Valproic acid (VPA) is a drug that is widely used to treat various types of epilepsy as well as bipolar disorder and certain neurologic conditions such as migraine and neuropathic pain1–3. VPA exerts its pharmacological effect through multiple mechanisms, among them an increase in the production of gamma-aminobutyric acid (GABA), a decrease in the synthesis of glutamate, and a blockade of voltage-gated sodium channels and T-type calcium channels4. Around 90% of VPA is bound to plasma proteins, chiefly albumin. This bond is dose-dependent and saturable which, together with VPA's narrow therapeutic margin and high pharmacokinetic variability, warrants close monitoring of its plasma levels1,5.

Most commonly, it is the concentration of total valproic acid (TVPA) that gets measured. However, in cases where the binding of VPA is weaker, an increase is observed in the free fraction of the valproic acid (FVPA) in plasma. This means that a higher concentration of the drug becomes available to exert its pharmacological effect which, however, also increases the risk of toxicity. The most usual adverse reactions are nausea and vomiting, drowsiness, tremor, confusion, weight gain, hyperammonemia and elevated liver enzyme levels1. Patients with hypoalbuminemia should have their free FVPA concentrations monitored, although VPA's therapeutic margin has not been clearly defined with different authors proposing different criteria6–8. As the free FVPA is currently not subject to routine determinations, several mathematical equations have been proposed to estimate it, based on albuminemia and TVPA9–12.

Hermida et al.9 proposed a method to predict free FVPA concentrations as a function of albuminemia, based on the relationship obtained by Parent et al.10:

In patients with hypoalbuminemia, the free FVPA is calculated as:

In patients with normal albumin levels, for the same free drug concentration, the free FVPA is calculated with the following formula:

The combination of equations 2 and 3 yields a formula is obtained that allows estimating the expected total drug concentration under hypoalbuminemic conditions:

Using a model derived from a multiple linear regression, Doré et al.11 concluded that total drug concentration and albuminemia are the two variables capable of predicting free drug concentrations:

Kodama et al.12 suggested that the free FVPA could be calculated using a Scatchard binding plot that integrates the mean association constant of the drug to albumin and the mean number of binding sites to albumin:

Where k is the mean association constant to albumin in the population and n(Pt) in the mean number of binding sites to albumin in the population.

Nevertheless, the estimation cannot be accurate in patients with hypoalbuminemia as it does not consider plasma albumin levels, which have a direct impact on free FVPA concentrations.

It must be said that none of the aquations above has been validated and wide variations are obtained when they are applied to populations different from those in clinical trials. Consequently, these methods cannot be used in lieu of laboratory techniques and monitoring the free FVPA is strongly recommended8–12.

The purpose of the present study is to determine the reliability of the methods used to estimate free FVPA levels in our patient population by means of a comparison between the free FVPA concentrations obtained in the laboratory and those estimated using both the previously described methods and a new method described by García et al.

A retrospective observational study was carried out at the Pharmacokinetics Unit of the Pharmacy department of the Severo Ochoa University Hospital. The data on the evaluated patients, all of them admitted between October 2017 and February 2019, were obtained from electronic medical records (Selene®), electronic prescriptions (Farhos®) and the Infinity® platform. Seventeen different free FVPA and TVPA levels were analyzed from 15 patients (8 females and 7 males), of which 11 were epileptic (73%) and 4 suffered from bipolar disorder (27%). Samples were extracted at the end of the dosing interval (trough concentrations).

Quantification of the free FVPA was carried out by an external laboratory by ultrafiltration or immunoluminiscence, which are associated with an inter and intra-assay accuracy of 6.3% and 4.6% respectively. TVPA levels were analyzed in the hospital's laboratory by an enzyme immuno-assay, with an inter- and intra-assay accuracy below 5%.

Free FVPA levels were determined with three previously published methods (Hermida9, Doré11, and Kodama12) and a method proposed by our own group (García et al), based on a modification of the method developed by Kodama12. The García method corrects the population mean value of albumin binding sites “n(Pt)” according to individual albuminaemia, multiplying this value by Hermida's αN/α ratio9:

The values estimated by thee four methods were compared with the free FVPA concentrations measured in the laboratory, and estimation errors (mean error [ME] and root-mean square error [RMSE]) were calculated to determine precision and accuracy, respectively13.

Demographic and clinical characteristics of the patients included in the study are shown in table 1. Table 2 shows the results obtained following application of the four methods mentioned above. The García et al method presented with the highest accuracy and precision levels while the Kodama method yielded the worst results. This was to be expected as the latter is only applicable to patients with albumin levels within the normal range.

Therapeutic concentrations of TVPA have been set at 50-100 μg/mL. The concentrations determined in the present study are for the most part below the therapeutic interval (38.6 ± 12.5 mg/L) because of the changes occurring in the free fraction. Alpha (a) is the ratio between free fraction and TVPA concentrations, and its value varies as a function of TVPA and albumin levels. Thus, in patients with normal albumin levels, a varies between 75% and 15% for TVPA concentrations between 50 mg/L and 100 mg/L, respectively. In patients with hypoalbuminemia, the free FVPA increases because of a reduction in the number of binding sites, resulting in VPA escaping from the usual sampling site (general circulation) and diminishing TVPA concentrations. For that reason, these concentrations are not reliable enough to be used as monitoring tools, with monitoring of real free FVPA concentrations being proposed as the best alternative. The present study found increased a values (16.38 ± 12.5%) due to hypoalbuminemia. As regards the TVPA concentration interval, Wallenburg et al.14 established an Interval of 4-12 mg/L, which could indicate that 87% of the subjects in our study present potentially toxic concentrations.

Nonetheless, routine determinations of VPA do not involve monitoring free FVPA. That is why some authors have proposed the use of mathematical equations to calculate them. However, discrepancies exist across the results obtained when those methods are used, which cast doubt on their usefulness in clinical practice.

The method that differs the most from real values is the one developed by Kodama13, as the equation was obtained from individuals with normal

serum albumin levels. Thus, all free FVPA levels estimated using the Kodama equations were lower than the real values, yielding the least precise and accurate results (ME: –8.9 mg/L, RMSE: 8.9 mg/L). Hermida9 underestimated 16 of the 17 VAP concentrations (ME: –4.9 mg/L, RMSE: 4.9 mg/L). In turn, Doré’s11 method was the one shown be conform to the studied population (ME: –1.5 mg/L, RMSE: 3.6 mg/L).

Based on our findings, we propose a change to the Kodama et al. method to allow free FVPA values to be adjusted as a function of the patient's albuminemia. The results obtained from the comparison between the observed free FVPA values and those predicted by the methods under analysis show that the method developed by García et al. is the most reliable one for the studied population, providing the most accurate and precise values (ME: –0.1 mg/L, RMSE: 3.3 mg/L). Therefore, should determination of free FVPA concentrations be unfeasible, we recommend that it be estimated using the García et al. method.

The small size of our sample as well as the fact that only patients with hypoalbuminemia were analyzed constitute the chief limitations of this study. In addition, four of the 17 determinations did not correspond to steady state VPA levels, which could have altered the precision of our results.

The results obtained in this study should prompt further investigations on the subject, with larger patient cohorts, in order to confirm the usefulness of the method proposed and establish new more reliable equations to estimate free FVPA concentrations given the latter's importance in the clinical outcomes of the available treatments.

No funding.

No conflict of interests.

65th National Congress of the Spanish Society of Hospital Pharmacists. Online. October 2020.