In this study, we model how biomedical topics influence one another, given they are organized in a topic hierarchy, medical subject headings, in which the edges capture a parent-child/subsumption relationship among topics. This information enables studying influence of topics from a semantic perspective, which might be very important in analyzing topic evolution and is missing from the current literature. We first define a burst-based action for topics, which models upward momentum in popularity (or 'elevated occurrences' of the topics), and use it to define two types of influence: accumulation influence and propagation influence. We then propose a model of influence between topics, and develop an efficient algorithm (TIPS) to identify influential topics. Experiments show that our model is successful at identifying influential topics and the algorithm is very efficient. © 2013 IEEE.