Biology - Tensegrity In Biology

The Bare Essentials of Life

The Shape Of Nature

Modern anatomy has taken many centuries to accumulate a body of knowledge that is now unrivalled in any other sphere. It has classified structures according to the thinking of the day and sought to understand their functions using the latest technologies, but established conventions have allowed many inconsistencies to survive long past their sell by dates. For example, orthodox views of human movement are based on the mechanics of man-made machines described in the seventeenth century and have remained essentially unchanged ever since, but biology is not constrained by the rules of classical mechanics and there is now a better way of looking at functional anatomy that is founded on some basic principles of self-organization.

Icosahedron Whenever nature uses the same principle in a variety of different situations there is probably an underlying energetic advantage to its appearance, and biological development and evolution will always favour those patterns and shapes that are the most energy-efficient in terms of stability, materials and mass. Even though they can appear to be rather complicated, at the most basic level, all living structures are the result of interactions between atomic forces and the orderly arrangements that they settle into.

Atoms interact with each other in many different ways – Van der Waal forces, electrostatics, covalency, steric interactions etc – but these can all be simplified into ‘those that attract’ and ‘those that repel’. The ‘forces’ themselves are invisible but ultimately cause the atoms to spontaneously form recognizable and tangible structures (crystals and molecules) through some basic principles of self-organization: geodesic geometry, close-packing and minimal-energy; and the same principles apply at every size scale where these ‘forces’ are frequently referred to as tension and compression. Thus, while the body itself has long been considered as a physical structure, a biotensegrity perspective recognizes that the particular configuration of invisible forces within it (closed-chain kinematics/tensegrity) is much more important in understanding what really enables it to do all the things it does. Living structures are the physical representations of the invisible forces within them.

Nature always does things in the simplest and most energy-efficient way possible, and a proper understanding of this simplicity now provides a powerful means to relate complex patterns and shapes with functional anatomy. Albert Einstein emphasized that the laws of physics must be the same in every place, which means that even the most complex organisms can be understood in terms of the same basic rules of organization.

Biotensegrity (modified from Bare Essentials 2014 issue 37)

Horse Image Biotensegrity recognizes that the forces of attraction and repulsion at the molecular scale are comparable with those of tension and compression at higher size scales, and are easily modelled using cables and struts, respectively. It is a simple re-evaluation of anatomy as a network of structures under tension and others that are compressed; parts that pull things together and others that keep them apart; basic physics!

Tensegrity models are similar to biological structures in that they are strong, light in weight and resilient to the effects of damaging forces, yet can change shape with the minimum of effort and always return to the same position of stable equilibrium. Their structural mechanics operate the same in any position, irrespective of the direction of gravity, and they have similar non-linear properties that influence movement and relate more to the newly-emerging field of soft-matter physics than classical mechanics. Each component part can be constructed from smaller ones within a complex structural heterarchy and innumerable hierarchies within it, with each part functionally related to all the others (because that is how they formed in the same place) so that the entire structure becomes united into a single functioning unit.

The recognition of biotensegrity as a unifying structural principle in living organisms began in the mid 1970’s with Stephen M. Levin (b. 1932), an orthopaedic surgeon who observed things at the operating table that could not be explained through orthodox biomechanical theory. He found that tightening up certain ligaments in the knee etc caused the bones to move apart, and that normal bones did not compress each other across their articular surfaces and often had a slight spacing between them, but there was no known mechanism that could make this possible; it was like the bones were suspended or appeared to ‘float’ within the tensional network of soft tissues. Further research on the skeletons of dinosaurs and other large animals eventually led to the realization that a then relatively little known structural principle called ‘tensegrity’ could provide an explanation for these findings and could be applied to every part of the body.

needle The term ‘tensegrity’ is a combination of the words tension and integrity, and this structural system was first recognized as a new structural principle in 1948 by Kenneth Snelson (1927-2016), a young sculptor who produced many impressive works that he described as “…unveil[ing] the exquisite beauty of structure itself”. Tensegrity models are particularly interesting because the struts remain isolated and do not compress each other at any point because they are suspended within the tension network. The architect Buckminster Fuller (1895-1983) recognized them as part of his theory of Synergetics, the study of nature’s coordinate system that considers that all natural structures are inherent displays of the forces within them; and the cell biologist, Donald Ingber, has described the structural lattice (cytoskeleton) within cells as a tensegrity structure that regulates cell function and applies at every size scale in the body. Mechanical engineers also appreciate the distinctive properties of tensegrity structures and are producing robots for use in the exploration of space etc. Both biologists and engineers now recognize that the simple principles of tensegrity can be applied to understanding the behaviour of more complex structures, but because certain aspects are not transferable between these different fields, Stephen Levin introduced the term biotensegrity to distinguish between them.

Biotensegrity models emulate biology in ways that were inconceivable in the past, but it has taken some time for the concept to become widely accepted because of its challenges to generally accepted wisdom. Biotensegrity explains how ‘joints’ can remain completely stable without over-stressing the soft tissues surrounding them, and demonstrates that the spine is essentially a tensioned structure that can function much the same in any position, with movement controlled by the very structure itself. It is attracting the attention of engineers, biologists, hands-on and movement therapists because it provides a better means to visualize the mechanics of the body in the light of new understandings about functional anatomy.

A note on the so-called power laws:

POWER-LAWS

So-called ‘power-laws’ are interesting because they offer an apparent link between complex and diverse phenomena, but their place in the grand scheme of things should be recognized for what it really is. While physicists and biomechanics use a system of engineering-based structural analysis for understanding natural phenomena based on equations, the underlying simplicity that underlies everything in the universe – geodesic geometry, close-packing and minimal-energy – is generally disregarded.

Investigations into biological organization have mostly started at the complex cellular level and moved upwards, and the power-scaling laws then emerge out of this, but recognizable patterns do not just appear out of nowhere but because of the interactions between some more basic principles described above.

Power-scaling patterns or ‘laws’ are a product of self-organized complexity but do not explain how or why the phenomena they link together developed in the first place. They are interesting and sometimes useful features in the emerging morphology but their significance has been overblown. In the same way, biological ‘fractals’ are not the result of some ongoing mathematical iteration but self-similar statistical probabilities that emerge independently as the developing structures formed. So, even though different processes at different size-scales can be compared through their fractal dimension, that does not necessarily mean that the structures themselvs are fractals. As for all those mathematical equations, they are simply subsets of the algorithms that determine how, why and in what way biology behaves in the way that it does, and are not causative in themselves.

Levin, S.M. 2016. Tensegrity: the new biomechanics. In: M. Hutson and A. Ward, eds., Textbook of musculoskeletal medicine., 2nd Ed; Oxford: Oxford University Press.
Scarr, G. 2018. Biotensegrity: the structural basis of life. 2^nd ed., Edinburgh: Handspring.

BIOTENSEGRITY is essentially an architectural system that maintains itself through the separation of tension and compression into different structures, and their distribution throughout the organism in an organized way that enables every part to potentially influence every other part. Such simplicity is due to the inter-relationship between those basic principles, and because this system relates to the property of super-stablility as the most energetically efficient arrangement (Connelly & Back), has enabled biological organisms of great complexity to develop, function and evolve in the myriad ways that they do. Tensegrity systems eliminate the need for bulky elements, and are lightweight structures with a high resiliency that depends on the integration of every part. They thus represent a paradigm shift in the way that we think about biology, and the human body in particular.

Many examples that illustrate the principles of biotensegrity can be found, but they often appear in obscure journals or are written in complicated scientific language, and are described here in the hope of making them more accessible. See the publications page for more information. Much experimental work has been carried out on cells, which are essentially complete organisms in their own right, while generalizations from a ‘whole-body’ perspective have mostly been reasoned from first principles and higher-level maths, or inferred from models and observation. Because biotensegrity describes living systems more thoroughly (Connelly & Back), it is only a matter of time before it becomes the standard approach to biomechanics.

Note that the biotensegrity concept represents a different way of understanding biology that is based on the interconnectivity beween every part (rather than the traditional reductionist approach), and because of that, no one aspect can be properly appreciated on its own. Don’t get bogged down in the detail but keep the overall simplicity in mind at all times.

CONTENTS: Structural heterarchies; Cellular cytoskeleton and morphogenesis; Cell cortex; Helix; Collagen; Fascial system; Cranial vault; Spider silk; Shoulder joint, Elbow and pelvis; Respiratory system of the bird; Mammalian lung.

Biological structures appear to be very different from the simple tensegrity models that we make with sticks and bits of string, but they conform to the same simple rules of geodesic geometry, close-packing and minimal-energy to build more complex structures (this is all expanded on the geodesic and models pages). Physical models are usually built with components on the same size scale but the essence of biotensegrity is structural and functional inter-dependency between components at multiple size scales. One particular aspect that is not often appreciated in simple models is that of structural hierarchies/heterarchies, and an example of one is shown here.

STRUCTURAL HETERARCHIES

Structural heterarchies are ubiquitous in biology and an inherent capability of tensegrity configurations. They provide a mechanism for the efficient packing of components,^Lakes the dissipation of potentially damaging stresses,^Gao^; ^Gupta and functionally connect at every level from the simplest to the most complex with the entire system acting as a unit. Each part of a heterarchy is a modular unit made from smaller parts that are nested and dependent on all those surrounding them at multiple size-scales, and often repeating in a self-similar fractal-like manner.^JelinekIn contrast, anatomical textbooks generally organize things in a hierarchical system of large ‘important’ structures at the top followed by smaller ‘less important’ ones below, but this is so misleading from a biotensegrity perspective. Heterarchies inevitably contain hierarchies within them, but is a much better umbrella term because it emphasizes the mutually-dependent relationship and small-world connections between every part.

klein bottle Tensegrity heterarchies display a significant reduction in mass (with the ‘spaces’ filled with other smaller structures), and as tension always tries to reduce itself to a minimum, they automatically balance in the most energy-efficient configuration. Because every part influences every other part, potentially damaging forces can be distributed throughout the network and harmful stress concentrations avoided.

The separation of tension and compression into separate components then means that their material properties can be optimized as these forces are transferred down to a smaller scale with the elimination of damaging shear-stresses and bending moments.^Levin At atomic and molecular levels, these forces automatically balance in the most stable and energetically efficient configuration to form crystals and more flexible molecules (or both), which are thus tensegrity structures in their own right.^Connelly^{; Edwards} While the forces of attraction and repulsion (tension and compression) always act in straight lines (geodesics), their structural representations can be arranged within structural heterarchies such that they form curves at higher size-scales; and curves are a common feature in biology (see definitions page). Curvature is just another means of minimizing energy, and biology is very good at finding the simplest way of doing things.

myosin hierarchy
The helix is an apparently curved structure and a common motif in protein structures, but a closer look reveals that the interactions between their component atoms are operating as straight-line geodesics. The helix is also a general model for coiled winding at multiple size scales throughout the body and its functional value has been demonstrated in a diverse group of organisms and described in relation to biotensegrity (also see the geodesics, helix and myofascial helix pages).

The heterarchical arrangement of helices in muscle shows this self-similar scaling up from molecules to much larger structures, and also illustrates the hexagonal close-packing geometry within the myofibril.

At the molecular level, tensegrity helices contribute to the mechanical behaviour of the cellular cytoskeleton – a semi-autonomous structural system amenable to such analysis because of its size.

CELLULAR CYTOSKELETON AND MORPHOGENESIS

Ingber showed how the cytoskeleton behaves as a multi-functional tensegrity structure that influences cell shape and activates multiple intra-cellular signalling cascades.^Ingber Within the cell, microtubules under compression are balanced by microfilaments of actin under tension^Luo with bundles of actin and spectrin fibres playing similar respective roles in the cell cortex.^Zhu Intermediate filaments (e.g. vimentin, keratin) link them all together from the nucleus to the cell membrane^Qin so that any change in force at one part of the structure causes the entire cytoskeleton to alter cell shape.^Wang; ^Mazumbder Tension is generated through the action of actomyosin ‘motors’ (for want of a better term) and polymerization of microtubules.

Many enzymes and substrates are immobilized on the cytoskeletal lattice and mediate critical metabolic functions including glycolysis, protein synthesis and messenger RNA transcription. DNA replication and transcription are also carried out on nuclear scaffolds that are continuous with the rest of the cytoskeleton. Changes in the cytoskeleton and cell shape thus alter cellular biochemistry leading to a switch between different functional states such as growth, differentiation or apoptosis.^Stamenovic

Experiments that allowed individual cells to assume certain shapes showed that those able to distort or spread had the highest rates of growth; rounded cells became apoptotic (died) while those intermediate in shape became quiescent and differentiated. Cells also tend to extend new motile processes (lamellipodia and filopodia) on sharp corners rather than blunt ones and this is linked with the cytoskeleton.

The cytoskeleton connects to the extracellular matrix (ECM) and other cells through adhesion molecules such as integrins and cadherins, respectively. These transmembrane proteins create a mechanical coupling that transfers tension generated within the cytoskeleton to the ECM and adjacent cells. Because a pre-stressed state of tension exists between them, so a change in ECM tension also causes a realignment of structures within the cytoplasm and the initiation of chemical signalling cascades that switch cell function; a process known as mechanotransduction.

Integrins act as strain gauges that respond to changes in tension on both sides of the membrane and their activation promotes the binding of proteins such as talin, vinculin, alpha-actinin, paxillin and zyxin. These physically link them to contractile actin bundles (‘stress fibres’) in the cytoskeleton and form part of a specialized complex called a ‘focal adhesion’.

budding 2 The transfer of tension from the ECM stimulates actomyosin tension generation, causing an increase in integrin binding and clustering, and the recruitment of more focal adhesion proteins that balance the ECM tension.^Vogel Force transfer is also transmitted via the cytoskeleton to other focal adhesions and integrins, stress-sensitive ion channels, cadherins, caveolae, primary cilia and nuclear structures etc.

The attachment of fibronectin molecules (ECM) to the outside of certain integrins (α5-β1) is what stimulates a reorganization of actin in the cytoskeleton and the accumulation of focal adhesions to the area. Changes in tension then feed back to cause unfolding of the fibronectin molecule and exposure of cryptic sites within it that lead to fibrillogenesis of itself and ultimately of collagen. The spacing of fibronectin nanofibrils on the outside of the membrane is proportional to the spacing of cross-linked actin bundles in the cytoskeleton and the cell is thus able to maintain tight regulatory control over collagen morphogenesis.^Wierzbicka

During embryogenesis, tension generated in the cytoskeleton is transferable to the ECM, and changes in matrix tension cause a realignment of structures within the cytoplasm and a change in cell function. Consequently, changes in enzymatic activity produce local and regional variations in the compliance of the basal membrane and cells adhering to these regions then distort more than neighbouring cells. Mitogen stimulation (chemical signalling) can then lead to the development of more complex tissue patterns such as budding, branching (alveoli) and tubular structures (capillaries)^Huang or produce motile cells that are able to migrate away (epithelial-mesenchymal transition).

Fractal Budding Branching can create a pattern similar to the ‘Koch snowflake’ fractal, and it has been found that the position of coronary artery lesions around the heart follows a pattern related to the Fibonacci sequence and Golden Mean, thus maximising perfusion of the myocardial bed.^GibsonSimple geometry seems to get everywhere because it is so energetically efficient!

As the reciprocal transfer of mechanical forces between the cytoskeleton and extracellular matrix orchestrates cellular growth and expansion, so complex multi-cellular tissue patterns can emerge based on the same principles,^Nelson and continuity of the extracellular matrix with the fascia extends this throughout the entire body.^{Guimberteau 1 and 2}

CELL CORTEX
The cellular cortex (cortical cytoskeleton) lies just beneath the cell membrane and is considered as part of the tensegrity cytoskeleton and modelled around an icosahedron.^Zhu It is essentially made from triangulated hexagons of the helical protein spectrin (tension) coupled to underlying bundles of the helical protein actin (which in this case are under compression). The network is organized into ~33,000 repeating units, each with a short central actin protofilament that is linked by 6 spectrin filaments to a lipid-bound suspension complex (tensegrity model). About 85% of these units appear as hexagons, with ~3% pentagons and ~8% heptagons, which suggests that the hexagonal arrangement is a biological preference (see the geodesic page).

The erythrocyte (diameter 8µm) has a composite membrane that distorts as it flows through smaller capillaries but allows the cell to recover its biconcave shape. Deformation of the membrane network may cause turbining of the actin protofilaments through the suspension mechanism thereby facilitating oxygen transfer from one side of the membrane to the other. The membrane is itself a bilayered structure of phospholipid molecules with outer heads under tension separated by hydrophobic tails under compression (see ‘spheres’ on the geodesics page).

THE HELIX

helixes The helix links to biotensegrity through a common origin in the geodesic geometry of the platonic solids (see geodesic and helix pages). Helical molecules behave as tensegrity structures in their own right as they naturally stabilize through a balance between attraction (tension) and repulsion (compression).^Connelly^{; Edwards} Globular proteins contain multiple helical domains and can polymerize into larger helixes such as those in the cytoskeleton described above. Similar helices can form into heterarchies as they wind around each other to form coiled-coils (eg. spectrin) or assemble into mechanically rigid rods or filaments,^Luo^;^Qin or further combine into more complex structures with specialized functions (eg. collagens). Collagens are major structural proteins that consist of several heterarchical levels of helices, and are the main structural protein within bones, tendons, ligaments and fascia.

helicosa Axial stretching or compression of a simple tensegrity helix initiates rotation in a direction that depends on the direction of twist or chirality. Inter linking it to another one with opposite chirality causes resistance as each helix counteracts the rotation of the other. Crossed-fibres of collagen scale up to form tubular helixes in the walls of blood vessels, the urinary system and intestinal tract^Gabella and influence their mechanical properties. Elastic arteries such as the aorta have walls organized into lamellar units, with collagen reinforcement and smooth muscle cells that form crossed-helices. Tension helical ‘walls’ will inevitably contain and interact with other structures under compression, and at different heterarchical levels. This chain of T-icosa shows how the (coloured) struts form both left- and right-handed helices, with each part remaining distinct, just like in these higher-level examples.

Having said all this, one of the characteristics of the tensegrity-icosahedron model (T-icosa) is that it consists of 3 struts arranged in a left-handed twist and 3 struts with a right-handed twist, and when opposite sides are pushed together, the entire structure contracts symmetrically around a central point and decreases in volume. In other words, tensegrities can demonstrate auxetic behaviour that was once considered impossible, and has now been shown in tendons, skin, bone and organs etc. So, some of the standard mechanical descriptions of helices given here may need some tweaking when we add this auxetic property, particularly in the way muscles function, but this is ongoing at present.

Capillary formation results from tension-dependent interactions between endothelial cells and an extra-cellular scaffold of their own construction and these cells form a selective barrier that allows vascular contents to pass out between capillary walls. The internal cellular cytoskeleton determines cell shape and orientation through tensegrity, is affected by signalling mechanisms and variations in fluid flow, and alters the tension between cells through adherens junctions, and thus ultimately affects tube permeability. This could perhaps be compared with the wall of a helical tensegrity model that has many gaps, but if the struts could be expanded into plates that just touched each other so that they ‘sealed’ the internal space; it could act just like the capillary cells.

helical angles pangolin In 1956, it was definitively shown that an optimum helical angle of ~55^o (relative to the main helical axis) balances both longitudinal and circumferential stresses,^{Clark; Shadwick} and thus allow pressurized tubes to bend smoothly without kinking and resist torsional deformation. Cardiac muscle fibre orientation varies linearly between inner and outer walls, from 55^o in one direction to 55^o in the other, with tangential spiralling in a transverse plane. The heart is a helical coil of muscle that contracts with left and right-handed twisting motions,^buckberg and has been described Stephen Levin as a simple tensegrity pump that may have relevance to cardiac dynamics, and has also been described using the ‘jitterbug’ mechanism (see Geodesic page).^Levin;^{Verheyen; Judge}

Similar helices form heterarchical ‘tubes within tubes’ in fascia that permeate and surround the muscles, limbs and body walls of a huge variety of species, all considered through biotensegrity (see myofascial helices page). Tubular organs that maintain constant volume throughout changes in shape have been described in the tongues of mammals and lizards, the arms and tentacles of cephalopods and the trunks of elephants.^Kier
The arrangement of scales on the pangolin illustrate the helix at the macro level, although notice how the orientations of left and right-handed helices on the body are different in the limbs, and this pattern in the limbs may be related to the Fibonacci sequence (see Palpatory phenomena and Traube-Hering-Mayer waves page). The thoraco-lumbar and abdominal fasciae also have a spiral appearance, if only in part, and helical fascial sheaths that transfer tensional forces within and between themselves have been described in controlling movement in a way that the nervous system is incapable of.^{Stecco and Myers}

COLLAGEN

collagen 2 Bones, tendons, ligaments and fascia are all arranged into complex heterarchy/hierarchies with collagen appearing at several different levels within them. In collagen type I, repeating sequences of amino acids spontaneously form a left-handed helix of procollagen, with three of these combining to form a right-handed tropocollagen molecule. Five tropocollagen molecules then coil in a staggered helical array that lengthens longitudinally by the addition of more tropocollagen to form a microfibril, and pack radially to form a fibril;^Charvolin with higher arrangements forming fibres and then fascicles. (see helix page).

The collagen molecule exists in twenty-eight different types, or configurations, and is a major structural contributor to the extracellular matrix (ECM) that surrounds virtually every cell. The matrix attaches to the cellular cytoskeleton through adhesion molecules in the cell membrane and forms a structural framework that extends through the fascia to every level in the body.

FASCIAL SYSTEM

Traditionally considered as mere packing tissue, fascia has been show to exert considerable influence over muscle generated force transmission.^Huijing; ^Stecco Fascial architecture consists of a complex network of tensioned fibres that envelop and enclose a heterarchical system of compressed compartments at multiple size-scales, and that are particularly noticeable in cross-section of the limbs as ‘tubes within tubes’. At the higher scale, these compartments contain muscles, bones and organs, while at the meso scale, the compartments are continuous with blood vessels, nerves and other tubes; with cells and proteoglycan-bound fluids of the extracellular matrix occupying the micro scale compartments; all of which operate as parts of a whole.

Within muscle a delicate network of endomysium surrounds individual muscle cells and is continuous with the perimysium ensheathing groups of fibres in parallel bundles, or fascicular compartments. Perimysial septa are themselves inward extensions of the epimysium, which covers the muscle and is continuous with the fascia investing whole muscle groups. These fascial tissues are reinforced by two helical crossed-ply sets of collagen with the ‘ideal’ resting fibre orientation of 55^o (axial) that varies with changing muscle length (see myofascial helices page).

Tension and compression are functionally interacting with each other, and because they always occur together, this combination of tensioned fibres and compressed compartments is what gives the body its form and the fascia its functions.

Over the last few years, the surgeon Jean-Claude Guimberteau 1 and 2 has observed and described the fibrous extracellular matrix system in vivo that forms a histological continuum between bones, tendons fascia, skin, muscles and vasculature etc, and allows them to glide in relation to each other during movement. The tensioned fibres form polyhedral ‘microvacuoles’ that contain fluid-bound proteoglycans and form the most basic level of tissue organization, where (at the microscopic level) there is no clear distinction between where one structure ends and another begins. The fibres are, in effect, the bars of a closed kinematic chain (CKC) system that enables each one to guide and regulate the position and motion of all the others within the system. CKCs are ubiquitous in biology and form the basic mechanics of the tensegrity model – they are described more fully here and in the book.

The following now gives some examples of how biotensegrity changes the way that we think about the human body.

THE HUMAN CRANIUM

tensegrity skull model Many aspects of normal cranial development are poorly understood, with many of the old ideas now outdated, and the biotensegrity model explains some of these and has the potential to improve our understanding of normal and abnormal cranial development. A more detailed explanation is given on the cranial vault page.

The skull is generally considered to be a solid box but is actually made up of 22 bones, most of which remain distinct throughout life, and several of these contribute to the cranial vault that surrounds and protects the brain. The sutural spaces between the bones are filled with fibrous tissue and are important to the mechanism that allows the cranium to grow larger and accommodate the developing brain. A tough dural membrane (dura mater) lines the internal surface of the bones and passes down through the cranial cavity to the base of the skull. Until recently the general opinion was that the growing brain pushes the bones outwards but this is now known not to be the case; and although an increase in dural tension does stimulate bone growth, the mechanism is much more complex than previously thought and is now better explained through biotensegrity.

geodesic straight curved In this example, the geodesic dome (icosahedron) is developed into a T-icosa model with the struts connecting opposite vertices (almost). The straight struts are then replaced with curved struts and these are replaced with curved plates (not shown) to produce the model skull with bones that surround a central space. The bones of the cranial vault are tensioned by the dura mater and configured as a tensegrity structure. Note that curved struts only make sense in biology because they are at the top of complex structural heterarchies (at least nine different levels within bone) and that extend from the molecular level to the complete structure at the macro level (see definitions page). It should also be recognized that the vault is also influenced by the outer muscles and fascia as well as the cerebral hemispheres and internal tissues.

curves Adult bones are separated by a sutural gap of about 100 microns and have large curves and smaller serrated outlines with a fractal relationship between them.^Yu The interaction between the collagen fibres within the dural membrane and bone convexities causes the bones to be held apart with the alignment of collagen fibres in the serrated sutures acting similarly,^Jasinoski and both contribute to the tensegrity configuration. (see definitions page).

During growth, the vault bones develop totally within the membrane, which they separate into an outer periosteum and inner dura mater membrane as they grow around their edges (bone fronts). Tension in the dural membrane beneath the sutures, plus chemical signals from the osteoblasts (bone-making cells) at the bone fronts, influence the cytoskeleton of cells within the membrane and beneath the suture through the process of mechanotransduction, and thus change cell activity that increases bone growth. It is a cyclic mechanism that both regulates bone development and maintains sutural patency up until the age of about seven years (when the brain stops growing). Even after this age the sutures normally remain patent up until at least the age of 70 years and contribute to the small amounts of bone mobility recognized by ‘cranial’ osteopaths and ‘cranio-sacral’ therapists (see Palpatory phenomena and Traube-Hering-Mayer pages).

cranial_hierarchy The bones form a dome that provides protection to the brain, compression struts of a tensegrity architecture that maintains sutural flexibility and accommodates brain growth, and a microstructure that transfers external forces down through through the heterarchy to the nano-scale. The centre of the bone is a honeycomb like structure made from collagen and mineral reinforcement. Curved-strut plates are still compatible with biotensegrity when considered in terms of heterarchies because the forces of tension and compression are always acting in straight lines at some smaller scale.

A biotensegrity configuration allows the skull to enlarge and remain one step in front of the growing brain rather than being physically pushed out by it. It also allows the skull to respond to the mechanical demands of external muscular and fascial structures and integrate the entire cranium. The dural membrane that lines the inner surface of the bones also extends into the cranial cavity; and it may be that ‘aberrant’ stresses in the base of the newborn skull are transferred to the bones of the vault (through the dura) and alter their normal growth pattern, thus leading to distortions in head shape (plagiocephaly) and sutural fusion (craniosynostosis).

SPIDER SILK

Spider silk can also be considered as a tensegrity structure at bothe the micro^Knight and macro levels.^Connelly It is a composite material with a heterarchical structure composed mainly of the proteins Spidroin I and II. Spidroin I consists of poly-alanine chains in anti-parallel beta-sheet conformation packed into an orthorhombic crystallite unit. These crystallites are interconnected by helical oligopeptides rich in glycine that form a polypeptide chain network within an amorphous glycine-rich matrix. The overall network shape contains circular segments (40-80 nm diameters) interconnecting in series to form a silk fibril, with many of these arranged laterally to form the silk thread with a diameter of 4-5 microns.^{Termonia; Du} It is the regular spacing and orientation of these crystallite units and heterarchical structure that suggests that it is a tensegrity structure.

wheels wheel An analogy can also be made between a spider’s web and the spoked wheel where cable tension is balanced by compression within the rim and central hub. If the cables were fairly flexible the central hub could be moved somewhat and always return to the same position of stable equilibrium – an important and most-efficient tensegrity characteristic called super-stability^Connelly.

THE BICYCLE WHEEL AND SHOULDER JOINT

gymnasts shoulder Fuller was the first to describe the bicycle wheel in terms of tension and compression(Fuller) while Levin used it as an analogy to explain some of the complexities of the human body in terms of biotensegrity.^Levin Here the outer rim and central hub are considered as compression elements held in place by a network of wire spokes in reciprocal tension. This type of wheel is a self-contained entity maintained in perfect balance throughout with no bending moments or torque, no fulcrum of action and no levers. He proposed that the scapula functions as the hub of such a wheel, in effect as a sesamoid bone, and transfers its load to the axial skeleton through muscular and fascial attachments. The sterno-clavicular joint is not really in a position to accept much compressional load and the transfer of axial compression across the gleno-humeral joint is at maximum only when loaded at 90^o abduction.
The joint is essentially a frictionless inclined plane which means that it must rely heavily on ligamentous and muscular tension in all other positions. The humerus as a hub model would function equally well with the arm in any position. Interestingly, different parts of the gleno-humeral capsule that transfer specific tensional stresses can only do so if the capsule is intact, even if those stresses do not apparently pass through the missing parts,^Moore but this makes perfect sense if the capsule is considered as a tensegrity sheet at a microscopic level.

In a similar way, the ulna can be compared to a hub within the distal humeral ‘rim’ of muscle attachments, where load bearing across the joint is significantly tensional, and compressional forces are contained within the bones and soft-tissue compartments, thus allowing the hand to lift much larger loads than would otherwise be the case (see the elbow page).

hinge The pelvis can also be compared with the wheel with the iliac crests, anterior spines, pubis and ischia representing the outer rim and the sacrum representing the hub tied in with strong sacro-iliac, sacro-tuberous and sacro-spinous ligaments. Similarly the femoral heads act like hubs within the ‘spokes’ of the ilio-femoral, pubo-femoral and ischio-femoral ligaments.

All these examples are huge simplifications of the anatomy but they do indicate the potential of looking at the body in this different way. Standard descriptions of synovial joints as hinges is very misleading because most bones follow complex helical pathways during movement, and it has been shown in the knee joint that there is no continuous compression between bones and cartilage, even when they are pushed together.^Hakkak The above biotensegrity description of the fascia as a complex system of tensioned fibres enclosing a multi-scale heterarchy of compressed compartments now offers an alternative means to explain this non-bone compression/joint spacing (see the elbow example).

diplodoccus camel According to Wolff’s law, tensional forces remodel the bony contours and alter the positions and orientations of their attachments, contributing to the complexity of shapes apparent in the skeleton. As part of a biotensegrity structure, each attachment would influence all the others and distribute forces throughout the system with points of potential weakness avoided, which is in contrast to a solid rod or truss that is vulnerable to buckling. Such a mechanism would be an advantage in long-necked animals such as giraffes, camels and dinosaurs, where the load from the head is distributed throughout the neck, as opposed to a stress-ridden cantilever system such as the Forth Bridge.

cuban acrobats forth The erect spine and bipedal weight bearing capability of humans has traditionally been viewed as a tower of bricks and compressed disc joints that transfer the body weight down through each segment until it reaches the sacrum; but a vertical spine is a relatively rarity amongst vertebrates. Most other species have little or no use for a compressive vertebral column which is frequently portrayed as a horizontal truss and cantilever support system. As the main difference in vertebrate anatomies is in the detail it seems reasonable to suppose that they have some structural properties in common. Tensegrities are omni-directional ie. they are stable irrespective of the direction of loading, and the spine, pelvis and shoulder all demonstrate this property (within physiological limits), enabling dancers to tip-toe on one leg and acrobats to balance on one hand.^Levin

RESPIRATORY SYSTEM OF THE BIRD

bird The respiratory system of the bird differs substantially from the mammalian lung; it is an exceptionally efficient gas exchanger that processes the large amounts of oxygen required to sustain flight. Some of the reasons for this are considered to be its geodesic design and heterarchical biotensegrity arrangement that mechanically couples each part into a functionally unified structure.^Maina The volume of the bird lung is about 27% less than that of a mammal of similar body mass although the respiratory surface area is about 15% greater. The lung is attached to a rigid ribcage and its volume changes relatively little during a respiratory cycle (1.4%); instead, separate air sacs act like bellows and cause unidirectional and continuous ventilation. The air passages of the lung have a heterarchical arrangement with two-thirds of the lung volume taken up with several hundred parabronchi; their polygonal atrial openings each give rise to several funnel shape ducts (infundibulae) that terminate in numerous air capillaries, the terminal respiratory units (fig. ?). Both blood and air capillaries anastomose and interdigitate to form a tightly packaged three-dimensional network.
The parabronchi develop from epithelial cells that are compressed due to space restraint and naturally form hexagons with lumens that enlarge during development. This geodesic packing arrangement persists into the adult and makes the most economical utilization of space, thus maximizing the potential respiratory surface area. The constitutive parts of the parabronchus act together to function as an integrated unit that prevents the air capillaries from collapsing under compression and blood capillaries from distending with over-perfusion; mechanically, it is rather similar to the tensegrity bicycle wheel described above.^Maina2010

bird lung Intertwined smooth muscle bundles and collagenous tissue surround the atrial openings into the central lumen and form a complex helical arrangement. The collagen forms an intricate system of longitudinal, transverse and oblique fibres that connect to elastic fibres in the interatrial septa and floor of each atrium, and continue as the interfundibula septa that eventually becomes the basement membrane surrounding the exchange tissues. The smooth muscle, collagen and elastic fibres surrounding the atrial openings form an internal parabronchial column that lies next to the lumen. The collagenous septa and exchange tissues are also continuous with the interparabronchial septa that enclose the walls of larger blood vessels and form an external parabronchial column. The exchange tissues and associated septa are thus suspended between the internal and external parabronchial columns like the spokes in a bicycle wheel.

Contraction of smooth muscles around the atrium tenses the interatrial and interfundibula septae and stretches the elastic fibres, with collagen limiting their stretchability; the elastic fibres then act as energy-storage elements and recoil when the muscles relax. The interatrial, interfundibula and interparabronchial septa thus balance the centripetal force produced by contraction of the smooth muscle. An outward centrifugal force is also produced, by surface tension generated within the air capillaries and the prevailing intramural pressure in the interparabronchial arteries, and this is balanced by the elastic and inflexible collagen fibres. The parabronchus thus exists in a dynamically tensed state, with the inward pull of the atrial smooth muscles (internal column/wheel hub) ultimately counterbalanced by the interparabronchial septa (external column/wheel rim) and surrounding parabronchi. The morphology of the parabronchus and its constitutive parts thus fits every definition of a tensegrity structure.

MAMMALIAN LUNG ALVEOLI

The matrix surrounding alveoli is considered to be a biotensegrity structure. “The septa between alveoli are very thin and contain a single dense capillary network. They are supported by a fine network of fibres that are interwoven with the capillaries and anchored at both ends in axial fibres that form the network of alveolar entrance rings in the wall of alveolar ducts; and peripheral fibres that extend through interlobular septa towards the pleura. This allows the spreading of the capillaries by mechanical tension on the fibres. Because of this disposition of capillaries and fibres, alveoli in the mature lung are not structural units that can be separated: each of their walls is shared by two adjoining alveoli, both in terms of gas exchange with the capillary and with respect to mechanical support. Even the epithelial lining is shared by two adjacent alveoli as it extends through the pores of Kohn… This disposition of the fibre system makes the lung a tensegrity structure, which means that, in terms of mechanics, the integrity of lung parenchymal structure is exclusively ensured by the tension of the fibre continuum that supports alveolar walls and their capillaries. If one fibre is cut, this causes collapse of the septum followed by rearrangement of the adjacent parts, as occurs in emphysema.^Weibel

Well, this page is the start of a vast amount of information that is accumulating about the value of biotensegrity to understanding biology, and the human body in particular. Because every part is in an inseparable relationship with every other part, no amount of writing can do justice to this subject on its own. So absorb what you can, read the books and it will transform the way the way we think about life and the treatment of its problems.

The Bare Essentials of Life

The Shape Of Nature

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