High-performance computational models and solid numerical analysis play an increasingly important role in many medical and biomedical applications. As a matter of fact, mathematical modeling and numerical simulations allow for the creation of patient-specic models, which can be used to study, e.g., the function of organs such as the human heart, or to evaluate and plan for individualized therapies. Building on the progress achieved during the last decades in the areas of modeling and simulation, nowadays "virtual" therapy planning is in principle possible. For example, mono- and bidomain equations are by now established models in cardiac electrophysiology, allowing for an "in-silico" evaluation of a patient's heart. Different validated models exist, describing with high accuracy the electrical activity in the myocardium.
Nonetheless, patient-specic simulation cannot yet be employed as a routine tool in the treatment of patients. One particular reason for this can be found in the data which are acquired in clinical practice. These data are in general not suciently detailed to provide accurate input parameters for numerical simulations. Often, these data can only be estimated based on the available measurements, for example MRI, or on general knowledge, for example analytical models. As a consequence, whenever a patient-specic simulation is carried out, the data could possibly contain huge uncertainties. For clinical practice, it is imperative to guarantee that the outcomes of in-silico models can be relied upon. This raises the question of how these measurement errors affect the modeling results. Using established forward models, different studies have been carried out, providing sensitivity analysis on the basis of forward simulations and a more or less straightforward sampling of the parameter spaces.
However, the newly developed ideas and mathematical insights from Uncertainty Quantication (UQ) do allow for a much more precise and efficient quantication of important sensitivities in cardiac simulations. It is therefore the goal of this project to exploit ideas and techniques from UQ for simulations in cardiology, in particular electrophysiology, and to develop simulation tools, which will provide reliable estimates of parameter sensitivities for patient-specic simulations in electrophysiology.