## 1 Introduction  
Levetiracetam, a second-generation antiepileptic drug (AED) with a unique mechanism of action, is approved by both the U.S. Food and Drug Administration and the European Medicines Agency (EMA) as an add-on therapy for the treatment of partial seizures, myoclonic seizures, and primary generalized tonic-clonic seizures. In Europe, it is also the only AED approved for the treatment of partial seizures in adults and adolescents aged 16 years and older [1].  
In critical care, levetiracetam has been studied for the treatment of status epilepticus, tumor-related seizures, and seizures following subarachnoid or intracerebral hemorrhage, trauma, and stroke [2, 3, 4, 5, 6, 7]. The pharmacokinetic and pharmacodynamic properties of this antiepileptic drug make it an advantageous option in the care of patients in the ICU. Compared to other AEDs, the pharmacokinetic profile of levetiracetam is favorable after both oral and intravenous administration (IV) [8, 9]. After oral administration, there is rapid and nearly complete absorption (95%) with dose-proportional pharmacokinetics, low protein binding (10%), and low within-subject variability. It is excreted primarily renally by glomerular filtration with partial tubular reabsorption and has a plasma elimination half-life of approximately 6-8 h in adults. There are no known clinically significant drug interactions, and it is not associated with the common hemodynamic or cardiovascular side effects of other AEDs [8; 10; 11; 12].  
A clear association between levetiracetam serum levels and therapeutic or toxic effects has not been demonstrated [10; 13]. In accordance with the International League Against Epilepsy (ILAE) guidelines for medication adherence monitoring, overdose and dose adjustment, a therapeutic range of 12-46 mg/L has been recommended [10; 14; 15]. However, different levetiracetam levels outside the reference range in different populations have been reported in the literature. Pregnant women, elderly and pediatric patients, and patients with end-stage renal failure or those requiring renal replacement therapy exhibit altered pharmacokinetics [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27].  
Relatively few studies in critically ill ICU patients have reported increased drug clearance (greater than 120-160 mL/min/1.73 m\({}^{2}\)) and treatment failure for seizures [28; 29; 30; 21]. Based on empirical evidence, therapeutic drug monitoring for levetiracetam has been classified as 'potentially useful' but increasing evidence that altered pharmacokinetics of levetiracetam may be observed in critically ill patients has increased the need for therapeutic drug monitoring and pharmacokinetic modeling to determine optimal dosing regimens to maximize therapeutic effect and limit toxicity [22].  
The aim of this study was to investigate the pharmacokinetics of levetiracetam in critically ill intensive care patients using nonlinear mixed-effect modeling approaches. The latter allow the identification of important pathophysiological factors (such as renal function) that could influence the kinetics of levetiracetam. Special emphasis was placed on the selection of the most suitable index for renal function and for this purpose several indices have been measured and investigated. Most of the patients participating in the study had from mild loss to severe loss of kidney function which allowed this exploration. Simulations were performed to assess the impact of important patient characteristics on the kinetics of levetiracetam. In addition, the potential influence of disease severity and renal function on epileptic status was investigated.