Mapmaker, mapmaker, where's the topography in a complex system?

Why, in the pattern, of course, and it's all mathematics.

Virgil J. Seutter,D.C.

Introduction

Mathematics in the biological sciences is not something taken lightly. Certainly it's much more complex and wonderful than I can imagine, let alone figure out. Somehow it deals with models. For the chiropractor, this doesn't mean too much. Focused on the subluxation, he doesn't see any pattern to his ritual that makes any sense except what he feels with his hands. On the other hand, for the embryologist, it means something more; like the formation of structure as a morphogenesis of cellular development (1,2). It gives the embryologist an idea of how the embryonic form might be created by understanding the pattern of development. In other words, it gives him "insight" into something relatively obscure (3).

Pattern generation has been linked to the Turing chemical pre-pattern approach where pattern and morphogenesis take place sequentially. Form in morphogenesis is important in understanding the emergence of structural changes from a cellular beginning. All this is based on reaction diffusion mechanisms as a mathematical model to understand the development of patterns in or on the body. Mathematical modeling can be used to study motion in biomechanics (4) as well as applications to geographic contour maps of the earth (5,6), the universe, or even to structural design of mechanical objects.

The real idea behind all this business about topographical mapping is the possibility of extracting information, useful information. That's sometimes difficult to envision. However, I might be able to give the reader some idea how this could be possible.

An eternity ago, when I was in the air force, I plotted weather maps. It was an education and an experience. The meteorological world has changed from my day using sophisticated computers and doppler radar and goodness knows what. In my day, plotting weather maps, whether surface (7) or upper air (8), was a tedious business. A surface map contained dots that represented the different cities with a weather station. Each dot was plotted with the necessary information. The data on the left contains only a portion of the data: city/town letter identification on the right bottom, barometric pressure top right, high temperature top left, and low temperature bottom left. A stick flag with little barbs pointing the direction of the wind and speed was symbolic to all maps. More was included: a symbol representing the type of cloud and whether it was overcast or clear, and much more. Now, mind you, all this had to be plotted within a circle no bigger than the size of a dime. Talk about eyeball strain! I'm not sure if a distant relative had similar problems as a cartographer ( 9,10,11), but he did an a-o-kay job.

Now, all this business about plotting maps is more than the eye can see for the moment. All the data on each city plot, when plotted for its similarities dot to dot or plot to plot, provided information that normally would not have been seen. After all, looking at each city plot meant nothing except that it was either hot or cold, windy or calm. Nothing exciting about that!

However, if we began to connect our dots to cities with the same information, we began to literally 'see' a pattern develop. Our cognitive minds grasped the significance of this pattern formation (it's exciting just to know our minds can do that!). This pattern began to show the areas of land mass in which the temperature was the same as it was at home, where the wind was blowing just as hard as it was at home, and where the clouds obscured the sun just as much as it did at home. That was nice to know, that other areas had the same weather as I did - at home. But what was noticed was that by visualizing all these patterns, it was possible to tell when the next mass of air might slide our way. It's wonderful to know something ahead of time. Sometimes it's just wonderful to know something!

Of course, I'm being facetious. But I'm trying to make a point. It's really a jab, you know, at how to acquire information without making a big fuss about it. It doesn't have to be absolutely right, you know. It's really just a theoretical projection of probable relationships. What it is though, is the ability to acquire information that might make some projection of a probable event or action down the road. And...

Well, it seems to me that chiropractors are having the same problem as some of the other sciences: the inability to find relationships between an action and an outcome (or reaction; now where have I heard that before?)(note1). What the chiropractor interprets as an entry point into body function is based upon either touch or palpation (12). The latter is similar to touch, just probably poking a little harder to find contour changes on a local area of the body, often the spine. He does a pretty good job, at least the patients seem to acknowledge some feeling of change and well-being as the result of some action called "manipulation."

But the problem is one of credibility and absolutes. On the one hand, the credibility is based upon a philosophy and a theory - a philosophy called "vitalism" that can't really be proved since innate function is just a description, not an answer to explain things. It has no life of its own, or no form that can provide a basis for the patient's response to a physical action on the body like an "adjustment;" there is nothing absolute to tie it down to a cause - effect relationship. And how it's all tied in is the pickle. How it all interrelates hasn't been found, probably because noone has a really good idea (or at least not very original), and ideas are just ideas with no substance.

On the other hand, the theory, more or less states that much of our body ills are due to something called a "subluxation" (a bone out of place) that sort of pinches on a nerve coming out of the spinal column. Well, that sounded good at one time when the reducibility of the anatomy could view a bone sort of pinching on a nerve... at least that was the thinking of the time. Lately, however, something called "ion channels" (13,14,15) and how it relates to touch as a molecular basis for explanation (16) suggests that a nonlinear system of communication exists in the nervous system as well. In other words, the old explanations can no longer support the neat explanations of a wiring system schema; it deals with something more nonlinear (and that ain't half the pickle if we can understand that it all ties into the brain cortex somewhere. Now that could reduce the importance of the spinal column even more!).

Oh, well, I'll be in more of a pickle unless I can spit out another idea. At least this idea can create something a little more substantive than just an innate something or other. Of course, this idea and the substantive form of the idea may have no real existence any more than the innate idea. But at least it can be plotted, that's more than one can do with the innate. In other words, it gives an "insight" into something relatively obscure.

But the trick of it is the implications of an idea. In other words, an idea is an abstraction. Now, the innate idea is also an abstraction. But the defining thing about it all is that an abstraction defines or expresses a quality that's apart from an object. The innate does a pretty good job at this. But it's something that can't be pinpointed without getting into heaps of trouble. And there's probably more to it since something abstract may have intrinsic form but relatively little or no pictorial representation. Now, that's a real problem since it implies that substance is virtually absent and very likely non-representable since even a picture perfect representation isn't possible.

Well, perhaps it's time to leave the innate and get with the program. Something plottable might work. At least it gives me something to picture, as well as something to think about, as well as something abstractly curious. What it means is that abstractions can be examined by science but only if we can translate it into something representational, something pictorial. Now, that's substance without form, i.e., it doesn't really exist except as an idea; more precisely, it isn't reducible since it's existence is somewhere in a nonlinear world and that means we have to jump into something that uses mathematics to translate the abstraction to understand the dynamic processes involved in the everyday world of function and form.

Well, let's try. Mathematics is about the only way to represent something tangible and yet, not tangible. That's a riddle in itself. But mathematical descriptions are not explanations, merely useful in presenting models of activity (17,18,19,20). And here's the meat of it: that a mathematical model is useful in providing a basis to simulate experiments and to get approximate quantitative solutions. Well, that's nice, but how do we ask the right questions unless we ask...

Now, that's a silly question, the leopard can't change its spots, or can it (21)? Of course this is a riddle and of course its got something to do with complexity science, and mathematics, and abstractions, and the whole ball-of-wax of nonlinear inquiry; it's got to do with mathematical modeling, simulating experiments and getting approximate quantitative solutions; that animal coat patterns can be generated with morphogen based reaction diffusion mechanisms.

figure 1

The hypothesis for consideration is this: that biomathematical applications based on the principles of Turing space (as a form of aberrant spatial patterning) may provide information for understanding provocative muscle testing procedure and its relation to therapy localization contact points. It assumes that the spots on a leopard can be mathematically correlated as instabilities in the diffusion of morphogenetic chemicals in the animals skins (22,23,24). Recent findings involving touch link the importance of ion channels as a chemical or molecular basis for touch. While linear mechanisms exist, speculation would suggest a nonlinear basis for analysis of the less tangible phenomena of therapy localization as somehow chemical related and nonlinear dependent as an information system. It attempts to delineate a neurocognitive component to the subluxation complex as distinct from the motor/sensory components of the physical (wiring) system. It attempts to examine the cognitive (programing) system as a constantly changing system of neuro-networking communication. It is an attempt to provide an innovative model for theoretical inquiry.

Now, there you have it; got it, right? Well, don't worry about it, I'm still mulling it over myself. I'll need the whiz kids to take the quantum leap to really get down to business. For now, ole Simon says "keep it simple." So, Simon says, "what's so different about a plot on a dot or a spot with a plot?" My question has to be simple since complexity seems to be a remote idea for some. My mapmaker background prompts the question whether plotting a contour map of relative complexity on weather data should be much different from plotting the imaginary spots (therapy localization (25)) on a virtual body? Is it possible to generate meaning (and that's precisely what we do, 'generate' meaning, since it is an implied function of the mathematics)?

Now that we know a little about complexity science, reaction - diffusion mechanisms, and plotting imaginary lines on weather maps, it should only be a stepping stone away to plot the body surface and extract some information from the process.

Of course, there's one big problem, a huge problem, really: how do we get the data? and what kind of data? Well, this is a problem since I'm not a researcher, I really didn't have access to tools that permit technical inquiry that could document the data as a recordable test or access to academia who could help me. But that was of secondary importance at this point since my objective was to determine whether the procedure of therapy localization used by techniques such as "Applied Kinesiology" might hold some water. The implication was that I had to use muscle testing (26) because at this point in time there didn't seem to be any other method to test muscle testing except by using it.

Furthermore, I suspected that a feasibility study could still be performed. A differentiating feature in this procedure was the consideration that while previous research attempts to compare consistency and/or reliability between different people challenging the test subject, my premise was that a coarse graining analysis (27,28,29) of the body surface might yield a form of data that could be analyzed for probability rather than absolute consistency (30,31,32). This is used in complexity science and computational analysis.

However, another problem had yet to be addressed: that was that if a change was to be obtained on the ventral body surface as a distal contact challenge to the cord level, a method had to be found to alter the impulses at the cord level in relation to the distal, ventral portion of the body. Previous search for information on methods to alter muscle testing in therapy localization challenges suggested the use of a electromagnetic influences to modify the test (33). A negative polarity strip magnet was found and taped to the side and level of the spinal column being tested. The rationale was that if magnetic influences had some effect upon muscle testing, that blocking a proximal nerve root ought to influence the muscle testing by creating an aberrant effect on the spatial patterns tested on the ventral or distal contact site as it correlated to the spinal level.

The procedure involved blocking the spinal cord level, then muscle testing the subject by having the subject contact each topographical ventral contact. These contact areas were designated by number for purposes of computer designation and followed the dots represented on figure 1. These were arbitrary contact sites complying with therapy localization sites often used by some of the techniques but also spatial parameters for referencing future testing and comparisons.

Each contact point was tested. Those contact points that demonstrated aberrant response (i.e., a positive test) were recorded. This took days since the test subject had to demonstrate a relative neutral response before the test challenge was deemed valid (i.e., no other interference). Also, because of constraints, i.e., fatigue, etc., only a few levels were tested each day.

 Table 1. Subluxation Pattern for reference point (above glabella on forehead) RT1, LC1, RC1,LC2,LC7,LT4,RT5,RT8,LT11/LC3,RC3,RC7 Graphic simulation pattern below from computationally correlated data. This was derived from topographical spatial reference points in therapy localization. It represents a behavior pattern of associated neurological probabilities in subluxation patterns. In an information context, the data provides an ability to graphically or visually associate tentative levels of influence. The clinician's intervention in manipulative procedure does not encompass awareness of associated levels of subsystem activity, i.e., the clinician is not always aware of the muscle groups that are recruited in a demonstration of compromise. Using computational methods, subsystem activity can be further elaborated visually to demonstrate possible muscle involvement as it relates to levels of the spinal cord. Computational approaches to information gathering could assist both the clinician and researcher by creating an awareness of the probable extent that manipulation might effect a muscle grouping, etc. It encourages a global perspective of clinical findings by referencing muscle groups, neurological pathways, etc. so the clinician can make more informed decision in either treatment or in research inquiry.

Graph 1 - therapy localization site above glabella.

The raw data was essentially unintelligible. In other words, testing the C1 level produced aberrant responses at more than one level of the ventral topography as did testing levels in the lumbar region. Analysis of the data produced identification of spinal levels as graphic display of these levels in graph 1. This represents the test site or therapy localization site on the forehead above the glabella. Note 2

I couldn't be sure what this meant and was disappointed to find that levels of the spine were represented throughout the analysis. The graphical display provided some visual insight indicating that some areas were more prominent with a higher percentage of the data in relation to other levels.

However, the next step was to use the data by manipulating and/or adjusting the level of the spine according to the data. This required more precise adjusting than manual manipulation offers, so instrumentation was used to localize the level to adjust. I adjusted from the high percentage level to the low, i.e., adjusting all the levels indicated by the data but in a sequence starting with the highest percentage.

Objective changes: The ability to detect neuromuscular pattern changes required examination of the patient's posture while standing along with muscle testing, rather than laying prone and palpating the spinal column. The inquiry eventually led to experimenting with postural evaluation as the patient therapy - localized the contact area.

In so doing, I became more aware of posture changes as different contacts were made by the subject on the ventral surface of the body. Postural evaluation included viewing the level of the iliac crests or innominates, the level of the scapula, shoulders, ears, occiput, position of the head, etc.

What was noted was that when the subject changed contact positions (therapy localization) at various locations on the ventral spatial reference, changes were noted on the level of the iliac crests, etc. In other words, as the subject moved to different areas of the ventral spatial reference point, changes could be detected in the way in which the patient changed posture.

Treatment using a manual instrument to the spine altered the deviation noted in postural examination. Objective changes could be noted in the posture but also in the subject's range of motion as well as the subject's subjective remarks that indicated they were either standing straighter, feel looser, can move better, etc.

Often preceding the objective changes, however, the patient began to describe subjective changes while laying on the table. Since chiropractic data reveals little about how a patient describes the treatment except "feeling better," "more relaxed," "no pain," etc., I was surprised by remarks the patients began to relate. Descriptions like "the sinuses are opening up," "I feel tingling in my arms, (legs, etc.). Other remarks included feeling warmth in the shoulders, neck, or the feet starting to warm up, or the stomach relaxing, or the headache easing, etc. These are sensations I had no way of measuring except by listening to the patient after the treatments as they lay on the table. These also appeared different from what I had experienced in diversified treatment of the spine.

The possibility that pattern analysis of spatially referenced topographical contact points on the ventral surface of the body could reveal information that relates to a neuro - reflexive mechanism may need to be considered for further research. However, the nature of the information suggests that both the philosophy and the theory may need revision before the chiropractor can understand that a transition from linear to nonlinear mechanisms is taking place. Furthermore, the ability to unveil the existence of patterns to variable spinal column levels reveal a deeper mechanism that might be more precise and predictable in treatment application. The advantage in the detection of patterns is that identification of multiple levels of lesion areas permit treatment of all levels rather than testing single levels either through muscle testing or leg length differentiation.

My original endeavour to uncover information about muscle testing protocols was to apply my understanding of mapmaking with a meager understanding of complexity science. I felt that topographical mapping could be possible as a way of extracting information. I also felt that the profession needed some method whereby information could be extracted that might provide an insight into something that has been relatively obscure in our ability to understand how or why things happen with the manual therapy protocols. Considering that a common denominator in all techniques involves "touch," I speculated that it might be possible that techniques could be analyzed on that basis if patterns could be demonstrated on the body surface.

What has become functional as a technique is not complete at this point since further experimentation and research is needed. However, what may have emerged in this pilot effort is the possibility that the techniques might be open to examination and/or question in a way that has not previously been possible. In other words, if the researchers can begin to think in terms of finding patterns to the subluxation idea, it might be possible to analyze how a technique might affect the body as a reflexive effect.

In experimenting with the above, I have already commented in other articles  (34)about the following observation: that both muscle testing and leg length checks are an illusion (35); that mere touch to a body surface can change the appearance of body posture as well as leg length. In other words, while the purist would view leg length changes as an unadulterated procedure relating to strict biomechanical explanation, I suggest that it engages mechanisms similar to those engaged in muscle testing and that the whole business is an illusion. This does not mean that the protocols cannot be used, merely that we need to understand what they "really" do rather than following more assumptions that lead us in the wrong direction.

Seutter, V. "Mapmaker, mapmaker, where's the topography in a complex system? Why, in the pattern, of course, and it's all mathematics." Chiropractic Resource Organization. 20 May 2001. ChiroZine ISSN1525-4550

References

Note 1
Somewhere in our basic understanding of science is the idea that for every action there is a reaction. For the health sciences, the emphasis has been placed on "outcome" as equivalent to the reaction one might view as a result of a specific action. For the chiropractor, the action is equated to a manual therapeutic application whereas for the medical community the action is also associated with a procedure of sorts or the introduction of a pharmaceutical substance.

Somehow I must be missing something. Somewhere the transition from an action to a reaction doesn't seem to have been answered. That which represents "outcome" often appears as a glossover of intermediary reactions that noone really understands, especially me. For the chiropractor to satisfy the outcome as a direct result from an action (i.e., manipulation), I would think it important to understand more about what happens the minute an adjustment is performed than to assume that the outcome is a direct effect of the adjustment. In other words, I'm more interested about what goes on between the action and reaction, what changes the objective findings of postural alteration after an adjustment. Or, for medicine, what changes occur that constitute an outcome as a direct reaction to a substance? Somewhere in-between the action and reaction is the elusive placebo that noone seems to understand, even though one might suspect that noone will ever understand the nature of outcome as a result of an action until one understands placebo.

Note 2
The nature of graphic displays of data is important in nurturing the cognitive visualization of patterns. If chiropractic is to inquire into the theoretical nature of its protocols, visual graphic pattern recognition should improve the ability to ask questions as a result of the graphic display. In other words, the graphic display ought to be able to inspire questions that normally would not have been conceived as a possible mode of action previously.

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 Contents

20 May 2001

 The morphological changes from cellular genesis to embryo began as a characteristic of chemical reaction - diffusion mechanisms. The inquiry into chiropractic technique may need to approach a non-linear dynamic that involves complexity science and information theory, hebbian learning and plasticity. [animal coat patterns / markings can be generated using a reaction diffusion principle in computer analysis, etc. Biomathematical applications based on the principles of Turing space (as a form of aberrant spatial patterning) may provide information for understanding provocative muscle testing procedure and its relation to therapy localization contact points.] Mathematical Biology I J.Mathematical Biology Math Biology Text