Using Bayes' Rule for Analysis of Microfluidic Particle and Cluster Sorting

Deterministic lateral displacement (DLD) and related microfluidic sorting devices are typically evaluated based on the size distributions of particles collected at each outlet, even though the more relevant measure of performance is the probability that a particle of a given size ends up in a specific outlet. Here, we use Bayes' rule to infer these size-dependent routing probabilities from experimentally accessible measurements of outlet size distributions, inlet size distributions, and outlet subpopulations. Using a DLD array designed to separate microspheres and microsphere clusters, we determine the probabilities that particles of different sizes are directed to each outlet and define a probabilistic critical size (DC) at which particles are equally likely to follow a zigzag and a displacement trajectory. Based on this, we calculate key performance metrics, purity, and yield. Our results demonstrate high-quality separations and show that routing probabilities provide a general and robust framework for benchmarking microfluidic sorting devices beyond traditional outlet-based analyses.