Regulation of Ion Gradients across Myocardial Ischemic Border Zones: A Biophysical Modelling Analysis

Abstract

The myocardial ischemic border zone is associated with the initiation and sustenance of arrhythmias. The profile of ionic concentrations across the border zone play a significant role in determining cellular electrophysiology and conductivity, yet their spatial-temporal evolution and regulation are not well understood. To investigate the changes in ion concentrations that regulate cellular electrophysiology, a mathematical model of ion movement in the intra and extracellular space in the presence of ionic, potential and material property heterogeneities was developed. The model simulates the spatial and temporal evolution of concentrations of potassium, sodium, chloride, calcium, hydrogen and bicarbonate ions and carbon dioxide across an ischemic border zone. Ischemia was simulated by sodium-potassium pump inhibition, potassium channel activation and respiratory and metabolic acidosis. The model predicted significant disparities in the width of the border zone for each ionic species, with intracellular sodium and extracellular potassium having discordant gradients, facilitating multiple gradients in cellular properties across the border zone. Extracellular potassium was found to have the largest border zone and this was attributed to the voltage dependence of the potassium channels. The model also predicted the efflux of from the ischemic region due to electrogenic drift and diffusion within the intra and extracellular space, respectively, which contributed to depletion in the ischemic region.

Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue

“…A very similar formalism was developed (in parallel) in the heart-cell community in the context of a model of ischemia [58]. Our buffering model accounted for electrodiffusive processes in the intra- and extracellular domain, and was essentially an expansion of the previous model by Qian and Sejnowski [64], which only considered the intracellular domain.…”

“…Along with other electroneutral models [53–56, 58, 65], the KNP formalism provides a means of deriving the local potential V from the physical constraint that the (intra- and extracellular) bulk solution is electroneutral [28]. This approximation was used as early as in 1890 by Planck, who described electrodiffusion in electrolytes [70].…”

“…This requires an extremely high spatiotemporal resolution, which makes PNP models computationally expensive and unsuited for predictions at the tissue/population level [52]. However, a series of modelling schemes have been developed that circumvent the charge relaxation processes, essentially by replacing Poisson’s equation by the constraint that the bulk solution is electroneutral [28, 52–58]. The electroneutrality condition is a physical constraint valid at a larger spatiotemporal scale, and thus allows for a dramatic increase in the spatial and temporal grid sizes in the numerical simulations.…”

The calcium–frequency response in the rat ventricular myocyte: an experimental and modelling study

“…This choice represents a limitation, as the concentration of free calcium in rat plasma remains contentious. Previous studies have measured the extracellular free calcium concentration to be between 1 and 1.3 mM in rats (Moore, 1970;Polimeni, 1974) and the plasma concentrations of potassium to be between 3.3 and 5.8 mM, as reviewed in Niederer (2013 The interplay between calcium, TnC and tension generation is not included in our analysis and represents a limitation in our model. The inclusion of a sarcomere model with tension-dependent Ca 2+ buffering feedback would address this, albeit with a significant increase in model complexity.…”

Effects of Propranolol and Verapamil on Changes in TQ and ST Segment Potentials During Graded Coronary Flow Reduction in a Porcine Myocardial Ischemia Model

“…Lethal ventricular tachyarrhythmias during acute myocardial ischemia have been related to ST-T alternans due to repolarization and depolarization alternans and spatial heterogeneity of the APD restitution, and extracellular K + gradient across the ischemic border zone leading to systolic and diastolic injury current, and verapamil lessened the standard deviation of E K of the center and margin of ischemic myocardium during early stage of the ischemia. 14,21,22,23) We demonstrated that the ATP-sensitive K + channel opener pinacidil lessened the rise in extracellular K + during acute myocardial ischemia mainly by a marked decrease of the action potential duration of the ischemic myocardium. 24) Recently, intracoronary administration of verapamil and nicorandil, an ATP-sensitive K + channel opener, has been shown to be effective for the treatment of slow/no flow phenomenon in the acute coronary syndrome.…”