Tensegrity- a primer

HELLADELICIOUS tensegrity skeleton frame

Here’s a follow up to the previous essay on the stress and strain design inside bone. It’s part of the conversation between bone and brain, especially a young brain as it grows inside what the anatomist’s call the cranial vault. Graham Scarr has taken the creative step to take a plastic model of a human skull, then using a delicate copping saw cut along the suture connections between the bones that make up the cranial vault. The sutures are like farmers fences between neighbors in this case the neighbors fields are 3 dimensional separations interlocking at the bone borders with each other. Then he has attached elastic connectors to make all the pieces hold together. It’s really an ingenious way to explain how our head bones connect and interact with protecting our brain. I’ve sourced a modified version from a paper presented in the International Journal of Osteopathic Medicine (11) 2008 80-89 by Scarr entitled, A model of the cranial vault as a tensegrity structure, and its significance to normal and abnormal cranial development.  Here’s my Canadian slant on tensegrity: think of a snow igloo as a geodesic dome held together on a crystalline level.

I found this amazing discussion concerning igloos as possible tensegrity structures from a Google search from a blogger, Gerald de Jong, this is his explanation for tensegrity: ‘You use the word “hub” but in a tensegrity all things you might call hub consist of the following things coming together: One bar, and a handful of cables in various directions, all pulling towards the other end of the bar.  Think of a circus tent suspended in the middle by a pole, but then imagine the circus tent being on a mirror so the pole also extends downwards.  The bars are suspended in space such that they don’t touch or cross each other but instead they are all held together by a network of tension wires.  Bars are alone, tension holds the whole together.  If you travel on one tension wire until the end you meet the ends of several other tension wires where they meet the end of a bar – always, so you can travel everywhere without “leaving” the tension.  If you travel on a compression bar you will just be able to go back and forth between its ends or you will leave this local “compression zone”. ‘ So- what gives in the igloo in terms of tensegrity might be asked?  ‘Generally there are not “vertical” and “horizontal” compression members, but rather all of them zig-zag instead, suspended in their network of tension. Generally there are not “vertical” and “horizontal” compression members, but rather all of them zig-zag instead, suspended in their network of tension.’ An igloo is then considered as made up of packed snow, the snow particles which are tetrahedral, joined into shapes held together against each other and supporting each other as the entire crystalline geodesic dome held together in a network of continuous compression. In terms of looking at biological cells it’s also the communication that the structure provides for sensing tension, both locally and through the entire structure, that is the spin-off to take away from this. Bone cells orient to both compression and tension in the design that is seen inside a bone. But it’s not just so-called hard substances when we think of bone,  because bone bends, it has enormous flexibility before it breaks. That flex capacity seems to be the core essence for tensegrity as design, things can change shape by sensing shape, things like a growing cranial vault as a network of tension.

Using a dis-articulated plastic model of the human skull, the shape of the cranial vault was evaluated by Scarr toward a discussion involving, “…that stability of the vault which is dependant on an underlying brain; and sutural patency merely facilitates cranial expansion. The influence of mechanical forces on the development and maintenance of cranial sutures is well-established, but the details of how they regulate the balance between sutural patency and fusion remain unclear. Previous research shows that mechanical tensional forces can influence intracellular chemical signalling cascades and switch cell function; and that tensional forces within the dura mater affect cell populations within the suture and cause fusion.”

One of the misconceptions with bone is the way we actually physically handle it like in an anatomy lab, the bone is preserved bone, like the cadavers that our medical students learn from. The elastic tissues existing between bone vault plates no longer have the elastic capacity generating the integrity over the tension net of the entire cranial vault, so the structural dynamics that are existing in a living bone net are lost. Its like an old football, all dessicated and entirely rigid. Tension in alive bone appears to be necessary for the regulation of new bone growth to replace the bone absorbed. During construction of his model skull Scarr noticed that the tension cords he added to keep all the bone pieces together had to be attached near to his cut edges of the bone segments.

So what is the concept of tensegrity for coming to terms with the architecture of assembled organism and assembling organisms? The wonder of it is the guidance that takes place to build the structure during the elaborated embryo stages. I will not attempt to describe this process in detail it is a monster load of microscale interactions. Kenneth Snelson was a sculptor who created free standing structures as art objects in the 1940s.

This is a tensegrity sculpture of suspended poles held together with compression cables. Snelson added the terms tension to integrity to arrive at tensegrity. So when the term tension net is used its everything working together. Buckminister Fuller also got into the tensegrity business deriving the mathematics that define the particular geometrical stability for tensegrity structures. In Montreal we have a Fuller geodesic dome as a remnant from the 1967 World’s Fair, Expo67. The other type of Fuller structure is termed pre-stressed. Fuller made these space frame types of structure using triangles to form the repeating pattern over the entire surface. The entire outside of a tensegrity structure is under tension, which is termed isometric tension. The tension poles cross the inside of the structure to connect to vertices essentially to push them apart. Instead of meeting at an edge the poles have cables replacing the edges everything is stable but under isometric tension balance since the inward pull of the cables is balanced by the outward push of the poles or struts. The compression elements appear to float within the tension network which is a balanced  integrity structure. Any load applied to this tensegrity structure causes a uniform tension change around all of the cables (edges) distributing the compression evenly into the struts, separated from each other, spaced without contact. If the edges (cables) disappear into each other as in a geodesic dome,  the structure becomes more rigid hence pre-stressed. If the struts are replaced with curved plates the structure maintains its stability. As Scarr emphasizes, ” A fundamental characteristic of pre-stessed tensegrity is as Fuller described it, ‘…continuous tension and discontinuous compression.’ ” The bone plates are the compression elements which are being pulled by the dural tension not making any contact with each other, as  if floating in discontinuous compression. If the bones are inspected in a circular naming sequence, each bone plate despite being pulled in different directions eventually gets around the circle to pull upon itself, as continuous tension. Recalling Newton’s Third Law of Motion translated as action and reaction being equal and opposite, therefore opposite direction tensional forces will will mean the forces cancel out. In other words all the tensional forces are balance even in zero gravity which is why pre-stressed tensegrity tension structure will perform in zero-gravity space.

The bone knitting sutures along all the edges remain under tension, the tension which is a necessary condition to stimulate bone growth. The next part of the description is complex in its various aspects, here is Scarr’s explantions. ” It is likely that the vault shape of the early foetus would be reliant on the expanding brain pushing outwards on the ectomeninx,(the layer of mesoderm from which the dura mater and much of the membrane bone of the skull develop in the higher vertebrate embryo ) But  pre-stressed tensegrity could become a significant factor after 8 weeks, as ossification stiffens the membranous tissue and transfers tensional stresses across the developing bone. Chondrification would transform the base into a more geodesic structure with greater stability, and reorient certain vectors of growth influencing the greater expansion of the vault.” (In embryogenesis, the skeletal system is derived from the mesoderm germ layer. Chondrification (also known as chondrogenesis) is the process by which cartilage is formed from condensed mesenchyme tissue, which differentiates into chondrocytes and begins secreting the molecules that form the extracellular matrix. Early in fetal development, the greater part of the skeleton is cartilaginous. This temporary cartilage is gradually replaced by bone (Endochondral ossification), a process that ends at puberty. In contrast, the cartilage in the joints remains unossified during the whole of life and is, therefore, permanent.) source Wikipedia: cartiledge

Scarr’s plastic head model with curved plates is representing  plates of cranial bone as the compression struts floating in the most immediate zones around edges in the dura mater as the elastic cables without direct bone to bone contact, acting as a compression union. Scarr concentrated his model on the cranial vault he did not cut outlines of the facial bones. Scarr did not elaborate his model onto various embryo shape transitions maintaining the outcome of the cranial vault was the focus of his explanations. For example at the cranial base the bones are shown according to Scarr, ‘as a pre-stressed structure potentially changing in the early embryo to a more geodesic type as the conversion of the cartilage growth plates replace membrane between the bones.’

“Fractals are common in natural structures. Their formal definition is rather obtuse for the purposes of this paper, but a working definition could be: ‘a shape or pattern which evolves as it changes, reappearing in a hierarchy of different size scales’. Although the frequencies and amplitudes of the ‘wave’ curvatures seen at the bone edges in Fig. 9a and b vary, they are both examples of a fractal nature with a similar pattern appearing at different size scales.51 Fractals are probably relevant to linking structural hierarchies throughout the body,2,32,35,36 thus making the icosahedron particularly versatile, because it also gives rise to structures with geodesic and pre-stressed tensegrity properties.
As the vault bones approximate each other, a sort of hybrid geodesic/pre-stressed tensegrity structure would provide the required rigidity for brain protection, but
with the facility for micro mobility at the sutures.1,2,15 Pre-stressed tensegrity in the cranium allows for flexibility during development, and whatever other functions that patent sutures might serve beyond cranial expansion.
4,7,15,21 The cranial base naturally develops a geodesic structure and provides a platform from which the vault bones could expand, through pre-stressed tensegrity, to accommodate brain growth. If the transfer of tensional
forces in the dura mater, and the suggested mechanisms illustrated in Fig. 9 really do form an essential part of sutural patency, an aberration in this system which leads to compressive bone contact at any point could be one step towards a rigid geodesic cranium.1,5,15 This may explain why cartilage sometimes appears in sutural joints.1,14 A local tensional stress generated within the cellular cytoskeleton could transfer to the extracellular matrix of the dura mater and produce effects on other cells at some distance, with structural rearrangements throughout the network. Long-distance transfer of mechanical forces between different tissues could contribute to dural development, and be responsible for spatially orchestrating bone growth and expansion.3,28e30,32,34,47,49,52
Similarly, an ‘aberrant’ tensile stress from elsewhere in the cranium could exert its effects on sutures some distance away, and contribute to a change in interactions
between the dura mater, bones and brain, ultimately leading to premature synostosis.1,2 4. Conclusion without relying on an expansive force from an underlying brain, a situation currently unresolved.1e6 Tensional forces in the dura mater have the effect of pushing the bones apart, whilst at the same time integrating them into a single functional unit. Sutural patency depends on the separation of cranial bones throughout normal development, and the model describes how tension in the dura mater achieves this, and influences sutural phenotype. Cells of the dura mater respond to brain expansion and influence bone growth, allowing the cranium to match the spatial requirements of the developing brain, whilst remaining one step ahead and retaining a certain amount of autonomy. Tensegrity may also be an integrating mechanism in a hierarchical structure that extends from the cell to the whole organism, with complex 3D patterns the outcome of a network of interactions which feedback on each other.2,29,30,32,36e40,47,52 This provides a context for this model and could indicate a new approach for understanding the pathologies seen in the neonate.
One of the most significant aspects of biology is the efficiency with which it packs multiple functions into minimal space. This presents a conundrum in physical
modelling, as any structure will inevitably be limited in its behavior if it is incomplete or in isolation. It must be emphasized that much of the supporting evidence for this model is circumstantial, and more research is needed to verify it, but it is compatible with current understandings of cranial physiology, and has a contribution to make to a hierarchical systems approach to whole body biomechanics” from Scarr’s descriptions about the tensegrity version as interpretation the plastic cranial bone vault of tension bones held together integrally over the entire structure. (I apologize for the citation numbers, they refer in the last paragraph to the bibliography from the original article by Scarr for the interested reviewer who may want to research further)

‘In the human body the type of tensegrity structure is found in the cytoskeletal cortex of most cells, and in the erythrocyte (red blood cell) the geodesic structure is considered a primary contributor to the functionality of its particular shape. Pre-stressed structures have been well described by Donald Ingber inside the inner cytoskeltons of living cells. Levine has also described the ubiquity of pre-stressed tensegrity structures within the shoulder joint, the pelvis and along the spine.’ sourced from Ingber Lab web site.

The Ingber Lab in Harvard is trying to unravel what tensegrity performs in biology the descriptions from their web site are insightful. Their web site describes :” Systems Biology is a new field that focuses on the problem of how specialized behaviors emerge from collective interactions within complex molecular networks. The common approach is to work from the “bottom-up” by accumulating huge data sets with massively-parallel techniques or molecular analytical approaches, and then use computational modeling to “reverse engineer” network topology and behavior. Our work on tensegrity revealed that great insight could be gained by viewing the system as a whole and working from the “top-down”. Specifically, we found that when trying to understand collective mechanical behavior within supramolecular assemblies, higher-order architecture and physical forces must also be considered. Tensegrity also explains how hierarchical structures may be comprised of systems within systems (molecules within cells within tissues within organs) and yet still exhibit integrated mechanical behavior. In addition, it reveals how robust behaviors, such as persistence, mechanical adaptability, and shape stability, can be generated using “sloppy” parts (e.g., flexible molecular filaments), a key feature of both complex networks and living systems. Thus, tensegrity may represent the “hardware” behind living systems.”  So this is part of the approach we are attempting to take in our own research especially concerning concussions. The basics of a concussion are violent movements within the cranial vault of the brain. If we are to understand this shape distortion I think we should understand how the brain shape works too normally,no? So that’s where tensegrity comes into play: if that is how Nature assembles a brain as it grows inside the cranial vault its the communication signals that provide the boney protection as if a conversation that we are paying attention to. The brain signals the bone to expand within a tensegrity tension network. The fascinating part is the shape tension of the entire cranial bone vault is coordinated. So if ever we get to understand this brain bone conversation happening through the tensegrity tension link we will begin to comprehend the down link when enough shape changes after a concussion have occurred as the brain tension net is altered.

If you’ve ever witnessed your own child’s birth you’ll know the profound impact that happens as the baby starts his life in front of your eyes, your baby. The time you first hold your own babies head, your relationship with your parents suddenly shifts. At that moment I found myself thinking from my parent’s point of view when I was born, “So this is what my first day started felt like,’ you mumble to yourself in mystic wonder. It seems so fragile what a miracle of birth such a complex thing now resting in the palm of your hand.

What I have attempted in this essay is to elaborate from a tensegrity type conversation point of view, is to describe  the major conversion that went into that little head growing inside the mother’s womb to now be held in your hand. The cell to cell shape conversation within the tension net between growing head plate bones accommodating a brain in development  guidance is beyond our greatest skills on making anything as elegant and complex as a babies brain ready to start a new life. But part of the magic is how tensegrity allows cells to shape themselves into sensing reacting changing altering growing learning while we stare on in dazed joy.

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Montreal Grandmother, Agnes Kent was saved by Raul Wallenberg from certain death, when he provided papers for her and her Mom to escape away from the Nazis. Today when asked what that escape meant, she replied,"Remind people, that while statesmen and whole countries remained silent and did nothing, a single individual chose to act, with ramifications that proved enormous. Similar choices confront us today. Write that simple truth she said, it can never be repeated often enough because the world keeps forgetting it."
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