### abstract

- This project will develop multiscale mathematical models that integrate neurophysiology, muscle mechanics, and fluid dynamics that govern the swimming of lamprey, the most basal living vertebrate. The models will be used to develop and test general principles for how animals manage to move stably and effectively through complex and changing environments. The PIs have developed the first mathematical model of a swimming organism to fully couple a surrounding fluid with a simulated animal. In this project, the PIs will add simulated nervous and sensory systems, in order to test broad hypotheses for how animals must respond to perturbations for stable and effective swimming. The approach of the project is to consider how the dynamics of swimming emerges from the inherent coupling of all of these elements. The PIs hypothesize that sensory feedback is necessary to support the locomotor pattern as oscillation frequency increases, but, at a particular oscillation frequency, mechanical interactions alone can be sufficient to stabilize the swimmer against both neural noise and fluid perturbations. To test these hypotheses, the PIs combine two different classes of mathematical models: (1) a high-fidelity computational fluid dynamic (CFD) model based upon the incompressible Navier-Stokes equations to estimate the forces and the motion of the body; (2) coupled oscillator models to describe the neural circuit that generates the locomotor pattern, called a central pattern generator (CPG) and its sensory inputs. The CFD model simulates aspects of the system where the governing equations and parameters are known, while the CPG models allow us to examine general principles about sensorimotor feedback for aspects where fewer details are known. All animals interact with their environment using flexible structures such as hairs, antennae, fins, limbs, and even their entire bodies, and all of these structures deform in response to both internal body forces and external environmental forces. And all animals that move have nervous systems that use electrical signals to activate muscles to produce force and to respond to sensory inputs that result from those environmental interactions. To understand how animals move effectively in the physical world, one must understand the interactions of many different forces, including forces from passive tissue properties, active muscular forces, and forces from the external environment. Such an understanding is critical to the development of next generation prosthetic limbs that enable adaptive and effective motion in complex environments, and to the progress of therapies for spinal cord injury that rely on the coupling between the damaged spinal circuits, the mechanics of legs, and the interaction with the external world. In this project, the PIs will investigate how the coupling among these different systems and forces contributes to the dynamics and stability of motion in a model swimming organism.