. Systemic dis-position of protein therapeutics in humans could be predictedreasonably well using allometric relationships:

P ¼ a × BWb ð19Þ

where P is a parameter of interest, BW is species body weight, anda and b are the coefficient and the exponent of the allometric equation.The value of the allometric exponents for clearance and the volume ofdistribution and the number of species required for the prediction hasvaried among studies (Mordenti et al., 1991; Mahmood, 2004, 2009;Ling et al., 2009; Wang and Prueksaritanont, 2010; Deng et al., 2011).Traditional allometry cannot be applied for drugs exhibiting a target-mediated disposition that results in dose-dependent pharmacokineticparameters (Woo and Jusko, 2007; Kagan et al., 2010). We havepreviously combined target-mediated disposition model with allome-tric principles to simultaneously capture the pharmacokinetics of typeI IFNs and exenatide in multiple species (Kagan et al., 2010; Chenet al., 2013).The quantitative information on species difference in the absorption

process is very limited. The first-order absorption rate constant forPEG-erythropoietin after subcutaneous injection was shown to scalewith an allometric exponent of 20.147 (based on four species), anda species-specific bioavailability parameter was used (Jolling et al.,2005). The absorption of erythropoietin was described by a combina-tion of zero- and first-order kinetics in three species (rats, monkeys,and humans) (Woo and Jusko, 2007). The relationship between theestimated parameters and species body weight was assessed using re-gression analysis, and the allometric exponent for the first-order ab-sorption rate constant was calculated as 20.349. Dose-dependent rateand extent of absorption (frequently reported for protein therapeutics)can further complicate interspecies analysis. For example, separatevalues for the absorption rate constant or bioavailability are sometimesused for each dose level (Mager et al., 2003; Ramakrishnan et al., 2003;Gao and Jusko, 2012). Although this approach might be useful forcapturing observed data, it provides little insight into the mechanism ofabsorption and cannot be used effectively for interspecies prediction.Michaelis-Menten kinetics were used to successfully capture dose-

dependent absorption of exenatide in multiple species, and species-specific parameters (Vmax and Km) were required (Chen et al., 2013).The ability of the model to predict exenatide pharmacokinetics inhumans after subcutaneous administration was evaluated by simula-tion using two approaches: 1) separate sets of Vmax and Km valuesfrom mice, rats, and monkeys; and 2) Vmax and Km for humans werecalculated using the allometric approach from three preclinical species.Interestingly, human data could not be adequately predicted usingmonkey absorption parameters, but rat Vmax and Km provided resultsconsistent with clinical data. The Vmax parameter was highly correlatedwith body weight (allometric exponent of 0.392, R2 = 0.996).Although Km appeared less correlated with body weight (allometricexponent of 0.605, R2 = 0.602), the combination of Vmax and Km

values obtained from the regressions provided a good prediction ofhuman data (Chen et al., 2013).Recently, a mechanism-based model that combines the absorption

of free and bound antibody with presystemic degradation was appliedto describe the pharmacokinetics of rituximab in rats and mice (Kaganand Mager, 2013; Kagan et al., 2014). Subcutaneous absorption ofrituximab was dose dependent in both species, but the absorptionprocess was faster in mice, and the magnitude of the nonlinearabsorption was less pronounced in mice as compared with rats. Similarstructural model was able to capture the dose-dependent subcutaneous

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TABLE2

Selectedstudiesthat

evaluatedsubcutaneous

absorptio

nof

proteintherapeuticsusingpopulatio

nanalysis(excluding

monoclonalantib

odiesandFc-fusion

proteins)

Drug

Species/Population

AbsorptionModel

AbsorptionParameters

BetweenSub

ject

VariabilityforAbsorption

Param

eters,CV%

Cov

ariatesforAbsorption

Param

eters

Reference

Anakinra

Rats

Sequentialzero-andfirst-order

Fractionof

zero-order

Yes

fork a

No

Liu

etal.,2011

Durationof

zero-order

k aDarbepoetin

alfa

Anemic

patientswith

chronic

kidney

disease

Zero-orderinputinto

thedepot

compartmentfollo

wed

bythe

first-orderabsorptio

n

FYes

No

Doshi

etal.,2010

Durationof

input k a

Darbepoetin

alfa

Health

yhumans

First-order

k aYes

fork a

Flin

earfunctio

nof

thedose

Agoram

etal.,2007

k a}

(Age/50)

20.951

Erythropoietin

dPediatric

patientswith

chronic

kidney

disease

First-order

FNo

No

Knebelet

al.,2008

k aErythropoietin

Health

yhumans(m

eta-analysis)

(1)Zero-orderinputinto

thedepot

compartmentfollo

wed

bythe

first-orderabsorptio

n

F-hyperbolic

functio

nof

thedose;

Yes

fork a,D1,

Tlag,

fractio

nof

(1)

k adecreasedwith

ageandbody

weight;

Olsson-Gisleskog

etal.,

2007

(2)Zero-orderafteralagtim

eaFractionof

(1),dose

dependent;

k alower

infemales

For

(1):k a,Durationof

zero-order

(D1)

Fincreasedwith

increase

inhemoglobin;

For

(2):Durationof

zero-order

(D2),Tlag

Fdecreasedwith

body

weight

Filg

rastim

Health

yadults

Parallelzero-andfirst-order

follo

wed

byfirst-order

FNo

No

Wiczlinget

al.,2009

Fractionof

zero-order

Durationof

zero-order

k aFilg

rastim

Health

yadults

First-order

FNo

No

Krzyzanskiet

al.,2010

k aGrowth

horm

one

Health

yhumansanddialysis

patients

Michaelis-M

enten

Vmax

No

Kmpopulatio

nspecific

Klitgaardet

al.,2009

Km

Insulin

Health

yhumans

First-order

with

atransitcompartment

FYes

k a}

BMI

Potocka

etal.,2011

k a1

k a2

Insulin

Rats

Parallelzero-andfirst-order

Fractionof

zero-order

No

No

Gopalakrishnanet

al.,

2005

Durationof

zero-order

Tlagforzero-order k a

F-dose-dependent

functio

nIFN-a2b

Hum

anhepatitisC

patients

Sequentialzero-andfirst-order

Fractionof

zero-order

Yes

No

Chatelutet

al.,1999

Durationof

zero-order

k aLeukemia

inhibitory

factor

Health

ypostmenopausalwom

enandinfertile

patients

Zero-order

Durationof

zero-order

No

No

Gogginet

al.,2004

Low

molecular

weight

heparin

Health

yhumans

Parallelzero-andfirst-order

follo

wed

byfirst-order

Fractionof

zero-order

Yes

fork a

andfractio

nof

zero-order

No

Abe

etal.,2013

Durationof

zero-order

Tlagforzero-order k a

Pegylated

human

erythropoietin

Rats,dogs,andmonkeys

First-order

FYes

fork a,F

k a}

BW

20.149

Jolling

etal.,2005

k aTlag}

BW

21.810

Tlag

F–speciesspecific

Peginesatide

Chronic

kidney

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First-order

FYes

k a}

BMI,creatin

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aThe

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h)(O

lsson-Gisleskog

etal.,2007).

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absorption in both species (with the exception of an absorption delayfor rats) (Fig. 5A). The binding affinity of rituximab to the receptor(presumably FcRn), the expression level of the receptor, and the rateconstant for presystemic degradation were shared between species.The rate constants for absorption of the free and bound antibody wereestimated separately for mice and rats, and decreased with increasingbody weight. Interestingly, the relationships between the absorption rateconstants and species body weight was similar to the relationship betweenthe distribution rate constants and body weight (Kagan et al., 2014).

Conclusions and Future Perspective

Subcutaneous absorption of proteins is regulated by a large numberof factors, which can be divided into species, subject, and drug/formulation specific. Predicting subcutaneous absorption in humans isa difficult task, and the best preclinical model has not been identified(McDonald et al., 2010). Species differences in skin morphology andtheir effect on the rate and extent of subcutaneous absorption, andapproaches for integrating this information into interspecies pharma-cokinetic models require further investigation. Some physiologicprocesses that take part in the subcutaneous absorption may be scaledwith body weight among species. Lindstedt and Schaeffer (2002)

reported that the skin blood flow can be described using an allometricexponent of 0.741 using data for mouse, rat, dog, and human.Interestingly, the lymph flow rate in the thoracic duct can be scaled withbody weight using an allometric exponent of 0.723–0.792 (Fig. 7).Insulin is an important paradigm that demonstrates that the

mechanistic insights into the absorption process can be exploited fordeveloping products with a wide range of properties (i.e., rapid-actingversus long-acting insulin analogs). As described before, some of themodel components were effectively shared among different insulintypes (Fig. 4). Similarly, it can be hypothesized that due to structuralresemblance, the absorption behavior of various mAbs and Fc-fusionproteins is governed by similar factors (e.g., binding to FcRn).Therefore, some of the model parameters can be shared within thisclass of drugs or predicted based on in vitro experiments (such asmeasurement of binding affinity of different IgG to FcRn usingsurface plasmon resonance technique). Furthermore, species differ-ences in the affinity and in the expression levels of FcRn can bepotentially used for interspecies prediction of the absorption kinetics.The contribution of many drug- and formulation-dependent factors

to the subcutaneous absorption of therapeutic proteins has not beensufficiently investigated (e.g., glycosylation, pegylation, the isoelectricpoint of protein, presence of binding proteins in the subcutaneous

TABLE 3

Selected studies that evaluated subcutaneous absorption of monoclonal antibodies and Fc-fusion proteins using population analysis

Drug PopulationPopulationMean F, %

Population Meanka, Day 1

Between SubjectVariability for

ka, CV%Covariates for ka References

Adalimumab Rheumatoid arthritis 58 Value not reported — — Velagapudi et al., 2005AMG317, fully human

IgG2Healthy humans 24.3 0.185 — Age (centered at

40 yr)Kakkar et al., 2011

20.72b

Canakinumab Human healthy and patients 63.3 or 70.0a 0.299 or 0.269a 64 Age (centered at34 yr)

Chakraborty et al., 2012

20.555b

Canakinumab Gouty arthritis 58.8–73.5a 0.193–0.296a 50.8 Age (centered at52 yr)

Chakraborty et al., 2013

20.319b

Denosumab Postmenopausal womenwith osteopenia orosteoporosis

63.8 0.212 63 Age (centered at64 yr)

Sutjandra et al., 2011

20.577b

Denosumab Bone metastasis 61.2 0.257 51.5 Age (centered at54 yr)

Gibiansky et al., 2012

20.509b

Efalizumab Psoriasis 56.4 0.242 — — Ng et al., 2005Efalizumab Psoriasis —

c 0.191 0 fixed — Sun et al., 2005Etanercept Juvenile rheumatoid arthritis 58c 1.2 215 — Yim et al., 2005Etanercept Rheumatoid arthritis —

c 0.797 24.3 (73.1d) — Lee et al., 2003Etanercept Psoriasis —

c 0.754 — — Nestorov et al., 2004Fc-osteoprotegerin Healthy postmenopausal

women7.19 0.314 — — Zierhut et al., 2008

Golimumab Psoriatic arthritis —c 0.908 — — Xu et al., 2009

Golimumab Rheumatoid arthritis —c 0.125 — — Hu et al., 2011

Golimumab Ankylosing spondylitis —c 1.010 78.6 — Xu et al., 2010b

IgG subcutaneous Primary immunodeficiency 66.0 0.439 — — Landersdorfer et al., 2013MTRX1011A, humanized

IgG1Rheumatoid arthritis 52.3 (IIV 18.9 CV%) 0.212 68.7 — Zheng et al., 2011

Omalizumab Asthma 62c 0.480 39.9 — Hayashi et al., 2007Omalizumab Asthma — 0.458 141 — Lowe et al., 2009Romiplostim Healthy subjects 49.9 0.610 — — Wang et al., 2010Sirukumab Healthy subjects —

c 0.77 60.0 — Zhuang et al., 2013TNFR-Fc fusion protein Ankylosing spondylitis —

c 1.452 (Tlag = 1 h) 55.6 (81.8 for Tlag) — Fang et al., 2010Ustekinumab Psoriasis —

c 0.354 0 fixed — Zhu et al., 2009Ustekinumab Psoriatic arthritis —

c 0.427 82.4 — Zhu et al., 2010

F, systemic bioavailability; IIV, inter-individual variability; ka, first-order absorption rate constant; TNF, tumor necrosis factor.aDepending on the drug product.bExponent for power model on centered covariate.cBioavailability was not modeled as a separate parameter; volume of distribution (Vd/F) and clearance (CL/F) were estimated. If the bioavailability value was reported, it was taken from previous

studies.dCV% for interoccasion variability.

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space). The absorption of nonglycosylated granulocyte colony-stimulating factor (filgrastim) was faster and resulted in a greaterAUC and Cmax (by 18 and 20%) as compared with glycosylatedgranulocyte colony-stimulating factor (lenograstim) after subcutane-ous injection of 5 mg/kg in normal subjects (no difference between theelimination half-lives was observed) (Watts et al., 1997). Sub-cutaneous absorption of erythropoietin a in pediatric patients was23% faster and resulted in a 43% lower bioavailability as comparedwith erythropoietin d (erythropoietin d is produced in a human cellline and has a different carbohydrate composition from Chinesehamster ovary [CHO] cell-derived erythropoietin a) (Knebel et al.,2008). Lower bioavailability was reported for mAbs with a higher pIvalues (more than ;9.0) in minipigs and humans (Zheng et al., 2012).Formulation related factors for subcutaneous injected biotherapeuticshave been reviewed recently (Kinnunen and Mrsny, 2014). However,quantitative characterization of the effects of formulation excipientsand absorption modifiers on the rate and extent of absorption oftherapeutic proteins should be investigated in future studies.For insulin and mAbs, binding at the absorption site was proposed

as a mechanism that modulates the systemic absorption (Mosekildeet al., 1989; Wang et al., 2008; Kagan et al., 2012); more informationis needed regarding the effect of endogenous proteins, solublereceptors, and antidrug antibodies in the interstitial space on ab-sorption of exogenous proteins. Presystemic degradation processes fortherapeutic proteins are poorly understood, and in vitro incubation insubcutaneous tissue homogenates, lymph (or lymph nodes), and bloodcan be used for evaluating drug stability and informing the modelingprocess (Wang et al., 2012; Zou et al., 2013). However, in vitro studiesmight not fully represent the complexity of the in vivo conditions.Human growth hormone was stable for 6 hours in the central lymph ofsheep, but there was a significant difference in the drug recoverybetween the peripheral and central lymph-cannulated groups (62 versus8.6%) (Charman et al., 2000). Measurement of the disappearance rate ofthe injected protein from the subcutaneous site (in addition to plasmaconcentrations) can help to identify rate-limiting steps in the absorptionprocess. A linear relationship was found between the half-life at theinjection site and the molecular weight of four fluorescently labeled

proteins (23 – 149 kDa) using whole-body imaging technique (Wu et al.,2012). The effect of various pathologic states on subcutaneous absorptionhas not been sufficiently characterized (e.g., obesity). Increased adipositywas associated with a reduced subcutaneous blood flow and a slowerabsorption of insulin in humans (Vora et al., 1992). Wang et al. (2012)reported that PEG40-erythropoietin exhibited approximately 2-fold lowerexposure in fat rats as compared with normal rats after body-weightnormalized subcutaneous dose administration.In conclusion, this review summarized current experience with

modeling of the pharmacokinetics of therapeutic proteins administeredby the subcutaneous route. Despite continuing research in this area,our understanding of the quantitative aspects of subcutaneous ab-sorption is still limited. It is anticipated that further development ofmechanism-based modeling will play a central role in resolvingcomplexities associated with absorption of these drugs.

Authorship ContributionsWrote or contributed to the writing of the manuscript: Kagan.

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Address correspondence to: Dr. Leonid Kagan, Department of Pharmaceutics,Ernest Mario School of Pharmacy, Rutgers, State University of New Jersey, 160Frelinghuysen Road, Piscataway, NJ 08854. E-mail: lkagan@pharmacy.rutgers.edu

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