Both medical research and clinical practice are starting to involve large quantities of data and to require large-scale computation, as a result of the digitization of many areas of medicine. For example, in brain research - the domain that we consider here - a single research study may require the repeated processing, using computationally demanding and complex applications, of thousands of files corresponding to hundreds of functional MRI studies. Execution efficiency demands the use of parallel or distributed computing, but few medical researchers have the time or expertise to write the necessary parallel programs. The Swift system addresses these concerns. A simple scripting language, SwiftScript, provides for the concise high-level specification of workflows that invoke various application programs on potentially large quantities of data. The Swift engine provides for the efficient execution of these workflows on sequential computers, parallel computers, and/or distributed grids that federate the computing resources of many sites. Last but not least, the Swift provenance catalog keeps track of all actions performed, addressing vital bookkeeping functions that so often cause difficulties in large computations. To illustrate the use of Swift for medical research, we describe its use for the analysis of functional MRI data as part of a research project examining the neurological mechanisms of recovery from aphasia after stroke. We show how SwiftScript is used to encode an application workflow, and present performance results that demonstrate our ability to achieve significant speedups on both a local parallel computing cluster and multiple parallel clusters at distributed sites.