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A modification of the variational iteration method (VIM) for solving systems of nonlinear fractional-order differential equations is proposed. The fractional derivatives are described in the Caputo sense. The solutions of fractional differential equations (FDE) obtained using the traditional variational iteration method give good approximations in the neighborhood of the initial position. The main advantage of the present method is that it can accelerate the convergence of the iterative approximate solutions relative to the approximate solutions obtained using the traditional variational iteration method. Illustrative examples are presented to show the validity of this modification.

IntroductionCurrent treatment strategies for primary upper extremity deep venous thrombosis (pUEDVT) range from conservative treatment with anticoagulation therapy to invasive treatment with thoracic outlet decompression surgery (TOD), frequently combined with catheter directed thrombolysis, percutaneous transluminal angioplasty, or stenting. Due to a lack of large prospective series with uniform data collection or a randomized trial, the optimal treatment strategy is still under debate. We conducted a multicenter observational study to assess the efficacy and safety of both the conservative and invasive treatment strategies for patients with pUEDVT.MethodsWe retrospectively collected data from patients treated in five vascular referral and teaching hospitals in the Netherlands between 2008 and 2019. Patients were divided into a conservative (Group 1), an invasive treatment group (Group 2) and a cross-over group (Group 3) of patients who received surgical treatment after initial conservative therapy. Follow-up consisted of outpatient clinic visits and an electronic survey. Primary outcome was symptom free survival defined as absence of any symptom of the affected arm reported at last follow-up regardless of severity, or extent of functional disability. Secondary outcomes were incidence of bleeding complications, recurrent venous thromboembolism, surgical complications, and reinterventions.ResultsA total of 115 patients were included (group 1 (N = 45), group 2 (N = 53) or group 3 (N = 27). The symptom free survival was 35.6%, 54.7% and 48.1% after a median follow-up of 36, 26 and 22 months in groups 1, 2 and 3 respectively. Incidence of bleeding complications was 8.6%, 3.8% and 18.5% and recurrent thrombosis occurred in 15.6%, 13.2% and 14.8% in groups 1–3 respectively.ConclusionIn this multicenter retrospective observational cohort analysis the conservative and direct invasive treatments for pUEDVT were deemed safe with low percentages of bleeding complications. Symptom free survival was highest in the direct surgical treatment group but still modest in all subgroups. Perioperative complications were infrequent with no related long term morbidity. Of relevance, pUEDVT patients with confirmed VTOS and recurrent symptoms after conservative treatment may still benefit from TOD surgery. However, symptom free survival of this delayed TOD seems lower than direct surgical treatment and bleeding complications seem to occur more frequently.

Introduction: Current treatment strategies for primary upper extremity deep venous thrombosis (pUEDVT) range from conservative treatment with anticoagulation therapy to invasive treatment with thoracic outlet decompression surgery (TOD), frequently combined with catheter directed thrombolysis, percutaneous transluminal angioplasty, or stenting. Due to a lack of large prospective series with uniform data collection or a randomized trial, the optimal treatment strategy is still under debate. We conducted a multicenter observational study to assess the efficacy and safety of both the conservative and invasive treatment strategies for patients with pUEDVT., Methods: We retrospectively collected data from patients treated in five vascular referral and teaching hospitals in the Netherlands between 2008 and 2019. Patients were divided into a conservative (Group 1), an invasive treatment group (Group 2) and a cross-over group (Group 3) of patients who received surgical treatment after initial conservative therapy. Follow-up consisted of outpatient clinic visits and an electronic survey. Primary outcome was symptom free survival defined as absence of any symptom of the affected arm reported at last follow-up regardless of severity, or extent of functional disability. Secondary outcomes were incidence of bleeding complications, recurrent venous thromboembolism, surgical complications, and reinterventions., Results: A total of 115 patients were included (group 1 ( N  = 45), group 2 ( N  = 53) or group 3 ( N  = 27). The symptom free survival was 35.6%, 54.7% and 48.1% after a median follow-up of 36, 26 and 22 months in groups 1, 2 and 3 respectively. Incidence of bleeding complications was 8.6%, 3.8% and 18.5% and recurrent thrombosis occurred in 15.6%, 13.2% and 14.8% in groups 1-3 respectively., Conclusion: In this multicenter retrospective observational cohort analysis the conservative and direct invasive treatments for pUEDVT were deemed safe with low percentages of bleeding complications. Symptom free survival was highest in the direct surgical treatment group but still modest in all subgroups. Perioperative complications were infrequent with no related long term morbidity. Of relevance, pUEDVT patients with confirmed VTOS and recurrent symptoms after conservative treatment may still benefit from TOD surgery. However, symptom free survival of this delayed TOD seems lower than direct surgical treatment and bleeding complications seem to occur more frequently., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (© 2022 de Kleijn, Schropp, Westerink, Nijkeuter, van Laanen, Teijink, Vos, Ünlü, Van Hattum, Petri and De Borst.)