Background: Milrinone has been suggested as a possible first-line therapy for preterm neonates to prevent postligation cardiac syndrome (PLCS) through decreasing systemic vascular resistance and increasing cardiac contractility. The optimal dosing regimen, however, is not known. Objective: To model the dosing of milrinone in preterm infants for prevention of PLCS after surgical closure of patent ductus arteriosus (PDA). Methods: Milrinone time-concentration profiles were simulated for 1,000 subjects using the volume of distribution and clearance estimates based on one compartmental population pharmacokinetic model by Paradisis et al. [Arch Dis Child Fetal Neonatal Ed 2007;92:F204-F209]. Dose optimization was based on retrospectively collected demographic data from neonates undergoing PDA ligation in Estonian PICUs between 2012 and 2014 and existing pharmacodynamic data. The target plasma concentration was set at 150-200 ng/ml. Results: The simulation study used demographic data from 31 neonates who underwent PDA ligation. The median postnatal age was 13 days (range: 3-29) and weight was 760 g (range: 500-2,351). With continuous infusion of milrinone 0.33 μg/kg/min, the proportion of subjects within the desired concentration range was 0% by 3 h, 36% by 6 h, and 61% by 8 h; 99% of subjects exceeded the range by 18 h. The maximum proportion of total simulated concentrations in the target range was attained with a bolus infusion of 0.73 μg/kg/min for 3 h followed by a 0.16-μg/kg/min maintenance infusion. Conclusion: Mathematical simulations suggest that in preterm neonates the plasma time-concentration profile of milrinone can be optimized with a slow loading dose followed by maintenance infusion.