Activation Dynamics
Let’s get back to our data processing.
In case you don’t remember (I can’t blame you, I’ve taken my time with these posts), here is a description of our experiment, our motion data and EMG data processing.
Following a series of steps that included rectification and filtering, we transformed our muscle activity signal from a squiggly to a smooth line, that is zero when the muscle is resting, and increases (to a maximum of 1) when the muscle is active.
For a single burst of activity, it looks like this:
In practice, the red line (our “processed EMG”) is not actually a line, but a series of discrete points. This is because we record and process our EMG ten times a second, not continuously. It actually looks like this (I’ve increased the scale so you can see it a bit better):
These points represent our estimate of the neural command that reaches the muscle and excites it. In our model, we call this “muscle excitation”. We recorded this particular EMG from the sensor placed over the muscle group that extends the middle, ring and little finger. (Overall we recorded from 4 EMG sensors.) This is part of the extensor digitorum communis muscle.
In our computer model, it looks like this:
We model it as three different muscles: the EDCM, EDCR and EDCL (Extensor Digitorum Communis for the Middle, Ring and Little finger).
So the processed EMG from one sensor is converted to excitation of three muscles in our model. The conversion looks like this:
The red circles are the processed EMG, which we calculate ten times a second. Then we apply a threshold of 0.05. This means that any values of the processed EMG that are below 0.05 are set to zero. We do this because in practice, even if the muscle is resting, there could be some low-level electrical activity picked up by our sensors, which would make our model fingers jitter continuously. By using a threshold, we make sure the muscles are either on or off, and during periods of rest our model is completely still.
The other thing you’ll notice is that the muscle excitation looks like a continuous line (the blue line in the graph above), instead of discrete points. It is actually a series of points, just more of them: 250 points per second.
Given a set of muscle excitations, our model calculates muscle forces and moments, accelerations of all the segments and finally joint angles (more on this later). Following this process, our model predicts the hand movement based on the muscle excitations. But it can only make a prediction for the very near future: just 4 milliseconds into the future.
So in one second, which is 1000 milliseconds, the model needs 1000 / 4 = 250 inputs, which is why the excitation looks like a continuous line. But as you can see it only actually changes ten times a second, because that’s how often we record and process our EMG.
Ok, we have our muscle excitations, which is our model input, so we are finally ready to start running our model!
Step 1: Activation Dynamics
When electrical signals from the brain reach a muscle, it does not generate force instantly. The action potentials (that I mentioned previously) propagate through the muscle, changing ion concentrations and forming bridges between certain proteins that result in muscle contraction.
The point is, it takes time for the neural command that reaches a muscle (what we call “muscle excitation”) to be translated into muscle activation. The higher the muscle excitation, the higher the muscle activation - but with a delay.
This process is called Activation Dynamics. You can read about the maths here, and you can see it in action in the graph below.
As the muscle excitation takes a step up, the muscle activation slowly builds up towards it. It’s similar with steps down, although de-activation is slower than activation.
Activation dynamics is the first step our model takes given processed EMG. Next, I’ll describe how the activation of muscles is translated into muscle forces, and muscles forces into hand movement.
