Fractal Geometry for Biomimetic Design of Biodevices - Advanced Design and Manufacturing Technologies for Biomedical Devices - page 108

Fig. 6.10 Scheme for fractal-based biomimetic design of biodevices (Patent pending: Spanish
Patent and Trademark Office P201030957)

as well as microsystems for studying cell motility can be found in Chaps. 10 , 11 and
12 , when focusing on the manufacture of biodevices with micro- and even
nanofeatures.
Until now the chapter has focused on the design process of biodevices based on
fractal surfaces, thus leading to textured devices but with an overall geometry
clearly “planar”, which may be somehow limited for obtaining three-dimensional
implants and prostheses.
Fractal models may also be of help for reproducing the spatial morphology of
tissues and organs and for providing a way of controlling aspects such as porosity,
surface/volume ratio, stiffness…, which are decisive for promoting some chemical
reactions and biological processes.
We would like to introduce here the use of “fractal spheres” or “fractal seeds”,
whose distribution for filling the 3D space and subsequent Boolean combination
with the solid object of a prosthesis, organ or structure can lead to three-dimensional
porous structures for being used as support for 3D cell growth, both in tissue engi-
neering and in the novel field of biofabrication.
The process is schematically described in Fig. 6.11 and is based on combining
“fractal spheres”, which can be defined by the equations detailed below. A fractal
sphere, by adapting the definition of fractional Brownian fractal surface, can be
defined by an almost randomly changing radius in the form:

∞
∑

− a k k

rx r C xA
k

() =+ • l • sin( l • + )

0 k

k = 1