Where **P**_{A} are the potentials in the atria,** T** is the transfer matrix, and **P**_{T} are the measured torso potentials. Computing this transfer matrix is not as easy as the formula may suggest. The problem is ill-posed, and finding a stable solution is complicated. Different regularization methods are employed to find a solution that is stable and gives the desired results. At the end of the day, however, no matter how sophisticated the regularization, and how accurate the resulting transfer matrix, there will be a limiting factor that is inherent to the transfer matrix: Each atrial potential in **P**_{A} (so each potential in a given place in the atria) can only be a linear combination of the torso potentials in **P**_{T}. Realistically, the relationship is most likely more complicated, and we need a mathematical model that can capture these more complex relationships.

The question that we need to answer are to model this relationship is what the underlying physical phenomena are that constitute this relationship. Or do we? In one of my previous blog posts we talked about knowledge driven, and data driven reasoning. We can either use existing knowledge to model relationships, or we can throw lots of data at a model and optimize the model such that it captures these relationships. I would love to tell you more, but the competition may be lurking in these blog posts to steal ideas, so let me get a head start on this, and share the progress in the next blog post. Until then, stay safe!