The helix is a common motif in protein structure and 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 the forces of 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 helixes 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 helixes, and are the main structural protein within bones, tendons, ligaments and fascia.
Axial stretching or compression of a helix initiates rotation in a direction that depends on the direction of twist or chirality. Linking it to another one surrounding it with opposite chirality causes resistance as each helical layer 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 tractGabella 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-helixes. It is likely that wall components under tension contain sub-structures under compression at a different heterarchical level, and vice versa. This chain of T-icosa shows how the (coloured) struts form both left- and right-handed helixes, with each part remaining distinct, just like in these higher-level examples.
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.
An optimum helical angle of ~55o balances longitudinal and circumferential stressesClark; Shadwick and helical fibre arrays allow pressurized tubes to bend smoothly without kinking and resist torsional deformation. Cardiac muscle fibre orientation varies linearly between inner and outer walls, from 55o in one direction to 55o 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 a simple tensegrity pump that may have relevance to cardiac dynamics has also been described using the ‘jitterbug’ mechanism.Levin; Verheyen; Judge
Similar helixes 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 helixes on the body are different in the limbs; the 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 Fascial tissues are also reinforced by two helical crossed-ply sets of collagen with the ‘ideal’ resting fibre orientation of 55o (axial) that varies with changing muscle length.
Bones, tendons, ligaments and fascia are all arranged into complex heterarchies 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 many different configurations and is a major component of 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.
Traditionally considered as mere packing tissue, fascia has been show to exert considerable influence over muscle generated force transmission.Huijing; Stecco It naturally develops into compartments, or ‘tubes within tubes’, particularly noticeable in cross-sections of the limbs. Within muscle a delicate network of endomysium surrounds individual muscle fibres and is continuous with the perimysium ensheathing groups of fibres in parallel bundles, or fasciculi. 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 55o (axial) that varies with changing muscle length (see myofascial helices page).
The fascial system has also been described as a tensegrity system, which might seem rather strange initially because there don’t appear to be any compression struts. The extracellular matrix/fascial system is a complex biological heterarchy which means that it is likely to be different to simple models. As tension and compression always occur together it must have structures under tension and others under compression.
Considering a sheet of tensioned fascia between two bones, or even both ends of the same bone, any two points along that tension line (x,y) will be separated by a pull from either end. The points are held apart by tension, but as one of the functions of a ‘strut’ is to hold two points apart (nodes), the tissue between them is behaving as such to other parts lower down in the tensegrity heterarchy. Tensioned collagen and compressed proteoglycans interact in a tensegrity way at the nano level. Fascia could thus be considered as a network of tensioned cables and [virtual] ‘struts’ but only if it is part of a larger biotensegrity system that includes ‘real’ struts such as bones at a higher level. The basic biotensegrity principles remain the same but the description starts to become a bit more complex (see definitions page).
At the macro level, bones (struts) are compressed by muscles and fascia under tension. Muscles are cables that generate axial tension on contraction, but the resulting changes in their diameter also make them variable length compression struts perpendicular to this, which probably contributes to the tension in associated fascia and force appearing at tendons.Maas The balance of so-called ‘agonist/antagonist’ muscle tensions has also been shown to reduce stress concentrations in long bones (bending stresses) making them compatible with the resiliency required of biotensegrity struts.Sverdlova
Over the last few years, the surgeon Jean-Claude Guimberteau 1 and 2 has observed and described a fibrous biotensegrity collagen system within the body that forms a histological continuum between bones, fascia, skin, muscles and vasculature, and allows sliding between all these tissues. The tensioned fibres enclose polyhedral ‘microvacuoles’ that contain proteoglycans, and are part of the basic network of tissue organization where (at the microscopic level) there is no clear distinction between one structure and those lying adjacent to it.
THE HUMAN CRANIUM
Many aspects of normal cranial development are poorly understood with some previously held views now outdated, but the biotensegrity model can explain some of these and improve understanding of normal and abnormal 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 membrane called the 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 mater tension does stimulate bone growth, the mechanism is much more complex than previously thought and is now better explained through biotensegrity.
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 seven different levels within bone) that extend from the molecular level to the complete structure at the macro level (see definitions page).
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 the 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 arrangement. (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).
The bones form a dome that provides protection to the brain, compression struts of a tensegrity structure 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 tensegrity when considered in terms of heterarchies because the forces of tension and compression are always acting in straight lines at some smaller scale.
A tensegrity configuration allows the skull to enlarge and remain one step in front of the growing brain rather than being pushed out by it. It also allows the skull to respond to the mechanical demands of external muscular and fascial structures and integrates 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 abnormal 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 can be considered as a tensegrity structure with some similarities to fascia.Knight 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.
An analogy might 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; although this idea remains controversial. If the cables were relatively elastic the central hub could be moved somewhat and always return to the same position of stable equilibrium. The common spider web is made from silk woven into a configuration of radial and spiral tension cables attached to a gate post and tree. These latter thus form a single compression element connected through the ground like the rim of the bicycle wheel. Each of the connecting nodes between cables represents one of many ‘hubs’ that can be displaced within the elastic tension network but that always returns to the same position of stable equilibrium, one of the properties of tensegrity. However this example of the spider’s web should probably be considered as on the limit of ‘tensegrity’ (see definitions page).
THE BICYCLE WHEEL AND SHOULDER JOINT
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 90o 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 could be likened to a hub within the distal humeral ‘rim’ of muscle attachments, where load bearing across the joint may be significantly tensional and compressional forces within the bones are distributed through this tensioned network, thus allowing the hand to lift much larger loads than would otherwise be the case (see the elbow page).
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 may act like hubs within the ‘spokes’ of the ilio-femoral, pubo-femoral and ischio-femoral ligaments.
Although these examples are huge simplifications of the anatomy they do indicate the potential of looking at the body in a different way.
For example, ‘hinge’ joints in the skeleton are very different to those in man-made structures, where a standard door hinge has metal plates screwed to the door and frame with one side of each pl
ate bending around a central metal rod. The rod acts as a fixed fulcrum that holds the door part of the hinge to the frame and is compressed between them as the door swings. However, most bones follow helical pathways during movement, and in the knee joint it has been shown that there is no continuous compression between bones and cartilage, even when they are pushed together. A biotensegrity ‘hinge’ joint does not need a single compression element to carry the entire load, and the tensegrity arm models clearly shows these features (see the elbow page for more anatomical details).
The body is made of many joints and they are all linked together through the fascial system. Theo Jansen is a Dutch artist who links multiple joint units together so that they can walk, and a comparison with the human locomotor system seems inevitable. A Janssen mechanism is a structure made of parts with specific lengths according to a precise formula so that they can move as a single entity. (link) (link)
Although these are not tensegrity structures, they are useful in demonstrating the importance of the 4-bar closed-chain kinematic system that is at the heart of biological structure and biotensegrity, and more details will hopefully be included in the not to distant future.
This model is a multi-joint tensegrity based on the same mechanism as the one above with each joint modelled with the six struts of a T-icosahedron. Some of the struts are elongated so that they become parts of two of these joints. The rotation then produces the same relative motion and interactions although it needs a bit more head scratching to work out which parts are pushing and pulling during the movement. The long thin struts between the ‘joints’ are substructures in a heterarchy where the next level above is comparable to the metal plates of the original Jansen mechanism. Apart from the fixings to the wooden block there are no fixed fulcrums, levers, or moments of inertia in this model. This model shows how the structure itself is able to control the movement of parts some distance away, and in a biotensegrity context, would enable muscles to refine that movement at a higher level of control. We can separate passive and active components in models but in biology they are often inseparable. This model still has a long way to go but it is one more step.
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.
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
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
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
THE CENTRAL NERVOUS SYSTEM
It may be that a biotensegrity mechanism is responsible for morphogenesis of the central nervous system, based on some particular characteristics of developing neurites and anatomy of the cerebral cortex.Van Essen Tension along axons in the white matter is considered to be the primary driving force for cortical folding and is counterbalanced by hydrostatic and growth-generated pressures.
When neurites are transiently stretched, their length increases in proportion to the applied tension, indicating simple elastic behaviour. Under sustained stretching, however, they display visco-elastic properties as the initially elevated tension passively relaxes to a lower level over a period of minutes. Active elongation occurs when tension is maintained above a threshold level and active retraction occurs when tension is fully released. Collectively these passive and active mechanical properties allow neurites to adjust their length by a negative feedback mechanism that tends to maintain a steady tension, much as a fishing line is reeled in or out to regulate tension on the line.
Early in development, neurons migrate to the cortical plate along radial glial cells, differentiate and emanate axons that reach specific target structures. Many structures have pronounced anisotropies in the orientation of axons, dendrites and glial processes; and are under tension. Consequently tissue elasticity will vary in different directions and expansion will occur preferentially in the direction with the greatest compliance, generally perpendicular to the main fibre axis.
The trajectories of long-distance processes arising or terminating in a given region of the cerebral cortex are biased towards one side as they enter and leave exclusively through the underlying white matter. During cerebral growth collective axon tension pulls strongly interconnected regions towards one another (conjoining arrows), forming outward folds (gyri) and allowing weakly connected regions to drift apart and form inward folds (sulci). Consequently cortical cell layers vary in thickness beneath gyri and sulci (similar to the effect of folding a paperback book).
The self-assembly of three-dimensional tensegrity nano-structures of the simplest 3-strut tensegrity model and platonic solids is now possible using single and double strands of synthetic DNA.Zheng;Liedl They confirm that the tensegrity concept can realistically be applied to the evolutionary development of biological structures.