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We study the existence of oscillatory and periodic solutions of a class of first order scalar impulsive delay differential equations with piecewise constant argument.

Background Cerebral vasospasm (CV) is a major cause of delayed morbidity and mortality in patients with subarachnoid hemorrhage (SAH). Various cerebral protectants have been tested in patients with aneurysmal SAH. We aimed to research the success rate of treatment of CV via intra-arterial milrinone injection and aggressive pharmacological therapy for refractory CV. Methods A total of 25 consecutive patients who received intra-arterial milrinone and nimodipine treatment for CV following SAH between 2014 and 2017 were included in the study. Patients who underwent surgical clipping were excluded. Refractory vasospasm was defined as patients with CV refractory to therapies requiring ≥3 endovascular interventions. Overall, six patients had refractory CV. Long-term neurological outcome was assessed 6–18 months after SAH using a modified Rankin score and Barthel index. Results The median modified Rankin scores were 1 (min: 0, max: 3) and Barthel index scores were 85 (min: 70, max: 100) From each vasospastic territory maximal 10–16 mg milrinone was given to patients; a maximum of 24 mg milrinone was given to each patient in a session and a maximum of 42 mg milrinone was given to a patient in a day. Both milrinone and nimodipine were given to three patients. There was a large vessel diameter increase after milrinone and nimodipine injections. No patient died due to CV; only one patient had motor dysfunction on the right lower extremity. Conclusion Higher doses of milrinone can be used effectively to control refractory CV. For exceptional patients with refractory CV, high dose intra-arterial nimodipine and milrinone infusion can be used as a rescue therapy.

Objective Ibuprofen and pregabalin both have independent positive effects on postoperative pain. The aim of the study is researching effect of 800 mg i.v. ibuprofen in addition to preoperative single dose pregabalin on postoperative analgesia and morphine consumption in posterior lumbar interbody fusion surgery. Materials and Methods 42 adult ASA I-II physical status patients received 150 mg oral pregabalin 1 hour before surgery. Patients received either 250 ml saline with 800 mg i.v. ibuprofen or saline without ibuprofen 30 minutes prior to the surgery. Postoperative analgesia was obtained by morphine patient controlled analgesia (PCA) and 1 g i.v. paracetamol every six hours. PCA morphine consumption was recorded and postoperative pain was evaluated by Visual Analog Scale (VAS) in postoperative recovery room, at the 1st, 2nd, 4th, 8th, 12th, 24th, 36th, and 48th hours. Results Postoperative pain was significantly lower in ibuprofen group in recovery room, at the 1st, 2nd, 36th, and 48th hours. Total morphine consumption was lower in ibuprofen group at the 2nd, 4th, 8th, 12th, and 48th hours. Conclusions Multimodal analgesia with preoperative ibuprofen added to preoperative pregabalin safely decreases postoperative pain and total morphine consumption in patients having posterior lumbar interbody fusion surgery, without increasing incidences of bleeding or other side effects.

a b s t r a c tThis paper presents a systematic development of the oscillatory results for the linear and nonlinear impulsive delay differential equations. We also discuss linearized oscillation theory, and give some applications to mathematical biology.

This paper summarizes a series of results on the oscillation of impulsive ordinary differential equations. We consider linear, half-linear, super-half-linear, and nonlinear equations. Several oscillation criteria are given. The Sturmian comparison theory for linear and half linear equations is also included.

A class of first order linear impulsive differential equation with continuous and piecewise constant arguments is studied. Sufficient conditions for the oscillation of the solutions are obtained.

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