Deriving the Bidomain Model of Cardiac Electrophysiology From a Cell-Based Model; Properties and Comparisons

The bidomain model is considered to be the gold standard for numerical simulation of the electrophysiology of cardiac tissue. The model provides important insights into the conduction properties of the electrochemical wave traversing the cardiac muscle in every heartbeat. However, in normal resolution, the model represents the average over a large number of cardiomyocytes, and more accurate models based on representations of all individual cells have therefore been introduced in order to gain insight into the conduction properties close to the myocytes. The more accurate model considered here is referred to as the EMI model since both the extracellular space (E), the cell membrane (M) and the intracellular space (I) are explicitly represented in the model. Here, we show that the bidomain model can be derived from the cell-based EMI model and we thus reveal the close relation between the two models, and obtain an indication of the error introduced in the approximation. Also, we present numerical simulations comparing the results of the two models and thereby highlight both similarities and differences between the models. We observe that the deviations between the solutions of the models become larger for larger cell sizes. Furthermore, we observe that the bidomain model provides solutions that are very similar to the EMI model when conductive properties of the tissue are in the normal range, but large deviations are present when the resistance between cardiomyocytes is increased.

Multifunctional Viologen-Derived Supramolecular Network with Photo/Vapochromic and Proton Conduction Properties

A supramolecular network [H4bdcbpy(NO3)2·H2O] (H4bdcbpy = 1,1′-Bis(3,5-dicarboxybenzyl)-4,4′-bipyridinium) (1) was prepared by a zwitterionic viologen carboxylate ligand in hydrothermal synthesis conditions. The as-synthesized (1) has been well characterized by means of single-crystal/powder X-ray diffraction, elemental analysis, thermogravimetric analysis and infrared and UV-vis spectroscopy. This compound possesses a three-dimensional supramolecular structure, formed by the hydrogen bond and π–π interaction between the organic ligands. This compound shows photochromic properties under UV light, as well as vapochromic behavior upon exposure to volatile amines and ammonia, in which the electron transfer from electron-rich parts to the electron-deficient viologen unit gives rise to colored radicals. Moreover, the intensive intermolecular H-bonding networks in 1 endows it with a proton conductivity of 1.06 × 10−3 S cm−1 in water at 90 °C.