Abstract
Traditional views of the human cranial vault are facing challenges as
researchers find that the complex details of its development do not
always match previous opinions that it is a relatively passive
structure. In particular, that stability of the vault is dependant on an
underlying brain; and sutural patency merely facilitates cranial
expansion. The influence of mechanical forces on the development and
maintenance of cranial sutures is well-established, but the details of
how they regulate the balance between sutural patency and fusion remain
unclear. Previous research shows that mechanical tensional forces can
influence intracellular chemical signalling cascades and switch cell
function; and that tensional forces within the dura mater affect cell
populations within the suture and cause fusion.
Understanding the developmental mechanisms is considered important to
the prevention and treatment of premature sutural fusion - synostosis -
which causes skull deformity in approximately 0.05% of live births. In
addition, the physiological processes underlying deformational
plagiocephaly and the maintenance of sutural patency beyond early
childhood require further elucidation.
Using a disarticulated plastic replica of an adult human skull, a
model of the cranial vault as a tensegrity structure which could address
some of these issues is presented.
The tensegrity model is a novel approach for understanding how the
cranial vault could retain its stability without relying on an expansive
force from an underlying brain, a position currently unresolved.
Tensional forces in the dura mater have the effect of
pushing
the bones apart, whilst at the same time integrating them into a single
functional unit. Sutural patency depends on the separation of cranial
bones throughout normal development, and the model describes how tension
in the dura mater achieves this, and influences sutural phenotype.
Cells of the dura mater respond to brain expansion and influence bone
growth, allowing the cranium to match the spatial requirements of the
developing brain, whilst remaining one step ahead and retaining a
certain amount of autonomy. The model is compatible with current
understandings of normal and abnormal cranial physiology, and has a
contribution to make to a hierarchical systems approach to whole body
biomechanics.
Introduction
For many years it has been widely accepted that the cranial vault
expands through an outward pushing pressure from the growing brain, with
the sutures merely accommodating its growth and fusing in the third
decade of life.
1,2 However, recent data suggests that daily
brain growth is too small to induce sutural osteogenesis, and that in
any case, substantial growth is over before the completion of sutural
growth.
3,4,5,6 Human facial sutures normally remain patent
until at least the seventh or eighth decade, whereas the timing of
sutural fusion in the cranial vault is extremely variable and unreliable
forensically.
7,8 Many factors affect cranial enlargement - some are genetic while others are epigenetic.
Understanding the developmental mechanisms of the cranium is
considered important to the prevention and treatment of the pathologies
affecting the neonatal cranium. Craniosynostosis is the premature fusion
of one or more of the cranial sutures resulting in skull deformity, and
occurs in roughly 1 in 2000 live births.
4 It may be
associated with specific genetic syndromes or occur sporadically, and
any cranial suture may be involved, although with differing frequencies.
2,9,10
Premature fusion results in arrested bone growth perpendicular to the
synostosed suture, with subsequent abnormal compensatory growth in the
patent sutures.
1,2,9,11 Another skull deformity, not due to
synostosis, is positional moulding or deformational plagiocephaly. When
present at birth it is the result of in-utero or intrapartum molding,
often associated with multiple births, forceps or vacuum-assisted
delivery; or post-natally resulting from a static supine positioning.
12
One of the difficulties during this period is differentiating premature
fusion from abnormal moulding. By the time children are diagnosed with
craniosynostosis, the suture has already fused and the associated
dysmorphology well established. Surgical intervention may then be
necessary for neurological or cosmetic reasons.
The adult skeleton is mostly capable of healing defects and
deficiencies via the formation of new bone. However, while children
under the age of 2 years maintain the capacity to heal large calvarial
defects, adults are incapable of healing the smallest of injuries. The
coordinating mechanisms behind normal and abnormal development are
currently incomplete,
10,13 and the model to follow presents a
novel approach to furthering our understanding of the processes
involved. Although many readers will have an extensive knowledge of the
cranium, others may be unfamiliar with the details which underlie the
significance of this model, and a brief overview follows.
The Cranial Vault or calvarium: 
The cranial vault, or calvarium, surrounds and encloses the brain, and
is formed from several plates of bone which meet at sutural joints,
unique to the skull, and which display a variety of morphologies
specific to each suture.
2,7,11,14,15 The high compressive and
tensile strength of bone provides mechanical protection for the
underlying brain, while the sutural joints provide a soft interface and
accommodate brain growth.
10 The
vault
bones are the frontal, parietals and upper parts of the occiput,
temporals and sphenoid. Inferior to the vault is the cranial base, or
chondrocranium, which is made up of the lower parts of the occiput and
temporals, the ethmoid and the majority of the sphenoid. In the embryo,
the vault bones develop through ossification of the ectomeninx - the
outer membranous layer surrounding the brain; while the cranial base
develops through an additional cartilaginous
stage,
2, 16
the significance of which will be discussed later (Individual bones
spanning both regions fuse at a later stage). Enlargement of the
neurocranium occurs through ossification of sutural mesenchyme at the
bone edges, and an increase in bone growth around their perimeters.
1,15
During this process, the ectomeninx becomes separated by the
intervening bones into an outer periosteim and internal dura mater. By
the time of full term birth, the growth of the different bones has
progressed sufficiently so that they are in close apposition, only
separated by the sutures which intersect at the fontanees (Figure 1). At
full-term birth, sutural bone growth is progressing at about 100
microns/day, but this rate rapidly decreases after this. Maintenance of
sutural patency is essential throughout for normal development of the
brain and craniofacial features.
2,4,10 The brain has usually
reached adult size by the age of 7 years but the sutures normally
persist long after this - until at least 20 years of age. Even after
this, there is considerable variation in the pattern and timing of
sutural fusion in the human adult throughout life.
2,7,8,16 Animal sudies of the cranial vault clearly demonstrate sutural patency throughout.
2,16
The Dura Mater:
The dura mater is the outer one of three membranes surrounding the
brain (fig. 2). Its outer surface – the endosteal layer, is loosely
attached to most of the inner bone surface, particularly in children,
but more firmly attached around the bone margins, the base of the skull
and foramen magnum. The inner meningeal layer of the dura mater
continues down through the foramen magnum and surrounds the spinal cord
as far as the sacrum. This layer also reduplicates inwards as four
sheets which partially divide the cranial cavity and unite along the
straight sinus - the falx cerebri, falx cerebellum and bilateral
tentorium cerebelli.
The internal structure of the dura mater consists of inner and outer
elastic networks and integumentary layers, and a collagen layer;
although abrupt boundaries between these ‘layers’ cannot be
distinguished histologically.
17 The collagen layer occupies
over 90% of its thickness, with collagen fibres arranged in parallel
bundles and differing orientations - varying from highly aligned to
apparently random, and arranged in lamellae.
18 Typically, with age, the dura mater thickness changes from 0.3 to 0.8 mm.
17,18
Collagen has the strongest mechanical properties of the different
structural proteins, and fibre orientation has been observed to coincide
with the direction of tensile stress.
9,18,19,20
The Sutures: Adjacent cranial vault bones are linked through fibrous mesenchymal tissue, referred to as the sutural ligament (fig. 2).
15 The
two layers which derive from the embryonic ectomeninx – the periosteum
and dura mater, continue across the suture, and also unite around the
bone edges.
15 In the cranial base, ossification occurs
through cartilage precursors, some of which fuse together in the foetus
or early childhood.
The synchondroses are the intervening cartilages between the bones of
the cranial base. The spheno-basilar synchondrosis normally ossifies in
the third decade, and the petro-occipital fissure (synchondrosis) in the
seventh.
21 The cranial base is relatively stable during development, with the greatest size changes taking place in the vault.
Morphogenesis and phenotypic maintenance of the sutures is a result of intrinsic differences within the dura mater.
1,5,10,16,20,22 The significant factors in this are cellular differentiation, intercellular signals and mechanical signals.
23
(1) Cells of
the dura mater beneath the suture undergo epithelial-mesenchymal
transitions - a mechanism for diversifying cells found in complex
tissues, and migrate into the suture as
distinct cell populations.23,24,25
Fibroblast-like cells in the centre produce collagen and maintain
suture patency. Those with an osteoblast lineage also produce a collagen
matrix, but lead onto bone formation at the suture margins, causing the
cranial bones to expand around their perimeters.13
Osteoclast mediated bone resorption may be necessary for changes in the
complex morphological characteristics at the sutures edges.26 A complex coupling between fibroblast, osteoblast and osteoclast populations determines the actual position and rate of sutural development.5,10,26,27
In addition, a critical mass of apoptotic cells within the suture is
essential to maintaining the balance between sutural patency and new
bone formation.
10,14
(2) Intercellular signalling
influences epithelial cell function through the production and
interactions of soluble cytokines such as the ‘fibroblast growth
factors’ and ‘transforming growth factors’.
23,25 The cells at
the approximating edges of the bones, either side of the suture (bone
fronts), set up a gradient of growth factor signalling which regulates
the sequential gene expression of other cells, and causes changes in the
spatial and temporal development of different cell populations.
10,13,22,28
(3) Mechanical signals.The
morphology of the suture also reflects the intrinsic tensional forces
in the dura mater, in the order of nano or pico Newtons.
1,3,27,28
Regional differentials in this tension create mechanical stresses which
interact and exert their effects on the cells, stimulating them to
differentiate and produce different cell populations.
4,20,23,27,28
The sensitivity of the cellular cytoskeleton to tensional forces, and
the particular pattern of stress application, has been shown to be
crucial in determining the cellular response through a process of
mechanotransduction.
2,28-34 Given that the cytoskeleton is
attached to the surrounding extracellular matrix through
mechano-receptors in the cell membrane, a mechanical force transfer
between them can produce global changes within the cell by altering the
cytoskeletal tension. Multiple chemical signalling pathways are
activated within the cell as a result, and together with intercellular
chemical signals, provides multiplexed switching between different
functional states such as differentiation, proliferation and cell death.
29,30,32
It
is actually not an essential requirement for a spherical tensional
structure to be maintained through an expansive force (such as a growing
brain) in order to remain stable.3,35 The proposal here is
that the calvarium of the neonate could be such a structure which
maintains its shape through other mechanisms, being influenced by the
expanding brain as a secondary factor.
THE TENSEGRITY MODEL
The concepts of tensegrity have become increasingly recognized over
the last thirty years as a model for understanding some of the
structural properties of living organisms.
29,30,35-42 This
appreciation follows from investigations in the 1940s by the sculptor
Kenneth Snelson, and the architect Buckminster Fuller, into novel
structures in free standing sculpture and building design.
35,41 Although Snelson actually discovered the concept, and has used it to great effect in his sculptures, it was Fuller
who
defined the basic geodesic mathematics. The word ‘tensegrity’ is
derived from the words ‘tension’ and ‘integrity’ and describes
structures which are inherently stable as a result of their particular
geometry.
Fuller found the icsoahedron to be a useful model
for describing certain aspects of geodesic geometry - the geodesic dome
and tensegrity.
35,36 The outstanding feature of
geodesic domes is that they have a rigid external frame maintaining
their shape, based on a repeating pattern of simple geometry (fig. 3a).
In the human body, this type of structure is found in the cytoskeletal
cortex of most cells;
43 and in the erythrocyte, the geodesic structure is considered a primary contributor to the functionality of its peculiar shape.
44
Tensegrity structures have been well described by Ingber in the inner cytoskeletons of cells;
29,30 and Levin in the shoulder, pelvis and spine,
36-40 suggesting their ubiquity throughout the organism.
In
development of the model, the icosahedron is converted into a
tensegrity structure by using six new compression members to traverse
the inside, connecting opposite vertices and pushing them apart (fig.
3b). Replacing the edges with cables now results in the outside being
entirely under isometric tension. The inward pull of the cables
is balanced by the outward push of the struts, providing structural
integrity so that the compression elements appear to float within the
tension network. A load applied to this structure causes a uniform
change in tension around
all the edges (cables), and distributes
compression evenly to the six internal struts, which remain distinct
from each other and do not touch.
35 (Some of the edges of the
geodesic dome (fig. 3a) have disappeared in the transition to
tensegrity (fig. 3b) because they now serve no structural purpose and
are redundant.) Replacing the straight struts (fig. 3b) with curved ones
(fig. 3c) maintains the same stability, but they now surround a central
space. In the same way, the curved struts can be replaced with curved
plates (not shown) and the structure still retains its inherent
stability.
The
use of curved struts in tensegrity can be understood through structural
hierarchies. In biology, it is common for component structures to be
made up of smaller structures, which are themselves made up of still
smaller substructures. Structural hierarchies provide a mechanism for
efficient packing of components, dissipation of potentially damaging
stresses and integration of all parts of the system. Thus, the
appearance of curves at one scale are seen to result from interactions
of components at a smaller scale, and the forces of tension (attraction)
and compression (repulsion) always act in straight lines within them.
The
plastic adult skull model illustrated in figures 4 - 7 shows curved
plates of cranial bone - representing the compression struts, apparently
‘floating’ in the dura mater - shown here as elastic tension cords. The
bones do not make actual contact with each other at any point. As this
paper essentially concerns the cranial vault, the facial bones have not
been separated. Bones of the cranial base are shown here as part of an
overall tensioned structure, in spite
of
the synchondroses being under a certain amount of compression in vivo.
Their development in the early embryo could be part of a tensegrity
structure, only changing to compression as the cartilage growth plates
replace membrane between the bones. They are shown as they are in order
to demonstrate the potential of the tensegrity principle
through
all stages of cranial development. Substituting the tension cords of
these model sutures with a compression union would not alter that
principle in the vault. The spheno-basilar synchondrosis (fig 7) has
been distracted in order to display the isolation of each bone within
the dura mater more clearly. (It also supports the unbalanced weight of
the face; but see the additional wire model below.) Internal cranial
structures have been omitted for the sake of clarity.
A fundamental characteristic of tensegrity structures is, as Fuller described it, “...
continuous tension and discontinuous compression”.
35
These concepts are illustrated in figure 8a which shows a schematic
diagram of the bones spread out in two dimensions. The bones are the
compression elements which are being pulled by dural tension (only a
small number of tension forces pulling in one general direction are
shown in this diagram). Here they remain distinct from each other and do
not make contact with each other at any point - ‘discontinuous
compression’. This contrasts with figure 8c, which shows the compressive
load of a stone wall bearing down through the keystone and both sides
of the arch - the compression force here is continuous.
Returning to figure 8a, the tension cords are pulling in different
directions, but a resultant tensional force develops (large arrows)
which is dependent on the size and direction of the contributing
tensions (the ‘parallelogram of forces’ in mechanics terminology).
Starting with the left temporal: the tension pulls the left parietal
(indirectly here) towards the left temporal in the direction of the
resultant force. At the same time, the left parietal is pulling on the
right parietal through the same mechanism, and this in turn is pulling
on the right temporal. The consequence of all this is brought together
in figure 8b, showing the same bones arranged in a circular
anatomical sequence, the resultant tension pulling on each bone in
turn, passing around the circle, and ultimately pulling on itself –
‘continuous tension’. Before running away with thoughts of perpetual
motion, it must be pointed out that an equal and opposite tensional
force will also be pulling in the opposite direction with the effect of –
zero – nothing happens! This same isometric tension is acting across
all the sutures in 3 dimensions, and because it is a tensegrity
structure, the consequence is that all the tensional forces are
balanced, the bones appear to float, and unless acted upon by another
force, the structure will remain as it is. The precise placement and
directions of the tensions is extremely important if the structure is to
maintain itself as described, and is detailed later. While the simple
6-strut model is useful for demonstrating tensegrity, such structures
can be made using any number of compression struts from two upwards,
with the compression members remaining distinct from each other.
45
The
model was constructed from a full size plastic adult skull obtained
from a medical suppliers and cut into the individual bones using a fine
coping saw, with the exceptions of the facial bones which remain as a
unit with the sphenoid. Although the intricacies of the serrate sutures
could not be followed exactly, comparison with a real bone skull
confirmed their essential similarities for the purpose described. Holes
drilled at the bone perimeters were threaded with an elastic cord, as
used in textile manufacture.The tension cords are positioned so that
they illustrate the nature of the tensegrity structure and do not
necessarily follow any particular anatomic structure. However, during
positioning of the attachment holes, it became apparent that they should
be as close to the edge as possible in order for the structure to work
effectively. It was also evident that the various curves of the bone
edges, in all three dimensions, facilitated a separation of the bones by
making alternate attachments between the peaks of opposing bone edge
convexities (fig 9a).
DISCUSSION
One of the difficulties found in constructing this model was the
unexpected vault shape changes caused by adjusting individual cord
tensions. Tensegrity structures have visco-elastic properties similar to
biological structures, and this can cause them to behave unpredictably
because of a non-linear relationship between stress and strain.
9,35,46 A summary of some of the significant mechanical aspects of tensegrity design and how they apply to the human skull follows:
3.1. Stability
Stability is achieved through the configuration of the
whole network,
and not because of the individual components. The model describes a
mechanism whereby the calvarial shape could be maintained independently
of any outward-pushing pressure from the brain within,
1-6 a
position currently unresolved. The sutures remain under tension (tension
being necessary for regulating bone growth), while the bones remain
mechanically distinct from the brain, being influenced through cells of
the dura mater to expand. It is likely that the vault shape of the early
foetus would be reliant on the expanding brain pushing outwards on the
ectomeninx,
2,4,10 but tensegrity could become a significant
factor after 8 weeks, as ossification stiffens the membranous tissue and
transfers tensional stresses across the developing bone (fig 8a).
23
Chondrification would transform the base into a more 'geodesic dome'
structure with greater stability (fig. 3a), and reorient certain vectors
of growth influencing the greater expansion of the vault.
1,2
During construction of the model, it became evident that it would only
work effectively if the tension cords were attached near the edges of
the bone. In children, the strongest attachments of the dura mater are
also around the bone margins, suggesting that this may be significant
and congruent with the mechanism being modelled.
20 Continuity
of dural tension is thus maintained beneath the bone and may affect
intercellular signalling from one side to another. Firmer attachments of
dura mater in the centre of adult bone would not affect the tensegrity
principle, but implies a change in that signalling, and may influence
the lack of bone healing capability in the skull after early childhood.
It must be emphasized that this model describes a structural mechanism
which may be functioning in living tissue. It would not work in
preserved skulls or cadavers where sutural and dural tissues have lost
their elastic resiliency, and the structure becomes fixed under
continuous compression (Figure 8c).
3.2. Balance
The tension and compression components are balanced mechanically
throughout the entire structure, which will optimize automatically so as
to remain inherently stable. The various curves of the bone edges, in
all three dimensions, facilitate a separation of the bones through
alternate tension attachments between opposing bone edge convexities
(fig 9a). The attachments on either side naturally settle along the
tension line. Consequently, if those attachments are at the peak of each
convexity, the bones will be pushed apart in a direction perpendicular
to the tension force, and held there. Directional tensile stresses in
the dura mater and collagen fibre orientations have been found.
9,18-20
For example, symmetrical fibre orientations in the temporal regions
were observed to be 6.3 degrees +/- 0.8 degrees in respect to the
sagittal suture.
18 At a different size scale, figure 9b
demonstrates the same principle in a serrated suture. The serrate
sutures increase the surface area between adjacent bones because of
their interlocking projections, but the tension attachments holding the
bones apart, as described above, would also decrease the potential for
sutural compression in this model. [Since the publication of this paper,
it has been shown that tensioned collagen fibres within the sutures are
aligned such that they resist compression, as described here. Jasinoski
SC, Reddy BD, Louw KK, Chinsamy A. 2010 Mechanics of cranial sutures
using the finite element method. Journal of Biomechanics 43:3104-3111.]
In figures 9a and 9b the tension cords are causing the bones to be
pushed apart. This is strange behaviour indeed, considering that tension is generally noted for
pulling,
and not pushing. It underlines how the non-linear relationship between
stress and strain in tensegrity and biological structures could be
brought about. Conflicting forces resolve themselves by taking
the
paths of least resistance, eventually settling into a stable and
balanced state of minimal energy. However, a living organism has a field
of force dynamics which are in a continuous state of flux, so that
stability and balance are constantly changing (if that is not a
contradiction in terms).32,47,48
Cells of the dura mater respond to brain expansion and influence bone
growth, allowing the cranium to match the spatial requirements of the
developing brain, whilst remaining one step ahead and retaining a
certain autonomy.
1-6 This position renders the vault more
adaptable to other functional requirements, such as the demands of
external musculo-tendinous and fascial attachments.
7,21A
tensegrity cranium balances its stability through all stages of
development, by allowing small and incremental changes compatible with
the mechanical demands of all connected structures.
3.3. Energetically efficient
Energetically efficient means it has maximum stability for a given
mass of material. The geodesic dome can enclose a greater volume for
minimal surface area, with less material than any other type of
structure apart from a sphere. When the diameter of a sphere doubles,
the surface area increases 4 fold and the volume increases 8 fold, which
makes it materially very efficient. The entire structure of the model
neurocranium resembles a sphere-like geodesic dome (fig. 3a), with a
dural ‘skin’ under tension and bones enmeshed as an endoskeleton. In
mechanical terms, a tensegrity structure cannot be anything other than
in a balanced state of minimal energy throughout.
35,45
3.4. Integration
In
a tensegrity structure, a change in any one tension or compression
element causes the whole shape to alter and distort, through reciprocal
tension, distributing the stresses to all other points of attachment.
29,30,32,35-41
In this model, the occiput is fixed at the condyles whilst the sphenoid
exerts an elastic compression through the spheno-basilar synchondrosis.
Apart from this, the frontal, ethmoid, sphenoid, occiput, temporals and
parietals do not make direct contact with each other at any point
(‘discontinuous compression’), and are suspended all around (‘continuous
tension’) (fig. 8). It has been known for a long time that cranial base
dysmorphology may be fundamental to the aetiology of premature suture
closure.
1,2
The cartilage growth plates in the chondrocranium
have been shown to respond to mechanical stresses, although normally
the spheno-basilar region is the only one to remain metabolically active
for very long after birth, and remains so until adolescence.
6,49,50 The dural sheets connecting across the neurocranium short cut mechanical stresses from one part to the other
1
- the falx cerebri/cerebelli linking the ethmoid, frontal, parietals
and occiput; and the tentorium cerebelli linking the sphenoid, temporals
and occiput with the falx along the straight sinus. [The wire model
shown is an extra figure, and the shapes correspond to the edges of the
inner bone surfaces. All the 'bones' in this model remain separated
because of the tensegrity configuration.]
The icosahedron has several attributes that are advantageous for modelling biological structures.
35,36
A full account is beyond the scope of this paper, but a few significant
points are worth mentioning. It is fully triangulated, which is the
most stable of truss configurations (figure 3a); it comes closest to
being spherical, with the largest volume to surface area ratio of all
the regular polyhedrons - making it materially efficient; its surfaces
can be divided equally into smaller triangles and the structure scaled
up into higher frequencies - making it even more energetically
efficient;
43-45 it provides a link between close-packing in 2
and 3 dimensions; and as a fractal generator, it can polymerize into a
sheet, stack in a column or helix, and create complex patterns and
shapes. Fractal analysis is commonly applied to natural structures.
Their formal definition is rather obtuse for the purposes of this paper,
but a working definition could be: ‘A shape or pattern which evolves as
it changes, reappearing in a hierarchy of different size scales’.
Although the frequencies and amplitudes of the ‘wave’ curvatures seen at
the bone edges in figures 9a and 9b vary, they are both examples of a
fractal nature – with a similar pattern appearing at different size
scales.
51 Fractals are probably relevant to linking structural hierarchies throughout the body,
2,32,35,36
thus making the icosahedron particularly versatile, because it also
gives rise to structures with geodesic dome and tensegrity properties.
As
the vault bones approximate each other, a sort of hybrid geodesic
dome/tensegrity structure would provide the required rigidity for brain
protection, but with the facility for micro-mobility at the sutures.
1,2,15 Tensegrity
in the cranium allows for flexibility during development, and whatever
other functions that patent sutures might serve beyond cranial
expansion.
4,7,15,21 [It is likely that this explains some of
the underlying mechanisms described by 'cranial' osteopaths.] The
cranial base naturally develops a geodesic structure and provides a
platform from which the vault bones could expand, through tensegrity, to
accommodate brain growth. If the transfer of tensional forces in the
dura mater, and the suggested mechanisms illustrated in figure 9 really
do form an essential part of sutural patency, an aberration in this
system which leads to compressive bone contact at any point could be one
step towards a rigid geodesic dome cranium.
1,5,15 This may explain why cartilage sometimes appears in sutural joints.
1,14
A local tensional stress generated within the cellular cytoskeleton
could transfer to the extracellular matrix of the dura mater and produce
effects on other cells at some distance, with structural rearrangements
throughout the network. Long-distance transfer of mechanical forces
between different tissues could contribute to dural development, and be
responsible for spatially orchestrating bone growth and expansion.
3,28,29,30,32,34,47,49,52
Similarly, an ‘aberrant’ tensile stress from elsewhere in the cranium
could exert its effects on sutures some distance away, and contribute to
a change in interactions between the dura mater, bones and brain,
ultimately leading to premature synostosis.
1,2
CONCLUSION
The
tensegrity model is a novel approach to understanding how the cranial
vault could retain its stability without relying on an expansive force
from an underlying brain, a situation currently unresolved.
1-6
Tensional forces in the dura mater [and suture] have the effect of
pushing
the bones apart, whilst at the same time integrating them into a single
functional unit. Sutural patency depends on the separation of cranial
bones throughout normal development, and the model describes how tension
in the dura mater achieves this, and influences sutural phenotype.
Cells of the dura mater respond to brain expansion and influence bone
growth, allowing the cranium to match the spatial requirements of the
developing brain, whilst remaining one step ahead and retaining a
certain amount of autonomy. Tensegrity may also be an integrating
mechanism in a hierarchical structure that extends from the cell to the
whole organism, with complex 3D patterns the outcome of a network of
interactions which feedback on each other.
2,29,30,32,36-40,47,52 This provides a context for this model and could indicate a new approach to understanding the pathologies seen in the neonate.
One of the most significant aspects of biology is the efficiency with
which it packs multiple functions into minimal space. This presents a
conundrum in physical modelling, as any structure will inevitably be
limited in its behaviour if it is incomplete or in isolation. It must be
emphasized that much of the supporting evidence for this model is
circumstantial, and more research is needed to verify it, but it is
compatible with current understandings of cranial physiology, and has a
contribution to make to a hierarchical systems approach to whole body
biomechanics.
Acknowledgement
I wish to express my sincere appreciation to Nic Woodhead, Chris
Stapleton and Andrea Rippe, for their contributions and thoughts during
discussions in the preparation of this paper.
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. The arrangement of scales in the pangolin and snake 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 geodesics 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. 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.
connecting opposite vertices. 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 (elastic cord in model) and configured as a tensegrity structure. The curved struts are at the top of a bone hierarchy (at least seven different levels within bone) that extends down to the molecular level (see definitions page).
and change cell activity that results in further bone growth. It is a cyclic mechanism that regulates bone growth and maintains sutural patency up until at least seven years of age (when the brain stops growing). Even after this age the sutures should remain patent and may contribute to the small amounts of bone mobility recognized by 'cranial' osteopaths and 'cranio-sacral' therapists.
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 is 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. It is the regular spacing and orientation of these crystallite units and hierarchical structure that suggests that it is a tensegrity structure.
where load bearing across the joint may be significantly tensional and allow compressional forces to be distributed through a tensioned network and the hand to lift loads much larger than would otherwise be the case (see the elbow page).
move as a single entity. 
six struts of a T6-sphere. 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 hierarchy where the next level above is comparable to the metal plates of the original TJ 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 movement of a tensegrity joint can cause other joints to move passively at a basic level and that muscles just refine that movement further down the chain as a higher active 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.
avoiding points of potential weakness, in contrast to a rod or truss which 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.
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.