Thank you for the references, I will follow these!

I think the basic idea is that when you're doing physical therapy that targets certain muscles, you have to find the muscle(s) that are limiting the motion! This is not obvious because they all interact.

Like if you have a back problem, you can try to exercise your back all you want, and that may not actually fix the problem. Because the real issue could be with your leg, which causes 16 hours a day of "bad" motion against your pelvis, which in turn messes up your back.

All the muscles in the body are interlinked and they often compensate for each other. When people have a problem in one area, they compensate in other ways.

So I have the same question as above: I think inverse kinematics is more about "modeling"? You would need to model every muscle, which is hard, and it is specific to a person?

I think his intuition is partly based on a mental model, but it's also probablistic. I think the model has to capture the things that are "invariant" across humans (i.e. basic knowledge of anatomy), and the variation between humans is the probablistic part. It's also based on variation in your personal health history / observed behavior, e.g. how you walk, how often you're sitting at a computer, etc.

So it does feel like an "inference" problem in that sense -- many factors/observations that result in multiple weighted guesses of the cause / effective therapies.

Inverse kinematics is about reconstructing body motion from position marker data, not really about modeling. For example, glue some tennis balls to a person's arms and legs, track their position from video of the person walking around, and use inverse kinematics to reconstruct their joint angles (their skeletal pose) across time. It's also possible to do this with marker-free methods.

Inverse dynamics takes the kinematics data from above and, in combination with ground reaction forces measured from a force plate (or instrumented footwear, etc.), calculates the forces and moments on each joint. Since control of the human musculoskeletal system is over-determined (the same motion, forces, and moments can be produced by multiple muscle activation patterns), EEG data or even ultrasound elastography is sometimes used to better constrain estimates of muscle activation patterns.

In your example the usual approach would be to use (elements of) the above methods to find out if a patient had unusual motion patterns, like the suspected abnormal leg motion in your back pain patient. Statistics comes into play once you have population data to classify as "good" or "bad", and when you're trying to determine if the hypothesized relationships between symptoms and particular motion / muscle activation patterns genuinely exist. Of course, it's fine to try different approaches (but don't forget to obtain IRB review and comply with the various regulations on human subjects research).