Many central problems in geometry, topology and mathematical physics reduce to questions regarding the behavior of solutions of nonlinear evolution equations. Examples are Thurston’s classification of compact 3-manifolds based on Hamilton’s Ricci flow and the work of Christodoulou and Klainerman on the nonlinear stability of Minkowski spaces. Examples of hyperbolic equations include the Einstein field equations of general relativity as well as semilinear wave equations. Ricci flow and semilinear reaction-advection-diffusion equations are of parabolic type. In all these equations, the global dynamical behavior of bounded solutions for large times is of significant interest. Specific questions concern the convergence to equilibria; the existence of periodic, homoclinic, and heteroclinic solutions; and the existence and geometric structure of global attractors. On the other hand, many solutions develop singularities in finite time. The singularities have to be analysed in detail before attempting to extend solutions beyond their singularities or to understand their geometry in conjunction with globally bounded solutions. In this context we have been particularly interested in global qualitative descriptions of blow-up and grow-up profiles.
Background: Hemolytic specimens are among the most challenging preanalytical issues in laboratory diagnostics. The type of blood collection tube in use is claimed to influence in vitro hemolysis. We aimed to examine this hypothesis and estimate the respective financial impact, evaluating routine blood samples from the past 4 years.
Methods: A total of 47,820 hemolysis index (HI) values from five different time intervals (IV1–IV5) were compared against each other, representing the following tubes: IV1-Sarstedt Monovette; IV2-8 mL/16×100 mm Greiner BioOne (GBO) Vacuette; IV3/IV4-5 mL/16×100 mm GBO Vacuette; IV5-4.5 mL/13×75 mm GBO Vacuette. For estimation of the economic impact, material, personnel and analytical costs were calculated.
Results: HI mean values in time interval IV2 were significantly higher than in all other intervals, while mean values amongst all other intervals were comparable. The number of moderately and severely hemolyzed samples increased with incrementing vacuum. Overall comparable costs between intervals IV1 and IV5 were €11,370, €14,045, €12,710, €11,213 and €8138 per 10,000 samples, respectively.
Conclusions: Aspiration tubes and low vacuum tubes show comparable hemolysis rates. Increasing vacuum levels are associated with higher hemolysis rates. By decreasing in vitro hemolysis, financial savings up to €5907 per 10,000 samples could be gained.