Population Pharmacokinetics of Cyclosporine in Transplant Recipients

Abstract

A number of classical pharmacokinetic studies have been conducted in transplant patients. However, they suffer from some limitations, for example, (1) the study design was limited to intense blood sampling in small groups of patients during a certain posttransplant period, (2) patient factors were evaluated one at a time to identify their association with the pharmacokinetic parameters, and (3) mean pharmacokinetic parameters often cannot be precisely estimated due to large intraindividual variability. Population pharmacokinetics provides a potential means of addressing these limitations and is a powerful tool to evaluate the magnitude and consistency of drug exposure. Population pharmacokinetic studies of cyclosporine focused solely on developing limited sampling strategies and Bayesian estimators to estimate drug exposure, have been summarized before, and are, therefore, not a subject of this review. The major focus of this review is to describe factors (demographic factors, hepatic and gastrointestinal functions, drug–drug interactions, genetic polymorphisms of drug metabolizing enzymes and transporters) that have been identified to contribute to the large portion of observed variability in the pharmacokinetics of cyclosporine in transplant patients. This review summarizes and interprets the conclusions as well as the nonlinear mixed-effects modeling methodologies used in such studies. A highly diversified collection of structural models, variability models, and covariate submodels have been evaluated and validated using internal or external validation methods. This review also highlights areas where additional research is warranted to improve the models since a portion of model variability still remains unexplained.

INTRODUCTION

Pharmacokinetics evaluates the time course of the processes of absorption, distribution, metabolism, and excretion of drugs. Pharmacokinetic modeling uses various pharmacokinetic parameters as descriptors of these processes and mathematically relates the concentration of drug in biological fluids, typically in blood or plasma, to the time after administration of the drug. Pharmacokinetic parameters are useful for understanding response/toxicity over time and are important for the determination of dose and formulation of the drug to be administrated. Important pharmacokinetic parameters include clearance (CL), volume of distribution (V_d), absorption rate constant (k_a), elimination rate constant (k), and half-life (T_1/2). Pharmacokinetic parameters can be determined by modeling drug concentration versus time profiles using either classical or population pharmacokinetic modeling techniques.

Classical modeling approaches normally employ linear and nonlinear regression to estimate individual pharmacokinetic parameters from each subject. Noncompartment analysis is the most commonly used classical approach. Parameters are often summarized as a mean value and standard deviation as a reflection of interindividual variability. Typically, the analysis is performed using Phoenix™ WinNonlin® (Pharsight Corp., Mountain View, CA). The data are sometimes averaged or pooled. Despite its simplicity, this approach may result in poorly estimated parameters and confound sources of variability.

Classical pharmacokinetic approaches suffer from some limitations, especially in transplant patients. First of all, the study design is limited to intense blood sampling in a small, relatively homogeneous groups of patients, resulting in insufficient data to make statistically significant conclusions. Furthermore, the homogeneity of the subjects (e.g., patients with comorbidities and the very young and very old) may not represent the variability observed in the entire population. Studies in transplant patient population are often conducted in a certain posttransplant period due to the large intra- and interindividual variability caused by the type of transplantation and postoperative time, which limits the routine clinical applicability of their conclusions to all transplant patients. Secondly, the association of patient factors with pharmacokinetic parameters can generally be evaluated only one covariate at a time, which does not take into account the interactions and coeffects of different factors. This limits its ability to identify all significant factors that contribute to the overall variability in drug exposure. Finally, classical approaches have difficulties in handling nonlinear pharmacokinetics and atypical pharmacokinetic profiles, which are frequently observed in transplant population as the physiological conditions of the transplant patients can change during one single study interval, resulting in large intraindividual and interindividual variability. As a result, the pharmacokinetic parameters estimated are time- and patient-dependent.

Population pharmacokinetic approach is a potential and powerful tool to address the above-mentioned limitations and has been developed as an alternative approach over the last two decades (1–9). First of all, population approaches can be used to analyze data that could not be analyzed using classical methods. It can take advantage of sparsely collected data from a large number of subjects with very few data points from each subject, such as retrospectively collected data from therapeutic drug monitoring. This is especially true for transplant patients since most of the patients are hospitalized and undergo routine monitoring of the immunosuppressive drugs. Data from highly diversified patient populations can be analyzed by estimating typical values of pharmacokinetic parameters together with interindividual and residual variability. The greater amount and heterogeneity of the data can represent the variability in the entire population to a higher degree. Furthermore, the flexibility in study design is essentially increased, for example, the data can be from different dosing intervals at any sampling time following different administration routes, and the number of data points from each subject can be different. Finally, patient factors significantly associated with pharmacokinetic parameters can be evaluated and identified in the model building process. The final covariate submodel could be used for dosage individualization through Bayesian forecasting, which is clinically relevant. In fact, many population pharmacokinetic studies have been conducted to reanalyze the data that have previously been analyzed using classical approaches (data from different studies may be combined), and have resulted in newer findings that could not be made by classical approaches mentioned above (10,11). Typically, nonlinear mixed-effects modeling is performed using NONMEM®, Phoenix® NLME™, Monolix, S-PLUS, SAS, and other software programs. Most studies summarized in this review used the NONMEM® program.

CYCLOSPORINE

The introduction of cyclosporine in the early 1980s, together with advances in surgical procedures, has revolutionized organ transplantation. Cyclosporine has been the cornerstone of most immunosuppressive regimens in organ transplantation until recently. The original brand name of cyclosporine is Sandimmune®, and it was available as soft gelatin capsules, oral solution, and intravenous formulation (12). Subsequently, the microemulsion formulation Neoral® that exhibits a more rapid and consistent absorption than Sandimmune has become available as soft gelatin capsules and oral solution (13).

The low exposure of cyclosporine has been shown to be associated with acute and/or chronic rejection (14,15), while the high exposure of cyclosporine is associated with serious adverse effects such as hypertension, posttransplant diabetes mellitus, dyslipidemia, intermittent renal hypoperfusion, and both reversible acute toxicity and irreversible tubulointerstitial fibrosis (15,16). It is difficult to predict the exposure of cyclosporine in a patient on a particular dose due to the large variability in its pharmacokinetics.

A number of classical pharmacokinetic studies of cyclosporine have been conducted in transplant populations, but they suffer from the certain limitations discussed previously. Therefore, population pharmacokinetic approach was used for the pharmacokinetic analysis of cyclosporine. The aim of this review is to provide an overview of 31 publications (17–54) that evaluated population pharmacokinetics of cyclosporine in transplant patients and to summarize and interpret the information to benefit clinical applications and future investigations.

CLASSICAL PHARMACOKINETICS OF CYCLOSPORINE

Cyclosporine is highly lipophilic and its oral absorption is slow and incomplete. Its oral bioavailability ranges from 10 to 89%. Food causes a clinically significant decrease in peak concentration and exposure of cyclosporine. Cyclosporine is extensively distributed in peripheral tissues. Its volume of distribution is 3 to 5 L/kg. Cyclosporine distribution in the blood is approximately 41 to 58% in erythrocytes, 33 to 47% in plasma, 5 to 12% in granulocytes, and 4 to 9% in lymphocytes. In plasma, cyclosporine binds primarily to lipoproteins and secondarily to albumin. Its fraction unbound is approximately 0.1. Cyclosporine is extensively metabolized in the liver via CYP3A pathway, and the metabolites are extensively excreted in the bile. The clearance of cyclosporine is 0.3 to 0.4 L/kg and the half-life ranges from 5 to 27 h (12,13).

POPULATION PHARMACOKINETICS OF CYCLOSPORINE

Literature Search

Publications reviewed were identified through a systematic search on MEDLINE/PubMed using the keyword “pharmacokinetics, cyclosporine, NONMEM” (44 studies found) or “pharmacokinetics, cyclosporine, bayesian” (55 studies found). Only population pharmacokinetic studies in human subjects were included in this review. Additionally, relevant sources identified in the bibliographies of reviewed papers were also included. Abstracts and other nonjournal publications were only included if sufficient details were provided. The exclusion criteria are duplicate publications of the same data or cohort, non-English language papers, sources lacking details in methodology or results, and review/summary papers. Population pharmacokinetic studies of cyclosporine focused solely on developing limited sampling strategies and Bayesian estimators to estimate drug exposure, have been summarized before (48,49), and are, therefore, not a subject of this review. Finally, 38 publications were included in this review.

STUDY DESIGN

The study design used in population pharmacokinetic studies of cyclosporine is summarized in Table I. Most of the studies were based on patients from Europe. Retrospectively collected data were used in 14 studies. Most of the studies were conducted in posttransplant period, while three studies were conducted in pretransplant period. One-third of the studies involved pediatric patients. Kidney, heart, lung, bone marrow, and liver transplant patients were all studied with kidney transplant patients in most of the publications. Sandimmune and Neoral were used in 12 and 20 studies, respectively. The pharmacokinetic models that adequately described the data and the parameters estimated using these models in these publications are summarized in Table II.

Table I.

Study Design and Significant Covariates of Population Pharmacokinetic Studies of Cyclosporine

References	Site	Cohort	MDL sub	Formulation	Covariatesa
					CL, CL/F	V d, V d/F	k a or k tr	Bioavailability
(17)	France	Adult/pediatric, bone marrow	188 + 60 (1,487)		NT	NT	NT
(18)b	France	Adult/pediatric, bone marrow	188 (1,487)		NT	NT	NT
(19)	France	Adult/pediatric, bone marrow	42 (462)		NT	NT	NT
(20)	USA	Adult, kidney	77 (301)	SAND	POT
(21)	China	Adult, kidney	60 (281)		WT, SEX, POT
(22)	Australia	Adult/pediatric, liver	25 (∼145)	SAND	NT	NT	NT
(23)	Australia	Adult, heart	36 (779)	SAND	WT, DIL			POT (−/+)
(24)	Australia	Adult/pediatric, cardiothoracic	182 (435)	SAND	MI
(25)	Denmark	Kidney, heart, lung	879 (3,617)	NEO
(26)	Spain	Adult, kidney	20
(27)	Australia	Adult, heart	46 (184)	SAND/NEO	WT, DAY TIME (+)			FORM, DIL, PIT (−/+)
(28)	Japan	Adult, kidney	69 (966)	SAND/NEO	WT
(29)	Switzerland	Adult, kidney	49 (350)	SAND/NEO		WT		FORM
(30)	France	Adult, kidney	20 (200)	NEO
(31)	France	Adult, lung	19	NEO	CF	CF	CF
(32)	USA	Adult, bone marrow	129 (740)	SAND/NEO	WT, POT (−)
(33)	France	Adult, kidney	70 (340)	NEO
(34)	France	Adult, kidney	20 (220)		NT	NT
(35)	Holland	Adult, kidney, heart	151	NEO	WT, 3A4
(36)	France	Adult, kidney	63	NEO
(37)	UK	Adult, heart, lung	48 (1,004)	SAND/NEO	ITR, CF, WT			POT (+)
(38)	China	Adult, kidney	99 (2,141)	NEO/Neocyspin/Tianke	POT (−), BIL, WT, AGE, INH, HCT
(39)	Canada	Adult, kidney	37 (2,204)	NEO/Pliva		WT, SEX	FORM
(40)	Spain	Adult, kidney	11 (315)	NEO	NT	NT	NT	POT (+)
(41)	China	Adult, heart	38 (694)	NEO	WT, DIL, HCT	WT
(42)	France	Adult (heart, lung, kidney), pediatric (kidney)	147 (3,072)	NEO	WT	WT	CF, POT
(43)	France	Pediatric, kidney	98 (1,260)	NEO	POT (+)	WT
(44)b	Finland	Pediatric, kidney	162	SAND (IV, PO) NEO (PO)	WT, ROUTE, HCT, SCr, CHL	WT, HCT, SCr, CHL
(45)b	Finland	Pediatric, kidney	104	SAND (IV, PO) NEO (PO)	NT	NT	NT	NT
(46)	Holland	Pediatric, stem cell	17	SAND (IV) NEO (PO)
(47)	Norway	Adult, kidney	49 (916)		AGE	WT, AGE	WT, POT, AGE
(48)	China	Adult, liver	124 (3,731)	NEO	DT, HCT, PR
(49)	China	Adult, kidney	146 (1,577)	NEO	WT, BIL, MDR1	SEX, MDR1
(50)	Korea	Adult, kidney	74 (2,394)		POT, PDD, BIL, WT, ALD
(51)	Netherlands	Adult, bone marrow	20 (436)	SAND (IV) NEO (PO)
(52)	China	Adult, Bone marrow	73 (281)		HCT, ALB, ITR
(53)	Tunisia	Adult, bone marrow	60 (600)	SAND
(54)	Korea	Adult, kidney	69 (2,034)	NEO	POT, CYP	SEX, WT, POT, ABCA, ABCB

Site the country where the patient cohorts were located, Cohort the type of transplantation, MDL sub model building subpopulation presented as number of patients (total number of samples collected), CL clearance, V _d volume of distribution for one-compartment model or volume of distribution in the central compartment (V _c) for two-compartment model, k _a absorption rate constant, k _tr transfer rate constant in Erlang/gamma absorption mode, SAND Sandimmune, NEO Neoral, Pliva Pliva cyclosporine soft gelatin capsules, WT body weight, POT postoperative time, ROUTE intravenous or oral administration, HCT hematocrit, SCr serum creatinine, CHL cholesterol, CF cystic fibrosis, DIL coadministered diltiazem, FORM formulation, BIL total bilirubin level, INH inhibitor (diltiazem/verapamil), PDD prednisolone dose, ALD amlodipine, ALB albumin, ITR itraconazole, 3A4 CYP3A4 genetic polymorphism, MDR1 multidrug resistance 1 transporter genotype, ABCA, ABCB ATP-binding cassette transporter genotypes, MI metabolic inhibitors (diltiazem/itraconazole/ketoconazole), NT not tested, SEX sex, AGE age, IV intravenous administration, PO oral administration

^aCovariates that are significantly associated with pharmacokinetic parameters. The sign in the parentheses denotes positive or negative correlation

^bPretransplant patients were studied

Table II.

Pharmacokinetic Models and Parameters of Population Pharmacokinetic Studies of Cyclosporine

References	Route	CMPT	CL (L/h)	CL/F (L/h)	V (L)	V/F (L)	F
(17)	IV	2	23.5		18a
(18)	IV	2	23.5		94.4
(19)	IV	3	23.3		127.6
(20)	PO	MM		53
(21)	PO	1		59.8		227
(22)	IV	None	0.53 L/h/kg		2.2 L/kg
(23)	PO	1		0.28 L/h/kg		4 L/kg
(24)	PO	None		46.4/34.1b
(25)	PO	2
(26)	PO	MM
(27)	PO	1		4.7		77.4
(28)	PO	2		13.4		507.8
(29)	PO	2		22.6		4.7 L/kg
(30)	PO	2		59.3		76.6a
(31)	PO	2		50		88/74c
(32)	IV/PO	None	22.3				27%
(33)	PO	2		26.3		119
(34)	PO	1
(35)	PO	2		30.7		241.3
(36)	PO	2		30		242.8
(37)	PO	1		23.1		202
(38)	PO	1		28.5		133
(39)	PO	2		8.59		179.6
(40)	PO	1		17		134
(41)	PO	1		21.6		4.5 L/kg
(42)	PO	2		32.6		234.3
(43)	PO	2		23.1		270.3
(44)	IV/PO	3	6.1		26.6		36%
(45)	IV/PO	3	0.88 L/h/kg3/4		2.3 L/kg		38%
(46)	IV/PO	2	11.3		43.4		38.6%
(47)	PO	2		26.9		1143.4
(48)	PO	1		23.1		105
(49)	PO	1		49.5		226
(50)	IV/PO	1		43.6		1,990
(51)	IV/PO	2	21.9		75.6		71%
(52)	IV/PO	None	28.2		1,080		71.1%
(53)	IV	2	25.4		506.9
(54)	PO	1		56	4,650

CMPT number of compartment in the model, MM Michaelis–Menten model, V and V/F total volume of distribution which is summarized here, CL clearance, F bioavailability, IV intravenous administration, PO oral administration

^aOnly volume of distribution in the central compartment was reported

^bCL/F was calculated using the data from the EMIT/TDx assays

^c V/F for patients with/without cystic fibrosis

MODEL BUILDING

The choice of fixed- and random-effects models may affect the adequacy of the model and the selection of significant factors and thus affect the reliability of the conclusions and clinical applicability of the final model for optimization of dosing regimens. Furthermore, the choice of fixed- and random-effects models is based on the type of data, which in turn depends on the properties of the drug and the study populations. Therefore, it is important to summarize how the fixed and random effects were modeled in literature for transplant patients to benefit further investigations and clinical applications. The final models of fixed and random effects are summarized in Table III.

Table III.

Model Building and Analytical Assays in Population Pharmacokinetic Studies of Cyclosporine

References	Forward	Backward	Absorption model	BSV	Error	Res	Assay
(17)							RIA
(18)							RIA
(19)			First-order				HPLC
(20)	0.005			Pro′			RIA
(21)	0.05		First-order	Exp	Exp′	0.31	HPLC/FPIA
(22)							FPIA
(23)	0.01	0.01	First-order	Pro′	Add	77.4	HPLC
(24)				Exp	PP		EMIT/FPIA
(25)			Zero-order
(26)	0.005			Exp	Add	13.9	FPIA
(27)			First-order, lag time	Exp	P+A	0.13 (Pro), 54 (Add)	HPLC
(28)	0.001		First-order, lag time				FPIA
(29)	0.001		First-order, lag time	Pro′	Pro	0.14 (Neoral), 0.43 (SAND)	FPIA
(30)			Gamma				LCMS
(31)			Gamma				EMIT
(32)	0.01	0.01		Exp	P+A		HPLC/UV
(33)	0.01	0.001	Erlang	Exp	P+A	0.05 (Pro), 27 (Add)	EMIT
(34)			Two-portion		P+A	0.13 (Pro), 21 (Add)	EMIT
(35)	0.05	NO	First-order, lag time	Pro′	Exp′	0.22	EMIT
(36)	0.025		Zero-order, lag time	Pro′	Pro	0.14	EMIT
(37)	0.05	0.005	First-order	Exp	P+A	0.44 (Pro), 76.4 (Add)	EMIT
(38)	0.05	0.001	First-order	Exp	P+A	0.31 (Pro), 42.4 (Add)	FPIA
(39)	0.05	0.05	Two-portion	Exp	P+A	0.22a	LCMS
(40)	0.01	NO	First-order	Exp	Pro	0.23	FPIA
(41)	0.001	0.001	First-order	Exp	Pro	0.3	FPIA
(42)	0.01	0.001	Erlang	Exp	P+A	0.11 (Pro), 37.9 (Add)	FPIA
						0.11 (Pro), 30.2 (Add)	LCMS
(43)	0.01	0.001	Erlang	Exp	P+A	0.09 (Pro), 87 (Add)	EMIT
						0.10 (Pro), 48.2 (Add)	EMIT
(44)	0.001	0.001	First-order	Exp	P+A (IV)	IV: 0.09 (Pro), 1.5 (Add)	RIA
					Pro (PO)	PO: 0.2
(45)							RIA
(46)			First-order		Pro	0.19
(47)	0.01	0.001	First-order, lag time	Exp	P+A	0.18 (Pro), 23 (Add)	CEDIA, LCMSMS
(48)	0.001	0.001	First-order	Exp	Exp′	0.19	FPIA
(49)	0.01	0.005	First-order	Exp	Add	33.6	FPIA
(50)	0.05	0.01	First-order	Exp	P+A	11.1 (Pro), 30.2 (Add)	RIA
(51)	0.01	0.01	First-order, lag time	Exp	P+A	8.8 (Pro), 65 (Add)	FPIA
(52)	0.05	0.01		Exp	P+A	0 (approx) (Pro), 0.004 (Add)	FPIA
(53)	0.01	0.01	First-order, lag time	Pro′	P+A	0.03 (Pro), 0.001 (Add)	HPLC/FPIA
(54)	0.05	0.01	First-order	Pro′	Pro	0.354	RIA

^aAdditive error not reported

Forward criteria (p value) used in the forward inclusion model building process, Backward criteria (p value) used in the backward exclusion model building process, BSV between-subject variability model, Exp exponential interindividual variability model: P _ij = TV(P _j) × exp(η _ij), Pro′ proportional interindividual variability model: P _ij = TV(P _j) × (1 + η _ij) (where P _ij is the ith individual’s estimate of the jth basic pharmacokinetic parameter, TV(P _j) is the typical value of the jth population parameter, and η _ij is a random variable for the ith individual and the jth basic pharmacokinetic parameter distributed with mean zero and variance of ω _j ²), Error residual variability model, Add additive error model: C _obs = C _pred + ε, Exp′ exponential model: C _obs = C _pred × exp(ε _ij), Pro proportional error model: C _obs = C _pred × (1 + ε), P+A a combined error model containing both proportional and additive errors: C _obs = C _pred × (1 + ε) + ε′, PP C _obs = C _pred + ε × C _pred ² (where C _obs and C _pred are the observed and predicted blood tacrolimus concentrations, respectively, and ε and ε′ are normal random variables with means of zero and variances of δ ² and δ′², respectively), Res residual variability estimate in the final model (unit for additive error is nanograms per milliliter), RIA radioimmunoassay, HPLC high-performance liquid chromatography, FPIA fluorescence polarization immunoassay, EMIT enzyme-multiplied immunoassay, LCMS liquid chromatography–mass spectrometry, LCMSMS liquid chromatography–tandem mass spectrometry, CEDIA cloned enzyme donor immunoassay, IV intravenous administration, PO oral administration

FIXED EFFECTS

Cyclosporine displays complex absorption profiles in transplant patients. Absorption lag time, gamma or Erlang distribution, and two-portion absorption models have all been used to significantly improve population pharmacokinetic models of cyclosporine (Table III).

Gamma/Erlang Distribution Absorption Model

Gamma-distributed absorption model, or also called Erlang distribution, best described the absorption profiles in five studies (30,31,33,42,43). This absorption model is a particular case of the gamma distribution function and assumes that there is a chain of several compartments (a) between the depot and central compartments (Fig. 1). Due to its flexibility, it is useful to describe flat and delayed absorption profiles with a correlation between the delay and the peak width, which normally is not zero order or first order (55), especially when a simple absorption lag time (T_lag) fails to describe a delay between two compartments. Another advantage of the gamma-distributed absorption model is that it requires estimating only one parameter (k_tr, transfer rate constant between the several compartments between the depot and central compartments), while a first-order absorption model requires estimating two parameters (absorption rate constant and T_lag). This is important especially for small dataset with limited sample size and for the development of limited sampling strategies as more parameters in the model may require more samples for an accurate estimation of drug exposure. k_tr between the compartments between the depot and central compartment could be assumed to be the same (single gamma-distributed absorption model (55–57)) or different (double/multiple gamma-distributed absorption model (55,58)). The number of serial compartments is normally determined iteratively by increasing this number until the model is reached no further improvement.

Fig. 1.

Scheme of the single gamma-distributed absorption model. A linear chain of identical compartments (cmpt) connected by an identical transfer rate constant (b). CL clearance, Vd volume of distribution

Two-Portion Absorption Model

Rousseau et al. and Fradette et al. (34,39) used two-portion absorption models to describe atypical pharmacokinetic profiles of cyclosporine (especially double-peak profiles) frequently observed after transplantation, especially in the early postoperative period. This model assumes discontinuous sequential absorption of the drug in two portions caused by gastrointestinal retention of a portion of the drug dose (Fig. 2) because of the delayed gastric emptying and decreased/variable gastrointestinal motility that has been frequently observed after transplant surgery (59,60). Rousseau et al. (34) described the delayed transfer of each portion by first-order processes with transfer rate constants and lag times and showed a significant difference between the two lag times, while Fradette et al. (39) only used lag times without showing any significant differences.

Fig. 2.

Scheme of the simplified two-portion absorption model (Cmpt compartment). The first fraction (F1) of the dose is transferred from the stomach to the gut first, while the transfer of the remaining fraction (F2 = 1 − F1) is more delayed. This delayed transfer of each portion was described by first-order processes with transfer rate constants (k _tr1 and k _tr2 for each portion) and lag times (T _lag1 and T _lag2 for each portion). Once transferred into the gut, the dose was absorbed immediately, which was described by first-order processes with an absorption rate constant (k _a)

The underlying physiological mechanism for this model is that the upper gastrointestinal tract is cleared periodically following a cyclic pattern called migrating motility complex cycle (MMCC) (61). The two-portion absorption happens when the drug dose is partially emptied in one MMCC with the remainder being emptied in one of the following MMCC. Therefore, it would make sense to compare the two-portion interval (difference between the lag times for the two portions) to MMCC periodicity (interval between two successive MMCC) and to compare the transfer rate constant to the normal value of gastric emptying rate, which was missing in these two studies.

RANDOM EFFECTS

Interindividual variability was best described by an exponential model in most studies (Table III). However, five studies chose a proportional model. None of the studies used an additive model. Residual variability was found to be best described by a combined error in most studies (Table III), while six studies used a proportional model and two studies used an additive model.

MODEL VALIDATION

Only 13 population pharmacokinetic studies of cyclosporine attempted to validate their model. The reason may be that developing and validating limited sampling strategies are more important than validating a priori model for cyclosporine, because cyclosporine dose has to be adjusted based on therapeutic drug monitoring rather than simply based on demographic factors due to its narrow therapeutic range and large variability in its pharmacokinetics.

External validation was performed in seven studies using data splitting or completely independent dataset to form the validation dataset. Studies that used data splitting have made sure that the data are splitted randomly and that the statistics of the patient variables are then compared. The sample size ratio of model building dataset over model validation dataset varied from 1 to 5 in these studies. Eight studies internally validated the model using bootstrapping and internal data splitting. The methods and results of model validation are summarized in Table IV.

Table IV.

Model Validation in Population Pharmacokinetic Studies of Cyclosporine

References	Validation methods	VLD sub	Mdl/Vld	MPE (ng/ml)	MAPE (ng/ml)	RMSE (ng/ml)
(19)	EV (DS)	16 (176)	2.6/2.6	1.63 (2.93%)		23.5
(22)	EV (DS)	25 (∼143)	1/1	−40		100
(23)	EV (DS)	33 (883)	1.1/0.9	21.3 (8.5%a)		92.5
(27)	BS200
(29)	EV (DS)	10 (100)	4.9/3.5	2.8%b
(36)	IDS	21
(38)	EV (DS), IDS	21 (397)	4.7/5.4	EV −2.26		EV 101.1
(40)	EV	9 (580)	1.2/0.5
(41)	BS200
(42)	IDS			3.5 ± 1.5%c	18 ± 1%c
(43)	IDS
(45)	BS100
(47)	EV, IDS	12 (239)	4.1/3.8	EV 17.6 ± 10%, IDS 27.2 ± 25%c	IDS 227
(48)	BS1000			5%	23.90%
(49)	BS600
(51)	BS2000
(52)	BS1000
(53)	NPDE1000, EV				10	37.7%
(54)	BS1000

The symbol ∼ denotes “about”

EV external validation, DS data splitting, BS bootstrapping, NPDE normalized prediction distribution error (the number denotes how many times the resampling was repeated), IDS internal data splitting, VLD sub model validation subpopulation presented as number of patients (total number of samples collected), Mdl/Vld the size ratio of model building dataset over model validation dataset, presented as ratio (number of patient) / ratio (number of samples), MPE mean prediction error presented with or without standard deviation, MAPE mean absolute prediction error, RMSE root-mean-square prediction error

^aRelative to average observed value

^bAUC was predicted

^cRelative to the actual observed value

COVARIATES ON PHARMACOKINETICS OF CYCLOSPORINE

Many factors are significantly associated with the clearance (CL), volume of distribution (V_d), and bioavailability (F) of cyclosporine (Table I), and these associations seem to be independent of the populations studied or organ transplanted. For the assessment of covariate effects, only 11 studies used stepwise model building methods with forward inclusion and backward exclusion procedures using slightly different criteria for statistical significance (Table III). The results of the other studies that only used forward inclusion method without backward exclusion or did not use stepwise model building methods should be interpreted with caution. The influence of covariates on pharmacokinetics of cyclosporine is described below.

Body Weight

The body weight-based dosing regimen is currently the most common method for dosing cyclosporine in clinical settings and is supported by population pharmacokinetic studies. Allometrically scaled body weight was shown to be significantly associated with CL or CL/F of cyclosporine in 11 studies and significantly associated with V_d or V_d/F of cyclosporine in seven studies (Table I). In addition, Porta et al. (26) demonstrated that a Michaelis–Menten elimination model best described the data and a weight-normalized K_m significantly improved the model fit. The dose of cyclosporine should be increased with an increase in the body weight in circumstances where routine therapeutic monitoring is limited or not routinely available or prohibitive in cost.

Postoperative Time

The CL/F of cyclosporine in patients during the first week after transplantation was significantly higher (27%) compared to that in patients 6 months after transplantation (21). A Michaelis–Menten elimination model best described these data as an increase in K_m with respect to the postoperative time (POT), which resulted in a decrease in intrinsic CL (V_m/K_m) in the first few months after kidney transplantation (20,26). A significant decrease in CL over POT, presumably related to reduced hepatic cytochrome P450 metabolism, enterohepatic recycling, or bile formation/excretion due to chemotherapy- or transplant-related toxicity, was also reported in bone marrow transplant patients (32). In contrast, Irtan et al. (43) reported a statistically significant increase in CL/F with POT after kidney transplantation. However, CL/F only increased minimally (0.006 L/h) in this study.

Oral absorption of cyclosporine is expected to improve with POT. Wu et al. (38) reported a decrease in CL/F over POT in kidney transplant patients, which was suggested to be due to an increase in F with POT. Falck et al. (47) showed a significant increase in cyclosporine absorption rate constant with POT in adult kidney transplant patients. Similarly, Saint-Marcoux et al. (42) reported a significant increase in cyclosporine transfer rate constant in an Erlang absorption model with POT in adult heart, lung, and kidney transplant patients. This is most likely caused by improved gastrointestinal function. Absorption of cyclosporine is limited to a specific region in the upper duodenum (62) and is therefore greatly influenced by gastrointestinal functions (63–65). Absorption of cyclosporine is very likely to be impaired immediately after transplant due to gastrointestinal complications of surgery, such as paralytic ileus and intestinal ischemia, which can be precipitated by splanchnic hypoperfusion (59,60). Decreased and variable cyclosporine absorption and bioavailability have been associated with paralytic ileus and intestinal ischemia after transplantation (59,60,66). The absorption of cyclosporine may be improved with POT due to recovery of gastrointestinal functions.

Rosenbaum et al. (37) and Lukas et al. (40) showed a possible decrease in bioavailability of cyclosporine with POT. Parke et al. (23,27) showed a possible decrease of bioavailability with POT during the first 5–7 days after heart transplantation and then possibly increased bioavailability with POT. However, these four studies only involved oral cyclosporine administration, and their conclusion was made based on the basis that incorporation of POT in the relative bioavailability expression improved the model. None of the population pharmacokinetic studies provided solid evidence for an association between oral bioavailability of cyclosporine and POT.

Coadministration of Inhibitors of CYP3A and P-glycoprotein

Transplant patients often receive multiple-drug therapy. CYP3A inhibitors have the potential to decrease the clearance of cyclosporine. Coadministration of diltiazem was significantly associated with lower CL/F of cyclosporine in different transplant populations (23,24,38,41). Diltiazem and cyclosporine are both substrates of CYP3A and P-glycoprotein. Diltiazem is also an inhibitor of CYP3A and P-glycoprotein. Therefore, coadministration of diltiazem could result in decreased hepatic and intestinal metabolism of cyclosporine (67–69) and thus a decrease in CL and an increase in F of cyclosporine, resulting in an overall decrease in CL/F of cyclosporine. Furthermore, McLachlan et al. and Rosenbaum et al. (24,37) demonstrated that coadministration of itraconazole was significantly associated with lower CL/F of cyclosporine. Coadministration of ketoconazole (CYP3A inhibitor) (24) and verapamil (P-glycoprotein inhibitor) (38) was also associated with lower CL/F of cyclosporine. In addition, Parke et al. (27) showed higher bioavailability of cyclosporine associated with coadministration of diltiazem. Although this finding is consistent with other studies, this study did not involve intravenous administration of cyclosporine as discussed above.

Hematocrit

High hematocrit values were significantly associated with low CL or CL/F of cyclosporine as demonstrated by Wu et al., Yin et al., and Fanta et al. (38,41,44) and with low V_d/F as demonstrated by Fanta et al. (44), which agreed with previous findings (70–72). Cyclosporine is distributed approximately 41 to 58% in erythrocytes (12). Therefore, its pharmacokinetics is expected to be sensitive to change in the extent of drug association with blood components. From a physiological point of view, an increase in hematocrit leads to an increase in binding of cyclosporine to erythrocytes. This could partly prevent cyclosporine extraction by the liver and distribution into peripheral tissues, which resulted in an increase in blood concentration and a decrease in the calculated CL (CL = Dose/AUC) and V_d of cyclosporine. From a pharmacokinetic point of view, an increase in hematocrit leads to a decrease in unbound fraction (f_u) of cyclosporine in the blood, resulting in a decrease in hepatic CL (CL_h) and V_d. Here, CL_h = f_u × intrinsic CL, for low-clearance drugs, such as cyclosporine, and V_d = V_b + f_u/f_t × V_t where V_d, V_b, f_t, and V_t denote apparent volume of distribution, volume of blood, unbound fraction of cyclosporine in tissues, and volume of total body water minus blood volume, respectively.

Cystic Fibrosis

Rousseau et al. (31) demonstrated a significantly higher elimination rate constant and lower exposure of cyclosporine in lung transplant patients with cystic fibrosis (CF). These patients require higher cyclosporine dose to achieve the same exposure as lung transplant patients without CF. Rosenbaum et al. (37) also demonstrated a significant increase (over 100%) in CL/F of cyclosporine in lung transplant patients with CF. Saint-Marcoux et al. (42) reported a significant association of CF with cyclosporine transfer rate constant in an Erlang absorption model. This agreed with previous findings and can be explained by the poor absorption of cyclosporine in lung transplant patients with CF (73).

Age

In adult kidney transplant patients, Wu et al. (38) showed a significant decrease in CL/F of cyclosporine with age, and Falck et al. (47) showed a significant decrease in CL/F, V_d/F, and k_a of cyclosporine with age. However, none of the pediatric population pharmacokinetic studies identified age as a significant covariate on the pharmacokinetics of cyclosporine. The possible reason is that the effect of age may be masked by the effect of body size as it is difficult to distinguish the interindividual variability caused by age-related factors from that caused by size-related factors.

Other Factors

Wu et al. (38) demonstrated that low CL/F was significantly associated with poor liver function indicated by elevated total bilirubin levels. Parke et al. (27) reported a slightly higher daytime CL/F, which agreed with previous report (74), likely due to reduced hepatic metabolism at night. However, the difference was small and would not warrant adjustment of day and night dosage. Hesselink et al. (35) reported that the objective function value was reduced upon introduction of the CYP3A4*1/*1B genotype into the model, suggesting a slightly higher CL/F in carriers of a CYP3A4*1B variant allele. Even though transplant type was reported to significantly influence the absorption of cyclosporine in solid organ (heart, lung, and renal) transplant patients (42), there are no population pharmacokinetic studies that compared bone marrow transplantation and solid organ transplantation. This could be due to most studies focused on a single transplanted organ.

ANALYTICAL METHOD

Immunoassays including fluorescence polarization immunoassay (FPIA, often on an Abbott TDx system or a newer AxSYM system), enzyme-multiplied immunoassay (EMIT), radioimmunoassay (RIA), and cloned enzyme donor immunoassay (CEDIA) are convenient and widely used in routine monitoring of cyclosporine blood concentrations in clinical settings. However, antibodies in the immunoassay cross-react with cyclosporine metabolites, resulting in higher and possibly more variable cyclosporine blood concentration measurement than the actual concentration of cyclosporine. In contrast, chromatography and mass spectrometry have the advantages of specifically measuring the parent drug without interference from the metabolites. Although they are less convenient and more expensive, they are increasingly being used in clinical settings. Cyclosporine blood concentrations measured using different assays are significantly different in transplant patients (75).

Population pharmacokinetic studies of cyclosporine showed that the results of immunoassays may be misleading for scientific and clinical purposes. First of all, bioavailability of cyclosporine cannot be reliably estimated using data obtained from immunoassays. Fanta et al. (44) showed that CL estimated after intravenous administration was 25% higher than that of oral administration using data obtained from RIA, resulting in a bioavailability estimate of 125%. The reason is that the large amount of cyclosporine metabolites formed during its extensive intestinal metabolism (76,77) cross-react with the antibodies used in the immunoassays, resulting in overestimation of cyclosporine concentrations and thus lower CL (CL = Dose/AUC) after oral administration than that of intravenous administration (78,79). Secondly, pharmacokinetic parameters may be misestimated using data from immunoassays, such as underestimation of CL/F. Furthermore, pharmacokinetic parameters estimated using data from different immunoassays are also different. McLachlan et al. (24) showed a higher estimated CL/F using EMIT than FPIA. Saint-Marcoux et al. (42) solved this problem by introducing a scaling factor and attributing different residual variability models to each assay, in order to apply the population model to data obtained from three types of assays. Finally, model-based dose prediction could be affected by the reasons mentioned above, which will be clinically relevant.

In addition, in population pharmacokinetic analysis, residual variability is partly due to the variation in the assay. Most of the studies used immunoassays. There seems to be no significant difference in residual variability estimated in all the studies as shown in Table III and that shown by Saint-Marcoux et al. (42). This suggests that all the assays are relatively well validated and consistent.

LIMITATIONS

Most of the studies did not include external validations. Many studies did not even evaluate the model performance (Table IV). Some studies used subsequently discovered flawed assays (Table III), and the studies reviewed were conducted for different purposes (describe cyclosporine PK (17–20,22,28–31,34,36,39,41,46,49,53), dedicated to test a specific covariate (40,51) and full screening of all available factors (21,23–27,32,35,37,38,42–45,47,48,50,52,54), and illustrate the application of a new statistical method for population pharmacokinetic analysis (18)). Not all the relevant covariates and conditions were evaluated in all the studies. A study that was performed by Falck et al. (47) used optimal study design, analyzed the samples using appropriate assay, selected a best-fit model, screened various covariates, evaluated the model performance, and adequately validated the model for the determination of appropriate dose of cyclosporine for renal transplant patients.

CONCLUSION

Twenty-two years after the introduction of population approaches into pharmacokinetic studies of immunosuppressive mediations in transplant patients, it is timely to review the methodologies and results of these studies. A review of these studies demonstrated that population pharmacokinetic approaches greatly increased the flexibility in study design and added to our understanding of the pharmacokinetics of cyclosporine in transplant patients. A highly diversified collection of structural models, variability models, and internal or external validation methods were employed in these studies to ensure the adequacy and validity of the models. Many factors have been shown to be significantly associated with the variability in pharmacokinetics of cyclosporine. Their relevance to dosing of cyclosporine is summarized in Table V. Body weight, coadministration of inhibitors of CYP3A, and hematocrit are the most important factors associated with clearance of cyclosporine in transplant patients. Postoperative time and cystic fibrosis are also significantly associated with the absorption of cyclosporine. Furthermore, coadministration of inhibitors of P-glycoprotein, age in adults, liver function, time of administration (day/night), presence of CYP3A4*1B mutated allele, and formulation could also be associated with variation in clearance and bioavailability of cyclosporine. Special attention should be paid to these factors in future investigations and in clinical applications of cyclosporine.

Table V.

Summary of Covariates Identified in Population Pharmacokinetic Studies of Cyclosporine and Their Relevance to Dosing

	Adjust dose with increased level of covariate	Covariates with definite effect	Covariates with possible effect	Covariates with no effect
Cyclosporine	Increase dose	Body weight and cystic fibrosis	Liver function	Renal function, gender, race, and other donor characteristics
	Decrease dose	CYP3A inhibitor, hematocrit, POT	P-glycoprotein inhibitor, age

POT postoperative time

Future studies are encouraged to collect more factors since a certain amount of pharmacokinetic variability still remained unexplained. Pharmacokinetic–pharmacodynamic modeling is also required to better understand the relationships between drug doses, drug concentrations, and clinical outcomes. This will allow definition of therapeutic range, optimization of dosing guidelines, and dose individualization to target concentrations and effects.