Search

Comparing tree topologies is an invaluable biological tool, though it is mathematically difficult to systematize. Tree comparisons are simpler to compute on ordered/labeled graphs, which are produced through the eutelic lineages of Caenorhabditis elegans development. We make use of this property to create novel approaches to compare the values and topologies of weighted graphs. This involves generalizing the euclidean norm to the weighted edges of tree structures to create a branch distance, incorporating the tree edit distance as a measure of topological distance, and normalizing the tree edit distance into the Jaccard Distance. These approaches are benchmarked by measuring cell cycle timing in embryonic cell lineages using this framework to categorize patterns of development and corroborating these findings with known developmental properties of this model organism.

Deep brain stimulation (DBS) is an established clinical therapy for Parkinson’s disease (PD). Experimental data suggests that DBS activates axons near the active electrode contact. However, the specific axonal pathways directly activated by DBS are not clearly defined. In this study, we used patient-specific computational models to provide insights of the pathways mediating the therapeutic response to subthalamic DBS.One such model, known as the field-cable pathway-activation model (FC PAM), is the current gold standard for predicting axonal activation on a patient-specific basis. However, FC PAMs require significant technical expertise and computational resources. Thus, the driving force (DF) and volume of tissue activated (VTA) methods, which are derived from simplified FC models, are typically used in clinical research studies. We compared the predictions of the FC PAM, DF PAM, and VTA PAM during subthalamic DBS. Unfortunately, none of these simplified models (i.e. DF PAM or VTA PAM) were able to match the results of the FC PAM in terms of stimulation thresholds or pathway activation estimates across all pathways and combinations of stimulus parameters.The pathways in the subthalamic region that mediate the therapeutic effects of DBS are not clearly defined. We constructed FC PAMs of three PD patients explicitly representing six axonal pathways. We calculated the pathways activated by the clinically-defined therapeutic stimulation setting in each patient. Our results suggest that therapeutic stimulation activates multiple pathways and these pathways were not consistent among the PD patients.We used an FC PAM to dissect the neural elements mediating cortical evoked potentials. Experimental recordings of cortical evoked potentials are used to evaluate the effects of subthalamic DBS and have components that occur at discrete times after each stimulus pulse. We compared the conduction times for small (5.7 microns), medium (10.0 microns), and large (15.0 microns) diameter corticofugal axons of both the hyperdirect and internal capsule pathways. We found that subthalamic DBS likely activates small diameter hyperdirect axons resulting in the medium latency cortical evoked potentials.This work lays the foundation for studies selectively targeting pathways in the subthalamic region with the use of FC PAMs to dissect the complex clinical response to stimulation.