Our bones: strength, lexibility and…fractals!

The combined hardness and toughness of bone cannot be explained by the mere mixture of proteins and calcium phosphate mineral. To solve this conundrum, a deeper insight into the structure of this remarkable material is required. Using advanced three-dimensional nanoscale imaging of the mineral in human bone,


I ma g e c r e d i t s : P i x a b a y -CC0
Each of us has a skeleton -that is ordinary. However, the bone of which a skeleton is made is anything but ordinary. From an engineering perspecive bone provides an incredibly versaile support structure that performs remarkably well in a circus contorionist, a sumo wrestler, a toddler who is climbing up a bookshelf, and in the toddler's grandfather leaping forward to prevent a bonebreaking fall. However, ater fracture, bones can heal without traces, and they are preserved as fossils for millions of years. Unil adulthood, bones increase in size a thousand-fold. But ater all, bones consist of abundant bioavailable elements such as calcium, phosphorus, and carbon. The secret of bones is that they are both strong and lexible at the same ime. In fact, many biological objects are strong and lexible: for example, wood, antlers, spider webs. Over millions of years of evoluion, nature developed a strategy to obtain maximal funcional eicacy from the cheapest inventorysomething called "hierarchical organizaion".
How do we study hierarchical materials? One important point is to keep track of the context of observaions. With modern characterizaion methods, it is possible to image at high magniicaion and thus to idenify details all the way down to the level of individual atoms. However, our high-resoluion informaion only makes sense if we know about its hierarchical context. Like when using The combined hardness and toughness of bone cannot be explained by the mere mixture of proteins and calcium phosphate mineral. To solve this conundrum, a deeper insight into the structure of this remarkable material is required. Using advanced threedimensional nanoscale imaging of the mineral in human bone, we highlighted the importance of its structural organizaion.
interacive maps, zooming into a beauiful remote town you want to visit won't help you to get there unless you also carefully look at the roads that lead to that town. In materials science, an important tool used for precise sampling is a focused ion beam coupled to an electron microscope. The ion beam acts as a ine knife and cuts samples a few hundred atoms thick from an interesing area of a larger specimen. This smaller sample from a known locaion and context can be further used for highresoluion imaging. The second crucial factor in the research of hierarchical materials is that all such materials are three-dimensional. Therefore, in order to understand and correctly interpret imaging data, it must obtained in 3D. An important technique for this is electron tomography, where a iny sample as thin as one thousandth of the thickness of a human hair is imaged in a sequence of hundreds of projecions, each one being slightly rotated with respect to the other. These projecion images can be digitally assembled into a 3D image of the object − this digital replica can then be viewed from any angle at any level and analyzed in detail.
In fact, our ability to combine these modern methods of sampling and imaging into a smooth worklow became possible only fairly recently. For more than 300 years bone is known to be hierarchically structured (the irst descripion of 5 levels of bone hierarchical organizaion was made by the English surgeon and scienist Clopton Havers in 1691). When we obtained a iny specimen of bone from a known locaion and of a known orientaion, and when we looked at the bone crystallites with the aim of revealing their 3D shape and size, we discovered that these crystallites were already hierarchical at the nanometer scale (one billionth of a meter)! Moreover, the thin crystals were slightly curved, like delicate petals splaying away from the pedicle, or like loosely braided hair.
Beyond this, the hierarchy repeated itself: curved and needle-shaped crystals were merging sideways into a platelet (like ingers and a palm), and several platelets were stacked together (like 2, 3 or 4 hands pressed together). These intricate hierarchical aggregates merged and further split.
When zooming out whilst recalling the context of these curved crystallites in bone, an intriguing picture emerges: enire bones such as a rib, or the collar bone, have a clearly twisted shape, as the grooves and ridges in long bones follow a slight screw-like course. Tiny capillaries, which nourish the bone, pierce the bone shat with a delicate, screwlike trajectory. Around the capillaries, bone material is organized into osteons − concentric layers, reminiscent of leek stems. These layers are made of narrow bundles twising around the central capillaries with a varying angle. The bundles are composed of mineralized collagen ibrils gently twising around the bundle axis, like threads of a rope. Collagen is a ibrous protein that exists in triple helices, and the mineral crystallites, as our study showed, are also twisted. Thus, the organizaion of bones is self-similar, with the repeaing patern being a helix. Therefore we call this organizaion of bone fractal-like.
At all levels, the organizaion of bone components follows a helical moif. This makes bone both resilient and strong, as is essenially required in real life so that indeed the toddler could fall from the shelf, and the grandfather would drop his newspaper and leap towards the baby, and both would not sustain skeletal injuries. Nature endlessly reuses successful design strategies, and skeletons are not an excepion: down to the bone, we are fractals.