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Everyone that has measured his heartbeat once, knows that this is very rhythmic. This rhythm is needed to make sure that blood keeps circulating in the body, and can be adapted according to the circumstances. A disturbance of this regular beating could lead to serious consequences, for example cardiac arrest. Such a disturbed rhythm is termed a ‘fibrillation’, and must be treated with high urgency when it arises. The most used method for this treatment is a defibrillator. This device applies a heavy electric shock to the heart and temporarily stops it, after which it hopefully resumes its normal rhythm. This approach shows that the heart rhythm is controlled by electricity. The muscle cells of the heart are activated when receiving an electric stimulus and pass this impulse on to the surrounding cells. These signals cause the muscle cells to contract at the right moment, such that a fluent motion pumps the blood out of the heart and into the body. Sometimes it is possible that some muscle cells are defective, causing a delay or complete stop of the signal. A disturbance of the heart rhythm is then inevitable. You can compare this with a delayed train, causing all other trains on the network to be disturbed. To treat these sick muscle cells we first need to know where they are located. This means we need to determine the electrical signals in the heart wall. It is possible to insert a small balloon, covered in measuring points, in the heart. The values we measure there, the electrogram (EGM) are, however, not the same as those on the heart wall, because they are separated by a few centimeters of blood and tissue. This is what is called ‘the inverse problem’. We have now arrived at the point where this thesis is applicable. The signals in the heart wall can be calculated from the measurements on the balloon using mathematical models and algorithms. Most of these methods, however, need a lot of calculations and thus also a long computation time. Luckily there also exists a method already tested for similar situations, that does not need as much calculation time, but on the other hand is less accurate. This is the ‘Method of Fundamental Solutions’, or MFS for short. In this thesis it was studied if this method also works for our situation with the balloon catheter. For different parameters coupled to this method it was also studied what their effect is on the quality of the solution of the MFS. It is for example necessary to regulate the solution by constraining the height of the calculated electrical signals. These tests were performed on a situation that could be checked by hand, a simulation of electrical signals on the heart and clinical data from a pig’s heart. From these studies it appears that MFS works well to solve the inverse problem of the balloon catheter.