Modeling The Spino- Neuromuscular System Terence Soule, Stanley Gotshall, Richard Wells, Mark DeSantis, Kathy Browder, Eric Wolbrecht

Goals/Motivation Build a biologically accurate model of (a small piece of) the spino-neuromuscular system Biological modeling – Hypothesis Testing – Injury modeling Better Robots

Physical Model Biceps equivalent Gravitational force  Biceps’ applied force Triceps equivalent Triceps’ applied force

Neural Model High Level Neural Networks (12 total) I User controlled input Renshaw Inhibition Muscle Fibers (6 per muscle)

Neural Model Detailed 52 Synaptic Connections x 6 Motor Units Per Muscle x 2 Muscles = 624 Synapses!

Some Feedback Loops Gamma MN Alpha-MN Renshaw Cell Intrafusal Fibers Extrafusal Fibers 1a Afferent

Neurons Neurons are ‘pulse coded’ Time Neuron Potential Threshold Input Signals Neuron Fires Refractory period

Goal: Desired Behavior

Inputs?? What input do you use to tell the arm to move up? Down? Move fast? Hold still? Encoding problem Arbitrary solution: – Up -> high frequency input ~60 Hertz – Down -> lower frequency input ~30 Hertz

Problem Anatomy/network is ‘known’ – Reflex pathways – Neuron types – Inhibitory/excitatory connections Strength of connections is unknown

Representation of Connections Array of connection strengths & muscle fiber strengths: 0.23 | 1.43 | 2.3 | … | Total Values Need to find a set of values that allows the model to behave properly. Inter-relation between values is very complex, i.e. non-linear.

Evolutionary Training Need to adjust the strengths of inter-neuron connections & muscle fiber strengths & … Population New Population Selection by fitness Crossover and Mutation Insert When the new population is full, evaluate the individuals and repeat ( potential) solutions w/ fitnesses

Fitness Root mean squared error Square root of the sum of the squared errors between actual and target motion at a series of points along the desired trajectory.

Crossover and Mutation 0.23 | 1.43 | 2.3 | 0.32 | 1.3 | … | | 0.14 | 2.3 | 1.67 | 1.5 | … | | 1.43 | 2.3 | 1.67 | 1.3 | … | | 0.19 | 2.3 | 0.32 | 1.5 | … | 0.21 Crossover Mutation New solutions (offspring) based on ‘parent’ solutions.

Results - Behavior

Results - Training

Co-activation, Tonic Tension

Recruitment

Results –  motor neuron

Stability Altering weight

Stability Altering arm weight 0.65kg approaches the peak faster than 0.55kg

Results - Generalizability Training on multiple cases improves behavior on ‘out of sample’ test cases.

Stability Altering speeds/frequencies

Training Algorithms

Conclusions Model is trainable Trainable with mixed variable types (connection strengths and muscle fiber strengths) Model produces fundamental biological behaviors Increasing complexity produced better behavior Model is robust, proper training helps

Future Work Train more complex behaviors Generalized movement Adaptation to injury Real robots ( w/simpler networks and neurons) – Non-pulse coded neurons – One `fiber’/actuator per muscle – Simpler networks – Known angles