Grid technologies have the potential to enable healthcare organizations to efficiently use powerful tools, applications and resources, many of which were so far inaccessible to them. This paper introduces a service-oriented architecture meant to Grid-enable several classes of computationally intensive medical applications for improved performance and cost-effective access to resources. We apply this architecture to fiber tracking [1,2], a computationally intensive medical application suited for parallelization through decomposition, and carry out experiments with various sets of parameters, in realistic environments and with standard network solutions. Furthermore, we deploy and assess our solution in a hospital environment, at the Amsterdam Medical Center, as part of our cooperation in the Dutch VL-e project. Our results show that parallelization and Grid execution may bring significant performance improvements and that the overhead introduced by making use of remote, distributed resources is relatively small.