Excitable cells are of vital importance in biology, and mathematical models have contributed significantly to understand their basic mechanisms. However, classical models of excitable cells are based on severe assumptions that may limit the accuracy of the simulation results. Here, we derive a more detailed approach to modeling that has recently been applied to study the electrical properties of both neurons and cardiomyocytes. The model is derived from first principles and opens up possibilities for studying detailed properties of excitable cells. We refer to the model as the EMI model because both the extracellular space (E), the cell membrane (M) and the intracellular space (I) are explicitly represented in the model, in contrast to classical spatial models of excitable cells. Later chapters of the present text will focus on numerical methods and software for solving the model. Also, in the next chapter, the model will be extended to account for ionic concentrations in the intracellular and extracellular spaces.

Short QT (SQT) syndrome is a genetic cardiac disorder characterized by an abbreviated QT interval of the patient’s electrocardiogram. The syndrome is associated with increased risk of arrhythmia and sudden cardiac death and can arise from a number of ion channel mutations. Cardiomyocytes derived from induced pluripotent stem cells generated from SQT patients (SQT hiPSC-CMs) provide promising platforms for testing pharmacological treatments directly in human cardiac cells exhibiting mutations specific for the syndrome. How- ever, a difficulty is posed by the relative immaturity of hiPSC-CMs, with the possibility that drug effects observed in SQT hiPSC-CMs could be very different from the corresponding drug effect in vivo. In this paper, we apply a multistep computational procedure for translating measured drug effects from these cells to human QT response. This process first detects drug effects on individual ion channels based on measurements of SQT hiPSC-CMs and then uses these results to estimate the drug effects on ventricular action potentials and QT intervals of adult SQT patients. We find that the procedure is able to identify IC50 values in line with measured values for the four drugs quinidine, ivabradine, ajmaline and mexiletine. In addition, the predicted effect of quinidine on the adult QT interval is in good agreement with measured effects of quinidine for adult patients. Consequently, the computational procedure appears to be a useful tool for helping predicting adult drug responses from pure in vitro measurements of patient derived cell lines.

Computational modeling has contributed significantly to present understanding of cardiac electrophysiology including cardiac conduction, excitation-contraction coupling, and the effects and side-effects of drugs. However, the accuracy of in silico analysis of electrochemical wave dynamics in cardiac tissue is limited by the homogenization procedure (spatial averaging) intrinsic to standard continuum models of conduction. Averaged models cannot resolve the intricate dynamics in the vicinity of individual cardiomyocytes simply because the myocytes are not present in these models. Here we demonstrate how recently developed mathematical models based on representing every myocyte can significantly increase the accuracy, and thus the utility of modeling electrophysiological function and dysfunction in collections of coupled cardiomyocytes. The present gold standard of numerical simulation for cardiac electrophysiology is based on the bidomain model. In the bidomain model, the extracellular (E) space, the cell membrane (M) and the intracellular (I) space are all assumed to be present everywhere in the tissue. Consequently, it is impossible to study biophysical processes taking place close to individual myocytes. The bidomain model represents the tissue by averaging over several hundred myocytes and this inherently limits the accuracy of the model. In our alternative approach both E, M, and I are represented in the model which is therefore referred to as the EMI model. The EMI model approach allows for detailed analysis of the biophysical processes going on in functionally important spaces very close to individual myocytes, although at the cost of significantly increased CPU-requirements.

Two mathematical models are part of the foundation of Computational neurophysiology; a) the Cable equation is used to compute the membrane potential of neurons, and, b) volume-conductor theory describes the extracellular potential around neurons. In the standard procedure for computing extracellular potentials, the transmembrane currents are computed by means of a) and the extracellular potentials are computed using an explicit sum over analytical point-current source solutions as prescribed by volume conductor theory. Both models are extremely useful as they allow huge simplifications of the computational efforts involved in computing extracellular potentials. However, there are more accurate, though 
computationally very expensive, models available where the potentials inside and outside the neurons are computed simultaneously in a self-consistent scheme. In the present work we explore the accuracy of the classical models a) and b) by comparing them to these more accurate schemes.

The main assumption of a) is that the ephaptic current can be ignored in the derivation of the Cable equation. We find, however, for our examples with stylized neurons, that the ephaptic current is comparable in magnitude to other currents involved in the computations, suggesting that it may be significant – at least in parts of the simulation. The magnitude of the error introduced in the membrane potential is several millivolts, and this error also translates into errors in the predicted extracellular potentials. While the error becomes negligible if we assume the extracellular conductivity to be very large, this assumption is, unfortunately, not easy to justify a priori for all situations of interest.

We consider mathematical models of a collection of cardiomyocytes (myocardial tissue) coupled to a varying number of fibroblasts. Our aim is to understand how conductivity (δ) and fibroblast density (η) affect the stability of the myocardial tissue. We provide mathematical and computational arguments indicating that there is a region of instability in the η-δ space. Mathematical arguments, based on a simplified model of the coupled myocyte-fibroblast system, show that for certain parameter choices, a stationary solution cannot exist. Numerical experiments (1D,2D) are based on a recently developed model of electro-chemical coupling between a human atrial myocyte and a number of associated atrial fibroblasts.

This paper describes an extension of the so-called Rush-Larsen scheme, which is a widely used numerical method for solving dynamic models of cardiac cell electrophysiology. The proposed method applies a local linearization of non-linear terms in combination with the analytical solution of linear ordinary differential equations, to obtain a second order accurate numerical scheme. We compare the error and computational load of the second order scheme to the original Rush-Larsen method. For a given error tolerance, the second order method is from nine to 500 times faster than the original scheme, depending on the choice of model and tolerance.

Knowledge of cardiac electrophysiology is e{ffi}ciently formulated in terms of mathematical models. Most of these models are, however, very complex and thus denies direct mathematical reasoning founded on classical and analytical considerations. This is particularly the case for the celebrated bidomain model, developed almost 40 years ago for concurrent analysis of extra- and intracellular electrical activity. Numerical simulations represent an indispensible tool to study electrophysiology based on this model. However, both steep gradients in the solutions and complicated geometries lead to extremely challenging computational problems. The greatest achievement in scienti{fi}c computing over the past 50 year was to enable solution of linear systems of algebraic equations arising from discretizations of partial di{ff}erential equations in an optimal manner; i.e. such that the CPU-e{ff}orts increases linearly in the number of computational nodes. Over the past decade such optimal methods have been introduced in simulation of electrophysiology. This development, together with the development of a{ff}ordable parallel computers, has enabled the solution of the bidomain model combined with accurate cellular models de{fi}ned on realistic geometries. However, in spite of recent progress, the full potential of modern computational methods has yet to be exploited for solution of the bidomain model. It is the purpose of this paper to review the development of numerical methods for solving the bidomain model. The {fi}eld is huge, and we have to restrict our focus to the development after year 2000.

When the function of the atria is hampered by irregular electrical activation, radiofrequency ablation therapy can be used to restore normal activation and rhythm. Electroanatomical mapping systems provide the clinician with a picture of the activation sequence, from which he/she can determine where to ablate. The purpose of this paper is to present an algorithm for incorporating data from these mapping systems into a numerical simulator of the atria. The method is applied to 3D test problems with synthetic mapping data. Convergence to the correct solution is observed provided that a sufficient number of mapping sites are used. For our simulations, we use the monodomain model coupled with FitzHugh-Nagumo cell dynamics.

Powerful end-systems and faster access networks make large-scale distributed multimedia applications such as streaming and gaming increasingly popular. This popularity does, of course, also mean that the increase in available computing power and network bandwidth does not solve all existing problems, but rather that other parts of distributed systems will become bottlenecks. To relieve these, RELAY addresses issues of resource utilization in such distributed systems by investigating network and operating system support that provides quantifiably better support than the state-of-the-art. One of our main goals is to integrate and combine mechanisms to get more scalable, less resource demanding, high performance systems for time-dependent large-scale distributed multimedia systems. RELAY designs, implements and evaluates algorithms, mechanisms and tools to improve resource utilization, increase throughput, reduce/hide latency and support soft Quality-of-Service. The development takes user experience into account, since adaptation specific to this can reduce the necessary resource consumption considerably. We consider architectural, application-level, kernel and protocol support to achieve our goals, and we investigate combinations of performance-enhancing mechanisms such that they do not counteract each other. RELAY's approach is application-driven, where the best way of achieving performance improvements determines the research methodology. As an example, we report several of our findings in investigating support for distributed interactive applications, and massive multiplayer games in particular.

Research background: Inaccurate estimation of software development effort is one of the most important reasons of IT-project failures. While too low effort estimates may lead to project management problems, delayed deliveries, budget overruns and low software quality, too high effort estimates may lead to lost business opportunities and inefficient use of resources. These IT-project problems motivated the BEST (Better Estimation of Software Tasks) project at Simula Research Laboratory to conduct research with the goal of improving effort estimation methods. Scientific challenges: The project's main focus is to improve judgment-based effort estimation (expert estimation), which is the estimation approach most frequently used by the software industry. We argue that a better understanding of the mental steps involved in expert estimation is necessary to achieve robust improvement of software development estimation processes. A great challenge when studying expert judgment is to understand the unconscious steps involved. To study these steps, we make use of multidisciplinary competencies, especially psychology and software engineering, and financial resources enabling studies in realistic software development effort estimation contexts. Obtained and expected results: In this section, we present the main results of the project from its beginnings in 2001 until today and describe how the project has benefited from being an integrated part of Simula Research Laboratory, especially through the opportunity to conduct large-scale, controlled experiments in field settings. The section includes practical results on how to improve estimation methods, scientific results leading to a better understanding of the mental processes involved in judgment-based effort estimation, and our innovative research methods in the field of empirical software engineering. Results of the BEST project are currently in use by several software companies, as well as by researchers in forecasting and psychology, and they are also included in project management and software engineering textbooks. The BEST project plans to continue its multidisciplinary effort with the goal of constructing and evaluating better models of the mental steps involved in judgment-based effort estimation. An improved model of these steps will enhance our ability to accurately estimate software development effort and to predict when different types of estimation methods can be expected to deliver accurate effort estimates. This will in turn lead to a reduction of the number of IT-project failures and make better use of scarce financial and human resources.