A model for the numerical simulation of the action of microbioreactor acting in the continuous flow mode was developed. The microbioreactor system was mathematically modelled by a two-compartment model based on transient reaction-diffusion equations containing a nonlinear term related to the Michaelis-Menten kinetics of the enzymatic reaction. The effectiveness of microbioreactor and the process duration were numerically and partially analytically analysed at transition and steady-state conditions in a wide range of model parameters. The computational simulation was carried out using the finite difference technique. The performed calculations showed nonlinear effects of the internal and external diffusion limitations on the effectiveness and process duration.
BackgroundTo evaluate if the combination of several quantitative parameters into a mathematical model would enhance the detection of myocardial ischemia during dobutamine stress echocardiography (DSE) when compared to conventional wall motion analysis.MethodsIn a prospective study design 151 patients (age 61.8 ± 9.2) in test group and 105 patients (age 64.0 ± 10.6) in validation group were selected and underwent DSE between January 2008 and December 2012. In all patients coronary angiography was performed within 6-8 weeks from DSE, considering at least one stenosis ≥50 % per patient as significant coronary artery disease (CAD). Results of DSE visual assessment and myocardial velocity, strain and strain rate parameters derived from speckle tracking imaging were imported automatically to an originally created software. A mathematical model calculating prognosis of at least one stenosis per patient and stenosis in separate arteries was constructed.ResultsMyocardial ischemia was visually detected in 60 (39.7 %) and in 58 (54.2 %) patients of the test and validation group, respectively. A total of 76 (50.3 %) patients in the test group and 69 patients (65.7 %) in the validation group had ≥50 % coronary stenosis. Sensitivity and specificity of the mathematical model per patient in the test group were 91.6 % and 86.3 % compared to 76.8 % and 89.0 % of the visual assessment, respectively. However, in the validation group the sensitivity, specificity, positive predictive value and negative predictive value dropped down significantly becoming lower to visual assessment.ConclusionsMyocardial deformation imaging may potentially replace visual assessment with an automated predictive model for stress-induced ischemia detection. However, a multiparametric mathematical model based on quantitative deformation markers did not demonstrate incremental value to visual assessment of wall motion.
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