Swimming simply: Minimal models and stroke optimization for biological systems

In this talk, we examine how to represent the kinematics of swimming biological systems. We present a new method of extracting optimal curvature-space basis modes from high-speed video microscopy images of motile spermatozoa by tracking their flagellar kinematics. Using as few as two basis modes to characterize the swimmer's shape, we apply resistive force theory to build a model and predict the swimming speed and net translational and rotational displacement of a sperm cell over any given stroke. This low-order representation of motility yields a complete visualization of the system dynamics. The visualization tools provide refined initialization and intuition for global stroke optimization and improve motion planning by taking advantage of symmetries in the shape space to design a stroke that produces a desired net motion. Comparing the predicted optimal strokes to those observed experimentally enables us to rationalize biological motion by identifying possible optimization goals of the organism. This approach is applicable to a wide array of systems at both low and high Reynolds numbers.