The Bones of Tensegrity
copyright T. Flemons 2012
(note: In this paper I assume some familiarity with tensegrity and the issues raised when applying it to vertebrate anatomy. My previous paper entitled ‘The Geometry of Anatomy’ provides the ground work for what is discussed here. It can be accessed on my web site www.intensiondesigns.com and for convenience I have included the key concepts discussed in it. I am not an anatomist nor a clinician; my understanding is in the field of applied tensegrity, and in recognizing possible homologous structures in vertebrate anatomy.)
This paper addresses one of the key questions raised by the theory of biotensegrity and discusses how and why it is likely a superior description of gross vertebrate anatomy. It looks at joint structures in the body and explain how they can best be analyzed using tensegrity principles. This is in sharp contrast to traditional bio-mechanical descriptions and it will show how different they are.
First, a brief overview of the two paradigms is needed. It is easy to miss the significant difference between tensegrity structures and continuous compression structures. With few exceptions most human edifices are based upon the latter strategy and the practice of monolithic construction favours materials that can withstand compressive loading much better than tensile loading. Bricks and stone for example, are easy to find or make, and work with. They have the advantage of gravity to stick them together and properly constructed, they last centuries. But they don’t do as well in tension, and their very strength also disqualifies them as a strategy for living structures. They are immoveable and any flexibility is a failure in the form not a feature. Wood construction for the most part follows the same strategy but lighter. This building style parallels an ‘either/or’ bias in Western thinking (Aristotelian) and a good part of global culture as well. It is the failure to recognize the interconnected, ‘both/and’ nature of everything. A building style where the failure of a west wall doesn’t always affect the east wall lends itself to a mode of thinking that is atomistic and partial rather than synergistic and global.
Nomad cultures in contrast, knew everything was connected and their constructions showed it. They primarily built light weight tent shelters such as tipis or yurts (made of hides or dense fascia-like felt) which are of course tension structures. Because they were nomadic, they had a different way of seeing than ‘set in stone’ monolithic civilizations. They needed to be mobile and flexible, to address problems of weight constraint and weather. Instead of proper foundations, straight walls and keystone arches, with their attendant problems of compression loading and shear forces, they thought in terms of membranes and were concerned with issues of lightness, durability, flexibility and stiffness, oscillation, torque, chafing and wear. Every part affects every other part.
These are the same issues that life has contended with throughout it’s evolution from single cell entities to complex vertebrate animals. It should be no surprise then that many of the solutions are similar. Life appears to prioritize tensile strategies over compressive ones. But how does this work and what variety of tensility is life using? Because, while tensegrities are tensile structures, not all tensile structures are tensegrities. However, modern elaborations and inclusions to the definition open the door to a number of interpretations as to what a tensegrity system is. -see eg. Rene Motro, Robert E. Skelton in references.
Structurally, vertebrate animals have the most complex requirements-they need to be contingently and constantly mobile and thus must be self supporting. A tent is in part supported by the ground it rests on, a spider’s web depends upon the branch it attaches to, but the branch does not need the web. It does however, need the tree for support and the tree needs the ground to anchor itself. At the microscopic and molecular level we can argue that all structure is tensegral but only in this expanded sense would we include the branch along with the web or the ground along with the tree.
Everyone recognizes the importance of tensile tissues in the support system of the body. But there is a difference between describing the tensile system that straps the bones together, securing them at some angle (ligaments, tendons) under compression, and the tensegrity network that floats the bones within it (fascia) under tension. I would argue both strategies operate in the body.
The first type of tensile stability compares support for the torso to guying a mast from a stable surface. Stuart McGill in his book Low Back Disorders (c2007) illustrates this with several analogies. (fig 1,2,) Figure 1 simplifies this to the extreme, while figure 2 diagrams the forces more complexly. For the purposes of illustration the pelvis is seen as a platform that muscles and tendons pull the spine towards to stabilize it. There are no stable platforms in the body however.
Others have likened the support we receive to how a sailboat mast is stayed-except the mast needs the boat for support and not the other way around. We can analyze a sailboat as a tensegrity system but we have to add in what is not obvious. The mast,deck, stays, and shrouds equates to one half of a tensegral octahedron. Its mirror image can be traced in the boat hull and the keel. (fig 3)
Note that this kind of analysis of a sailboat discloses lines of tension embedded in the boat’s design. The geometry of a sailboat is self supporting, though relatively rigid and its range of motion is deliberately restricted. While a sailboat is a tensegrity system imposed on a boat which is not, it is far too rigid to qualify as a useful analogy for living forms.
Life ontologically assembles itself, from cells, to tissues, organs and finally to a regulating autonomous body that self repairs. Tensegrity provides a new means to analyze life systemically. It can establish a new paradigm-a bio-mechanical science of living structure that offers a comprehensive description of how we and everything that lives is stuck together and stays stuck together.
With tensegrity, torque is not a significant problem because of the way forces are distributed. Chafing or wear is distributed by multiple and redundant attachments and shear is not a separate force but tension and compression acting at some angle to each other. Technically, there are no shearing actions in tensegrities because separate forces act on different components. In a class one tensegrity, (Robert Skelton's classification system) there is no contact between compression members so there is nothing that shears. A class two tensegrity will have compression members meet but will not carry a compressive load across their intersection. They are flexible, economical of material and energy, durable and possess multiple paths of redundancy to failure. Living structure relies on tensegrity strategies also because they can demonstrate self assembly (i.e. larger scale tensegrities are built up from smaller scale tensegrities) hierarchically.
It has been well established (Ingber, Levin, et al) that tensegrity provides verifiable physical descriptions of cellular structure, bone matrix, tissue and organs. However, reasoning from these levels of organization to a new understanding of anatomical structure poses several questions. In a previous paper, The Geometry of Anatomy, several paths were proposed. This paper examines one in greater detail.
Parts and Wholes
It is very difﬁcult to address the complexity of the body without focusing on parts. It seems built into the language and Aristotelian paradigm that parts take precedent over the whole. We dissect cadavers and separate out aspects of the whole to serve our purposes. We study organ systems in exhaustive detail and only then link what we learn to some larger description of the whole body. We declare war on cancer and attempt to eradicate it without considering the inner (and outer) terrain that created the conditions that allowed it to thrive. And we sometimes neglect considering, that systems within systems are somehow nested at increasing and decreasing magnitudes of scale and a change at one level concatenates through the body at all other levels. Tensegrities are by their nature systemic and hierarchical and so should provide a better description of this biological process. This investigation has to link parts together as nested interconnecting tensegrities.
It now seems reasonable to adopt a syncretic system, such as tensegrity, as a new description of how vertebrate anatomy works-after all anatomic descriptions haven’t changed much since the 16th century (Andreas Vesalius). Bio-mechanists still persist in measuring forces acting on joints, bones and muscles based upon fictitious fixed fulcrums and still use linear analysis to delve into the parts that don’t simply add up to the whole. The spine is described as a vertebral ‘column’ of stacked vertebrae, with attached muscles and ligaments. The whole contraption is pulled together in a compression model - a pile of parts bound up for stability. It’s increasingly clear that such theories miss the mark and spawn any number of therapeutic interventions such as fusing of spines, and hip and knee replacements which might be avoided if a better understanding of the body’s tensional integrity were available. Challenges to the ruling paradigm are cropping up everywhere, from myofascial manipulation to neuro-repatterning of muscles that have sensory and motor amnesia. But the overarching theory that tensegrity provides still needs elucidation.
Understanding how tensegrity actually operates at the level of vertebrate anatomy has proven to be difficult to conceive. Bio-tensegrity theory is not superficial but it’s adoption has been. Many clinicians use the term in their practice without any comprehensive understanding of how it might actually work. The complexity of vertebrate anatomy demands a more complete and encompassing explanation-and must include the role fascia plays in seamlessly meshing the tensile elements with the harder, denser tissues. Tensegrity can best illustrate how it all hangs together, and a better description will net better prescriptions in terms of clinical practices.
A topic worth examining is the contentious issue surrounding simple joint articulations such as the finger, toe or knee. The challenge takes the form of two related questions that must be addressed: can tensegrity describe the articulations of joints, and can it demonstrate that loads are carried by a continuous tensile net with the compressive elements floating inside it? In other words can we describe a means by which a linked series of compression elements is suspended and/or supported by a tensile net rather than acting as a compressive column guyed down by muscles, tendons and ligaments.
Articulation of Joints
First, the simplest definition of tensegrity is any structure that remains integral (i.e. coheres or is stable) by means of a continuous tension network that fixes discontinuous compression elements within its boundaries. Applying tensegrity to the body implies that somehow the compressive elements (bones) are floating within a tensile mesh (fascia). It can show that the fascia working with muscles and bones will at least maintain and at best create space between articulating bones where there is no apparent means to achieve this.
No broad definition of tensegrity yet takes into account articulating segments or their behaviors. In fact a tensegrity system is stable precisely because it inhibits degrees of freedom and allows only a very limited range of motion in the form of slight oscillations. But a little reflection shows that they can change shape radically by altering the tension in the system.
Karl Ioganson, a Russian Constructivist, is sometimes credited with the first tensegrity construction in the 1920’s. He made a simplex tensegrity prism composed of three struts and nine tension members that completely collapsed when one of the tension members was missing or released. Correspondingly by adding the missing tension element back in, the structure reorganizes itself and climbs as if by magic off the ground to form a stable form capable of supporting a load. (fig 4)
Tensegrities depend on their tension net for their integrity. Kenneth Snelson insists that a tensegrity by definition must include a measure of its pre-stress, the built in tension level in the system that maintains its shape. Alter the tension variably anywhere in the system and the system changes as Ioganson’s structure demonstrates.
There is nothing in theory that prevents a tensegrity structure from altering shape by manipulating the tension or even the compression components. The question is how could life make this work? And how then to account for the varied joints and articulating surfaces found in the body? This question goes to the centre of the issue. Two comments here sum up the debate as it stands:
There are some mathematical calculations that support the biotensegrity model at the knee such as the actual calculable contact surface, the softness and friability of the cartilage, the slipperi-ness of the joint, the lack of distortion of the cartilage and menisci when the joint is under load as demonstrated by standing arthrograms.
Dr. Stephen Levin M.D., Orthopedic Surgeon and progenitor of the theory of Biotensegrity.
Considering the body on a macro level-bones as struts, organs as incompressible but deformable balloons, and connective tissue as tension members with muscles to immediately adjust the tension and nerves to shorten and lengthen the muscles-the idea of utter and strict tensegrity is hard to assert. Examining the actual human knee, it is hard to see that kind of mechanism at work: the tibial plateau simply does not extend high enough for any soft tissue fiber to go down from there to the lower edge of the femur. Close examination (which I have made in the dissection lab) does not reveal any substantial fibers that could possibly support the weight involved. The finger and toe joints present a similar problem.
Tom Myers, Anatomist and author of Anatomy Trains
To unpack the argument, picture a rod with a cup affixed to its end and another rod with a ball on its end. The ball fits into the cup and can rotate and roll around, causing the attached rods to hinge in relation to each other. At its simplest this could represent a finger or toe joint. The question then is, how to attach the two together? Connecting them directly with ligaments and tendons serves to increase compression forces by pulling them towards each other. What the bio-mechanists interpose between these surfaces are essentially cushions-cartilage, menisci, and the synovial capsule. It is a common agreement among many anatomists and orthopedic surgeons, that this capsule and these tissues are all that keeps the bones of a joint apart, protecting them from wear. Yet Levin has claimed that during arthroscopic surgery, when the synovial fluid has been drained to facilitate the surgery, a gap remains between the bone surfaces, even under direct loading. Further more he points out that the menisci can not handle the kinds of forces demanded of it. Cartilage is not suited to the abuse of repeated impact forces. John Sharkey, an anatomist, physiologist, and senior lecturer at the National Training Centre (Ireland) and the University of Chester England has pointed out that:
It makes little sense that cartilage tissue could withstand the bounding of three to six timesour body weight crashing up and down on it over a sustained duration such as someonerunning a marathon. I am not aware of any tissue that could withstand such forces.
Sharkey is referring to tissues compressively loaded. Research in the last 10 years has demonstrated that fascia under tension has the requisite strength and properties to effect joint integrity and augment the work of muscles. (Schleip, Gracovetsky) I think it’s likely that tensegrity can disclose how this works in the fascia.
One answer describes a tensegrity that is a saddle joint relying on two ‘y’ struts that interpenetrate. They can be attached by means of a tension sling that will prevent the two compression members from touching while creating a hinge. We could modify the ball and cup by affixing a membrane across the mouth of the cup which is formally similar. Now the ball is resting on a trampoline surface which is under constant tension as the two compression rods close with each other. (fig 5) In very crude form this seems a plausible tensegrity description for how an articulating joint works. But as Myers points out, he could not identify any tension fibers in the proper orientation that might carry the weight required. What isn’t spelled out but is equally problematic is that the knee is a rolling hinge joint. It is difficult to account for how soft tissue fibers or membranes can connect these two compression members in a suspended tensegrity configuration that allows this range of movement.
Previously there was an attempt to model the knee joint as a constellation of two discrete tensegrities. One represents the condyle surfaces of the femur, the other the eminence of the tibia plateau and the two attached together by means of a tension sling that is formally identical to the above mentioned membrane. (fig 6) While this solution is suited to a robotic or prosthetic application this is probably not how the body achieves a rolling joint. So how does it work in the body? Answering this question requires a closer look at tensegrity masts.
There are three genres of tensegrity masts, each dependent on different geometries. An X mast is based on Snelson’s first tensegrity sculpture. It is composed of two X forms rotated 90 degrees to each other and suspended by means of a tension sling and attendant stabilizers. Adding more X pieces creates an extendable mast. (fig 7a)
A Fuller mast is composed of stellated tetrahedral forms reminiscent of vertebral bodies suspended one above the other by similar means. (fig 7b, 10)
The third type of mast is a spiral Snelson type mast and is composed of chiral tensegrity prisms stacked in a variety of ways, either clockwise, counterclockwise, or interwoven with each other. (fig 8) Snelson, in a paper on three-dimensional weaving, notes the close correlation between these types of masts and three-dimensional linear weaving patterns. They are found in rope, wire, and also the well-known Chinese finger puzzle.
These tensegrity masts have interesting properties, they can act like a spring, compressing under load but, unlike a spring they can also self-extend. By applying circumpherential forces to segments of the mast, e.g. squeezing or constricting the mast laterally, they narrow, becoming longer and stiffer, acting like a compression member and are able to bear significant loads. When the load is released it becomes more flexible, bending and shortening. This is because the weaving pattern forms four-fold rhombic facets which are free to shift shape, scissoring open and flexible, or closed and stiffer. When these facets are banded laterally, they become triangulated and the entire structure stiffens completely. (fig 9)
Any cylindrical object that is semi-flexible will demonstrate this; it doesn’t have to be a tensegrity. For example, a wooden barrel will flex very slightly under stress-add a cinching band to its middle and it will elongate and strengthen. Similarly, a crushing weight applied to the top will cause it to bulge at its middle until the triangulation inherent in the material fails and the barrel bursts. Tensegrity discloses how these forces operate.
Tensegrity masts and these equivalent structures are built around a hollow core. Thus their integrity depends upon a level of stiffness in the materials used. But what happens when the hollow core is filled? Plastic water bottles are much stiffer if they are full than empty for example. Squeeze the bottle and water wants to squirt out the top. Screw down the cap tight and you have a compression column able to withstand considerable forces. This concept is key to what follows.
Looking for equivalent structures in the body, we find muscles, ligaments, tendons crossing and securing the joint, with fascia wrapping each component and the entire joint latitudinally and obliquely in a complex multi-tiered manner. In other words, a tensegral weave pattern is connected via the periosteum to the bones.
I don’t think that fascia on its own could withstand much compression but muscles are essentially myofascial tubes within tubes (endo, peri and epimysium), with muscle fibres filling the spaces in between, and will compress across their bulk and probably longitudinally to some extent, bones obviously provide the largest compression component to the system.
Graham Scarr MSB, DO http://www.tensegrityinbiology.co.uk/
The fascia is thus more than just another layer of compressive wrapping. When the equivalent of lateral bands triangulate the complex mesh of the fascia, a condition of pre-stress is formed which will cause the bones on opposite sides of a joint to separate and create a gap that is not completely supported by cartilage or joint capsules. The fascial sheath under lateral constriction and direct loading becomes more rigid and acts as an exterior compression stent or brace surrounding the joint. Release the compression force which supplies the pre-stress and the joint immediately becomes fluid and recovers its range of motion and degrees of freedom. This becomes a tensile solution to a compression problem. When any oblique wrappings contract and shorten they also somewhat exert this lateral banding force which shortens the tissue and carries the bones of the joint apart from each other. It may seem counterintuitive that tensile tissues can act in unison to create a compression structure but that is what the geometry indicates. Just as bone can carry a tensile load, so fascia can support a compression column. There exists more than enough beneficial geometry to keep the bones floating and suspended in the fascial net. As fascia has been shown to contract and relax in short intervals and as the contractions needed are small adjustments relative to the whole, this explanation can account for a joint that is alternatively stiff and yielding. It also explains how the compressive forces bearing down on a joint can be mediated so the cartilage is spared the constant loading involved in any activity.
“Recent ultrasound based measurements indicate that fascial tissues are commonly used for a dynamic energy storage [catapult action] during oscillatory movements such as walking, hopping or running. During such movements the supporting skeletal muscles contract more isometrically while the loaded fascial elements lengthen and shorten like elastic springs (Fukunaga et al. 2002).”
Schleip et al. 2010
A similar solution seems to exist for coupled vertebrae. Could it be the case that the discs alone carry all of the compressive forces in a gravity field? How does the fascia assist in distributing the loads? The thoracolumbar fascia wraps the vertebral bodies in diagonal and lateral strands like a woven sleeve with multiple attachments to the vertebrae. Pre-stress maintains the integrity of the spine and slight contractions laterally or even diagonally can extend it, ameliorating compressive loading, separating the vertebrae and sparing the discs. The geometry of the vertebral bodies themselves in the thoracic and the lumbar spine bear resemblance to a Fuller tensegrity mast. Spinous and transverse processes in the thoracic and articular facets in the lumbar spine are slung one above the other by tensile tissues i.e. the fascia. (fig 10) Picture a Fuller mast embedded in a Snelson mast, both working together synergistically to maintain vertebral and disc integrity.
The muscles and tendons as prime movers create range of motion and degrees of freedom, leveraging against the fascia which keeps the joint capsule apart and intact. But the fascia also augments and assists muscles in their tasks. Multiple paths of redundancy and a dynamic homeostasis are hallmarks of tensegrity structures and this appears to be the best explanation for how our bodies stay intact and handle the loads imposed upon them. Fascial sleeves that wrap all of our joints have the ability to maintain integrity by keeping the bones apart as they flex and contract through spiraling oblique and circumpherential force vectors. Intact fascia carry some of the pre-stress in the body and allow the gaps between bony surfaces to become the default position. Failure of these fascia membranes leads to compression injuries or arthritic degeneration over time.
The implications of this are far reaching-to salvage a compromised knee joint or repair a compressed spine, tightening or augmenting the collateral fascial tissues that envelop the bones would go a long way to restoring joint integrity. For example an external ‘smart’ tensegrity brace could assist a compromised leg, contracting and relaxing as needed. (fig 11) Additionally, augmenting or retraining the fascia to do it’s job seems a far superior strategy than fusing bones or building compression joints. Spinal fusion is directly anathema to a tensegrity paradigm that respects the whole system as a tensile integrity. Like so many interventions that work from an atomistic perspective it moves the problem down the chain to the next weakest link.
Research into bio-tensegrity is still at a nascent stage and more needs to be done. When professionals are convinced that this systemic approach has merit, the science of bio-mechanics will change and new inventions and discoveries will be made in fields such as therapeutic sports braces, prosthetics, robotics, and exoskeletons. It is hoped this paper inspires others to look further into these and other fields where tensegrity may be of use.
Buckminster Fuller is credited with exploring and developing the concept of tensegrity (discovered by his student Kenneth Snelson) in a comprehensively scientiﬁc manner. http://bﬁ.org/
Serge Gracovetsky PhD, http://sites.google.com/site/gracovetsky/home
Donald Ingber M.D. PhD, http://web1.tch.harvard.edu/research/ingber/homepage.htm
Valentín Gómez Jáuregui, Controversial Origins of Tensegrity, http://www.tensegridad.es/Publications/Controversial_Origins_Of_Tensegrity_by_GOMEZ-JAUREGUI.pdf
Stephen Levin MD., Orthopedic Surgeon, Progenitor of Biotensegrity http://biotensegrity.com/Private correspondence
Stuart McGill PhD, University of Waterloo, Ontario, Canada Low Back Pain-evidence based prevention and rehabilitation, 2nd edition 2007 http://www.amazon.com/Low-Back-Disorders-Second-Edition/dp/0736066926/ref=sr_1_1?s=books&ie=UTF8&qid=1330795933&sr=1-1
René Motro PhD, Tensegrity: Structural Systems for the Future 2003, http://www.amazon.com/Tensegrity-Structural-Systems-Ren%C3%A9-Motro/dp/1903996376/ref=sr_1_3?ie=UTF8&qid=1330795500&sr=8-3
Tom Myers, A Fuller View c2012, Chapter 2, L Steven Sieden, http://www.amazon.com/Fuller-View-Buckminster-Fullers-Abundance/dp/1611250099/ref=sr_1_1?s=books&ie=UTF8&qid=1330795971&sr=1-1
Graham Scarr MSB, DO http://www.tensegrityinbiology.co.uk/ Private Correspondence
John Sharkey, anatomist, physiologist, and senior lecturer at the National Training Centre Ireland and the University of Chester England. Private correspondence
Robert E. Skelton, Mauricio C. de Oliveira, Tensegrity Systems 2010, http://www.amazon.com/Tensegrity-Systems-Robert-E-Skelton/dp/1441944915/ref=sr_1_fkmr1_1?s=books&ie=UTF8&qid=1330795707&sr=1-1-fkmr1
Robert Schleip, Fascia Research Project, Institute of Applied Physiology, Ulm University, Ulm, Germany Adjo Zorn, Fascia Research Project, Institute of Applied Physiology, Ulm University, Ulm, Germany Frank Lehmann-Horn, Fascia Research Project, Institute of Applied Physiology, Ulm University, Ulm, Germany Werner Klingler, Department of Anesthesiology, Ulm University Germany, The fascial network: an exploration of its load bearing capacity and its potentialrole as a pain generator http://www.fasciaresearch.de
Kenneth Snelson, http://www.kennethsnelson.net/ Kenneth Snelson is generally regarded as the discoverer of tensegrity and has had a very successful career as a sculptor and inventor for over 60 years.