Fractals, brains, Pi

A fellow-traveler on SomaSimple found this blogpost, Fractal Thoughts on Fractal Brains by David Pinkus, an interesting sequence of thoughts spurred by an open access article, Broadband Criticality of Human Brain Network Synchronization.

The word "fractal" always conjures up in my mind an image of the Norwegian coastline, then another little tidbit that always has stuck with me, about pi,

"Pi also appears as the average ratio of the actual length and the direct distance between source and mouth in a meandering river (Stølum 1996, Singh 1997)."

From the blogpost:

"The design, results and context for this study are very sophisticated, and the implications are quite abstract. So I’m going to do my best to be clear. First the context: Many natural systems exhibit fractal organization and behavior. A fractal is a branchlike structure. Think of a tree: (1) Trees have many more small branches than large ones. This characteristic is also sometimes called a “power-law” or “inverse power law” or a “1/f” organization. Each of these terms means that there are exponentially more small branches compared to big ones. (2) Trees are “self-similar,” meaning that small branching patterns resemble larger ones. This characteristic is also sometimes called “scale invariance” or “scale free” because no matter the size you are looking at, the general branching shape is the same. (3) The complexity of tree branching patterns can be quantified. Fractals are called “fractals” because they exist in fractional dimensions. A line fits perfectly in one-dimension. A plane (like a piece of paper) fits in two-dimensions. Fractals fit in between a line and a plane (or in the real world between two and three dimensions). More simply, because they are so complex, with huge numbers of tini tiny branches, trees never quite reach three dimensions. If you put them in a box, there will always be some space left over.

You may quickly recognize that many other natural structures besides trees are fractals: Neurons, rivers, the respiratory system, the circulatory system, geological fault lines, snow-flakes, and so on."

As if fractal form doesn't sound complex enough, there is fractal behaviour, apparently:

"Natural systems also produce fractal behavior over time or in dynamics. Earthquakes are a common example. There are many more small earthquakes than large ones (which is nice by the way). Other examples include the size of extinction events in animal species, numbers of academic publications (a few researchers do huge amounts of work and the rest of us do just a little), numbers of hits to web-sites, wait times in stop-and-go traffic, and word usage in literature (i.e., zipf’s law)."

Fractals as verbs as well as nouns. I've often thought of the brain as more verb than noun.

The kinesthetic senses

This paper came to my attention yesterday: The kinesthetic senses by Uwe Proske and Simon Gandevia, in Australia. By some refreshing turn of events, it is open access. It provides an historical backdrop to nearly everything we as physical therapists are about. We are all about restoring this function, kinesthesia, to people in whom it would seem to have gone missing. We always have been. Without good kinesthesia, motor control goes offline. When motor control goes off line, so does maximal function.

The paper begins with a brief intro to kinesthesia. It states at the outset that muscle and skin receptors account for most of the receptor input that helps the brain make motor choices. It specifically states,

"Peripheral receptors which contribute to kinaesthesia are muscle spindles and skin stretch receptors. Joint receptors do not appear to play a major role at most joints."

Wow. Right there, we can see a huge erosion under the sea shore of one of the defining organizational principles of orthopaedic manual therapy, which is that getting to and wiggling or popping the right joint in the right way will jumpstart a better motor output. Orthopaedic manaual therapy (and chiro) have used this idea to build themselves and have perpetuated it for decades, for a century. It's just not valid. It was a false hypothesis, and finally research has begun to trickle out that suggests this is the case.

After a brief description of the contribution of muscle spindle receptors to the kinesthetic senses, Proske and Gandevia begin to discuss receptors found in skin:

"Concerning the possible contribution to kinaesthesia from other receptor types, the summary view is that while a good case has been made for some cutaneous receptors, the evidence is less convincing for joint receptors. The cutaneous receptor most likely to subserve a kinaesthetic role is the skin stretch receptor, the slowly adapting Type II receptor served by Ruffini endings (Chambers et al. 1972; Edin, 1992). For kinaesthesia at the forearm, stretch of skin over the elbow during elbow flexion can provide information about both position and movement. Movement illusions generated by stretch of skin of the hand and over more proximal joints, when combined with muscle vibration were greater than when either stimulus was applied on its own (Collins et al. 2005). The authors made the point that this was not just a matter of skin input facilitating the muscle input and that cutaneous input generated by skin stretch contributed to kinaesthesia in its own right. More recent observations have shown that skin input can also have an occluding action. Signals from local, rapidly adapting receptors evoked by low-amplitude, high frequency vibration can impede movement detection (Weerakkody et al. 2007).(....)
While joint receptors were first thought to be all-important in kinaesthesia, the present-day view is that their contribution at most joints is likely to be minor. Typically they respond to joint movement, but often with response peaks at both limits of the range of joint motion (Burgess & Clark, 1969). They are now thought of as limit detectors. However, there are examples in the literature of responses across the full range of joint movement (Burke et al. 1988) and here joint receptors may play a role under circumstances in which input from muscle and skin is not available (Ferrell et al. 1987). "

My bolds.

This paper is an important one for manual therapists who seek to understand how it is that "light" manual techniques seem to do as well to help patients' brains connect up in terms of improved, observable motor output, as heavy joint-based, manipulative or mobilizing ones.

Proske, U., & Gandevia, S. (2009). The kinaesthetic senses The Journal of Physiology, 587 (17), 4139-4146 DOI: 10.1113/jphysiol.2009.175372