# Motor Control (9/21/2016)

Motor Control: walk, run, hop, stand on one foot, etc…

What makes motor control difficult?

• External forces (i.e. gravity)
• Sequence of muscle movements (extreme coordination)
• Uncertainty in the environment
• Optimization on the fly is computationally difficult
• Time latency (transmission time between neurons)

## Bernstein’s paper (1935)

Simplified model: one muscle and one external force (gravity).

F (the momentum of a muscle) is a function of E (innervation), $\alpha$ (the angle of articulation), and the rate of change of $\alpha$:

$F = F(E, \alpha, \frac{d\alpha}{dt}$)

Angular acceleration of a limb is directly proportional to F and one external force G (gravity, which is a function of $\alpha$), and inversely proportional to I (the moment of inertia):

$\frac{d^2\alpha}{dt^2} = \frac{F+G(\alpha)}{I}$

$I \frac{d^2\alpha}{dt^2} = F(E, \alpha, \frac{d\alpha}{dt}) +G(\alpha)$   (i)

Which factors does E depend on? 3 hypotheses are possible:

(a) E($\alpha, \frac{d\alpha}{dt}$): only depends on $\alpha, \frac{d\alpha}{dt}$.

Problem: The formula (i) now depends only on the initial conditions, which does not really correspond to physiological reality and in effect completely ignores the role of the central nervous system -> “central paralysis”.

(b) E(t): only depends on time.

Problem: The result of interactions from the formula (i) now cannot be foreseen or regulated on the fly because the changes in excitation is independent -> “ataxia”

(c) E(t, $\alpha, \frac{d\alpha}{dt}$): So, E must be both a function of time (“central nervous system”) and of muscle length and its rate of change (“proprioceptive reflex”).

General conclusions:

1. There must be higher-level representations of motor actions.
Consider a simple motor task such as writing a letter ‘A’ on a paper. Once you learn how to do this in a stable position, you can also do it while you are standing, sitting down, laying down, using the other hand, using foot, etc. You can also write a letter ‘A’ in different sizes and shapes without any problem. Each of these environments require different sequence of muscle innervations, and therefore, there must be higher level representation of letter ‘A’ that activates the right set of muscles depending on the environment. (An even simpler example is rotating your arm in a circle).
2. Muscle control cannot be localized.
Suppose muscle control is localized, i.e., the innervation of a muscle is controlled by a particular neuron (or set of neurons). Let’s call the sequence of neurons that are activated to achieve a particular motion the activation pattern for that sequence. Then, every repetitive movements will have different activation patterns because of external factors (environment), since different muscles will have to be innervated to different extents. Suppose that this repetitive movement is a conditioned motor reflex. Then, it will also show different activation patterns, meaning that conditioned reflexes are not localized. This contradicts the more common assumption that conditioned reflexes are localized (since response seems independent of circumstance and without intent). Therefore, muscle control cannot be localized.
3. Topology vs. Metrics
Sensory systems appear to be able to recognize topology while being robust to large differences in metric.
E.g. Try to draw stars in succession and compare them. They can be metrically very different, but regardless of these metric differences, they are still all “stars”.