Read here about research into how tensegrity can help explain many aspects of the birth process.
While there is little literature applying biotensegrity concepts to the organism as a whole in the process of birth, the behavior of meiosis, uterine muscle tissue, spindle fibers, and the orthogonal positioning of the centrioles in all animal cells indicates that such research may bear fruit.
The female uterus is better explained by a tensegrity structural anatomical model than the traditional, classical Newtonian model. As Levin wrote, " If governed by simple Newtonian mechanics, urinary bladders will burst when full, pregnant uteruses will rupture with strong contractions, and, with each heartbeat, arteries will lengthen enough to crowd the brain out of the skull." 
Myofibroblasts (MFBs) are cells that exert clinically significant contractile force in particular circumstances. They play a critical role in normal mammalian birth, being present in the ovaries and uterus .
Tom Myers writes in Anatomy Trains, MFBs play a key role in birth. These cells occur in healthy fascia, and in fascial sheets in particular--such as the lumbar fascia, fascia lata, crural fascia, and plantar fascia. They have also been found in ligaments, the menisci, tendons, and organ capsules. The density of these cells may vary positively with physical activity and exercise, but in any case, the density is highly variable among people.
Myers wrote that one very surprising aspect of these cells is that their contraction--unlike every other muscle cell in the body, smooth or striated--is that they are not stimulated to contract via the usual neural synapse. Therefore they are beyond the reach of conscious control, or even unconscious control as we would normally understand it. The factors that induce the long-duration, low-energy contraction of these cells are 1) mechanical tension going through the tissues in question, and 2) specific cytokines and other pharmacological agents such as nitric oxide (which relaxes MFBs) and histamine, mepyramine, and oxytocin (which stimulate contraction). Unexpectedly, neither norepinephrine or acetylcholine (neurotransmitters commonly used to contract muscle), nor angiotensin or caffeine (calcium channel blockers) has any effect on these MFBs. Many MFBs are located near capillary vessels, the better to be in contact with these chemical agents... The manner in which the MFB contacts and tenses the fiber matrix of the ECM is instructive, and will lead us into the wonderful world of tensegrity on a cellular level.
Regular fibroblast cells contain actin, as do most cells, but they are incapable of mounting the degree of tension or forming the kinds of intracellular and extracellular bonds necessary to pull significantly on the ECM (Fig 1.71A). Under mechanical stress, however, the fibroblast will differentiate into a proto-MFB, which builds more actin fibers and connects them to the focal adhesion molecules near the cell surface (Fig. 1.71B). Further mechanical and chemical stimulation can result in full differentiation of the MFB, characterized by a complete set of connections between the fibers and glycoproteins of the ECM through the MFB membrane into the actin fibers connected with the cytoskeleton (Fig 1.71C).
The contraction produced by these cells--which often arrange themselves in linear syncitia as muscle cells also do, like boxcars on a train - can generate stiffening or shortening of large areas in the sheets of fascia where they often reside (Fig. 1.72).
This discovery, though still in its early stages in terms of research, promises myriad implications about the body’s ability to adjust the fascial webbing. This form of ‘pre-stress’--a middle ground between the immediate contraction of pure muscle and the fiber-creation remodeling shown by the pure fibroblast - can prepare the body for greater loads or facilitate transfer of loads from one fascia to another. In terms of the responsiveness of fascia, we see a spectrum of contractile ability from the instant and linear pull of the skeletal muscle through the more generalized spiral contraction of the smooth muscle cell on into the varying degrees of MFB expression to the more passive but still responsive fibroblast at the other end of the connective tissue spectrum.
Given how these MFBs can be stimulated by mechanical (fibrous) loading or by fluid chemical agents, we can also discern in this system the dance among the neural, vascular, and fibrous web that goes into making what we have here termed ‘Spatial Medicine’, how the body senses and adapts to changes of shape caused by internal or external forces.
Returning to our discussion of tensegrity, we introduced the myofibroblasts at this point because they show how the body can alter the ‘pre-stress’ of the body’s tensegrity to stiffen it for greater loading. Because of the time involved, there has to be an anticipation of further stress and loading to put the contraction in place. Thus one is tempted to question whether emotional stress can induce similar loading and MFB response, creating a generally ‘stiffer’ (literally), less sensitive (interstitial sensory nerve endings would be rendered inert), and less adaptable person biochemically.
Moving to the other end of the scale, this discussion also leads us to how microtensegrity works to connect the entire inner cell workings to the ECM of the fascial net. It is not only MFBs that are capable of hooking up to the ECM. On this microscopic level, the tensegrity applications are more unambiguous, and have every promise of revolutionizing our approach to medicine by bringing to the fore the spatial and mechanical aspect as a complement to the predominant biochemical view.
The cytoskeleton is shown by Ingber to have many properties best explained by tensegrity. For example, "Internal microtubule struts are used to stabilize local regions of the cytoplasm to stiffen the mitotic spindle." 
The cytoskeleton performs critical functions in birth. These include meiosis (division of duplicated chromosomes in sperm and egg cells), sperm motility, mitosis, cell proliferation, cell migration and changes in cell shape which accompany differentiation, the expression of cell form and function.
Hameroff wrote, "The cytoskeleton is crucial to all steps in reproduction, growth, trophism and differentiation. If chromosomes are maldistributed in meiosis or mitosis, nonviable or abnormal offspring can occur. Such maldistribution may be related to cytoskeletal dysfunction, an early theory for the cause of cancer. Variability in tubulin isozymes and MAPs could explain tissue and cell specificity based on differences in the molecular composition and activities of the cytoskeleton." 
Some fertile areas of speculation.
Compression and tension in birth
In mammalian birth, alternating waves of tension and relaxation, called labor in human birth, enforce a rhythmic sequence of signaling to pass from the uterus to the fetus being born. This compresses and expands the infant's tensegrity structure, see the portal to structural anatomy.
While the connection is dubious, it is at least amusing to see tensegrity cited in the patent below.
Glenn Austin and Lisa Tam of Seattle, Washington, filed US patent 7047975 for a female birth control device that employs tensegrity. From the patent text: "The female condom is configured such that when the condom is inserted into a woman's vagina, the woman's introitus acts on a proximal section of an elongated pouch extending between internal and external biasing members (e.g., rings) of the condom. Inward compressive forces exerted by the introitus on the inner ring of the condom cause the inner ring to be pushed distally within the vaginal canal, and the proximal pouch section to become a tension member pulling against the external ring. This causes a 'tenting' of the proximal pouch section against the introitus. The resulting interaction of compression and tensile forces (a tensegrity effect) serves to provide the condom with a high degree of internal and external stability, including resistance to twisting and slippage." See http://www.freepatentsonline.com/7047975.html
Links and References
 Opposing Views On Tensegrity As A Structural Framework For Understanding Cell Mechanics By Donald E. Ingber, Steven R. Heidemann, Phillip Lamoureux, And Robert E. Buxbaum, J Appl Physiol 89:1663-1678, 2000.
 Biomolecular Consciousness and Nanotech by Hameroff
 Levin, The Tensegrity-Truss as a Model for Spine Mechanics: Biotensegrity, citing Morris, J. M. and Lucas, D B (1964), Biomechanics of spinal bracing, Arizona Medicine 21:170-176.
 Schleip wrote, "Compared with striated muscle cells, smooth muscle cells offer a more efficient transformation of chemical energy into mechanical strength. It has long been known that fibroblasts often transform into myofibroblasts which contain smooth muscle actin fibers and can therefore actively contract.... MFBs are found regularly in healthy skin, in the spleen, uterus, ovaries, circulatory vessels, periodontal ligaments and pulmonary septa. " Fascial plasticity – a new neurobiological explanation, Part 2, by Robert Schleip, Journal of Bodywork and Movement Therapies (2003), doi:10.1016/S1360-8592(02)00076-1