Emerging Synergisms Between Drugs and Physiologically-Patterned Weak Magnetic Fields: Implications for Neuropharmacology and the Human Population in the Twenty-First Century

Synergisms between pharmacological agents and endogenous neurotransmitters are familiar and frequent. The present review describes the experimental evidence for interactions between neuropharmacological compounds and the classes of weak magnetic fields that might be encountered in our daily environments. Whereas drugs mediate their effects through specific spatial (molecular) structures, magnetic fields mediate their effects through specific temporal patterns. Very weak (microT range) physiologically-patterned magnetic fields synergistically interact with drugs to strongly potentiate effects that have classically involved opiate, cholinergic, dopaminergic, serotonergic, and nitric oxide pathways. The combinations of the appropriately patterned magnetic fields and specific drugs can evoke changes that are several times larger than those evoked by the drugs alone. These novel synergisms provide a challenge for a future within an electromagnetic, technological world. They may also reveal fundamental, common physical mechanisms by which magnetic fields and chemical reactions affect the organism from the level of fundamental particles to the entire living system

Sixth-order adaptive non-uniform grids for singularly perturbed boundary value problems

In this paper, a sixth order adaptive non-uniform grid has been developed for solving a singularly perturbed boundary-value problem (SPBVP) with boundary layers. For this SPBVP with a small parameter in the leading derivative, an adaptive finite difference method based on the equidistribution principle, is adopted to establish 6th order of convergence. To achieve this supra-convergence, we study the truncation error of the discretized system and obtain an optimal adaptive non-uniform grid. Considering a second order three-point central finite-difference scheme, we develop sixth order approximations by a suitable choice of the underlying optimal adaptive grid. Further, we apply this optimal adaptive grid to nonlinear SPBVPs, by using an extra approximations of the nonlinear term and we obtain almost 6th order of convergence. Unlike other adaptive non-uniform grids, our strategy uses no pre-knowledge of the location and width of the layers. We also show that other choices of the grid distributions lead to a substantial degradation of the accuracy. Numerical results illustrate the effectiveness of the proposed higher order adaptive numerical strategy for both linear and nonlinear SPBVPs

Transient integral boundary layer method to calculate the translesional pressure drop and the fractional flow reserve in myocardial bridges

BACKGROUND: The pressure drop – flow relations in myocardial bridges and the assessment of vascular heart disease via fractional flow reserve (FFR) have motivated many researchers the last decades. The aim of this study is to simulate several clinical conditions present in myocardial bridges to determine the flow reserve and consequently the clinical relevance of the disease. From a fluid mechanical point of view the pathophysiological situation in myocardial bridges involves fluid flow in a time dependent flow geometry, caused by contracting cardiac muscles overlying an intramural segment of the coronary artery. These flows mostly involve flow separation and secondary motions, which are difficult to calculate and analyse. METHODS: Because a three dimensional simulation of the haemodynamic conditions in myocardial bridges in a network of coronary arteries is time-consuming, we present a boundary layer model for the calculation of the pressure drop and flow separation. The approach is based on the assumption that the flow can be sufficiently well described by the interaction of an inviscid core and a viscous boundary layer. Under the assumption that the idealised flow through a constriction is given by near-equilibrium velocity profiles of the Falkner-Skan-Cooke (FSC) family, the evolution of the boundary layer is obtained by the simultaneous solution of the Falkner-Skan equation and the transient von-Kármán integral momentum equation. RESULTS: The model was used to investigate the relative importance of several physical parameters present in myocardial bridges. Results have been obtained for steady and unsteady flow through vessels with 0 – 85% diameter stenosis. We compare two clinical relevant cases of a myocardial bridge in the middle segment of the left anterior descending coronary artery (LAD). The pressure derived FFR of fixed and dynamic lesions has shown that the flow is less affected in the dynamic case, because the distal pressure partially recovers during re-opening of the vessel in diastole. We have further calculated the wall shear stress (WSS) distributions in addition to the location and length of the flow reversal zones in dependence on the severity of the disease. CONCLUSION: The described boundary layer method can be used to simulate frictional forces and wall shear stresses in the entrance region of vessels. Earlier models are supplemented by the viscous effects in a quasi three-dimensional vessel geometry with a prescribed wall motion. The results indicate that the translesional pressure drop and the mean FFR compares favourably to clinical findings in the literature. We have further shown that the mean FFR under the assumption of Hagen-Poiseuille flow is overestimated in developing flow conditions