BIOMIMETIC COMPUTER-AIDED DESIGN AND

MANUFACTURE OF COMPLEX BIOLOGICAL SURFACES

Andrés Díaz Lantada, Pilar Lafont Morgado, Javier Echávarri Otero, Enrique Chacón Tanarro,

Eduardo de la Guerra Ochoa, Juan Manuel Munoz-Guijosa and José Luis Muñoz Sanz

Grupo de Investigación en Ingeniería de Máquinas – E.T.S.I. Industriales – Universidad Politécnica de Madrid,

C/ José Gutiérrez Abascal, nº 2. 28006, Madrid, Spain

Keywords: Biological Systems Modeling, Computer-aided Design, Biomimetics, Computational Geometry, Fractals,

Surface Topography.

Abstract: Conventional computer-aided design software does not yet provide special tools oriented to modeling the

complexity of biological systems, as such programs are mainly developed for promoting information

exchange in tasks related to industrial design and to parts with regular smooth surfaces. The process

explained in this study allows defining and precisely controlling the topography of surfaces from the design

stage, with help of computer-aided design tools. Its application to obtaining a biomimetic surface based on

the leaves of the Lotus flower (Nelumbo nucifera), renowned for its outstanding self-healing and

tribological properties, is shown as example. Some reflections on potential remarkable applications, linked

to the development of implants and prototypes with applications in several industries, have also been

included.

1 INTRODUCTION

Several studies have focused on the importance of

surface topography and microtexture for promoting

positive effects in all kinds of biomedical devices,

from implantable prosthesis to extra-cellular

matrixes and scaffolds for cell growth and tissue

engineering. These textures have a significant

influence in osseointegration of prosthesis, cell

proliferation and tissue growth given that those cells

and tissues seem to be more “comfortable” and

spread more quickly when faced with biodevices

with similar surface properties.

In addition the use of biomimetic surfaces can

help to introduce numerous desirable phenomena in

machine, mechanical and structural elements, thus

improving contact between parts, reducing wear or

even obtaining self-cleaning objects. However, the

process of introducing desired roughness on the

surfaces of man-made objects is still mainly linked

to carrying out machining operations, laser

processing or chemical attacks. In all these cases,

post-processing operations can be difficult to control

and it would be very positive to directly impose

special topographies from the design stage.

The use of fractal models for mimicking such

natural surfaces can prove to be useful for design

tasks. Fractals are rough or fragmented geometric

shapes that can be split into parts, each of which is

(at least approximately) a reduced-size copy of the

whole. The term fractal was coined by Benoît

Mandelbrot in the late 1970s / beginning of 1980s

and derives from the Latin fractus meaning “broken”

or “fractured” (Mandelbrot, 1982). The term is used

to describe complex geometries that are too intricate

to be formulated in conventional Euclidean terms,

with properties like self-similarity and defined

usually with simple recursive procedures.

Since the early works linked to fractal geometry,

it became clear that they could be used for

describing the geometries, patterns and roughness of

natural objects. Although fractals are commonly

considered to be infinitely complex (due to their

usual recursive definitions) “approximate fractals”

are easily found in nature, which usually display

self-similar structure over an extended, but finite,

scale.

By limiting the steps applied in a recursive

definition of a conventional fractal, approximate

fractals can be obtained, which mimic complex

natural geometries. Natural objects that are

approximated by fractals include clouds, mountains,

286

Díaz Lantada A., Lafont Morgado P., Echávarri Otero J., Chacón Tanarro E., de la Guerra Ochoa E., Munoz-Guijosa J. and Muñoz Sanz J..

BIOMIMETIC COMPUTER-AIDED DESIGN AND MANUFACTURE OF COMPLEX BIOLOGICAL SURFACES.

DOI: 10.5220/0003889002860290

In Proceedings of the International Conference on Biomedical Electronics and Devices (BIODEVICES-2012), pages 286-290

ISBN: 978-989-8425-91-1

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

lightning bolts, coastlines, snowflakes, various

vegetables and several corporal and animal

geometries (Mandelbrot, 1982, Falconer, 2003).

During the last decade, increasing attention has

been paid to using fractals for promoting modeling,

design and simulation tasks in several areas of

Bioengineering. The most remarkable ones include

“modelling the behaviour of microorganisms”

(Tsyganov, 2007), “modelling complex organisms

and their systems (including human anatomy)” (Lin,

2004) and “modelling the surfaces of organs and

tissues” (Longoni, 2010).

In fact, very recent interest has appeared in the

use of fractals for mimicking the surfaces of organs

and tissues and thus improving the designs and in

vivo performance of several prosthetic devices,

although some limitations linked to the design

procedure still have to be overcome.

The process explained in this study allows

defining and controlling the texture and roughness of

surfaces from the design stage, with help of

computer-aided design tools. Its application to

obtaining a biomimetic surface based on the leaves

of the Lotus flower (Nelumbo nucifera), famous for

its remarkable tribological properties, is shown as

example (Barthlott, 1997).

The mentioned computer-aided design,

calculation and manufacturing technologies (CAD-

CAE-CAM), have become essential tools for

developing products. They allow 3D geometries and

alternative designs (to which calculations of stress,

deformations, ergonomics, dynamic response can be

applied) to be rapidly manufactured.

Moreover, these technologies can also be

employed to test materials and designs. They can

also prove to be extremely beneficial when applied

to the development of biomimetic devices with

advanced properties, even promoting personalization

of devices and special contact phenomena.

2 DESIGN PROCEDURE: FROM

MATHEMATICAL SURFACE

MODEL TO SOLID CAD FILE

2.1 Combining Euclidean

and Non-euclidean Geometry

We propose and explain in this section the use of

mathematical fractal models for designing the

complex and highly irregular surfaces of biomimetic

objects. In this way, parameters such as roughness,

waviness, skewness can be controlled from the

design stage and adapted in a more efficient way to

the requirements of final application.

Final multi-scale surface z(x,y) can be considered

as the sum of two different surfaces (z

(x,y) and z

(x,y)), each providing a relevant component at a

different scale level. In our case, the microscopic

bump-like behavior of the Lotus flower leaves can

be approximated by using a regular surface defined

by z

(x,y), for obtaining 10 μm size details. For

introducing an additional level of precision

(irregularities in the range of hundreds of

nanometers) z

(x,y) proves to give positive results if

based on fractal models.

In this study we have selected a fractional

Brownian fractal surface model for z

(x,y), which

has previously proved to be useful when carrying

out designs of natural surfaces (Falconer, 2003). The

following equations give the height “z” of the

surface, when assessing the function over a grid of

points given by their (x,y) coordinates.

The model uses several random functions (A

, B

), several control constants (λ, α, k) and an initial

height function “z

” can also be introduced.

According to the model, fractal dimension “D” of

the generated surface can be obtained from the

expression “D = 3 - α”, for having an indication on

how completely the fractal appears to fill space.

10/]))·sin()·cos([·sin(·),(

)10/)·sin(10/sin(·10),(

),(),(),(

∑

∞

−

++=

kkk

AByBxCyxz

yxzyxz

yxzyxzyxz

λλ

ππ

2.2 Surface Generation

The calculations have been carried out with help of

Matlab software (Mathworks, version R2009) and

the data obtained have been stored in three-column

matrixes [X, Y, Z].

The command “surf” helps to represent the

surfaces linked to the mentioned matrixes. Figure 1

shows the result of evaluating function z(x,y) over a

grid of 300 x 300 points (corresponding to 30 μm x

30 μm). Consequently, distance between points of

the grid is similar to the scale of irregularities

(around 100 nm size) introduced by z

(x,y). Number

of iterations “k” has been limited to 10, enough for

introducing the fractal random-like irregularities,

and the following design values have been used:

λ = 1.5; α = 0.4; z

= 0.

Similarity with original topography of the Lotus

flower leaves is noteworthy, as can be seen if

compared with the photos from references

BIOMIMETIC COMPUTER-AIDED DESIGN AND MANUFACTURE OF COMPLEX BIOLOGICAL SURFACES

287

(Barthlott, 1997) or with the results from alternative

biomimetic manufacturing approaches (Groenendijk,

2007).

Figure 1: Mathematical surface mimicking the micro- and

nano-topography of the Lotus flower leaves.

2.3 Exporting Geometry to CAD

Software

Once the mathematical surfaces have been obtained,

the information stored in the form [X, Y, Z] can be

converted into .stl universal format, so that the

surface can be recognized and imported with a CAD

program, for additional design operations (i.e.

providing the surface with a thickness, copying the

surface atop a previously designed geometry…).

Different special software packages and “mesh to

solid” tools can be used for directly handling data in

.stl and enabling subsequent CAD operations. Figure

2 shows below the surface after importing the .stl

file with the help of NX-7.5 (Siemens AG) and the

solid body obtained after applying standard Boolean

design operations, for launching manufacture

through the 3D Lightyear

software (3D Systems).

Figure 2: Handling the surface with CAD software for

obtaining a solid model.

2.4 Process Summary and Actuations

regarding Computer-aided

Engineering & Rapid

Manufacturing

Once obtained, CAD files enable the development of

several kinds of design validations (assembly,

relative movements…) and simulations (mechanical,

thermal, fluidic…) with the help of computer-aided

engineering resources, especially based on the use of

F.E.M. calculations.

Additionally the use of CAD tools can be very

beneficial when combined with a new set of

manufacturing techniques and technologies that have

appeared in the last two decades called “Rapid

prototyping and manufacturing technologies”.

These technologies help to address market

requirements in an ever more customized way, as

well as optimized in terms of time and cost, and

provide support for research work where physical

models (or prototypes) are needed for tests and

trials.

They are usually based on automatic “layer

manufacturing technologies” (like “laser

stereolithography”, “3D printers” or “selective laser

sintering”), rapid shape-copying processes, or

manufacturing processes through the elimination of

material (such as in computer-driven high speed

numerical control machining).

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The different technologies available allow

prototypes to be obtained rapidly in a wide range of

metallic, ceramic or polymeric materials with

remarkable precision. The whole proposed design,

simulation and manufacturing process is

summarized in Figure 3.

Figure 3: Process scheme. OEPM P20103947 (Díaz

Lantada, 2010a).

Regarding the manufacture of fractal surfaces, our

previous research has helped to validate the use of

rapid prototyping for obtaining physical prototypes

with details in the range of 0.4 to 4 mm (Díaz

Lantada, 2010b).

The manufacture of more precise geometries, such

as the examples shown in this study, can be

accomplished by using some technologies such as

two-photon polymerization (Inführ, 2007), micro-

stereolithography (Choi, 2009), digital light

processing (Stampfl, 2007) and X-ray based

micromachining (Gad-el-Hak, 2002), for details

even down to hundreds of nanometers.

In any case Figure 4 provides an example of

prototype (30 x 30 mm

) manufacture through laser

stereolithography with a magnified scale due to

precision limitations. Further miniaturization can be

accomplished by using some of the aforementioned

technologies.

3 BRIEF DISCUSSION

OF POSSIBLE APPLICATIONS

The possibility of designing parts with surfaces

mimicking those from natural organisms can prove

to be of great value for incorporating advanced

Figure 4: Design and prototype manufactured using laser

stereolithography.

contact phenomena into devices for several

industries, thus promoting interactions with

surrounding elements (if the part is integrated within

a complex device) or tissues or organs (in the case of

an implant).

Among most promising applications we would

propose to focus in the near future on the design of

implants with optimized biocompatibility, devices

with self-cleaning properties, devices with ad-hoc

improved hydrophobicity or hydrophilicity,

scaffolds for cell and tissue growth and prototypes

for research linked to tribological phenomena,

including adhesion, lubrication, friction and wear.

BIOMIMETIC COMPUTER-AIDED DESIGN AND MANUFACTURE OF COMPLEX BIOLOGICAL SURFACES

289

In addition, combining novel advances in micro-

CT and medical imaging software (i.e. Mimics,

Materialise NV) for obtaining precise CAD data of

organs and biostructures (Shi, 2008, Guo, 2010),

with the possibility of incorporating even

nanometric features in a similar way to the presented

study, can be of great help for research linked to

enhanced modelling of biosystems.

4 CONCLUSIONS

A novel method for defining and controlling the

topography of surfaces from the design stage, even

mimicking the characteristics of biological systems,

has been presented. It is based on the combination of

regular surfaces for describing the micrometric

structure and additional fractal components for

providing the final nanometric details. As

application example a biomimetic design of the

surface of the Lotus flower leaves has been

explained.

Manufacture of such complex geometries can be

directly accomplished with help of additive rapid

prototyping technologies, what supposes a focus

change, from a more conventional “top-down”

(micro-machining, chemical etching, laser ablation),

to a more versatile “bottom-up” approach. The

flexibility of additive manufacturing also enables the

application of similar surface microtextures to the

complex geometries of prostheses and biodevices,

thus helping to introduce beneficial contact

properties for enhancing aspects such as wear

endurance or biocompatibility.

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