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  • Articulated Tensegrity Systems
    A Tensegrity Model for Understanding the Body In Movement and in Stillness

    Tensegrity systems consist of pressurized and tension elements.
    Pressurized elements (or expansion elements) press outwards or resist being pressed inwards. They float relative to each other to maintain adjustability during change.
    Tensioned elements pull inwards or resist being pressed outwards. They are connected in a network that distributes stresses among themselves.

    Where pressurized elements give the structure shape and volume, tensioned elements hold the structure together, integrating it, hence the term tensegrity, a combination of the words tension and integrity.

    Articulated Tensegrity Systems

    Articulated Tensegrity Systems are a special type of tensegrity designed to change shape while maintaining tensegrity at key points in the system. An example of this is our individual bodies.

    Tensegrity Systems Allow Growth

    An important quality of tensegrity systems is that they allow growth while remaining their integrity.

    A balloon is a tensegrity system with air comprising the pressured elements and the rubber skin of the balloon the tension element. Fill a balloon with air and it expands in all directions. Allow the air to escape and the balloon shrinks.

    The skin of the balloon, the tensioned element, can freely redistribute stress because the molecules of air inside the balloon can move freely with respect to each other.

    Non-Destructive Brain Growth and Birthing

    This idea of being able to grow (or simply "change") while retaining integrity is important biologically.

    Imagine the brain growing. In order to accommodate the increase in side the bones of the skull have to expand. The sutures (tension elements or T-elements) which hold the bones of the skull (P-Elements) in place are what allow the individual bones to grow and the skull as a whole to expand outwards. The cranial sutures hold the bones in a relatively fixed relationship to each other while at the same time floating them so that they don't come into direct contact with each other.

    The pelvis is another structure which can rely on tensegrity to hold it together, particularly during an event like child birth. But even as the pelvis grows it is important that its bones be allowed to adjust to each other to maintain integrity while also allowing growth. The SI joints and to a lesser extent the pubic synthesis maintain the floating relationship between the sacrum and hip bones so that they can maintain their relationship even as they change or are subject to change.

    Skeletal articulations, where bone meets bone to form joints, also allow growth. Synovial joints are made up of joint capsules which have an envelope of connective tissue holding the ends of bones together while within the envelope is synovial fluid which presses the bones apart. Bones can grow and the growth can be accommodated by the joint capsule without losing joint integrity.

    The Tensegrity Model So Far

    In the previous article on tensegrity I talked about modifying a bicycle wheel so that the relationship between the hub and the rim was both controllable (or responsive) and sensible. Smart spokes would have built in tension motors for adding tension as well as stretch sensors for measuring stretch. At any moment in time the information from stretch sensors in the wheel could give the relative position of rim and hub. The tension creating motors controlled tension to allow the relationship between hub and rim to be changed or maintained.

    This Smart Wheel (version 1.0a) could be used to approximate the hip joint. Albeit a hip joint that doesn't connect to a lower back, or knee joint. The idea was to show how the the hip joint might be controlled (by the brain), and also how we might be able to consciously interact with the hip joint, directly feeling and controlling the muscles that act on it and the positions of the bones relative to each other at the joint itself.

    Types of Change
    (Internal Change, External Change and No Change)

    To make tensegrity systems easier to understand it may be useful to think in terms of two environments: the external, that is whatever is outside of the tensegrity system, and the internal, what is going on inside the system itself. The system boundary connects the internal to the external environment. It is where the internal environment relates to the external.

    Change could be defined as anything that tries to alter a relationship. The relationship being altered could be between parts of the system (within the internal environment) or the relationship between the internal and external environment.

    Change could be externally driven (i.e. coming from the external environment) or internally driven (i.e. created by the components of the wheel itself, the internal environment.)

    Looking at our smart wheel (1.0a) and assuming no externally driven changes we can assume the following basic scenarios:
    the smart spokes might be totally relaxed,
    they might be active and maintaining the relationship between hub and rim,
    they might be active and shifting the relationship between hub and rim.

    These scenarios are very simple and are the equivalent of learning to ride a bicycle in an empty car park. Because there are no external environmental factors to worry about the focus can be on learning to deal with the bicycles systems.

    Assuming that now there is externally driven change, we can assume these scenarios:
    the smart spokes might be relaxed so that the rim flops around relative to the rim, driven by the external change,
    they might be active and maintaining a particular relationship between hub and rim despite the external change,
    they might be active and trying to change the relationship despite the external change.

    Carrying on with the metaphor of learning to ride a bike, we could first practice dealing with regular predictable changes, then from there move on to dealing with random changes.

    When external change is present, a sensitivity to external as well as internal change can be beneficial. Then, when appropriate external change can be used to help drive the change the desired internal change. Less effort is then expended to create the desired change in relationship.

    One area in which our smart wheels (version 1.0a) are lacking is direct sensitivity of the external environment. For this it might be helpful to add pressure sensors to the rims to sense what part of the rim is in contact with the ground (or some other object or surface.) This could be used to augment information from the tension sensors. And so now we have an upgrade to smart wheels (version 1.0b)

    Where the tension sensors in the smart spokes could help determine the current relationship between hub and rim, pressure sensors in smart rim could help determine the current relationship between the wheel and the earth (or between the wheel and anything else externally contacting it).

    Creating a More Complete Model

    A regular bicycle wheel is more than just a rim, spokes and a hub. While this structure provides strength and durability while at the same time being light, it doesn't do a lot to absorb the small shocks and jolts of riding (even with smart spokes and rims).

    Stick a tire on, inflate it, we not only have a smoother ride, we also have another example of a tensegrity system.

    Tire Tensegrity Systems

    With a bike that is ridden, and focusing on the rear wheel (since it generally bears more weight than the front wheel), the weight of the rider passes through the frame stays to the hub. The uppermost spokes transfer that weight to the rim, which at it's point of contact with the ground, transfers the weight of the bike and the rider to the earth.

    Between the rim and the earth is an air filled tire, a tensegrity system in its own right. Assuming just enough air to keep the rim from contacting the earth, but not enough air to make the tire rigid, the tire will bulge near the point of contact with the earth. The air molecules inside redistribute and the rubber in this part of the tire bulges to accommodate the weight of the rider and bike pressing down into the earth. As the wheel rolls the bulge moves around the tire following the point of contact.

    If the tire doesn't have enough air pressure, or the rider is too heavy, the tire bulges to the point that the rim contacts the earth. The result is a rougher, potentially damaging ride. If the tire has alot of pressure, the rim is in no danger of contacting the earth but the ride becomes less comfortable and the tire itself could conceivably wear out faster because of the high pressure.

    With just the right amount of pressure the ride is comfortable, tire life is potentially longer and the rim is in no danger of bouncing on the ground. (There can be other considerations, more tire pressure gives better handling and less rolling resistance, lower tire pressure can give better grip, particularly with knobbly tires.)

    Smart Tires

    Ideal tire pressure will depend on the weight of the rider. For a heavier rider we need more tire pressure, for a lighter rider, potentially less. For smart tires we need a mechanism for sensing weight, or changes in weight. We could build stretch sensors into the walls of the tire.

    So that changes in weight could be acted upon we could have a mechanism within the tire to increase tire pressure when the stretch sensors are activated. This could be some sort of pump and reservoir that could both add air to the tire and extract it again. Of course then the whole tire would be stretched by the increase in pressure. And so sensors would have to be differentiated. In addition some protocol would have to be in place to signal when to reduce pressure.

    Another means of making the tire smart would be having some means of varying the flexibility of the tire itself so that for a heavier rider the tire become less flexible (stiffer) and for a lighter rider, more flexible. The tire could be designed in such a way that only the area that bulges is induced to become stiffer. So as the wheel rolls, the part of the tire that is most bulge prone becomes stiffer (while parts less bulge prone become less stiff). Note that this could work as a pressure sensor. Now we can potentially upgrade our smart wheels (version 2.0a beta).

    How is this relevant to understanding the body?

    In two words (describing one idea): joint capsules.

    Articulated Tensegrity Systems

    Joint capsules consist of an envelope that holds the ends of two or more bones together. Within the envelope is synovial fluid. The envelope could be thought of as a tensioned element and the fluid the pressurized element. The two together could be used to prevent the ends of bones pressing into each other. The envelope maintains the relationship of the bones while the fluid helps them to float relative to each other.

    How would the joint capsule as a whole adjust to handle changes in weight?

    Probably not with the equivalent of a device inside the tire that varies the pressure of the fluid. More likely is some method of adjusting the flexibility and/or tension of the joint capsule envelope. An increase in overall tension could be used to increase synovial fluid pressure, resisting the tendency of bones bumping into each other when they are subjected to greater forces. A decrease in overall tension could be used to decrease synovial fluid pressure in the cases where forces acting on the bones is less.

    This would be equivalent to the whole tire of a smart wheel (version 2.0a beta) being compressed.

    If, during bending of the hip joint part of the joint capsule bulged, tension would have to be added to reduce the bulge. What mechanism could be used to reduce joint capsule bulging (or more specifically, bulging of the joint capsule envelope)?

    We turn to the Dutch for the answer.

    The Dynament
    A Fundamental Architectural Building Block

    Traditionally ligaments are viewed as passive structures. They tend to be thought of as activating only at extreme positions to protect the joint. But what if they are directly affected by muscle tension? This would make them active structures!

    The Dutch and Dynaments

    Almost 30 years ago, a Dutch doctor, Jaap van der Wal PhD, did some anatomic dissections which where aimed at keeping the connective tissue at the joints intact. He noted that ligaments, as we often see them in anatomy texts, are fabrications. The actual ligaments as we see them are created by the anatomists knife. In reality ligaments don't exist as separate structures, much the way each individual transistors aren't separate structures in an integrated circuit. While their function is present, actual ligaments as separate and easy to discern structures within the connective tissue network don't exist.

    And so part of the problem with anatomic dissections as they normally tend to be done is that they remove connections between muscle and ligaments while leaving connections between muscles and tendons intact. With this in mind Jaap van der Wal suggests a basic functional building block called a dynament that includes the muscle belly and at either end of the muscle, the ligaments and tendons. The important aspect of this functional building block, particularly with respect to articulated tensegrity systems, is that when a muscle is activated it directly adds tension to both tendons and ligaments.

    Ligaments are Active Structures

    Based on this understanding, ligaments are not passive structures as we tend to generally think of them. They experience increases in tension as muscle tissue is activated and decreases in tension as muscle tissue is relaxed. And since ligaments form part of the joint capsule envelopes (and in some cases tendons do also), muscle activity can thus affect joint capsule envelope tension via the ligaments (and possibly the tendons).

    Thus muscle activation causing a joint to bend can also stiffen a joint capsule envelope to eliminate bulging which in turn adds pressure to the fluid inside the joint capsule causing it to push outwards against bones with greater force.

    Maintaining Tensegrity (at the Joints)

    Why would it be so important for the joint capsules to keep the bones from contacting? To maintain tensegrity. If the bones are prevented from contacting each other, or at the least from strongly pressing into each other, they can then adjust or float relative to each other. This in turn allows the joint capsule envelope to freely redistribute stress.

    This in turn could help explain injury muscle mechanics. If a muscle is injured, the brain might reprogram the body not just to keep the muscle safe, but to help keep the joint capsule itself safe.

    Assembling the Model

    Looking at what is possible in movement and in stillness it can be difficult to reconcile what the body does with tensegrity, particularly if we look at just tension in the muscles and connective tissue. However if we focus on the joints instead, with the idea that tensegrity is maintained at the joints, then the idea of tensegrity makes sense.

    With an articulated tensegrity system, the priority is on maintaining tensegrity at the joints so that the structure as a whole can be positioned freely. This gives the option of creating postures or movements that act like tensegrity systems or don't. In either case tensegrity is maintained at the joints.

    The brain varies muscle action so that joint capsules have just enough tension to keep the bones from pressing against each other. At the same time it controls muscle tension to create or maintain the desired movement or posture.

    These two jobs can be simplified to one job, assuming that the body isn't damaged in any way. A particular muscle action not only creates a desired movement, it also creates the required tension in the joint capsule envelope at the same time.

    If there are problems, the brain might limit movement not just to protect a muscle, but to protect the joint capsule. And it might call other muscles into play to simulate the affect of the damaged muscle on the joint capsule, to help keep the joint capsule intact.

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