RESUMO
We study a quasi-one-dimensional steady-state Poisson-Nernst-Planck type model for ionic flows through a membrane channel with three ion species, two positively charged with the same valence and one negatively charged. Bikerman's local hard-sphere potential is included in the model to account for ion sizes. The problem is treated as a boundary value problem of a singularly perturbed differential system. Under the framework of a geometric singular perturbation theory, together with specific structures of this concrete model, the existence and uniqueness of solutions to the boundary value problem for small ion sizes is established. Furthermore, treating the ion sizes as small parameters, we derive an approximation of individual fluxes, from which one can further study the qualitative properties of ionic flows and extract concrete information directly related to biological measurements. Of particular interest is the competition between two cations due to the nonlinear interplay between finite ion sizes, diffusion coefficients and boundary conditions, which is closely related to selectivity phenomena of open ion channels with given protein structures. Furthermore, we are able to characterize the distinct effects of the nonlinear interplays between these physical parameters. Numerical simulations are performed to identify some critical potentials which play critical roles in examining properties of ionic flows in our analysis.
RESUMO
BACKGROUND: Acute myocardial infarction (AMI) is a leading cause of mortality. Early reperfusion to restore blood flow is crucial to successful treatment. In the current reperfusion regimen, an increasing number of patients have benefited from direct percutaneous coronary intervention (PCI). In order to understand whether there is a correlation between the components of coronary thrombosis and the absence of reflow or slow blood flow after coronary stent implantation in direct PCI, we collected data on direct PCI cases in our hospital between January 2016 and November 2018. AIM: To investigate the correlation between intracoronary thrombus components and coronary blood flow after stent implantation in direct PCI in AMI. METHODS: We enrolled 154 patients (85 male and 69 female, aged 36-81 years) with direct PCI who underwent thrombus catheter aspiration within < 3, 3-6 or 6-12 h of onset of AMI between January 2016 and November 2018. The thrombus was removed for pathological examination under a microscope. The patients of the three groups according to the onset time of AMI were further divided into those with a white or red thrombus. The thrombolysis in myocardial infarction (TIMI) blood flow after stent implantation was recorded based on digital subtraction angiography during PCI. The number of patients with no-reflow and slow blood flow in each group was counted. Statistical analysis was performed based on data such as onset time, TIMI blood flow. RESULTS: There were significant differences in thrombus components between the patients with acute ST-segment elevation myocardial infarction and non-ST-segment elevation myocardial infarction (P < 0.01). In the group with PCI < 3 h after onset of AMI, there was no significant difference in the incidence of no-reflow and slow-flow between the white and red thrombus groups. In the groups with PCI 3-6 and 6-12 h after onset of AMI, there was a significant difference in the incidence of no-reflow and slow-flow between the white and red thrombus groups (P < 0.01). There was a significant correlation between the onset time of AMI and the occurrences of no-reflow and slow blood flow during PCI (P < 0.01). CONCLUSION: In direct PCI, the onset time of AMI and color of coronary thrombus are often used to predict whether there will be no reflow or slow blood flow after stent implantation.
