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

GammaMN

Alpha-MN

RenshawCell

Intrafusal Fibers

Extrafusal Fibers

1aAfferent

Neurons• Neurons are ‘pulse coded’

Time

Neu

ron

Pote

ntial

Threshold

Input Signals

Neuron Fires

Refractory period

Goal: Desired Behavior

0

1

2

3

0 200 400 600 800 1000 1200Time Step

Jo

int

An

gle

(R

ad

ian

s)

Trained

Target

(1:2)

(1:3)

(0)

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 | … | 0.21 631 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 TrainingNeed 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 | … | 0.210.43 | 0.14 | 2.3 | 1.67 | 1.5 | … | 1.320.23 | 1.43 | 2.3 | 1.67 | 1.3 | … | 1.320.43 | 0.19 | 2.3 | 0.32 | 1.5 | … | 0.21

Crossover

Mutation

New solutions (offspring) based on ‘parent’ solutions.

Results - Behavior

0

1

2

3

0 200 400 600 800 1000 1200Time Step

Jo

int

An

gle

(R

ad

ian

s)

Trained

Target

(1:2)

(1:3)

(0)

Results - Training

-300

-250

-200

-150

-100

-50

0

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000

Iteration

Fitn

ess

Best w/ Renshaws Avg. w/ RenshawsBest w/o Renshaws Avg. w/o Renshaws

Co-activation, Tonic Tension

Recruitment

StabilityAltering weight

StabilityAltering arm weight

0.65kg approaches the peak faster than 0.55kg

Results - Generalizability

1

10

100

1000

10000

0.5 0.55 0.6 0.65 0.7 0.75 0.8

Lifted Weight (kg)

Fit

nes

s -

Mat

ch t

o D

esir

ed B

ehav

ior

Training points

Test Points Training on multiple cases improves behavior on ‘out of sample’ test cases.

StabilityAltering speeds/frequencies

StabilityAltering 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