Table II.

Summary of published pharmacokinetic (PK) models: parameter estimates, covariates, model variability and assessment

Study	Outline of PK model	Software	EHC model	PK parameter estimates	Model variability	Covariates	Model assessment	Model schematic
Funaki (1999)[67]	3-compartment based on a 1-compartment disposition modela	NONMEM	Yes	CL/F (L/h) 25–46b V1/F (L) 31.6–142c V1/F (L) 43–193.3a ke (h−1) 0.271–0.859 ka (h−1) 0.409–13.70 tlag (h) 0.412c tlag (h) 0.274b	NS	Food, race on ka, Food, race on ke, Food, race, WT, Maalox®, CLCR on V1/F, Maalox® on tlag	NS	Figure 2a
Shum et al. (2003)[83]	2-compartment model with tlagd	NONMEM	Noe	CL/F (L/h) 27.1 [1.42] V1/F (L) 97.7 [12.6] ka (h−1) 2.27 [0.18] Q/F (L/h) 25.7 [3.45] V2/F (L) 206 [55.7] tlag (h) 0.145 [0.02]	BSV CL/F 0.039 [0.024] V1/F 0.31 [0.18] V2/F 2.27 [2.22] BOV CL/F 0.017 [0.013] V1/F 0.9 [0.27] V2/F 0.26 [0.23] ka 3.4 [0.7] tlag 0.1 [0.36] RUV Exp 0.12 [0.076] Add (mg/L) 0.57 [0.5]	NS	Diagnostic plots
Le Guellec et al. (2004)[84]	2-compartment model with zero-order absorption	NONMEM	Noe	CL/F (L/h) 15.7 [5]f V1/F (L) 36 [19] V2/F (L) 137 [17] Q/F (L/h) 25.9 [36] D1 (h) 0.69 [7]	BSV CL/F (%) 28 V1/F (%) 63 Q/F (%) 45 D1 (%) 11 RUV Prop NS Add (mg/L) 2.04	WT on CL 0.246	Diagnostic plots
Staatz et al. (2005)[85]	Bi-exponential elimination model with first-order absorptiong	NONMEM	Noe	CL/F (L/h) 34.9h,i/25.4i,j V1/F (L) 65 [7] V2/F (L) 496 [20] Q/F (L/h) 30.7 [10] ka (h−1) 0.64 [14]	BSV CL/F (%) 32 [29] Q/F (%) 78 [28] ka (%) 109 [21] BOV CL/F (%) 35 [14] RUV Prop (%) 41 [4]	Alb and ciclosporin dose on CL	Diagnostic plots, bootstrap
Van Hest et al. (2005)[86]	2-compartment model, first-order absorption with lag timek	NONMEM	Noe	CL/F (L/h) 33 [5.4] V1/F (L) 91 [7.2] V2/F (L) 237 [10] Q/F (L/h) 35 [5.3] ka (h−1) 4.1 [6.8] tlag (h) 0.21 [1.3]	BSV CL/F (%) 31 [15] V1/F (%) 91 [13] V2/F (%) 102 [25] ka (%) 111 [15] BOV CL/F (%) 20 [11] V1/F (%) 53 [17] ka (%) 116 [11] RUV Add (mg/L) 0.45 [2.3]	CLCR on V1/F -0.62 [16] Alb on V1/F -1.13 [23] Sex on V1/F 1.11 [4.3] CLCR on CL/F -0.12 [30] Alb on CL/F -1.07 [11] Ciclosporin on CL/F 0.31 [11]	Diagnostic plots, bootstrap
Payen et al. (2005)[68]	2-compartment model with zero-order absorption and lag timek	NONMEM	Noe	CL/F (L/h) 17 a (h−1) 7.5 b (h−1) 0.0072 [28.6] k21 (h−1) 0.017 [31.3] V1/F (L) 5 [17] ka (h−1) 0.63 [19.2] tlag (h) 0.69 [4.7]	BSV CL/F (%) 50.8 V1/F (%) 35.1 β (%) 32.1 k21 (%) 22.4 ka (%) 44.1 tlag (%) 99.5 RUV Prop (%) 26.5 Add (mg/L) 0.57	WT on V1/F 4.75 [29.7]	Diagnostic plots	Figure 2b
Premaud et al. (2005)[87]	Double gamma absorption model, de novo patients (day 3, 7, 30)l	In-house software MMF®	Noe	Day 3 a1 9.45 [6.25] b1 15.92 [8.97] a2 16.59 [9.79] b2 5.82 [4.47] A 1.76 [1.22] λ1 1.13 [0.62] MAT1 (h) 0.71 [0.39] MAT2 (h) 3.61 [1.86] CL/F (L/h) 40.16 [18.87] Day 7 a1 12.75 [8.4] b1 25.57 [12.92] a2 34.9 [15.15] b2 12.25 [5.41] A 1.49 [0.95] l1 1.03 [0.61] MAT1 (h) 0.56 [0.34] MAT2 (h) 3.38 [2.34] CL/F (L/h) 42.85 [15.21] Day 30 a1 13.43 [8.82] b1 21.79 [14.93] a2 15.38 [10.14] b2 5.46 [3.7] A 2.49 [1.44] λ1 1.95 [1.38] MAT1 (h) 0.69 [0.26] MAT2 (h) 3.01 [1.47] CL/F (L/h) 34.05 [13.8]	NS	NS	Diagnostic plots
	Single gamma absorption model, stable (>3 months)l			>3 months a 5.38 [2.5] b 10.39 [4.7] A 5.59 [5.1] λ1 7.36 [4.04] B 0.9 [0.6] λ2 0.69 [0.53] MAT (h) 0.53 [0.14] CL/F (L/h) 31.63 [15.38]
Cremers et al. (2005)[42]	4-compartment model with rate constant describing transfer from fourth to first compartment for EHCm	NONMEM	Yes	CL/F (L/h) 14.1h/11.9 [1.75]i Q/F (L/h) 20.1h/11.2i V1/F (L) 11.7h/10.3 [4.09]i V2/F (L) 465h/183 [75]i V4/F (L) MPAG 5.6h/8.9 [2.3]i k40(MPAG) (h−1) 0.16h/ 0.12 [0.03]i k41(MPAG) (h−1) 0.04 [0.02]i	RUV PropMPA (%) 35i PropMPAG (%) 14i	CLCR on k40	Diagnostic plots	Figure 2c
Van Hest et al. (2007)[88]	2-compartment model, first-order absorption with tlagk	NONMEM	Noe	CL/F (L/h) 23 [2] V1/F (L) 69 [6] V2/F (L) 298 [8] Q/F (L/h) 34 [7] ka (h−1) 4 [7] tlag (h) 0.24 [1]	BSV CL/F (%) 36 [9] V1/F (%) 90 [16] Q/F (%) 60 [21] ka (%) 101 [14] BOV CL/F (%) 21 [10] V1/F (%) 71 [12] ka (%) 116 [10] Q/F (%) 41 [39] RUV Add (mg/L) 0.44 [2]n	Ciclosporin on ka 9.8 × 10−4 [20] Alb on V1/F −1.2 [17] CLCR on V1/F −0.49 [10] Antacids on V1/F 1.4 [8] Ciclosporin on CL 4.8 × 10−4 [16] Alb on CL −0.72 [13] CLCR on CL −0.22 [7] Hb on CL −0.48 [16]° BSV CLCR on CL (%) 66 [29] Alb on CL (%) 112 [44]	Bootstrap
Jiao et al. (2008)[26]	5-chain-compartment model with gallbladder compartmentg	NONMEM	Yes	CL/FMPA (L/h) 10.2 [5.7] CL/FMPAG (L/h) 1.38 [6.9] V2/F (L) 12.5 [8.3] V3/F (L) 213 [9.1] V4/F (L) 4.4 [6.4] Q/F (L/h) 16.1 [5.1] EHCP 29.1 [10.4] tlag (h) 0.096 [15.8] k12 (h−1) 3.53 [12.4] k51 (h−1) 67.5 [12.7]	BSV CLMPA/F (%) 18.9 [35.6] V2/F (%) 34.5 [48.7] V3/F (%) 22.7 [39.2] V4/F (%) 23.1 [37.3] Q/F (%) 13.7 [48.9] EHCP (%) 29 [49.3] tlag (%) 57.3 [44.5] k12 (%) 60.3 [31.9] θ (%) 1.33 [27.2] RUV PropMPA (%) 45.3 [9.3] PropMPAG (%) 20.8 [16]	WT onCLMPA,Q and V3	Diagnostic plots, cross-method validation, VPC	Figure 2d
de Winter et al. (2008)[89]	2-compartment model with first-order absorption and eliminationp	NONMEM	No	tlag(EC-MPS, M1) (h) 0.95 tlag(EC-MPS, M2) (h) 1.88 tlag(EC-MPS, M3) (h) 4.83 tlag(EC-MPS, EV) (h) 9.04 tlag(MMF) (h) 0.3 ka(EC-MPS) (h−1) 3.0 ka(MMF) (h−1) 4.1 V1/F (L) 40 CL/F (L/h) 16.0 V2/F (L) 518 Q/F (L/h) 22 POPtlag(EC-MPS, M1) 0.51 POP tlag(EC-MPS, M2) 0.32 POP tlag(EC-MPS, M3) 0.17	BSV tlag(EC-MPS, M) (%) 8.0 tlag(EC-MPS, EV) (%) 40 tlag(MMF) (%) 11 CL/F (%) 39 V1/F (%) 100 V2/F (%) 490 Q/F (%) 78 ka (%) 187 RUV Add (mg/L) 0.39	NS	Diagnostic plots, bootstrap, VPC
Zahr et al. (2008)[90]	1-compartment model with first-order elimination convoluted with a triple gamma distributionl	In-house software MMF®	No	CL/F (L/h) 40.3 [50.7] V1/F (L) 32.7 [18.6]	NS	NS	Diagnostic plots, jack-knife method
Yau et al. (2009)[69]	5-compartment drug and metabolite model with EHCl	WinNonLin	Yes	CL/FMPA (L/h) 15 [5.6]q/ 18.2 [12.5]r CL/FMPAG (L/h) 0.85 [0.4]q/ 0.86 [0.3]r CLf/F (L/h) 13.2 [5.1]q/ 17.7 [11.9]r CL/FMPAG,bile (L/h) 0.4 [0.3]q/0.7 [0.1]r V1/F (L) 15.1 [10.9]q/7.6 [4.4]r V2/F (L) 188 [154]q/68 [39]r Vd/F (L) 203 [161]q/76 [43]r Vm/F (L) 3.74 [1.5]q/6.4 [4.2]r Q/F (L/h) 20.2 [11.9]q/ 9.7 [11.0]r ka (h−1) 1.57 [1.04]q/2.6 [0.39]r km (h−1) 1.69 [2.12]q/3.3 [3.45]r kbile (h−1) 0.12 [0.09]q/ 0.13 [0.06]r kr (h−1) 0.12 [0.1]q/0.11 [0.13]r kr,m (h−1) 0.13 [0.1]q/ 0.02 [0.01]r tlag (h) 0.13 [0.2]q/0.2 [0.3]r tbile (h) 9.4 [1.2]q/6 [2.1]r τgall (h) 1.4 [0.8]q/0.7 [0.3]r	NS		Diagnostic plots	Figure 2e
Sam et al. (2009)[70]	Initial 2-compartment model, linear elimination of MPAG and AcMPAG with EHC of MPAs	NONMEM	Yes	MPA ka (h−1) 0.67 [24.8] CL/F (L/h) 10.6 [11.1] V1/F (L) 25.9 [34.9] Q/F (L/h) 8.11 [24.2] V2/F (L) 39.6 [86.9] MPAG FMAG (L−1) 0.38 [27.3] k30(h−1): GFR <80 mL /min/ 1.73 m2 = a×(GFR/51.6)a, where a = 0.17 [34.7], b 0.33 [262] k30(hr−1): GFR >80 mL /min/ 1.73 m2 = 0.32 [28.4] k3G (hr−1) 0.15 [28.8] KGB (h−1) 0.007 [167] AcMPAG FMAC (L−1): GFR ≤60mL/ min/ 1.73 m2 = c×(GFR/45.3)e, where c 0.014 [17.5] d−1.95 [11.7] FMAC (L−1): GFR ≤60mL / min/ 1.73 m2 = 0.013 [15.1] k40 (h−1) 0.21 [13.8] k4G (h −1) 0.15 [26.5]	BSV MPA CL/F (%) 21.4 [66.1] V1/F (%) 87.8 [32] V2/F (%) 239 [248] MPAG FMAG (%) 34.6 [85.8] a (%) 29.1 [199] k30 (%) 29.1 [199] kGB (%) 35.9 [260] AcMPAG c (%) 24.6 [68.7] FMAC (%) 24.6 [68.7] k40 (h−1) 48.8 [47.1] k4G (h−1) 67.3 [41.1] RUV MPA (%) 69.9 [15.3] MPAG (%) 19.4 [32.1] AcMPAG (%) 17.8 [23]	GFR on k30	Diagnostic plots, VPC	Figure 2f
de Winter et al. (2009)[71]	2-compartment model, EHC of MPA with absorption of MPA described with 2 first-order processes (short and long lag time)k	NONMEM	Yes	Ffast 0.71 [9] tlag short (h) 0.287 [5] tlag long (h) 0.643 [3] ka (h−1) 6.2 [22] CL/F (L/h) 8.27 [5] V1/F (L) 52.4 [17] V2/F (L) 262 [5] Q/F (L/h) 16.2 [222] TGB1 (h) 6 TGB2 (h) TGB1+ 4 DGB (h) 0.1 EHCP 0.37 k63 (h−1) 1	BSV tlag short (%) 32 ka (%) 182 [40] CL/F (%) 34 [41] V1/F (%) 53 [48] TGB1 (%) 200 EHCP (%) 35 RUV (%) 0.414 [6]	CLCR on CL/F 0.42 [26]	Diagnostic plots, bootstrap, VPC	Figure 2g
Musuamba et al. (2009)[91]	2-compartment model with first-order absorption and elimination, with MPAG and EHC compartmentsk	NONMEM	Yest	tlag (h) 0.26 [7.4] k12 (h−1) 1.83 [32] V1/F (L) 14.7 [22] V2/F (L) 250 [32] V3/Fm (L) 6.31 [17] CL/F (L/h) 14.7 [11] k20 (h−1) 0.36 [23] Q/F (L/h) 21.1 [0.8] k20 (h−1) 0.36 [23] k40 0.12 [10.7]	BSV V1/F (%) 3.2 [12] Q/F (%) 17 [8] k40 (%) 2 [16] BOV k12 (%) 62 [18] V1/F (%) 21 [31] CL/F (%) 13 [26] k40 (%) 5 [39] RUV PropMPA (%) 0.4 [59] PropMPAG (%) 0.2 [0.4] AddMPA (μg/mL) 0.2 [63]	Sirolimus on k41 0.1 [14] GFR on k40 0.008 [41] AST/ALT on CL 3.1 [33]	Diagnostic plots, bootstrap, cross-method validation, VPC
de Winter et al. (2009)[92]	2- and 1-compartment models for unbound MPA and unbound MPAG, with EHC compartment	NONMEM	Yes	tlag (h) 0.231 ka (h−1) 4.0 V1/F fmPA (L) 189 CL/F fmPA (L/h) 747 V2/F fmPA (L) 34300 Q/F fmPA (L/h) 2010 k24 (h−1 mmol−1) 0.153 Bmax (mmol) 35100 k42 (h−1) 169 V1/F fMPAG (L) 8.56 k56 (h−1 mmol−1) 0.0133 k65 (h−1) 93.1 CL/F fMPAG (L/h) 4.75 TGB (h) 7.9 DGB (h) 1 k72 (h−1) 10 k57 (h−1) 0.0796	BSV tlag (%) 161 V1/F fmPA (%) 116 CL/F fmPA (%) 97 Bmax (%) 48 CL/F fMPAG (%) 106 TGB (%) 141 k57 (%) 71 RUV tMPA (mmol/L) 0.52 fMPA (mmol/L) 0.993 tMPAG (mmol/L) 0.18 fMPAG (mmol/L) 0.55	CLCR on CL fMPAG 1.36 Alb on Bmax 1.39 Ciclosporin on k57 0.002	Diagnostic plots, VPC

^aValues are range of mean PK parameters among races and fasted, after-meal and before-meal states.

^bIt was unknown if Maalox® was taken.

^cNo Maalox® taken.

^dSummary of results of the final base model, mean estimates [SE].

^eConsidered but not in final model.

^fBased on median study weight (kg) with corticosteroid co-medication.

^gPopulation PK estimates given as mean [SE%].

^hCiclosporin co-therapy.

ⁱTacrolimus co-therapy.

^jBased on median study albumin 26g/L.

^kFinal population PK model estimates given as mean [CV%].

^lPK parameters values are expressed as mean [SD].

^mFinal population PK estimates given as mean [SE].

ⁿRUV is on a natural logarithmic-scale as data were logarithmically transformed.

^oDuring first 6 months post-transplant.

^pFinal population PK model estimates expressed as mean.

^qReceived MMF, ciclosporin and prednisolone.

^rReceived MM F and prednisolone.

^sParameter estimates of final population PK model expressed as mean [%RSE].

^tEHC model only developed in those patients receiving concomitant medication with sirolimus.

α=apparent rate constant of distribution; β=apparent rate constant of elimination; θ=covariate effects and correlation between CL/F_MPAG and Q/F; λ₁, λ₂ = disposition rate constants of the 2 compartments; τ_gall=gallbladder emptying interval; a, b = gamma distribution parameters with single gamma absorption model; a₁,b₁, a₂, b₂=gamma distribution parameters with double gamma distribution model; A, B = disposition coefficient standardized per 100 mg dose; AcMPAG = MPA acyl-glucuronide; Add=additive error; Alb = plasma albumin concentration; bile=amount of MPAG in the gallbladder compartment; B_max=maximum number of binding sites; BOV=between-occasion variability; BSV= between-subject variability; CL = apparent total clearance; CL_CR=creatinine clearance; CL/F=apparent oral clearance; CL_f=apparent formation clearance of MPA to MPAG; CV=coefficient of variation; D₁,=duration of input (absorption); D_GB=duration of gall bladder opening; EC-MPS=enteric-coated mycophenolate sodium; EHC=enterohepatic circulation; EHCP=% of MPA recycled into the body; EV=evening; Exp = exponential; F_fast=part of dose ending up in the fast absorption compartment; F_m=fraction of the MPA dose converted to MPAG; FM_AG= ratio of the fraction of MPA metabolized to MPAG to the volume of distribution of MPAG; fMPA = unbound MPA; fMPAG = unbound MPAG; GFR=glomerular filtration rate; Hb = haemoglobin; k_xy=transfer rate constant from compartment x to y; k_a=absorption rate constant; k_bile=biliary excretion rate constant of MPAG; k_e = renal elimination constant; k_GB = rate constant for the release of recirculated MPA from MPAG and AcM PAG into the depot compartment; k_m=formation rate constant of MPAG; k_r = renal excretion rate constant of MPA; k_r,m = renal excretion rate constant of MPAG; Lag_long = lag time long absorption; Lag_short= lag time short absorption; M = morning; M1 =morning 1; M2 = morning 2; M3=morning 3; MAT=mean absorption time with single gamma absorption model; MAT₁, MAT₂ = mean absorption times with double gamma absorption model; MMF = mycophenolate mofetil; MPA=mycophenolic acid; MPAG=7-O-MPA-β-glucuronide; NONMEM = nonlinear mixed-effects modelling; NS = not stated; POP = part of the population; Prop = proportional error; Q/F = apparent intercompartmental clearance; RSE=relative standard error; RUV=residual variability; SD=standard deviation; SE=standard error; T_bile=time of bile release after dosing; T_GB„=time of nth opening gallbladder compartment; t_lag=lag time; tMPA=total MPA; tMPAG=total MPAG; V₁/F = apparent volume of distribution in the central compartment after oral administration; V₂/F=apparent volume of distribution of the peripheral compartment of MPA; V₃/F = apparent volume of distribution of the central compartment of MPAG; V₄/F = apparent volume of distribution of MPAG; V_d = apparent volume of distribution (V₁/F + V₂/F) for MPA; V_m=volume of central compartment for MPAG; VPC=visual predictive check; WT=bodyweight.