A systematic review of population pharmacokinetics of valproic acid

Janthima Methaneethorn

doi:10.1111/bcp.13510

. 2018 Feb 28;84(5):816–834. doi: 10.1111/bcp.13510

A systematic review of population pharmacokinetics of valproic acid

Janthima Methaneethorn ^1,^2,^✉

PMCID: PMC5903263 PMID: 29328514

Abstract

Aims

Population pharmacokinetics is an essential tool that helps guide individualized dosing regimens. The aims of this systematic review are to provide knowledge concerning population pharmacokinetics of valproic acid (VPA) and to identify factors influencing VPA pharmacokinetic variability.

Methods

PubMed and Embase databases were systematically searched from inception to June, 2017. Relevant articles from reference lists were also included. All population pharmacokinetic studies of VPA conducted in humans and that employed a nonlinear mixed effect modelling approach were included in this review.

Results

Twenty‐six studies were included in this review. Most studies characterized VPA pharmacokinetics as a one‐compartment model. Three studies reported a two‐compartment model. Body weight, dose and age were significant predictors for VPA volume of distribution (V _d). The estimated V _d for one‐compartment models ranged from 8.4 to 23.3 l. For two‐compartment models, peripheral volumes of distribution ranged from 4.08 to 42.1 l. Frequently reported significant predictors for VPA clearance (CL_VPA) included body weight, VPA dose, concomitant medications, gender and age. The estimated CL_VPA ranged from 0.206 to 1.154 l h⁻¹ and the inter‐individual variability ranged from 13.40 to 35.90%. Two studies reported population pharmacokinetics/pharmacodynamics of VPA in patients with epilepsy. Seventeen studies evaluated the performance of their final models.

Conclusions

Significant predictors influencing VPA pharmacokinetics as well as model methodologies are highlighted in this review. For clinical application, CL_VPA could be predicted using body weight, VPA dose, concomitant medications, gender or age. For future research, there is a knowledge gap regarding population pharmacokinetics/pharmacodynamics of VPA in a population other than epileptic patients.

Keywords: nonlinear mixed effect modelling, population pharmacokinetics, systematic review, valproic acid

What is Already Known about this Subject

Valproic acid is a narrow therapeutic index drug with high pharmacokinetic variability.
Several population pharmacokinetics of valproic acid were developed. However, no systematic literature reviews concerning pharmacokinetic variability of valproic acid have been reported.

What this Study Adds

This review systematically summarizes knowledge pertaining to population pharmacokinetics of valproic acid.
Three covariates were found to affect valproic acid volume of distribution, i.e. body weight, dose and age.
The most frequently identified factors that affect valproic acid clearance included body weight, valproic acid dose, concomitant medications, gender and age.
There are only a few studies that reported population pharmacokinetics/pharmacodynamics of valproic acid. A population pharmacokinetics/pharmacodynamics of valproic acid in a population other than epileptic patients is lacking.

Introduction

Valproic acid (VPA) is a broad spectrum antiepileptic drug used in the treatment of both generalized and partial seizures 1, 2, 3. Its activities are also extended to bipolar disorder and some neurological conditions including migraine and neuropathic pain 1, 2, 3. The exact mechanism of action of the drug is uncertain. However, several studies have proposed that VPA potentiates gamma aminobutyric acid (GABA) effects in the central nervous system 1. Several VPA formulations are available including conventional tablets, enteric coated tablets, sustained‐release tablets, capsules, oral solution and intravenous solution. The drug is rapidly and completely absorbed. However, differences in the rate of VPA absorption and bioavailability among formulations have been documented. The available data suggest that the bioavailability of VPA approaches 1.0 for intravenous solution, oral solution and capsules, whereas the bioavailability for sustained‐release tablets is approximately 0.8–0.9 4. For the rate of absorption, the reported times to maximum concentration (T _max) of VPA for oral solution, enteric coated tablet and sustained‐release tablet formulations are 1–2 h, 3–6 h and 10–12 h, respectively 1.

Approximately 90–95% of VPA is bound to albumin 5, 6. The binding becomes saturated when VPA concentrations are above 50 mg l⁻¹, resulting in a disproportionate increase in VPA concentrations 4. Several factors can affect VPA protein binding such as age, concomitant medications, renal and hepatic diseases and pregnancy status 1, 3, resulting in a high variability in apparent volume of distribution ranging from 0.1 to 0.5 l kg⁻¹ 4, 7.

VPA is mainly metabolized by the liver, with only a small amount of unchanged form being excreted in the urine 1. VPA exhibits high inter‐individual variability, particularly when enzyme‐inducing or ‐inhibiting drugs are coadministered 1. Three routes of VPA metabolism in humans have been proposed, including glucuronide conjugation, β‐oxidation in mitochondria and cytochrome P450 (CYP450) mediated metabolism 8, 9, 10. Of these, the last is considered a minor route of metabolism accounting for only 10% of administered dose 9, 10. Three isoforms CYP2C9, CYP2A6 and CYP2B6 are known to play a role in desaturation of VPA to the terminal olefin ∆⁴‐VPA 6, 11. Moreover, the drug has the potential to inhibit CYP2C9 11, 12, resulting in increased plasma concentrations of comedications. Glucuronyltransferase (UGT) isoforms participating in VPA metabolism include UGT1A3, 1A4, 1A6, 1A8 and 1A9 13. An average clearance value for VPA is 8 ml kg⁻¹ h⁻¹ with a range of 6–10 ml kg⁻¹ h⁻¹. For half‐life, an average value is 10–12 h, with a range of 4–17 h 4. Higher VPA clearances and shorter half‐lives have been reported in children 4. The drug is slightly removed (<20%) by standard haemodialysis, but is greatly eliminated via high‐flux haemodialysis 13. Given its relatively short half‐life, steady state VPA concentrations are usually achieved within 24–48 h.

Because VPA has a narrow therapeutic window, therapeutic drug monitoring (TDM) of VPA is a crucial part of drug therapy. The recommended VPA therapeutic range for the treatment of epilepsy is 50–100 mg l⁻¹. A slightly higher range of 50–125 mg l⁻¹ is proposed for bipolar disorder therapy 4, 14, 15. VPA levels greater than the recommended range may result in gastrointestinal side effects including nausea, vomiting and diarrhoea 4. Tremor and thrombocytopenia can occur at higher concentrations. When VPA concentrations exceed 175–200 mg l⁻¹, CNS toxicity is generally seen 13. Monitoring of VPA concentrations should be employed in most patients to ensure efficacy and avoid adverse effects. Given the reported diurnal variation in VPA concentrations 16, 17, trough concentrations in the morning should be used for TDM, as they are the most consistent levels from day to day 13. Currently, the method used to initiate VPA dosing is to use average VPA parameters obtained in other patients with similar conditions. Subsequently, the dose is modified based on the clinical status of patients. Because of the high variability in VPA pharmacokinetics 4, 5, 13, the method previously mentioned might result in too high or too low doses of VPA treatment. Moreover, this conventional approach has some limitations when the available VPA concentrations are not at steady state or the sampling time is not appropriate.

A population pharmacokinetic approach with Bayesian estimation allows clinicians to incorporate several factors affecting VPA pharmacokinetics into individualized drug therapy. In addition, this approach is more flexible in clinical settings where difficult situations such as non‐steady state drug concentrations or clinically unstable patients are present 5. Several population pharmacokinetic models for VPA have been reported. Given the continual use of VPA in clinical settings, knowledge concerning factors affecting pharmacokinetic variability of VPA is important. The objectives of this systematic review are to provide information on population pharmacokinetics of VPA and to summarize significant covariates affecting VPA pharmacokinetics which will be of benefit in clinical application and future research.

Methods

Population pharmacokinetic studies of VPA were systematically searched from PubMed and Embase databases from inception to June 2017. The following search terms were employed: ((‘valproic acid’ OR ‘sodium valproate’ OR ‘valpro*’ OR ‘VPA’) AND (‘population pharmacokinetic’ OR ‘pharmacokinetic model*’ OR ‘nonlinear mixed effect*’ OR ‘NONMEM’)). Reference lists of the identified articles were also checked. In addition, abstracts and non‐journal publications were reviewed if they provided sufficient details.

Inclusion criteria

Identified studies were eligible to be included in this review if they met the following criteria:

Study population: human studies (healthy volunteers or patients).
Treatment: VPA as a studied drug.
Analysis: population pharmacokinetic analysis of VPA employing a nonlinear mixed effect modelling approach.

Exclusion criteria

Studies were excluded from this review if:

They were review papers or focused on methodology/algorithm or software/program considerations.
The studies were conducted in vitro or in animals.
Approaches other than mixed effect modelling were employed.
They were published in non‐English language articles.
Information on methodology or pharmacokinetics was insufficient.

Data Extraction

The following information was extracted from each included article: (i) study characteristics (e.g. types of study, sampling time, number of collected samples, dosage regimen and VPA formulations), target population (patients or healthy subjects), population characteristics (e.g. age and weight range, gender, disease, concomitant medication), and (ii) information on population pharmacokinetic analyses such as structural models, statistical models (i.e. inter‐individual and residual variability), parameter estimates, covariates retained in the model as well as their criteria for significance, and approaches employed for model evaluation (e.g. internal or external validation).

Results

Study identification

A total of 103 and 160 studies were identified from PubMed and Embase databases searches, respectively. One additional record was identified from reference lists. Following title and abstract screening, 46 studies were available for eligibility assessment. Of these, 20 studies were excluded based on the exclusion criteria: (i) eleven articles were not population pharmacokinetic studies; (ii) four studies were review articles or methodology considerations; (iii) two studies did not use a mixed effects approach; (iv) one record was a non‐English language article; and (v) two studies did not provide sufficient information on methodology or pharmacokinetic parameters. Therefore, a total of 26 publications fulfilled the final criteria for this review. A PRISMA diagram of study identification is presented in Figure 1.

Study characteristics

All studies were published between 1995 and 2017. Table 1 summarizes the characteristics of each study. Most of the models were developed in patients with epilepsy 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38. One study reported a model incorporating data from both epileptic and psychiatric patients 39. One study was conducted in patients with mania 40. One study was performed in patients with acute VPA poisoning 41 and the other one was conducted in healthy subjects 42. The sample size of subjects used for model development ranged from 14 to 902. The number of VPA levels per individual for all studies ranged from 1 to 16. The VPA doses of the included studies ranged from 2.4 to 87.9 mg kg⁻¹ d⁻¹. Use of sustained‐release formulation was reported in nine studies 21, 28, 31, 34, 37, 38, 40, 41, 42. Fluorescence polarization immunoassay (FPIA) and enzyme multiplied immunoassay (EMIT) were used in 57.7% and 15.4% of the studies, respectively.

Table 1.

Characteristics of population pharmacokinetic studies included in the systematic review

No	Author	Country	Sample size	Gender (%) M/F	Age (y) Mean ± SD [Range]	Weight (kg) Mean ± SD [Range]	Formulation	Dosage regimen	Dose [Range]	Total samples [per patients]	Sampling time	C _ss (mg l ⁻¹ ) Mean ± SD [Range]	VPA assay [LOQ]
1	Botha et al. 18	South Africa	52	73/27	7.6 ± 4.2 [1.2–16]	24.2 ± 12.5	syrup, tablet, EC tablet	NR	NR	97 [1–6]	NR	NR	EMIT, FPIA
2	Yukawa et al. 44	Japan	250	50/50	10.1 ± 5.6 [0.3–32.6]	31.7 ± 15.3 [5.2–90]	tablet, syrup	2–3 times per day	15.89 ± 5.38 mg kg⁻¹ d⁻¹ [2.38–46.78] mg kg⁻¹ d⁻¹	474	2–6 h after morning dose	62.3 ± 20.7 [6.5–159.4]	FPIA (%CV <10)
3	Yukawa et al. 19	Japan	207	53/47	15.7 ± 8.2 [0.3–54.8]	42.6 ± 18.0 [4.5–86.0]	tablet, syrup	2–3 times per day	20.14 ± 7.66 mg kg⁻¹ d⁻¹ [5.56–60.0] mg kg⁻¹ d⁻¹	479	2–6 h after morning dose	56.0 ± 16.1 [14.7–107.7]	FPIA (%CV <10)
4	Yukawa et al. 20	Japan	400	50/50	11.5 ± 7.2 [0.3–54.8]	34.6 ± 16.9 [5.2–93.0]	tablet, syrup	2–3 times per day	16.5 ± 6.0 mg kg⁻¹ d⁻¹ [2.4–46.8] mg kg⁻¹ d⁻¹	792	2–6 h after morning dose	60.7 ± 20.3 [6.5–159.4]	FPIA (%CV <10)
5	Tanikawa et al. 21	Japan	215	54.4/45.6	22.0 ± 19.7 [0–79]	41.9 ± 18.6 [8.1–103]	conventional (tablet, granule, syrup), slow release (tablet, granule)	NR	NR	344 [~1.6]	1–39.3 h after dose	NR	FPIA
6	Blanco‐Serrano et al. 22	Spain	208	51.7/48.3	27.3 [14–95]	64.1 [27–100]	EC tablets, oral solution	2–3 times per day	17.2 mg kg⁻¹ d⁻¹ [5.03–50.0] mg kg⁻¹ d⁻¹	534	C_tr	56.6 [21.0–123.0]	FPIA (%CV < 10)
7	Blanco‐Serrano et al. 23	Spain	255	49/51	7.8 [0.1–14]	31.3 [4.0–74.0]	EC tablets, oral solution	2–3 times per day	24.20 mg kg⁻¹ d⁻¹ [15.7–50.0] mg kg⁻¹ d⁻¹	770 [2–5]	C_tr	65.3 [25.7–157]	FPIA (%CV < 10)
8	Park et al. 24	Korea	102	64.7/35.3	45.4 ± 19.2 [16–81]	60.4 ± 10.8 [40–91]	IV	2–4 times per day	17.80 ± 3.8 mg kg⁻¹ d⁻¹ [5.5–33.3] mg kg⁻¹ d⁻¹	352	C_p: 10–60 min after end of LD, C_tr: 60 min before next dose	NR	FPIA
9	El Desoky et al. 25	Egyptian	81	64.2/35.8	20 [3–58]	48.4 [15–75]	EC tablets, oral solution	2 times per day	18.8 mg kg⁻¹ d⁻¹, 790 mg d⁻¹ [1.4–44 mg kg⁻¹ d⁻¹, 200–1750 mg d⁻¹]	81 [1]	C_tr	44.4 [11.5–126]	FPIA (%CV < 10)
10	Jankovic et al. 26	Serbia	93	43/57	16.88 ± 12.69 [1–58]	47.81 ± 24.33 [9.65–115]	EC tablets, syrup	2 times per day	893.81 ± 353.83 mg d⁻¹ [200–1750] mg d⁻¹	97 [1]	C_p, C_tr	75.33 ± 24.63 [12.95–131.7]	FPIA (%CV < 10)
11	Birnbaum et al. 39	USA	146	35.6/64.4	77 [65–99]	64 [32–112]	NR	NR	NR	405 [1–16]	C_tr of morning dose	NR	NR
12	Dutta et al. 27		Cohort 1: 20	65/35	37.2 ± 14.3 [20–77]	89.9 ± 27.6 [55–159]	IV	single dose	1796 ± 552 mg [1090–3180] mg	160 [8]	0, 5, 10, 15, 30, 45, 60, and 240 min post infusion	C_ss was not achieved	Ultrafiltration immunoassay [0.7 mg l⁻¹]
12	Dutta et al. 27		Cohort 2: 20	70/30	40.8 ± 15.0 [19–70]	73.3 ± 13.9 [53–100]	IV	single dose	2192 ± 428 mg [1595–3000] mg	80 [4]	0, 30, 60, 240 min post infusion	C_ss was not achieved	Ultrafiltration immunoassay [0.7 mg l⁻¹]
13	Jiang et al. 28	China	317	61.5/38.5	8.78 [0.28–16]	33.69 [6–113]	NR (have SR formulation)	NR	21.82 mg kg⁻¹ d⁻¹ [2.96–80.8] mg kg⁻¹ d⁻¹	624 [1–10]	0–27.5 h	68.07 [5.47–160]	FPIA (%CV < 4)
14	Ueshima et al. 29	Japan	108 (divided into 3 groups) Gr 1: monotherapy		Gr 1: 4.6 [1–18.3]	Gr 1: 16 [3.4–51]	tablet, syrup, powder	2–3 times per day	Median = 33.3 mg kg⁻¹ d⁻¹ [4.8–87.9] mg kg⁻¹ d⁻¹	Gr 1: 88	3 h after morning dose	99.6 [19.6–179.8]	FPIA (%CV < 10)
			Gr 2: combination therapy		Gr 2: 4.9 [1–18.9]	Gr 2: 16.8 [3.4–63.3]				Gr 2: 147		92.8 [5.5–153]
			Gr 3: polytherapy		Gr 3: 8.1 [1.0–18.9]	Gr 3: 18.4 [6.6–61.0]				Gr 3: 107		80.7 [17.9–151.4]
15	Correa et al. 30	Mexico	110	57.3/42.7	7.0 ± 4.5 [0.5–17]	27.1 ± 16.5 [8–68.5]	tablet, oral solution	2–3 times per day	700.7 ± 370.8 mg d⁻¹ [100–1800] mg d⁻¹ 29.3 ± 14.2 mg kg⁻¹ d⁻¹ [9.1–70] mg kg⁻¹ d⁻¹	119	C_tr before morning dose	63.51 ± 24.6 [12–128.3]	CEDIA (%CV < 10) [sensitivity = 3.0 mg l⁻¹]
16	Jiang et al. 31	China	177	61.6/38.4	24.54 [2.83–77]	56.34 [12.5–99]	NR (have SR formulation)	NR	14.88 mg kg⁻¹ d⁻¹ [3.64–36] mg kg⁻¹ d⁻¹	319 [1–7]	0.25–24 h	64.10 [14.6–129.28]	FPIA
17	Vucicevic et al. 32	Serbia	129	55.8/44.2	34.3 ± 11.6	72.1 ± 14.2	film coated tablets	1–3 times per day	1108 ± 412 mg d⁻¹	200 [1–2]	C_tr before morning dose	72.3 ± 35.7 [0.5–185.5]	EMIT (%CV <10) [LLOQ: 1 mg l⁻¹ (if presence: LLOQ/2)]
18	Jankovic et al. 33	Serbia	Pediatric: 58 Adult: 60	48.3/51.7 41.7/58.3	7.21 ± 3.63 [1–14] 33.97 ± 16.41 l[15–65]	27.07 ± 13.08 [4–75] 69.67 ± 15.60 [37–106]	film coated tablets or syrup	1–3 times per day	596.92 ± 269.28 mg d⁻¹ [200–1250] mg d⁻¹ 1053.97 ± 326.77 mg d⁻¹ [500–2000] mg d⁻¹	65 63	C_p or C_tr C_p or C_tr	70.21 ± 30.36 [20.81–150] 68.65 ± 27.44 [26.30–150]	FPIA (%CV < 5) [Sensitivity = 0.7 mg l⁻¹]
19	Williams et al. 34	USA	Total: 52 Clinical trial: 10	69.2/30.8	NR [1–17]	NR	IV, syrup, capsule, EC sprinkle, EC tablet)	Clinical trial: Single iv infusion	Clinical trial: 14 mg kg⁻¹ d⁻¹ [12–15] mg kg⁻¹ d⁻¹	231 [1–15] 57	0, 5, 30 min, 1, 2, 3, 4, 5, 6 h after end of infusion	NR	Clinical trial: FPIA (%CV < 5) [LLOQ: 12.5 mg l⁻¹]
19	Williams et al. 34	USA	TDM: 42					TDM: NR	TDM: 23 mg kg⁻¹ d⁻¹ [3–60] mg kg⁻¹ d⁻¹	174	0–15 h (after last dose when C_ss has been reached)		TDM: VITROs VALP assay (%CV < 5)
20	Ibarra et al. 42	Uruguay	14 (bioequivalence study)	50/50	[19–35]	Male: 79 ± 9.7 Female: 59 ± 8.3	divalproex‐sodium delayed release formulation	Single dose	500 mg single dose under fasting condition	105 [15]	0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 16, 24, 36, 48 h	NR (C_ss not achieved)	HPLC‐UV–Vis (%CV < 8) [1.5 mg l⁻¹]
21	Ogusu et al. 43	Japan	PK analysis: 237	57.8/42.2	17.2 ± 8.3 [2.2–52.2]	48.8 ± 20.9 [9.6–120.5]	SR	NR	934.3 ± 540.2 mg d⁻¹ [100–2600] mg d⁻¹	827	0–24 h	68.15 ± 26.54 [7.70–165]	EMIT (%CV <10) [1 mg l⁻¹]
21	Ogusu et al. 43	Japan	PK‐PD analysis: 169	60.4/39.6	18.0 ± 7.8 [3.0–52.2]	51.0 ± 20.1 [13.0–120.5]	SR	NR	903.8 ± 502.7 mg d⁻¹ [100–2600] mg d⁻¹	42 γ‐GT levels		67.8 ± 25.7 [7.7–143.0]
22	Nakashima et al. 36	Japan	77 (conducted among the same population of epileptic patients reported in study no. 21)	62.3/37.7	15.2 ± 8.2 [0.8–36.9]	NR	NR	NR	1120 ± 592.5 mg d⁻¹ [50–3200] mg d⁻¹	729	0–24 h	predictive trough: 69.3 ± 19.9 [11.8–130.1]	EMIT (%CV <10) [1 mg l⁻¹]
			age ≤18: n = 56		11.7 ± 4.41
			age >19: n = 21		26.16 ± 5.34
23	Ding et al. 37	China	902	60.6/39.4	5.7 ± 3.8 [3 week‐14.0]	21.6 ± 11.9 [2.6–70.0]	syrup, conventional and SR tablets	1–4 times per day	27.1 ± 9.2 mg kg⁻¹ d⁻¹ [5.1–63.2] mg kg⁻¹ d⁻¹	1107	6–27.5 h	67.5 ± 24.5 [15.0–149.4]	FPIA (%CV < 10)
24	Lin et al. 38	China	199	57.3/42.7	26.6 ± 11.7 [14–66]	60.2 ± 12.5 [21–101]	SR and conventional tablets	1–4 times per day	884.5 ± 317.7 mg d⁻¹ [250–1800] mg d⁻¹	247	C_tr before morning dose	61.9 ± 26.8 [3.2–140.3]	FPIA (%CV <10) [0.7 mg l⁻¹]
25	Jawien et al. 41	Poland	20 (acute VPA poisoning)	50/50	40.4 [20–63]	NR	Depakine Chrono 500, Depakine Chrono 300, Convulex 500, Depaquine	NR	median 19.9 g [6–65 g]	80	Twice a day during 1^st and 2^nd days, then once a day until VPA level decreased to a therapeutic level.	NR	Gas chromatography (%CV < 10%) [VPA, 4‐ene VPA, 2‐ene VPA, and 3 keto VPA: 1.0, 0.05, 0.1. and 1.0 mg l⁻¹]
26	Methaneethorn et al. 40	Thailand	206	51.5/48.5	39.3 ± 13.1 [18.2–73.1]	63.2 ± 13.0 [40.0–107.2]	EC and SR tablets	1–4 times per day	1035.9 ± 382.7 [250–2000] mg d⁻¹	309	C_tr	NR	EMIT (%CV < 10) [1 mg l⁻¹]

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CEDIA, cloned enzyme donor immunoassay; C_p, peak concentration; C_tr, trough concentration; EC, enteric coated; EMIT, enzyme multiplied immunoassay technique; FPIA, fluorescence polarization immunoassay; IV, intravenous; LD, loading dose; LLOQ, lower limit of quantification; NR, not reported; SR, sustained release; TDM, therapeutic drug monitoring; %CV, % coefficient of variation; γ‐GT, γ‐glutamyltransferase

Population pharmacokinetic models of valproic acid

Most of the included studies aimed at describing variability in VPA pharmacokinetics, that is, to determine the magnitude of both inter‐individual variability (IIV) and residual variability (RV), as well as the influence of several covariates on VPA pharmacokinetics. One study investigated VPA protein binding 27. One study characterized the relationship between total and unbound serum VPA concentration based on the Langmuir equation, taking into account the IIV 29. Population pharmacokinetics/pharmacodynamics of VPA was performed in two studies (one study determined the optimal concentration of VPA based on clinical characteristics using a receiver operating characteristic (ROC) curve 36, the other determined the impact of superoxide dismutase 2 (SOD2), glutathione S‐transferase mu 1 (GSTM1) and glutathione S‐transferase theta 1 (GSTT1) on the relationship between VPA exposure and the risk of γ‐glutamyltransferase (γ‐GT) elevation 43). One study proposed a non‐linear model for VPA pharmacokinetics based on protein binding saturation 37. One study applied population pharmacokinetics to describe the time course of VPA and its metabolites in an overdose situation 41. Only seven studies provided an application of the proposed models such as dosage recommendations to achieve target level, simulations of VPA concentrations based on the proposed dosage regimens, and γ‐GT elevation based on VPA dose and SOD2 polymorphism 20, 23, 30, 34, 38, 40, 43.

Approximately 85% of the studies were TDM studies. Almost all of the studies described VPA pharmacokinetics as a one‐compartment model (n = 18). Only three studies reported a two‐compartment model. Additionally, a steady state model (C_ss = Dose/(CL * τ)) was employed in three studies 19, 20, 44. Rate of absorption was characterized as a first order process in most of the studies. However, zero order absorption was reported in one study in which liquid oral dosing was administered 34. Absorption lag time was reported in five studies 21, 34, 36, 42, 43 and enterohepatic circulation (EHC) was reported in one study 42. Influence of formulation on absorption rate was taken into accounted in six studies 21, 28, 30, 31, 34, 40. Of these, three studies fixed the absorption rate constant (k_a) at literature values 30, 34, 40. Elimination was characterized as a linear process, with the exception of two studies in which a dose‐dependent maximum effect model (DDE) 37 and a Michaelis–Menten kinetics for β‐oxidation process 41 were employed. NONMEM software was the most frequently used software for population pharmacokinetic model development. Table 2 summarizes information on population pharmacokinetic models with respect to study type, model structure and model validation.

Table 2.

Population pharmacokinetic models described in the included studies

No	Author	Type of study	Model	Model validation	Software
1	Botha et al. 18	TDM study	1 CPT (linear model with first order absorption)	NR	NONMEM
2	Yukawa et al. 44	TDM study	Steady state model	NR	NONMEM
3	Yukawa et al. 19	TDM study	Steady state model	NR	NONMEM
4	Yukawa et al. 20	TDM study	Steady state model	NR	NONMEM
5	Tanikawa et al. 21	TDM study	1 CPT (linear model with first order absorption)	NR	MDGP
6	Blanco‐Serrano et al. 22	TDM study	1 CPT (linear model with first order absorption)	External validation (n = 30)	NONMEM
7	Blanco‐Serrano et al. 23	TDM study	1 CPT (linear model with first order absorption)	External validation (n = 45)	NONMEM
8	Park et al. 24	TDM study	1 CPT (linear model without absorption)	NR	NONMEM
9	El Desoky et al. 25	TDM study	1 CPT (linear model without absorption)	External validation (n = 20)	NONMEM
10	Jankovic et al. 26	TDM study	1 CPT (linear model without absorption)	External validation (n = 20)	NONMEM
11	Birnbaum et al. 39	TDM study	1 CPT (linear model with first order absorption)	Internal validation (bootstrap)	NONMEM
12	Dutta et al. 27	PK study	1 binding site protein binding model	NR	NONMEM
13	Jiang et al. 28	TDM study	1 CPT (linear model with first order absorption)	External validation (n = 100)	NONMEM
14	Ueshima et al. 29	TDM study	Relationship between total and unbound concentration of VPA using Langmuir equation	NR	NONMEM
15	Correa et al. 30	TDM study	1 CPT (linear model with first order absorption)	External validation (n = 40)	NONMEM
16	Jiang et al. 31	TDM study	1 CPT (linear model with first order absorption)	External validation (n = 110)	NONMEM
17	Vucicevic et al. 32	TDM study	1 CPT (linear model with first order absorption)	External validation (n = 24)	NONMEM
18	Jankovic et al. 33	TDM study	1 CPT (linear model without absorption)	External validation (n = 115 for pediatric and 15 for adult)	NONMEM
19	Williams et al. 34	Clinical trial and TDM studies	2 CPT (linear model with first order absorption for solid oral dosing and zero order for liquid oral dosing)	Internal validation (bootstrap and VPC) and external validation using clinical trial data in SMA patients	NONMEM
20	Ibarra et al. 42	PK study	2 CPT (linear model with first order absorption plus enterohepatic circulation)	NR	NONMEM
21	Ogusu et al. 43	TDM study	1 CPT (linear model with first order absorption) for PK data, and logistic regression model for γ‐GT elevation	Internal validation (bootstrap, VPC, visual inspection)	NONMEM
22	Nakashima et al. 36	TDM study	1 CPT (linear model with first order absorption)	Internal validation (bootstrap, VPC, visual inspection)	NONMEM
23	Ding et al. 37	TDM study	Non‐linear model based on protein binding saturation	Internal validation (bootstrap and NPDE) and external validation: 2 datasets	NONMEM
24	Lin et al. 38	TDM study	1 CPT (linear model with first order absorption)	Internal validation (bootstrap, NPDE) and external validation	NONMEM
25	Jawien et al. 41	VPA toxicity study	2 CPT with metabolites (VPA‐2‐ene, VPA‐4‐ene)	Internal validation (visual inspection, VPC, NPDE)	Monolix
26	Methaneethorn et al. 40	TDM study	1 CPT (linear model with first order absorption)	Internal validation (bootstrap and NPDE)	NONMEM

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CPT, compartment; NPDE, normalized prediction distribution error; NR, not reported; PK, pharmacokinetic; SMA, spinal muscular atrophy; TDM, therapeutic drug monitoring; VPA, valproic acid; VPC, visual predictive check; γ‐GT, γ‐glutamyltransferase

Several covariates were tested during model development. Age, body weight, gender, co‐medication and VPA dose were the most frequently tested covariates, accounted for in 88%, 85%, 77%, 73% and 58% of the studies, respectively. However, gender and age were found to significantly affect VPA pharmacokinetics in only six and seven studies, respectively. CYP2C9 and CYP2C19 genotypes were investigated in two studies 31, 43. Only one of them found significant effects of CYP2C9 and CYP2C19 genotypes on VPA clearance 31. Investigated and significant covariates as well as criteria for statistical significance are summarized in Table 3.

Table 3.

List of tested and significant covariates in the models

No	Study	Tested covariates	Covariate selection	Significant covariates
1	Botha et al. 18	WT, age, gender, race, co‐medication (PB, PHT, CBZ)	Stepwise addition/stepwise deletion	WT and co‐medication on CL
2	Yukawa et al. 44	WT, age, VPA dose, gender	P < 0.05	WT, VPA dose, gender on CL
3	Yukawa et al. 19	WT, age, VPA dose, CBZ dose, gender, co‐medication (CBZ)	Stepwise addition/deletion (P < 0.05)	WT, VPA dose, CBZ dose, gender, co‐medication on CL
4	Yukawa et al. 20	WT, age, VPA dose, gender, co‐medication (PB, CBZ)	P < 0.005	WT, VPA dose, gender, co‐medication on CL
5	Tanikawa et al. 21	Age	P < 0.0001	age on CL
6	Blanco‐Serrano et al. 22	WT, age, VPA dose, gender, co‐medication (CBZ, PHT, PB)	Stepwise addition (P < 0.05)/backward elimination (P < 0.01)	WT, VPA dose, co‐medication on CL
7	Blanco‐Serrano et al. 23	WT, age, VPA dose, gender, co‐medication (CBZ)	Stepwise addition (P < 0.05) and stepwise deletion (P < 0.01)	WT, VPA dose, co‐medication on CL
8	Park et al. 24	WT, age, height, VPA dose, BMI, gender	Stepwise addition (P < 0.05) and stepwise deletion (P < 0.01)	WT on CL and V_d
9	El Desoky et al. 25	WT, age, gender, VPA dose, co‐medication (CBZ), CBZ dose, indication of VPA measurement (uncontrolled epilepsy)	Stepwise addition (P < 0.05) and stepwise deletion (P < 0.005)	co‐medication, VPA dose, age, uncontrolled epilepsy on CL
10	Jankovic et al. 26	WT, age, VPA dose, co‐medication (CBZ), gender	Stepwise addition (P < 0.05) and stepwise deletion (P < 0.005)	WT, age on CL
11	Birnbaum et al. 39	WT, gender, co‐medication, route of administration, formulations	stepwise addition (P < 0.005) and stepwise deletion (P < 0.001)	gender, co‐medication, formulation on CL
12	Dutta et al. 27	WT, age, gender, race, co‐medication (CBZ, PHT, PMD, PB, OCP) on binding association constant (K)	Stepwise addition (P < 0.05)	none
13	Jiang et al. 28	WT, age, gender, co‐medication (PHT, CBZ, PB, TPM, LTG), formulation, height, creatinine clearance	Stepwise addition (P < 0.05) and stepwise deletion (P < 0.01)	formulation on K_a, WT on V_d, co‐medication and age on clearance
14	Ueshima et al. 29	Effect of co‐medication (ZNS, ESM, PHT, CZP, CBZ, CLO) and polytherapy on B_m (apparent maximum concentration of the binding site of VPA) and K_d (apparent dissociation constant of VPA)	P < 0.05	Effect of ESM on K_d and effect of polytherapy on B_m and K_d
15	Correa et al. 30	WT, age, gender, height, BSA, VPA dose, co‐medication (CBZ, PB)	Stepwise addition (P < 0.05) and stepwise deletion (P < 0.001)	WT, VPA dose, co‐medication with PB on CL/F
16	Jiang et al. 31	WT, age, height, formulation, genotyping	stepwise addition (P < 0.05) and stepwise deletion (P < 0.01)	genotype and age on CL/F, weight on V/F, and formulation on K_a
17	Vucicevic et al. 32	WT, age, VPA dose, co‐medication (LTG, BZD, TPM, CBZ, PB), CBZ dose, PB dose, gender, tobacco smoking,	Stepwise addition (P < 0.05)/backward elimination (P < 0.05)	WT, co‐medication with TPM and VPA dose of greater than 1000
18	Jankovic et al. 33	WT, age, gender, VPA dose, co‐medication (CBZ, LTG, PB)	stepwise addition (P < 0.05) and stepwise deletion (P < 0.01)	Pediatric model: WT and co‐medication with CBZ on CL Adult model: WT and co‐medication with PB on CL
19	Williams et al. 34	WT, age co‐medication, race	Stepwise addition (P < 0.05) and stepwise deletion (P < 0.001)	WT on CL, WT and age on V_c, WT on V_p and WT on Q
20	Ibarra et al. 42	WT, age, gender and contraceptive therapy	Stepwise addition (P < 0.05) and stepwise deletion (P < 0.01)	WT on K_a and V_c, gender and contraceptive therapy on CL, F_E, and T_lag
21	Ogusu et al. 43	PK model: – WT, age, gender, VPA dose, CYP2C9 genotype, CYP2C19 genotype, and co‐medication (CBZ, CLO, GBP, PB, PHT, TPM, ZNS) on CL/F – WT and VPA dose on V/F PK‐PD: – WT, age, gender, VPA dose, duration of VPA therapy, CYP2C9, CYP2C19, SOD2, GSTM1, and GSTT1 genotypes, complication with intellectual disability and co‐medication (CBZ, CLO, GBP, PB, PHT, TPM, ZNS) on Base – WT, age, gender VPA dose, duration, CYP2C9, CYP2C19, SOD2, GSTM1, and GSTT1 genotypes, intellectual disability, co‐medication (CBZ, CLB, GBP, PB, PHT, TPM, ZNS) on slope	Stepwise addition (P < 0.05) and stepwise deletion (P < 0.05)	PK model: – VPA dose on V_d – VPA dose, gender, co‐medication with CBZ, PB, PHT, CLO on CL/F PK‐PD model: ‐ Intellectual disability and SOD2Val/Val genotype on base ‐ VPA dose on slope
22	Nakashima et al. 36	Age, gender, seizure locus, seizure type, complication with intellectual disability, co‐medication (CBZ, CZP, CLO, GBP, LTG, PB, PHT, TPM and ZNS)	Stepwise addition (P < 0.05) and stepwise deletion (P < 0.05)	age, CBZ, CZP, SCN1A G/A genotype, SCN1A A/A genotype on intercept partial seizure, PHT, TPM, SCN1A G/A genotype, SCN1A A/A genotype on slope
23	Ding et al. 37	WT, age, gender, VPA dose, formulation and co‐medication (CBZ, CZP, TPM)	Stepwise forward addition and backward elimination (P < 0.001)	WT, age, VPA dose, co‐medication with CBZ on CL/F WT on V/F
24	Lin et al. 38	WT, age, gender, VPA dose, formulation, co‐medication (CBZ, PHT, PB, TPM)	Stepwise forward addition (P < 0.05) and stepwise backward elimination (P < 0.01)	WT, VPA dose and co‐medication on CL/F; WT on V/F
25	Jawien et al. 41	Previous VPA therapy on V_max and decontamination on V_p/F	AIC value	Previous VPA therapy on V_max and decontamination on V_p/F
26	Methaneethorn et al. 40	WT, BMI, age, gender, co‐medication (PNZ, THP, CZP, RPD, HPD, CPZ), VPA dose	Stepwise addition (P < 0.05) and stepwise deletion (P < 0.001)	VPA dose and WT on CL/F

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AIC, Akaike information criterion; BMI, body mass index; BSA, body surface area; BZD, benzodiazepine; CBZ, carbamazepine; CL, clearance; CLO, clobazam; CPZ, chlorpromazine; CZP, clonazepam; ESM, ethosuximide; F_E, reabsorbed fraction; GBP, gabapentin; GEN, gender; GSTM1, glutathione S‐transferase mu 1; GSTT1, glutathione S‐transferase theta 1; HPD, haloperidol; K_a, absorption rate constant; LTG, lamotrigine; OCP, oxcarbazepine; PB, phenobarbital; PHT, phenytoin; PNZ, perphenazine; PMD, primidone; Q, inter‐compartmental clearance; RPD, risperidone; SOD₂, superoxide dismutase 2; THP, trihexyphenidyl; T_lag, lag time; TPM, topiramate; V_c, central volume of distribution; V_d, volume of distribution; V_max, maximum rate of metabolism; V_p, peripheral volume of distribution; VPA, valproic acid; WT, weight; ZNS, zonisamide

Exponential models (n = 11) were the most frequently used error models for IIV, followed by proportional (n = 10) and additive (n = 2) error models, respectively. For RV, additive (n = 10) and proportional (n = 10) models were the most commonly used, followed by combined proportional and additive (n = 2), and exponential (n = 2) models, respectively. The magnitude of IIV on VPA clearance ranged from 13.4% to 49.1%. Estimated pharmacokinetic parameters, magnitude of IIV and RV as well as relationship between covariates and pharmacokinetic parameters of each study are summarized in Table 4.

Table 4.

A summary of fixed and random effect models described in the included studies

No.	Study	Fixed effect parameters	IIV		RV
No.	Study	Fixed effect parameters	Relationship	Variability	Relationship	Variability
1	Botha et al. 18	CL (l h⁻¹) = [exp(0.022 * WT (kg) − 1.38)] * M where M = 1 for VPA monotherapy or VPA with PB or VPA with PHT; M = 1.6 for VPA with CBZ K_a (h⁻¹) = 1.9 (fixed)	Additive	16.30%	Additive	24.6%
2	Yukawa et al. 44	CL (ml kg⁻¹ h⁻¹) = 18.9 * WT (kg)^−0.276 * VPA dose (mg kg⁻¹ d⁻¹)^(0.142) * gender where gender = 1 for male, 0.887 for female	Proportional	13.4% (95% CI = 8.3–17.1)	Proportional	18.6% (95%CI = 16.3–20.6)
3	Yukawa et al. 19	CL (ml kg⁻¹ h⁻¹) = 6.06 * WT (kg)^‐0.168 * VPA dose (mg kg⁻¹ d⁻¹)^0.414 * CBZ dose (mg kg⁻¹ d⁻¹)^0.095 * 0.943^gender *1.10^CO where gender = 0 for males, gender = 1 for females, CO = 0 for VPA + CBZ, 1 for VPA + CBZ + one or more AED (PB, PMD, PHT, CZP)	Proportional	15.8% (95% CI = 13.2–18.1)	Proportional	16.3% (95%CI = 14.4–17.9)
4	Yukawa et al. 20	CL (ml kg⁻¹ h⁻¹) = 15.6 * WT (kg)^−0.252 * VPA Dose (mg kg⁻¹ d⁻¹)^0.183 * 0.898^gender * CO^PB * CO^CBZ where gender = 1 for female, CO^PB = 1.1 if patient treated with PB, CO^PB = 1 if patient not treated with PB, CO^CBZ = 0.769 * CBZ dose (mg kg⁻¹ d⁻¹)^0.179 if patient treated with CBZ, CO^CBZ = 1 if patient not treated with CBZ	Proportional	14.1% (10.9–16.8)	Proportional	18.4% (95%CI = 16.8–19.9)
5	Tanikawa et al. 21	VC: K_a (h⁻¹) = 8.14 VR: K_a (h⁻¹) = 0.230 Age < 12: k_e (h⁻¹) = 0.0673 (1 – 0.0221 * age) Age ≥ 12: k_e (h⁻¹) = 0.0495 V_d (l kg⁻¹) = 0.212 T_lag = 1.25 h	Proportional	K_a,_VC: 246% K_a,_VR: 1% K_e: 8.0% V_d: 2.1% T_lag: 63.1%	Proportional	VC = 18.6% VR = 7.1%
6	Blanco‐Serrano et al. 22	CL (l h⁻¹) = 0.004 * WT (kg) * VPA Dose (mg kg⁻¹)^0.304 * 1.363(CBZ) * 1.541(PHT) * 1.397(PB) (effect of co‐medication is bi‐therapy, cannot be applied to three or more concomitant medication) V_d (l kg⁻¹) = 0.2 (fixed) K_a (h⁻¹) = 1.2 (fixed)	Proportional	23.39% (95% CI = 4.04–42.7)	Additive	SD = 11.36 mg l⁻¹ (95% CI = 1.1–21.5 mg l⁻¹)
7	Blanco‐Serrano et al. 23	CL (l h⁻¹) = 0.012 * WT (kg) ^0.715 * (VPA Dose (mg kg⁻¹ d⁻¹))^0.306 * (1 + 0.359 * CBZ) where CBZ = 1 if patient treated with CBZ V_d (l kg⁻¹) = 0.24 (fixed) K_a (h⁻¹) = 1.9 (fixed)	Proportional	21.40%	Additive	23.90% for concentration 65 mg l⁻¹
8	Park et al. 24	CL (l h⁻¹) = 0.849 * (WT/60)^0.702 V_d (l) = 15.1 * (WT/60)^0.604	Exponential	CL: 32% V_d: 18%	Exponential	26.70%
9	El Desoky et al. 25	CL (l h⁻¹) = 0.105 + 0.151(CBZ) + 0.000248(VPA dose (mg d⁻¹)) + 0.0968(age (y)/20) + 0.0803(INDI) where CBZ = 1 if patient treated with CBZ, INDI = 1 if indication for VPA measurement is uncontrolled epilepsy V_d (l) = 11.5 (fixed)	Proportional	23.6%	Additive	SD = 5.24 mg l⁻¹
10	Jankovic et al. 26	CL (l h⁻¹) = 0.164 + 0.00365 * WT (kg) + 0.00464 * age (y)	Exponential	27.2%	Exponential	29.70%
11	Birnbaum et al. 39	CL/F (l h⁻¹) = 0.843 * 0.729 (if female) * 1.41 (if taking CBZ or PHT) * 1.25 (if formulation is syrup) V_d (l) = 14.0 l (fixed) K_a (h⁻¹) = 1.0 (fixed)	Exponential	32.9%	Combined	Proportional: %CV = 18.2% Additive: SD = 10.6 mg l⁻¹
12	Dutta et al. 27	Binding association constant (K) = 15.5 ± 2.28 mM⁻¹ Number of binding sites (N) = 1.98 ± 0.087	Proportional	K: 32%	Proportional	14%
13	Jiang et al. 28	K_a (h⁻¹) = 0.251 + 2.24(1‐HS) where HS = 1 for sustained release formulation V/F (L) = 2.88 + 0.157 * WT (kg) CL/F (l h⁻¹) = 0.106^(0.98*^CO) + 0.0157(age) where CO = 1 when co‐medication exists	Additive after log transformed	K_a: 11.00% V/F: 49.10% CL/F: 25.10%	Additive	SD = 13.2 mg l⁻¹
14	Ueshima et al. 29	For VPA monotherapy: B_m (μg ml⁻¹) = 130.0 (SE = 4.5 μg ml⁻¹) K_d (μg ml⁻¹) = 7.8 μg ml⁻¹ (SE = 0.7 μg ml⁻¹) For combination therapy with Ethosuximide K_d (μg ml⁻¹) = 7.8 * 0.872^Ethosuximide For polytherapy B_m (μg ml⁻¹) = 130.0 * 0.814^polytherapy K_d (μg ml⁻¹) = 7.8 * 0.538^polytherapy	Proportional	NR	Proportional	NR
15	Correa et al. 30	CL/F (l h⁻¹) = [0.0466 + 0.00363(WT (kg)) + 0.000282(VPA dose(mg d⁻¹)] * [1 + 0.236(PB)] where PB = 1 if patient treated with PB K_a (h⁻¹) = 1.2 (fixed) V_d (l kg⁻¹) = 0.24 (fixed)	Proportional	14.10%	Additive	SD = 17.3 mg l⁻¹
16	Jiang et al. 31	CL/F (l h⁻¹) = 0.0951 * (1 + exp(0.0267 * (3‐G)) + 0.0071(age) where G = 1, 2, or 3 for wild type, heterozygous and homozygous genotypes of CYP2C19 and CYP2C9, respectively V/F (l) = 6.54 * exp(0.0133 * weight (kg)) K_a (h⁻¹) = 0.424 * exp(2.768 * (1 − SR)) where SR = 1 for sustained release tablets	Exponential	CL/F: 29.30% V/F: 71.90% K_a: 36.70%	Additive	SD = 10.1 mg l⁻¹
17	Vucicevic et al. 32	CL/F (l h⁻¹) = 0.517 * (WT (kg)/70)^0.556 * 1.43^VPA * 0.765^TPM where VPA = 1 if dose is greater than 1000 mg d⁻¹, or 0 otherwise, TPM = 1 if patient co‐treated with TPM, or 0 if not. V/F (l kg⁻¹) = 0.14 (fixed) K_a (h⁻¹) = 0.67 (fixed)	Exponential	31.90%	Combined	Proportional: %CV = 23.8% Additive: 13.2 mg l⁻¹
18	Jankovic et al. 33	Pediatric: CL (l h⁻¹) = 0.137 + 0.00258 * WT (kg) + 0.159 * CBZ where CBZ = 1 if patient treated with CBZ, or 0 otherwise Adult: CL (l h⁻¹) = 0.0712 + 0.00502 * WT (kg) + 0.539 * PB where PB = 1 if patient treated with PB, or 0 otherwise	Exponential	Pediatric: 19.80% Adult: 20.25%	Additive	Pediatric: 23.22% Adult: 20.78%
19	Williams et al. 34	CL (l h⁻¹) = 0.854(WT (kg)/70)^0.75 V_c (l) = 10.3 (WT (kg)/70)^1.0 * (age/8.5)^−0.267 V_p (l) = 4.08 * (WT (kg)/70)^1.0 Q (l h⁻¹) = 5.34*(WT (kg)/70)^0.75 K_a for capsule (h⁻¹) = 2 (fixed) K₀ for syrup (mg/h) = 410 (fixed) K_a for sprinkle (h⁻¹) = 1.2 (fixed) Lag time for sprinkle (h) = 1 (fixed) K_a for tablet (h⁻¹) = 4.1 (fixed) Lag time for tablet (h) = 2 (fixed)	—	CL: 35.90% V_c: 19.60% V_p: 101.50%	Proportional	TDM: %CV = 34.8% Clinical trial: %CV = 4.6%
20	Ibarra et al. 42	K_a (h⁻¹) = 2.91 – 0.0184 * WT (kg) V_c (l) = 9.60 – 0.134 * (WT (kg)/70) V_p (l) = 4.95 CL_d (l h⁻¹) = 0.559 l CL (l h⁻¹) = 0.581 * (1‐S‐CT) + 0.9 * (S + CT) F_E = 0.462 * (1‐S‐CT) + 0.218 * (S + CT) T_lag (h) = 2.21(1‐S‐CT) + 2.00 (S + CT) T_EHC (h) = 8.27 K_EHC (h⁻¹) = 1.20 where S (sex) = 0 for women, 1 for men, CT (contraceptive therapy) = 1 if women treated with contraceptive, or 0 for the rest of subjects)	Exponential	K_a: 24.40% V_c: 21.20% V_p: 23.90% CL_d: 16.00% CL: 21.20% F_E: 41.10% T_lag: 37.70% T_EHC: 18.90% K_EHC: 38.70%	Proportional	σ = 0.00524
21	Ogusu et al. 43	K_a (h⁻¹) = 0.109 V_d/F (l) = 21.4 * (VPA dose (mg d⁻¹)/1000)^1.52 CL/F (l h⁻¹) = 0.559 * (VPA dose (mg d⁻¹)/1000)^0.596 * 0.917^female * 1.19^CBZ * 1.12^PB * 1.43^PHT * 0.906^CLO where female = 1, male = 0; CBZ, PB, PHT or CLO = 1 if CBZ, PB, PHT or CLO was co‐treated and = 0 otherwise A_lag (h) = 3.00 (fixed) Logit (Pr) = −6.63 + 3.62^{intellectual disability} + 1.96^{SOD2Val/Val genotype} + Dose^1.55 * AUC where intellectual disability = 1 if an intellectual disability was present and = 0 otherwise; SOD2 Val/Val genotype = 1, SOD2 Val/Ala or Ala/Ala genotype = 0	Exponential	ω² on K_a = 7.77 * 10⁻⁷ ω² on V_d/F = 1.83 * 10⁻⁷ ω² on CL/F = 0.0587 ω² on A_lag = 4.48 * 10⁻⁹ ω² on Logit (Pr) = 12.3	Proportional	σ² = 0.0617
22	Nakashima et al. 36	Age ≤ 18 y: Logit (Pr) = 7.73 – 4.88^CBZ − 1.93^PB − 4.75^{SCN1A GA genotype} − 4.30^{SCN1A AA genotype} − (10.9 – 4.73^CBZ + 3.86^PHT − 7.62^{SCN1A GA genotype} − 7.60^{SCN1A AA genotype}) * predicted trough concentration of VPA Age > 19 y: Logit (Pr) = 10.3 – 2.56^CZP − 9.88^{SCN1A GA genotype} − 14.3^{SCN1A AA genotype} * predicted trough concentration of VPA where CBZ, PB, PHT, CZP = 1 if CBZ, PB, PHT, CZP was co‐administered, and 0 otherwise; SCN1A G/A genotype or SCN1A A/A genotype = 1 for carriers of each genotype, and 0 for carriers of other genotypes	NR	NR	NR	NR
23	Ding et al. 37	CL/F (l h⁻¹) = $0.3 * {1.43}^{CBZ} * {(\frac{BW (kg)}{70})}^{0.791 - \frac{0.096 {Age}^{8.63}}{{0.802}^{8.63} + {Age}^{8.63}}} * (1 + \frac{2.8 {TDD}^{1.68}}{{37.4}^{1.68} + {TDD}^{1.68}})$ V/F = 22.2 (WT (kg)/70) where CBZ = 1 for patients co‐treated with CBZ, or 0 otherwise, TDD: total daily dose of VPA (mg kg⁻¹) K_a (h⁻¹) = 2.64 (fixed), 1.57 (fixed), 0.46 (fixed) for syrup, conventional tablets and SR tablets, respectively.	Exponential	ω = 0.195	Additive	13.3 mg l⁻¹
24	Lin et al. 38	CL/F (l h⁻¹) = 0.1(WT (kg)/60)^0.7VPA dose (mg d⁻¹)^0.2 1.36 (if co‐treated with CBZ) * 1.25 (if co‐treated with PHT) * 1.11 (if co‐treated with PB) V/F (l) = 0.14*WT (kg) K_a (h⁻¹) = 1.9 (fixed)	Exponential	18.0%	Additive	8.5 mg l⁻¹
25	Jawien et al. 41	Vc/F (l) = 3 (fixed) Vp/F (l) = 42.1 β_Vp/F (l) = 0.382 K₁₀ (h⁻¹) = 0.670 K₂₀ (h⁻¹) = 0.528 K₃₀ (h⁻¹) = 0.786 K₁₂ (h⁻¹) = 0.00143 K_M (mg l⁻¹) = 23 V_max (mg l⁻² h⁻¹) = 3.64 β_Vmax = 0.441 Q (l h⁻¹) = 58.8 Q₂ (l h⁻¹) = 0 Q₃ (l h⁻¹) = 27.5 T_lag (h) = 0 T_k0 (h) = 4.79 LnV_max = LnV_max0 + β_Vmax * VPAther LnV_p/F = Ln(V_p/F)₀ + β_Vc/F * Decont where VPAther (previous VPA therapy) and Decont (decontamination) = 1 if the feature is present, or 0 otherwise	NR	NR	NR	NR
26	Methaneethorn et al. 40	CL/F (l h⁻¹) = 0.464 * (VPA dose (mg kg⁻¹ d⁻¹)/17)^0.402 * (WT (kg)/60)^0.779 K_a (h⁻¹) = 0.78 (fixed) or 0.38 (fixed) for enteric coated and sustained release dosage form, respectively V_d (l) = 23.3	Exponential	CL/F: 19.1%	Proportional	0.163%

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AED, antiepileptic drug; A_lag, absorption lag time; B_m, apparent maximum concentration of the binding site of VPA; BW, body weight; CBZ, carbamazepine; CL, clearance; CL_d, distribution clearance; CLO, clobazam; CZP, clonazepam; F_E, reabsorbed fraction; IIV, inter‐individual variability; K_a, absorption rate constant; K_e, elimination rate constant; K_d, apparent dissociation constant of VPA; K_EHC, reabsorption rate constant; K_m, Michaelis constant; K₀, zero order rate constant; NR, not reported; Q, intercompartmental clearance; PB, phenobarbitone; PHT, phenytoin; PMD, primidone; RV, residual variability; SOD₂, superoxide dismutase 2; TDM, therapeutic drug monitoring; T_EHC, time of reabsorption onset; T_lag, lag time; TPM, topiramate; VC, conventional formulation of valproic acid; V_c, central volume of distribution; V_d, volume of distribution; V_max, maximum rate of metabolism; V_p, peripheral volume of distribution; VPA, valproic acid; VR, slow‐release formulation of valproic acid; WT, weight.

Approximately 65% of the studies evaluated performance of the final models (Table 2). Of these, external datasets were used in nine studies. The sample size of external datasets ranged from 20 to 130 subjects. Five studies evaluated the models by means of internal validation such as bootstrapping, visual predictive check (VPC) or normalized prediction distribution error (NPDE). Both internal and external validation were employed in three studies.

Discussion

VPA is one of the most widely used antiepileptic drugs. The drug has also been used to treat bipolar disorder and other neurological conditions. Several pharmacokinetic studies of VPA have been reported. This is the first review article that aimed to summarize knowledge concerning population pharmacokinetics of VPA, focusing on the nonlinear mixed effects modelling approach.

Even though VPA is almost completely absorbed, the absorption rate of the drug depends on dosage form. However, among the 15 studies that reported rate of VPA absorption, only six studies accounted for the influence of dosage form on absorption rate constant (k_a) and only four of them were able to estimate the k_a values. The ranges of estimated k_a values and magnitude of variability were 0.109–0.424 h⁻¹ and 1–36.7%, respectively. The estimated k_a values for tablet dosage form are more variable with a range of 1.0–8.14 h⁻¹ and a variability of 11–246%. The high variability in k_a (246%) of tablet dosage form is likely due to the limited number of samples per subject (~1.6), resulting in little information during the absorption phase. Additionally, it has been known that VPA concentrations are subject to diurnal variation 13. Given the wide range of sampling time (1.0–39.3 h), such high variability in k_a is not surprising. Estimated population k_a values for dosage forms other than conventional and slow‐release tablets are not available.

Eleven studies reported estimated values of volume of distribution (V_d). Of these, three studies characterized VPA pharmacokinetics as a two‐compartment model. The estimated V_d for one‐compartment models and peripheral volume of distribution (V_p) for two‐compartment models ranged from 8.4 to 23.3 l and 4.08 to 42.1 l, respectively. The variability in V_d was relatively high, with the range of 2.1–49.0% and 23.9–101.50% for V_d of one‐compartment and V_p of two‐compartment models, respectively. The authors proposed that the high variability in V_p (101.50%) could be attributed to the variability in protein binding which was not taken into account in the model 34. Given that a sparse sampling strategy was employed, it was not possible to estimate the magnitude of IIV in some studies and was therefore set at zero. For the effect of covariates, the reported significant factors influencing V_d included body weight, VPA dose and age. V_d of VPA increased with body weight and VPA dose. The increase in V_d with higher doses could be explained by the saturable protein binding 45. Regarding protein binding, Dutta et al. 27 reported that a one binding site model best described the VPA protein binding, with the population estimates for number of binding sites (N) and binding site association constant (K) of 1.98 and 15.5 mM⁻¹, respectively.

The estimated VPA clearance (CL_VPA) ranged from 0.206 to 1.154 l h⁻¹, with the magnitude of IIV of 13.40–35.90%. Significant covariates on CL_VPA frequently identified were body weight, VPA dose, concomitant medications, gender and age. Several studies reported an increase in CL_VPA with increasing body weight. This finding is expected given an association between body weight and organ development responsible for drug elimination. However, studies by Yukawa et al. have shown that CL_VPA decreased with increasing body weight during the maturation process 19, 20, 44. Regarding the effect of age, higher CL_VPA in young children compared with adults has been reported. However, the effect of age on CL_VPA in the children population is controversial. Tanikawa et al. 21 reported the decrease in CL_VPA with increasing age up to 12 years, which is consistent with a study by Cloyd et al. 46 in that CL_VPA decreases with maturation and reaches adult values around age 14–16 years. Even though, the reason for this finding is unknown, it has been reported that liver volume per unit body weight linearly decreases with increased age throughout childhood 47. However, El Desoky et al. 25, Jankovic et al. 26 and Jiang et al. 28, 31 reported a linear relationship between age and CL_VPA. They proposed that the increase in CL_VPA with increasing age could be explained by the developmental changes in drug metabolism in children. As for gender effect, lower CL_VPA in females has been observed in five studies 19, 20, 42, 43, 44. As previously mentioned, VPA is mainly metabolized via three routes including glucuronidation, β‐oxidation and CYP450 enzymes 8, 9, 10. Evidence showing lower UDP‐glucuronosyltransferases activity in females has been documented 48. Moreover, Ibarra et al. 42 tested the effect of gender on VPA pharmacokinetics incorporating an EHC process and found that the reabsorbed fraction of VPA in women was higher than in men. In addition, a 21.5% increase in CL_VPA was observed in women taking contraceptive therapy. The authors proposed that this could be attributed to an inductive effect of ethinylestradiol on glucuronosyltransferase activity.

An increase in CL_VPA with increasing VPA dose was reported by several studies. One possible explanation for this could be protein binding saturation, resulting in higher free VPA available for elimination. Moreover, a TDM effect could be another factor contributing to the increased CL_VPA since individuals with high CL_VPA tend to receive a higher dose. To better characterize this non‐linearity, Ding et al. 37 compared the ability of three models (i.e. the power exponent model, the dose dependent maximum effect (DDE) model and the protein binding model). The authors found that the DDE model best described VPA data, based on the standard evaluation criteria.

Concomitant drugs commonly found to influence CL_VPA included carbamazepine, phenobarbitone and phenytoin. These drugs are enzyme inducers 4, 5, leading to an increase in CL_VPA when co‐administered with VPA. The magnitude of CL_VPA elevation varies across studies. However, some studies did not find the effects of these enzyme‐inducing agents on CL_VPA, which might be due to the limited number of subjects using these drugs. In addition, Jiang et al. 31 reported a significant effect of CYP2C9 and CYP2C19 genotypes on CL_VPA. Although pathways other than CYP‐mediated elimination have been proposed, this finding is of importance in clinical settings where a test for CYP2C9 and CYP2C19 genotypes is available 8, 9, 10.

In terms of concentration–response relationships, a therapeutic range of VPA of 50–100 mg l⁻¹ in the treatment of epilepsy is widely accepted 4, 5. However, consensus on such relationship is questioning since this range was based on two small poorly controlled studies of patients on antiepileptic drug polytherapy. Moreover, this relationship does not take into account the active metabolites of VPA, 2‐propyl‐4‐pentanoic acid and 2‐propyl‐2‐pentanoic acid, that contribute to the anticonvulsant activity 49, 50. Beydoun et al. 49 reported the efficacy of VPA monotherapy in poorly controlled partial epilepsy randomly assigned to high (80–150 mg l⁻¹) or low (25–50 mg l⁻¹) VPA concentration level groups. They found that patients in the high VPA level group had higher reduction in seizure frequency from baseline as compared to those in the low VPA level group. However, adverse events, including tremors, thrombocytopenia, diarrhoea, vomiting and anorexia, were significantly higher in the high VPA level group as well. In addition, Panomvana Na Ayudhya et al. reported that seizure uncontrolled paediatric patients had a significantly higher elimination rate constant (K_e) and a significantly shorter half‐life of VPA. However, the sample size of this study was relatively small and future study with a larger sample size is required to confirm the results 51. With regard to psychiatric patients, even though a therapeutic range for mood‐stabilizing activity of VPA has not yet been published, several studies reported that a concentration of at least 50 mg l⁻¹ might be required to achieve clinical response in patients with bipolar disorder 50, 52, 53, 54, 55. However, these studies were relatively small, with sample sizes ranging from 24 to 59 patients. Further studies with larger sample size are still needed.

Only two studies characterized the relationship between VPA concentration levels and therapeutic/toxic effects by means of population pharmacokinetics and pharmacodynamics 36, 43. For the relationship between VPA exposure and seizure control, Nakashima et al. 36 utilized a logistic regression model to predict the probability of attaining at least 50% seizure frequency reduction. In addition, the authors determined an optimal cut‐off point for such probability using the receiver operating characteristic (ROC) curve. Significant predictors for achieving at least 50% seizure frequency reduction included age, seizure types, SCN1A rs3812718 polymorphism and comedication. The optimal VPA trough concentration for each patient can be calculated using the covariate–parameter relationship and the optimal cut‐off point with a logit (Pr) value of 0.1 from the proposed population pharmacokinetics/pharmacodynamics models as summarized in Table 4. For example, the optimal trough concentration for a patient with SCN1A G/G genotype, aged 10 years with generalized seizure, receiving VPA with phenytoin, is estimated to be 92.0 mg l⁻¹, whereas the optimal trough concentration in patients with the same conditions aged 10 years carrying SCN1A A/A genotype is estimated to be 142.4 mg l⁻¹. These findings imply that some patients might require VPA trough concentrations of greater than the generally accepted range of 50–100 mg l⁻¹ to achieve at least 50% seizure frequency reduction. Therefore, for patients with poorly controlled seizures, the optimal VPA trough concentrations might be obtained from the proposed population pharmacokinetics/pharmacodynamics model, instead of exclusively relying on the generally accepted range of 50–100 mg l⁻¹. Regarding the relationship between VPA exposure and the risk of developing toxicity, Ogusu et al. 43 investigated the impact of polymorphisms of antioxidant enzyme genes (SOD2, GSTM1 and GSTT2) on the elevation of γ‐GT, an enzyme used as a liver function marker commonly found in hepatocytes and biliary epithelial cells, during VPA therapy. The authors found that SOD2 Val16Ala polymorphism significantly influenced the relationship between VPA exposure and γ‐GT elevation and concluded that SOD2 genotyping may play an important role in preventing VPA‐induced γ‐GT elevation. However, the complexity of their model meant that the influence of enzyme‐inducing antiepileptic drugs could not be successfully included.

Key aspects pertaining to population pharmacokinetics of VPA for clinical use and future research have been highlighted by this review. For the clinician, VPA therapy could be optimized by population pharmacokinetic models and significant predictors, summarized in this review (Table 4), with an incorporation of Bayesian estimation to obtain optimal individual doses. However, predictive performance of these published models should be performed in a target population prior to use in clinical settings, particularly equations that were proposed without model validation (Table 2). Moreover, the choice to adopt these models for clinical use should be based on study design and factors associated with a patient population. For example, a one‐compartment model developed from routine monitoring data that incorporated the effect of antiepileptic comedication might be a better choice for patients receiving antiepileptic drug polytherapy. For researchers, this review provides information concerning model structure, population characteristics as well as sources and magnitudes of pharmacokinetic variability. For future studies, a population pharmacokinetic study of VPA in patients with psychiatric and other neurological disorders should be conducted. As for a population pharmacokinetics/pharmacodynamics model, some limitations still exist and future studies are needed to confirm such results. These include a population pharmacokinetics/pharmacodynamics study for seizure control in ethnically diverse populations to ensure the generalizability of the model for seizure control. Moreover, a population pharmacokinetics/pharmacodynamics of VPA in populations other than patients with epilepsy (i.e. patients with bipolar disorder and other psychiatric illness) is still lacking. Finally, more studies in regard to a relationship between VPA exposure and adverse effects, other than an elevation of γ‐GT, such as thrombocytopenia by means of population pharmacokinetics/pharmacodynamics are recommended.

Conclusion

Most of the reported population pharmacokinetic studies of VPA were conducted using TDM data, employing a one‐compartment model. Significant covariates influencing VPA pharmacokinetics were discussed and summarized. One third of published population pharmacokinetic models for VPA did not perform model validation and need to be evaluated for their predictive performance.

Competing Interests

There are no competing interests to declare.

Methaneethorn, J. (2018) A systematic review of population pharmacokinetics of valproic acid. Br J Clin Pharmacol, 84: 816–834. doi: 10.1111/bcp.13510.

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[bcp13510-bib-0001] 1. Johannessen CU, Johannessen SI. Valproate: past, present, and future. CNS Drug Rev 2003; 9: 199–216. [DOI] [PMC free article] [PubMed] [Google Scholar]

[bcp13510-bib-0002] 2. Landmark CJ. Antiepileptic drugs in non‐epilepsy disorders. CNS Drugs 2008; 22: 27–47. [DOI] [PubMed] [Google Scholar]

[bcp13510-bib-0003] 3. Lagace DC, O'Brien WT, Gurvich N, Nachtigal MW, Klein PS. Valproic acid: how it works. Or not. Clin Neurosci Res 2004; 4: 215–225. [Google Scholar]

[bcp13510-bib-0004] 4. Winter ME. Basic Clinical Pharmacokinetics, 5th edn. Philadelphia, PA: Lippincott Williams & Wilkins Health, 2010. [Google Scholar]

[bcp13510-bib-0005] 5. Bauer LA. Applied Clinical Pharmacokinetics, 3rd edn. New York: McGraw‐Hill Education, 2014. [Google Scholar]

[bcp13510-bib-0006] 6. Silva MFB, Aires CCP, Luis PBM, Ruiter JPN, IJlst L, Duran M, et al Valproic acid metabolism and its effects on mitochondrial fatty acid oxidation: A review. J Inherit Metab Dis 2008; 31: 205–216. [DOI] [PubMed] [Google Scholar]

[bcp13510-bib-0007] 7. Kodama Y, Kodama H, Kuranari M, Tsutsumi K, Ono S, Yukawa E, et al Gender‐ or age‐related binding characteristics of valproic acid to serum proteins in adult patients with epilepsy. Eur J Pharm Biopharm 2001; 52: 57–63. [DOI] [PubMed] [Google Scholar]

[bcp13510-bib-0008] 8. Fagundes S. Valproic acid: review. Rev Neurosci 2008; 16: 130–136. [Google Scholar]

[bcp13510-bib-0009] 9. Ghodke‐Puranik Y, Thorn CF, Lamba JK, Leeder JS, Song W, Birnbaum AK, et al Valproic acid pathway: pharmacokinetics and pharmacodynamics. Pharmacogenet Genomics 2013; 23: 236–241. [DOI] [PMC free article] [PubMed] [Google Scholar]

[bcp13510-bib-0010] 10. Perucca E. Clinically relevant drug interactions with antiepileptic drugs. Br J Clin Pharmacol 2006; 61: 246–255. [DOI] [PMC free article] [PubMed] [Google Scholar]

[bcp13510-bib-0011] 11. Johannessen SI, Landmark JC. Antiepileptic drug interactions – principles and clinical implications. Curr Neuropharmacol 2010; 8: 254–267. [DOI] [PMC free article] [PubMed] [Google Scholar]

[bcp13510-bib-0012] 12. Patsalos PN, Perucca E. Clinically important drug interactions in epilepsy: general features and interactions between antiepileptic drugs. Lancet Neurol 2003; 2: 347–356. [DOI] [PubMed] [Google Scholar]

[bcp13510-bib-0013] 13. Murphy JE. Clinical Pharmacokinetics, 5th edn. Bethesda, MD: ASHP, 2011. [Google Scholar]

[bcp13510-bib-0014] 14. American Psychiatric Association . Practice guideline for the treatment of patients with bipolar disorder (revision). Am J Psychiatry 2002; 159 (4Suppl): 1–50. [PubMed] [Google Scholar]

[bcp13510-bib-0015] 15. Leo RJ, Narendran R. Anticonvulsant use in the treatment of bipolar disorder: a primer for primary care physicians. Prim Care Companion J Clin Psychiatry 1999; 1: 74. [DOI] [PMC free article] [PubMed] [Google Scholar]

[bcp13510-bib-0016] 16. Bauer LA, Davis R, Wilensky A, Raisys V, Levy RH. Valproic acid clearance: unbound fraction and diurnal variation in young and elderly adults. Clin Pharmacol Ther 1985; 37: 697–700. [DOI] [PubMed] [Google Scholar]

[bcp13510-bib-0017] 17. Bauer LA, Davis R, Wilensky A, Raisys V, Levy RH. Diurnal variation in valproic acid clearance. Clin Pharmacol Ther 1984; 35: 505–509. [DOI] [PubMed] [Google Scholar]

[bcp13510-bib-0018] 18. Botha JH, Gray AL, Miller R. A model for estimating individualized valproate clearance values in children. J Clin Pharmacol 1995; 35: 1020–1024. [DOI] [PubMed] [Google Scholar]

[bcp13510-bib-0019] 19. Yukawa E, Honda T, Ohdo S, Higuchi S, Aoyama T. Detection of carbamazepine‐induced changes in valproic acid relative clearance in man by simple pharmacokinetic screening. J Pharm Pharmacol 1997; 49: 751–756. [DOI] [PubMed] [Google Scholar]

[bcp13510-bib-0020] 20. Yukawa E, Hideto T, Ohdo S, Higuchi S, Aoyama T. Population‐based investigation of valproic acid relative clearance using nonlinear mixed effects modeling: influence of drug–drug interaction and patient characteristics. J Clin Pharmacol 1997; 37: 1160–1167. [DOI] [PubMed] [Google Scholar]

[bcp13510-bib-0021] 21. Tanikawa K, Matsumoto Y, Matsumoto M, Fukuoka M, Yamamoto R, Endo K, et al Population pharmacokinetic parameters of valproic acid: conventional and slow release formulation. Jpn J Clin Pharmacol Ther 1998; 29: 489–494. [Google Scholar]

[bcp13510-bib-0022] 22. Blanco‐Serrano B, Otero MJ, Santos‐Buelga D, Garcia‐Sanchez MJ, Serrano J, Dominguez‐Gil A. Population estimation of valproic acid clearance in adult patients using routine clinical pharmacokinetic data. Biopharm Drug Dispos 1999; 20: 233–240. [DOI] [PubMed] [Google Scholar]

[bcp13510-bib-0023] 23. Blanco Serrono B, Garcia Sanchez MJ, Otero MJ, Santos Buelga D, Serrano J, Dominguez‐Gil A. Valproate population pharmacokinetics in children. J Clin Pharm Ther 1999; 24: 73–80. [DOI] [PubMed] [Google Scholar]

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PERMALINK

A systematic review of population pharmacokinetics of valproic acid

Janthima Methaneethorn

Abstract

Aims

Methods

Results

Conclusions

What is Already Known about this Subject

What this Study Adds

Introduction

Methods

Inclusion criteria

Exclusion criteria

Data Extraction

Results

Study identification

Figure 1.

Study characteristics

Table 1.

Population pharmacokinetic models of valproic acid

Table 2.

Table 3.

Table 4.

Discussion

Conclusion

Competing Interests

References

ACTIONS

PERMALINK

RESOURCES

Cite

Add to Collections

PERMALINK

A systematic review of population pharmacokinetics of valproic acid

Janthima Methaneethorn

Abstract

Aims

Methods

Results

Conclusions

What is Already Known about this Subject

What this Study Adds

Introduction

Methods

Inclusion criteria

Exclusion criteria

Data Extraction

Results

Study identification

Figure 1.

Study characteristics

Table 1.

Population pharmacokinetic models of valproic acid

Table 2.

Table 3.

Table 4.

Discussion

Conclusion

Competing Interests

References

ACTIONS

PERMALINK

RESOURCES

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