Proprioceptive feedback amplification restores effective locomotion in a neuromechanical model of lampreys with spinal injuries

Abstract

Spinal injuries in many vertebrates can result in partial or complete loss of locomotor ability. While mammals often experience permanent loss, some nonmammals, such as lampreys, can regain swimming function, though the exact mechanism is not well understood. One hypothesis is that amplified proprioceptive (body-sensing) feedback can allow an injured lamprey to regain functional swimming even if the descending signal is lost. This study employs a multiscale, integrative, computational model of an anguilliform swimmer fully coupled to a viscous, incompressible fluid and examines the effects of amplified feedback on swimming behavior. This represents a model that analyzes spinal injury recovery by combining a closed-loop neuromechanical model with sensory feedback coupled to a full Navier-Stokes model. Our results show that in some cases, feedback amplification below a spinal lesion is sufficient to partially or entirely restore effective swimming behavior.

Keywords: computational fluid dynamics; locomotion; neurophysiology; sensory feedback.

Fig. 1.

Schematic of the lesion models. (A) Schematic of the computational lamprey body, with an inset showing the details of the springs connecting the structural points (full construction given in ref. (14)). Panels (B–E) show the coupled oscillators that drive the activation wave along the body. For all models, filled circles indicate the oscillator’s natural frequency ω, and empty circles indicate ω = 0. Gray arrows show the connections among all oscillators on each lateral side with distance-dependent strength α. Cross-connections (blue arrows) connect oscillators across a single segment to enforce antiphase relationships on the same segment. The yellow η indicates the oscillator feedback, while gη indicates amplified feedback. The dotted red line with the scissor icon indicates the lesion, and the vertical gray dash-dot line indicates left–right symmetry. (B) “Normal” uninjured CPG. (C) “SL type” (spinal lesion). (D) “LC type” (loss of connections). (E) “AO type ” (all off).

Fig. 2.

Waveforms of injured computational and living lampreys. (A) Wake of a computational lamprey simulation with no injury, where red and blue represent counterclockwise and clockwise vorticity, respectively. The dark red body outline shows the starting point of the simulation. (B) Computational lampreys shown at the same point in simulated time with injury at 30% body length (L), magnitude-only feedback, and “SL,” “AO,” and “LC” type connections as labeled. The gray swimmer is the base case (no feedback, no injury). Each of the remaining colors has a different multiplier amplifying feedback below the injury: orange = 0× (no feedback below tail), pink = 1× (normal feedback), blue = 4×, and black=10×. “Start” shows the starting point of each of the simulations. Images of swimming larval lampreys (C) before injury, (D) 1 wk postinjury (WPI), (E) 3 WPI, and (F) 11 WPI. Images provided by Dr. Hilary Katz, Western Kentucky University.

Fig. 3.

Traveling waves and synchronized activity can be produced with sufficiently high feedback gain. Panels show results from the base case and the AO and SL type injuries with a lesion at 60%L (red dashed line). Columns represent different feedback models: 1, Base; 2, AO; 3, SL magnitude-only g = 4 below the injury; 4, SL magnitude-only g = 10 below the injury; 5, SL directional g = 4 below the injury; 6, SL directional g = 10 below the injury. (A) Activation signals along the body, where dark gray and light gray represent left and right side activation, respectively. Representative activity from panel B is shown superimposed. (B) Activation signals on the right side, above the lesion, and at two positions below the lesion for the first 4 s of simulated time. (C) Rayleigh’s R metric of synchronization, which indicates stable phase offsets between oscillators across the lesion (solid line) and between the two positions below the lesion (dashed line), where 1.0 represents perfect synchronization and 0 indicates completely unsynchronized signals. Methods for details. The panels outlined in bold indicate the recovery of a stable traveling wave (column 4) close to the base case (column 1).

Fig. 4.

Midline movements and swimming speed for different feedback types and gains. (A) Midline traces of the base case, and AO- and SL-type injured lampreys over a full tailbeat cycle. The red dashed line indicates the site of the injury. The head of the lamprey is on the left of each plot. (B) Center of mass speed for each of the midline cases shown in the corresponding row to the left. The first row shows data from lesions at 30% and the second row at 60%. Columns represent different feedback types.