A Modification of Ripley’s K Function to Measure Aggregation About a Mass

We present a methodology that detects spatial patterns of 3-dimensional point processes that include a mass within the study region. Spatial patterns such as clustering, randomness, or repulsion are considered in respect to the mass surface. Our method closely resembles Ripley’s K Function but is modified to discern the pattern about the mass surface. We walk though the definition and derivation of Ripley’s K Function and then follow this process to define the Modified K function. We develop this novel function according to the definition: the Modified K function times the intensity is the expected number of events within a distance h of a mass. Special consideration of edge effects is taken in order to make the function invariant to the location of the mass within the study region. Significance of spatial patterns is determined using Monte Carlo confidence envelopes similar to Ripley’s K Function. Simulations are performed to inform researchers how the Modified K function performs under different types of aggregation. Finally, we apply the Modified K function to neuroscience as a novel analysis tool by examining the spatial pattern of neurotransmitter release sites as events about a neuron. Supplemental materials for this article are available online.