Mathematical Modeling to Investigate Antiarrhythmic Drug Side Effects: Rate-Dependence Role in Ionic Currents and Action Potentials Shape in the O’Hara Model

Sudden cardiac death due to ventricular arrhythmia is one of the leading causes of mortality in the world. In the last decades, it has proven that anti-arrhythmic drugs, which prolong the refractory period by means of prolongation of the cardiac action potential duration (APD), play a good role in preventing of relevant human arrhythmias. However, it has long been observed that the “class III antiarrhythmic effect” diminish at faster heart rates and that this phenomenon represent a big weakness, since it is the precise situation when arrhythmias are most prone to occur. It is well known that mathematical modeling is a useful tool for investigating cardiac cell behavior. In the last 60 years, a multitude of cardiac models has been created; from the pioneering work of Hodgkin and Huxley (1952), who first described the ionic currents of the squid giant axon quantitatively, mathematical modeling has made great strides. The O’Hara model, that I employed in this research work, is one of the modern computational models of ventricular myocyte, a new generation began in 1991 with ventricular cell model by Noble et al. Successful of these models is that you can generate novel predictions, suggest experiments and provide a quantitative understanding of underlying mechanism. Obviously, the drawback is that they remain simple models, they don’t represent the real system. The overall goal of this research is to give an additional tool, through mathematical modeling, to understand the behavior of the main ionic currents involved during the action potential (AP), especially underlining the differences between slower and faster heart rates. In particular to evaluate the rate-dependence role on the action potential duration, to implement a new method for interpreting ionic currents behavior after a perturbation effect and to verify the validity of the work proposed by Antonio Zaza using an injected current as a perturbing effect.

Electrolyte disorders in the human ventricle. A simulation study.

Ventricular cells are immersed in a bath of electrolytes and these ions are essential for a healthy heart and a regular rhythm. Maintaining physiological concentration of them is fundamental for reducing arrhythmias and risk of sudden cardiac death, especially in haemodialysis patients and in the heart diseases treatments. Models of electrically activity of the heart based on mathematical formulation are a part of the efforts to improve the understanding and prediction of heart behaviour. Modern models incorporate the extensive and ever increasing amounts of experimental data in incorporating biophysically detailed mechanisms to allow the detailed study of molecular and subcellular mechanisms of heart disease. The goal of this project was to simulate the effects of changes in potassium and calcium concentrations in the extracellular space between experimental data and and a description incorpored into two modern biophysically detailed models (Grandi et al. Model; O’Hara Rudy Model). Moreover the task was to analyze the changes in the ventricular electrical activity, in particular by studying the modifications on the simulated electrocardiographic signal. We used the cellular information obtained by the heart models in order to build a 1D tissue description. The fibre is composed by 165 cells, it is divided in four groups to differentiate the cell types that compound human ventricular tissue. The main results are the following: Grandi et al. (GBP) model is not even able to reproduce the correct action potential profile in hyperkalemia. Data from hospitalized patients indicates that the action potential duration (APD) should be shorter than physiological state but in this model we have the opposite. From the potassium point of view the results obtained by using O’Hara model (ORD) are in agreement with experimental data for the single cell action potential in hypokalemia and hyperkalemia, most of the currents follow the data from literature. In the 1D simulations we were able to reproduce ECGs signal in most the potassium concentrations we selected for this study and we collected data that can help physician in understanding what happens in ventricular cells during electrolyte disorder. However the model fails in the conduction of the stimulus under hyperkalemic conditions. The model emphasized the ECG modifications when the K+ is slightly more than physiological value. In the calcium setting using the ORD model we found an APD shortening in hypocalcaemia and an APD lengthening in hypercalcaemia, i.e. the opposite to experimental observation. This wrong behaviour is kept in one dimensional simulations bringing a longer QT interval in the ECG under higher [Ca2+]o conditions and vice versa. In conclusion it has highlighted that the actual ventricular models present in literature, even if they are useful in the original form, they need an improvement in the sensitivity of these two important electrolytes. We suggest an use of the GBP model with modifications introduced by Carro et al. who understood that the failure of this model is related to the Shannon et al. model (a rabbit model) from which the GBP model was built. The ORD model should be modified in the Ca2+ - dependent IcaL and in the influence of the Iks in the action potential for letting it him produce a correct action potential under different calcium concentrations. In the 1D tissue maybe a heterogeneity setting of intra and extracellular conductances for the different cell types should improve a reproduction of the ECG signal.