Prions consist of pathological aggregates of cellular prion protein and have the ability to replicate, causing neurodegenerative diseases, a phenomenon mirrored in many other diseases connected to protein aggregation, including Alzheimer's and Parkinson's diseases. However, despite their key importance in disease, the individual processes governing this formation of pathogenic aggregates, as well as their rates, have remained challenging to elucidate in vivo. Here we bring together a mathematical framework with kinetics of the accumulation of prions in mice and microfluidic measurements of aggregate size to dissect the overall aggregation reaction into its constituent processes and quantify the reaction rates in mice. Taken together, the data show that multiplication of prions in vivo is slower than in in vitro experiments, but efficient when compared with other amyloid systems, and displays scaling behavior characteristic of aggregate fragmentation. These results provide a framework for the determination of the mechanisms of disease-associated aggregation processes within living organisms.