Tensegrity Skull Model

Jeanine Looman1, Gabriel Venne2 DO, PhD, Dorothea Blostein3 PhD, Graham Scarr4 DO

Physical and Simulated Tensegrity Models of the Skull Bones and Fascia using CT Bone-Shape Data

1 Dept. Bioengineering, McGill University, Montreal, Canada.

2 Dept. Anatomy and Cell Biology, McGill University, Montreal, Canada.

3 School of Computing, Queen's University, Kingston, Ontario, Canada.

4 Independent Researcher, Nottingham, UK.



Assessing the mechanical response of the fascia and other soft tissues to physical forces has long presented a challenge because of the difficulties inherent within current methodologies. Finite-element modeling of the skull, for example, has placed an emphasis on the bones but not captured the physical differences between them and the intervening sutures[1-3]. We describe our ongoing research into modeling the mechanics of the skull using CT bone-shape data, CAD and simulation software[4]. Our model directly follows from a previous description of the cranial vault as a tensegrity structure[5]. This modeling has potential applications in concussion research, in the treatment of developmental pathologies of the skull, in investigations of fascial force transmission patterns, and in research into the mechanisms of cranial osteopathy/cranio-sacral therapy.


Accurate bone shapes were obtained through CT scanning of a disarticulated human skull. This data was used to create 3D printed replicas of the bones; these were assembled into a physical model of the neurocranium by using elastic membranes to represent the falx cerebri and tentorium cerebellum. The same CT-derived data was also imported into 3D CAD and ArtiSynth biomechanical modeling software. In Artisynth the bones were linked via elastic cables to create a simulated tensegrity model[6, 7]. The precise position and stiffness of each link was determined through iterated adjustments based on observed simulation performance, with the goal of achieving an equilibrium state of the tensegrity model that closely resembles the natural arrangement of the skull bones.


Surprisingly, the elastic membranes of the physical model were sufficient to maintain overall integrity, with the bony bevels stabilizing the sutures in a way similar to a jigsaw puzzle. In addition, the versatility of the simulated tensegrity model demonstrated that changes to a single parameter mechanically affect the entire structure, thus mimicking a characteristic similar to living tissues.


The ArtiSynth model demonstrates the capability of this software to model complex biomechanics through tensegrity, adding to a research field that is increasingly recognized for its novel descriptions of functional anatomy.[6-8]


Computational Head Models

Computational head models provide many benefits compared to classical physical experiments. They are easily adaptable, time and cost effective, provide more valuable information and are not limited by physical resources[9]. The most popular is the finite element head model (FEHM), which together with improvements in imaging and material testing are increasing the reliability and complexity of computational analysis. Such models, however, use a single, rigid body to simulate the skull [3, 9, 10] and are unable to capture the flexibility inherent in sutural patency, which naturally limits their mechanical analysis.


Postnatally, the timing of normal sutural fusion shows considerable variation, with the metopic suture fusing completely within 7 months (67% of children)[11], the lateral and basilar parts of the occiput within 7 years[1], and most of the remaining sutures fusing inconsistently from the third decade onwards. The premature fusion of the cranial sutures in early childhood (craniosynostosis) can have significant cosmetic consequences (head shape) as well as severely impairing normal sensory, respiratory, and neurological function, and in extreme cases leads to blindness[12-14]. Surgical correction is often required and increasingly relies on 3D models for planning and improving outcomes[15]. As knowledge of the biomechanical forces involved in development of the cranial vault remains incomplete, FEHMs that take sutural flexibility into account could provide important information in the planning of surgical treatments[2, 12].

Children below the age of 10 are also in the highest incidence category for traumatic brain injury (9 per 1000 in the US (2010)), and a more complete understanding of concussion and cranial mechanics would be likely to improve their management[16], as well as supporting the methods of cranial osteopathy, craniosacral therapy, and fascial research in general.


The term ‘tensegrity’ refers to an architectural framework that consists of a set of discrete compression elements suspended within a continuous network of tensioned elements, and is increasingly recognized in biological research because of its characteristics that are similar to living tissues in many ways.[6-8] Such structures are flexible, resilient, have a high strength/weight ratio, and the ability to remain intrinsically stable throughout changes in shape – properties well-suited to a developing skull[5].


Acquisition and Segmentation of CT data

A disarticulated human skull (private collection) was CT scanned at a slice thickness of 0.625 mm with a General Electric LightSpeed þ XCR 16-slice CT scanner (GE Healthcare, Milwaukee, WI, USA) at Kingston General Hospital Imaging center, Ontario. The CT scan data of the entire disarticulated skull was imported into commercially available Mimics software (Materialise, Leuven, Belgium) in order to segment the bones. A combination of automated and manual segmentation was used to create a separate .stl file for each bone.

Graham Scarr 3D Printed Model Graham Scarr Wireframe Model Elastic Placement in Fusion360

Figure 1: (left) Physical tensegrity models of the cranial vault (Scarr, G. 2018 ©Handspring), and (right) the 3D CT scan data imported into Fusion360, showing the planning of the connections.

The 3D CT reconstructed models of individual bones were assembled in Fusion 360[17]. This software was also used to plan initial placement of tensile connections, based on physical models and a previous study of the cranial vault as a tensegrity structure (refer to figure 1) [5].

Simulating the Tensegrity Structure in ArtiSynth

The computational model was created by transferring the 3D data into ArtiSynth[4], making use of custom code to maintain the positions of bones and connections. The data in ArtiSynth was imported from .stl files into a Polygonal Mesh format. A program was written to interact with ArtiSynth and the model, allowing easy manipulation of key factors such as the material properties of the simulated bones and their connections. The Artisynth user interface was used to adjust of the location of connections.

In the Artisynth simulation, connections are elastic cables that link the bones to form a tensegrity structure. In Figure 2, connection attachments are shown as red spheres. The connections are purely tensile components with a resting length of zero. Resting length is defined as the minimum length at which the connection exerts a tension force. The magnitude of the tension force is proportional to the amount that the connection’s current length exceeds the resting length.

During Artisynth’s physics simulation, the tension forces in the links cause them to elastically shorten, thus moving the bones from their expanded initial position to an equilibrium state. We iteratively adjusted the position and stiffness of links in order to achieve an equilibrium state of the tensegrity model that closely resembles the natural arrangement of the skull bones (Figure 2).

Force Abstraction

In this simplified initial model, the bones have homogenous material properties, with linear connections providing a simplified equivalent to the tensional force within a continuous elastic sheet of connective tissue in vivo (Dural membrane). In future work we plan to modify the simulation to include known literature values relating to the mechanical properties of bones, dura mater and sutural ligaments.

Discussion & Future Work

Simulation in ArtiSynth Simulation in ArtiSynth

Figure 2: Initial and final frames of the physics simulation performed by Artisynth.


The novelty of this computational model is that it includes the sutures within the biomechanical analysis. The model demonstrates that tensegrity principles lead to an equilibrium state that closely resembles the natural arrangement of skull bones. Thus, tensegrity provides an alternative to the traditional view that in utero and in infancy the cranial vault expands through an outward-pushing pressure from the growing brain. The tensegrity model illustrates an alternative hypothesis that it is the dura mater that creates the separation between bones[5]. The model demonstrates the counter-intuitive result that dura mater (even though it is under tension) can act to create separation between the bones, while maintaining proper anatomical relationships between the bones.

3D Printed Physical Model 3D Printed Physical Model 3D Printed Physical Model

Figure 3: 3D Printed physical model.

Model Validation

The intention of this work was to demonstrate the capability of physics simulation software[4] in modelling the bones and sutures of the skull as a tensegrity structure. The model has not yet been specifically validated apart from the observations made above. Currently, head-impact models are validated by comparing experimental data from simulations with corresponding physical experiments. The physical experiments range from the use of cadavers to reconstructed physical models, and include the measurement of accelerations and pressures at various locations on the cranial vault during impact[3, 10]. There is also cadaveric data on the effect of facial impact, intracranial ventricular pressure, and brain displacement relative to the skull[18], and these could be included in future models. Further improvements could model the skull bones as multiple layers to represent the non-homogeneous material variations that occur within skull bones in vivo. ArtiSynth can also track acceleration and pressure from different points within the model[4], thus enabling the replication and comparison of many different impact and acceleration scenarios.


The computational ArtiSynth model consistently reaches an equilibrium state that closely resembles the natural arrangement of the skull bones. This demonstrates that tensegrity provides a viable structural framework that could be incorporated into new computational head models, thus furthering the understanding of cranial vault development, traumatic brain injuries and therapeutic protocols.


[1] S. Celik, C. Tomruk, D. E. Tanriover, Y. Uyanikgil, O. Bilge, and M. Turgut, "Embryological and Histological Features of the Cranial Sutures," in The Sutures of the Skull: Springer, 2021, pp. 19-42.

[2] J. Libby, A. Marghoub, D. Johnson, R. H. Khonsari, M. J. Fagan, and M. Moazen, "Modelling human skull growth: a validated computational model," Journal of the Royal Society Interface, vol. 14, no. 130, p. 20170202, 2017.

[3] E. G. Takhounts, R. H. Eppinger, J. Q. Campbell, R. E. Tannous, E. D. Power, and L. S. Shook, "On the development of the SIMon finite element head model," SAE Technical Paper, 2003.

[4] J. E. Lloyd, I. Stavness, and S. Fels, "ArtiSynth: A fast interactive biomechanical modeling toolkit combining multibody and finite element simulation," in Soft tissue biomechanical modeling for computer assisted surgery: Springer, 2012, pp. 355-394.

[5] G. Scarr, "A model of the cranial vault as a tensegrity structure, and its significance to normal and abnormal cranial development," International Journal of Osteopathic Medicine, vol. 11, no. 3, pp. 80-89, 2008.

[6] G. Scarr, "Biotensegrity: What is the big deal?," Journal of Bodywork and Movement Therapies, pp. 134-137, 2020.

[7] S. M. Levin, "Tensegrity: the new biomechanics," Textbook of Musculoskeletal Medicine., pp. 150-162, 2015.

[8] C.-M. Boghdady, N. Kalashnikov, S. Mok, L. McCaffrey, and C. Moraes, "Revisiting tissue tensegrity: Biomaterial-based approaches to measure forces across length scales," APL bioengineering, vol. 5, no. 4, p. 041501, 2021.

[9] K. M. Tse, S. P. Lim, V. B. C. Tan, and H. P. Lee, "A review of head injury and finite element head models," Am. J. Eng. Technol. Soc, vol. 1, no. 5, pp. 28-52, 2014.

[10] F. Turquier et al., "Validation study of a 3D finite element head model against experimental data," SAE transactions, pp. 1912-1923, 1996.

[11] H. L. Vu, J. Panchal, E. E. Parker, N. S. Levine, and P. Francel, "The timing of physiologic closure of the metopic suture: a review of 159 patients using reconstructed 3D CT scans of the craniofacial region," Journal of Craniofacial Surgery, vol. 12, no. 6, pp. 527-532, 2001.

[12] E. P. Buchanan, Y. Xue, A. S. Xue, A. Olshinka, and S. Lam, "Multidisciplinary care of craniosynostosis," Journal of Multidisciplinary Healthcare, vol. 10, p. 263, 2017.

[13] D. Johnson and A. O. Wilkie, "Craniosynostosis," European Journal of Human Genetics, vol. 19, no. 4, pp. 369-376, 2011.

[14] M. L. Moss, "Functional anatomy of cranial synostosis," Pediatric Neurosurgery, vol. 1, no. 1, pp. 22-33, 1975.

[15] N. R. Saber et al., "Generation of normative pediatric skull models for use in cranial vault remodeling procedures," Child's Nervous System, vol. 28, no. 3, pp. 405-410, 2012.

[16] J. D. Corrigan, A. W. Selassie, and J. A. L. Orman, "The epidemiology of traumatic brain injury," The Journal of head trauma rehabilitation, vol. 25, no. 2, pp. 72-80, 2010.

[17] Fusion360. (2022). Autodesk Inc. [Online]. Available: https://www.autodesk.ca/en/products/fusion-360/overview

[18] L. Zhang et al., "Recent advances in brain injury research: a new human head model development and validation," Stapp Car Crash Journal, vol. 45, 2001.