Numerical treatment of cardiac diseases using optimal control theory

AbstractWe propose a mathematical modelization and optimization of the action of some drugs such as β-blockers—a particular drug (tertatolol) studied in Servier laboratories is specially examined. Linear compartmental models are first tried but they are not convenient for explaining the experimental data. Then a dose effect relation is directly seeked. One obtains a nonlinear relationship between the dose, the plasmatic concentration and the drug's effect. Using some optimal control methods allows one to define an optimal therapeutic giving the optimal doses and possibly the optimal times optimizing some given criteria

A mathematical model of the circle of Willis in the presence of an arteriovenous anomaly

AbstractThis paper deals with a complete model of the flow in the Willis circle and its vicinity. We study: (a) the normal case; and (b) the influence of the presence of an arteriovenous anomaly. We have simulated the therapeutic procedures in order to confirm the treatment

Additional degrees of parallelism within the Adomian decomposition method

4th International Conference on Computational Engineering (ICCE 2017), 28-29 September 2017, DarmstadtThis is the author accepted manuscript. The final version is available from Springer via the DOI in this record.The trend of future massively parallel computer architectures challenges the exploration of additional degrees of parallelism also in the time dimension when solving continuum mechanical partial differential equations. The Adomian decomposition method (ADM) is investigated to this respects in the present work. This is accomplished by comparison with the Runge-Kutta (RK) time integration and put in the context of the viscous Burgers equation. Our studies show that both methods have similar restrictions regarding their maximal time step size. Increasing the order of the schemes leads to larger errors for the ADM compared to RK. However, we also discuss a parallelization within the ADM, reducing its runtime complexity from O(n^2) to O(n). This indicates the possibility to make it a viable competitor to RK, as fewer function evaluations have to be done in serial, if a high order method is desired. Additionally, creating ADM schemes of high-order is less complex as it is with RK.The work of Andreas Schmitt is supported by the ’Excellence Initiative’ of the German Federal and State Governments and the Graduate School of Computational Engineering at Technische Universit¨at Darmstadt

Inhibition of CD203c membrane up-regulation in human basophils by high dilutions of histamine: a controlled replication study

none5noPrevious research suggests that human basophil activation may be inhibited by histamine even at extremely low doses (high dilutions). In our experiment, membrane up-regulation of CD203c, which proved to be a more consistent activation marker than CD63, was significantly inhibited in samples treated with histamine at the dilutions of 2C, 12C, 14C, 15C and 16C. Control water dilutions/succussions did not show any significant effect. Therefore, using a strictly standardized flow cytometry protocol and a new dilution/succussion procedure, we have shown that low and high dilution of histamine do inhibit CD203c up-regulation in anti-IgE stimulated basophils.mixedS. Chirumbolo; M. Brizzi; R. Ortolani; A. Vella; P. BellaviteS. Chirumbolo; M. Brizzi; R. Ortolani; A. Vella; P. Bellavit