Proceedings of DETC’05
ASME 2005 Design Engineering Technical Conferences
September 24-28, 2005, Long Beach, California, USA,
SWEPT VOLUME REPRESENTATION OF MATERIAL DEPOSITION PROCESSES
FOR TISSUE SCAFFOLD FABRICATION
Jie Li, William Regli, Wei Sun
Department of Computer Science
Department of Mechanical Engineering and Mechanics
College of Engineering
Drexel University
Philadelphia, PA 19104
{jie.li, regli, sunwei}@drexel.edu
ABSTRACT
Solid freeform fabrication (SFF) techniques represent a
class of manufacturing processes for creating 3D tissue
scaffolds. A SFF method being developed at Drexel uses
material deposition of polymers from a nozzle that undergoes
piecewise linear motion in the plane. This work develops a
process model for this manufacturing device using a swept
volume representation of the capabilities of the tool.
Specifically, a swept volume describes the tool path information
and defines the scaffold to be fabricated. This swept volume
based model can be used to simulate the scaffold fabrication
process, and to generate a virtual scaffold prototyping.
1. INTRODUCTION
Tissue engineering techniques generally require the use of
scaffold, which provides the necessary support for cells to
attach, proliferate, and maintain their differentiated function [1].
There are various methods for modeling of tissue scaffold with
the requirement of cell growth and material degeneration.
Generation of functional tissue or organ structure requires a
scaffold to guide the overall shape and three-dimensional
organization of multiple cell types. Hence, scaffold
representation and fabrication is a key aspect of computer aided
tissue engineering.
This work examines the use of swept volume models to
model tissue scaffolds and capture the manufacturing process
associated with their creation. Swept volumes have had an
important application in manufacturing design and practice, but
usually in traditional mechanical domains in which material
removal by machining is the common operation. The swept
volumes are almost subject to the motion of object, which plays
a significant role in the design and implementation of a
manufacturing process.
This paper uses a swept volume of cylinder to capture the
process of material deposition to fabricate a tissue scaffold.
We provide a description of the implementation of the
technique and an analysis on how this method might be
improved and extended.
2. BACKGROUND AND LITERATURE REVIEW
Tissue Engineering
3D tissues are required and this is achieved by seeding the
cells onto porous matrices, known as scaffolds, to which the
cells attach and colonise[13]. Scaffold therefore plays an
important role in tissue engineering.
With the development of tissue engineering, especially, it
requires computer aided techniques to make the process of
tissue developing more efficient, such as modeling and
reconstructing 3D tissue, designing tissue scaffold models, and
fabricating physical models for tissues scaffolds. Computeraided tissue engineering (CATE) is such a utilization of
computer-aided technologies in tissue engineering [7]. An
important field in CATE is to design and manufacture tissue
scaffolds. Scaffolds are porous, degradable structures fabricated
from either natural materials or synthetic polymers [6]. The steps
for successful tissue scaffolds based on CATE is usually,
1. generating tissue structural view from computed
tomography (CT) or magnetic resonance imaging (MRI);
2. reconstructing CAD model of external structure;
3. designing internal architecture as well as determining
scaffold materials and internal pattern;
4. selecting appropriate techniques to fabricate scaffold due
to the external and internal properties;
5. evaluating the fabricated scaffolds.
Heterogeneous model of scaffold, in the contrary of
homogeneous model having unique internal architecture, is
developed by various materials or homogeneous internal
structure. Rather than homogeneous scaffold, heterogeneous
tissue scaffold would satisfy both biological requirements and
mechanical requirements. For example, bone is considered
heterogeneous calcified tissue at multi-hierarchical organization
levels. Composite unit cells are then imported for scaffold
modeling [8].
1
Copyright © #### by ASME
There are various scaffold fabrication techniques that can
be selected in the above step 4, such as freeze drying [10], fibre
meshes/fibre bonding [11], photolithography methods [12], and
solid freeform fabrication (SFF). Because of the incapability of
conventional fabrication techniques in precisely controlling
scaffold’s pore size, pore geometry, spatial distribution of pores
and construction of internal channels within the scaffold, SFF
are considered an advanced technique to produce scaffold with
customized external and internal architectures. SFF builds 3D
objects by layered manufacturing strategies. The general
process of SFF involves producing a computer-generated model
using computer-aided design (CAD) software. The computer
representation is a layer-by-layer slicing of the shape into
consecutive two dimensional layers, which can then be fed to
the control equipment to fabricate the part.
SFF entails several different approaches to fabricate:
3D printing: applies a thin layer of powder on a chamber
surface. The ink-jet style spray head deposits a liquid adhesive
onto the powder in a 2-D pattern, bonding the layer to form the
object. It is a kind of high speed and low materials cost
fabrication [14].
Fused Deposition Modeling (FDM): uses a moving nozzle to
extrude a fibre of polymeric material (x- and y-axis control)
from which the physical model is built layer-by-layer[9][15].
3D plotter: involves a moving extruder head (x-, y- and z-axis
control) and uses compressed air to force out a liquid or
pastelike plotting medium[16].
Stereolithography (SLA): is the first process ever developed in
rapid prototyping field with the meaning of 3-dimensional
printing. It uses a light-sensitive liquid polymer and a laser
beam traces out the shape of each layer and hardens the
photosensitive resin [17].
Swept volume representation is important in simulating the
interference between a moving solid and its environment [18].
The application of swept volume computation problem contains
generating finite-element meshes for engineering analysis [],
numerical control (NC) machining verification [], robot
workspace analysis [], collision detection [], geometrical
modeling [], motion planning [], Swept volume is geometric
method for defining a spatial domain [19]. Sweep differential
equation is used to determine the boundary of swept volumes.
In order to determine stationary points, Jacobian matrix is
studied for rank deficiency [20][22].
3. OVERVIEW OF TISSUE SCAFFOLD FABRICATION
3.1 Description of the Manufacturing Process
Freeform fabrication provides an effective process tool to
manufacture many advanced scaffolds with designed properties.
Fig. 1 shows a manufacturing process of PCL scaffold using
Precision Extruding Deposition techniques. The machine
consists of an XYZ position system, a material extruder system,
and a temperature control system [5]. Here, materials are
deposited according to the process tool path, which is generated
by data processing software, to form a layered 3D scaffold.
Fig. 1. Scaffold fabrication using Precision Extruding
Deposition (PED) process
Fig. 2 shows the nozzle motion during the fabrication.
.
other representations (implicit surfaces, i.e. work at Uwash
by Gantner et al).
Process model description?
Fig 2 nozzle motion
3.2 Fabricating Tissue Scaffolds
Traditionally, one technique on fabricating scaffolds of tissue
engineering is solid freeform fabrication[4]. In the process of
SFF, CAD scaffold models are sliced first and then fabricated
using the sliced information. Tool paths are kept in the sliced
models to control the fabrication. The following is the three
2
Copyright © #### by ASME
steps in the scaffold fabrication process:
a. Input scaffold model;
b. Slice the model;
c. Manufacture the model slice by slice.
After including swept volumes into fabricated scaffold, we
can fabricate the swept volumes directly (Fig. 2).
Solid Model
Swept Volumes
Sweeping
Extract
Fabricate
Tool Path
Fig. 2. Fabricating scaffold by swept volume based model
4. SWEPT VOLUME REPRESENTATION
4.1 Overview of the Sweep Equation
Swept volume is the volume generated by the motion of an
arbitrary object along an arbitrary path (or even a surface)
possibly with arbitrary rotations [2]. It is widely used in the field
of numerically controlled machining verification, robot analysis
and solid modeling.
The basic equation of swept volumes is as follows[3]:
 ( w)   (t )  R(t )
Where  characterizes the set of all points inside and on the
boundary of the swept volume.  (t ) is a (3  1) vector
representing 3D specified path, which is actually replacement
function. R(t) is a rotation function of the swept volumes and
  [ x1 ,..., xM ]T , which is parameterized surface used as the
base of sweeping.
Here t is a variable in the range of [0..1],
  x
 u
 
y
J (u , v, t )  
 u
  z
 u

 x
v
 y
v
 z
v
 x 
t 
 y 

t 
 z 
t 
Since it is a square matrix, its determinant is an analytic
function. Set the function to be zero, we can get the singular
points of the sweep equation. Singular surfaces will be got by
substituting these singular points into sweep equation. In our
case, the boundary of swept volumes comes from sweeping the
boundary of surface  and singular surfaces.
4.2 Mathematical Model of Swept Volumes for Process
Modeling
To approximate the model in manufacturing scaffold process,
we consider two key issues: sweep primitive and sweep path.
Especially, sphere and cylinder are regarded as two appropriate
primitives of swept volumes in our paper in order to make the
sweep efficient.
4.2.1 Two basic primitives of swept volumes for scaffold
process modeling
According to the different materials extruded from the nozzle
and different temporary they are heated, we considered the
following primitives as the base of swept volumes.
(a) Sweep-sphere volume
If the material is soft or of high temporary, it is mostly
approximately to sphere soon after extruded. The diameter of
the sphere is near to the diameter of nozzle of fabrication
machine.
As an example, we sweep a sphere along a parabola.
and w  [ x1 ,..., xM , t ] .
To form the boundary of swept volumes, singular surfaces are
found by Jacobian rank deficiency method[22]. Jacobian row
rank deficiency condition is used to determine all entities that
appear internal or external to swept volume. The matrix
T
  ( w) 
J ( w)   i

 w j 
Sweep along the curve
is called the Jacobian of the sweep. Consider a 3D surface
parameterized in terms of two variables as a (3×1) vector
given by
Jacobian is
  [ x(u, v), y(u, v), z (u, v)]T , the sweep
(b) Sweep-cylinder volume
If the material is a little bit hard or of low temporary, we use
a cylinder to approximate this process model. The diameter of
the cylinder is near to the diameter of nozzle of fabrication
machine, and the height of the cylinder is equal to its diameter.
If we sweep the cylinder along the same parabola curve, the
swept volume is as below:
3
Copyright © #### by ASME
4.2.2 Two kinds of paths to sweep
(a) Spline sweep
Spline curve can be created by some sampling points from
the boundary of layered surface. To make the swept volume fill
in the surface symmetrically, we select equidistant points of the
boundary, which are symmetrical of the y-axis. The following
figure is an example of spline sweep filling in a circular surface,
Where 5 points from the circle boundary are used to create a 3degree spline curve. The number of sampling points depends on
the size of the surface and the size of primitive.
Fig 4
5. IMPLEMENTATION
As an example, we considered how to represent the process
of generating a bone scaffold as a swept volume. We used
Quickslice to slice the CAD model and create swept volumes by
Maple 9.
First, the STL file of the bone is sliced layer by layer, where
each layer is full with connected lines. To simplify the
representation of sliced file, we represented lines as point pairs.
Second, we read the sliced file and put the points into an array
and then get lines from the array as the paths of swept volume.
Finally, we create swept volumes based on the above paths with
a primitive sphere, which approximate the motion of the nozzle
performing material deposition. Fig. 5 is a swept volume of the
bone.
(b) Piecewise line sweep
Even though spline curve is smooth, which is easy for
fabrication, it makes the mathematical model complex. In
real manufacturing process, it is also difficult to control
spline curves. Thus line, as most easily controlled curve, is
more widely used in real word. We consider piecewise line to
fill the surface. In the circle boundary of above example, we
create a piecewise line from 12 points picked up from the
boundary, and then sweep along the piecewise line using a
sphere.
Fig. 5. Swept volume implementation of bone
4.3 Mesh model of Swept Volumes for Process Modeling
The cost of computing mathematical model of swept volume
is very expensive. Fig 4 shows mesh model of swept volumes
by Pro/E.
6. DISCUSSION AND FUTURE WORK
To simulate the real manufacturing process and make the
swept volume model approximate to real objects fabricated by
the machine, the paths are very dense, that means it should cost
large of memory and a long time to calculate the whole model.
There are several ways to simplify the density.
(a) Reduce the number of paths. For example, pick up every
two paths, so the density is reduced to 50% of the origin. Also,
the density can be adjusted according to the feature distribution
of the object. In some layers, if there are no extra detail features
inside such as hole, the paths can be sparse.
(b) Since the size of basic circle to be swept can be changed,
in some sparse areas, we can choose a bigger circle to sweep to
4
Copyright © #### by ASME
make sure the total volume is the same. That is to say, some
paths of small circle can be combined into one path of large
circle. This is similar to unite the swept volumes.
7. ACKNOWLEDGMENTS
The authors would like to acknowledge funding support from
NSF/DARPA-0310619 grant for this research.
8. REFERENCES
[15] Scott CS, “Apparatus and method for creating three-dimensional objects”,
US Patent 5121329, 1991.
[16] Landers R, Mulhaupt R, “Desktop manufacturing of complex objects,
prototypes and biomedical scaffolds by means of computer-assisted
design combined with computer-guided 3D plotting of polymers and
reactive oligomers”, Journal of Macromolecular Materials and
Engineering Vol 282, 2000: 17-21
[17] Hull C (1990) Method for production of three-dimensional objects by
stereolithography. US Patent 4929402
[1]
Hutmacher DW., “Scaffold design and fabrication technologies for
engineering tissues--state of the art and future perspectives.” J Biomater
Sci Polym Ed. 2001;12(1):107-24.
[2]
K. Abdel-Malek, D. Blackmore, K. Joy, “Swept volumes: Foundations,
Perspectives, and Applications”, International Journal of Shape
Modeling, 2004
[3]
D. Blackmore, M.C. Leu, F. Shih, “Analysis and modelling of deformed
swept volumes”, Computer Aided Design, V26 n 4 pp. 315-326
[20] Leu M. C., Park S. H., Wang K. K, “Geometric presentation of
translational swept volumes and its applications”, ASME Journal of
Engineering for Industry, Vol 108, 1986 :113-119
[4]
Starly, B. Lau, A., Sun, W. Lau, W. and Bradbury T., “Direct Slicing of
STEP Based NURBS Models for Layered Manufacturing,” ComputerAided Design, Vol 37, Issue 4, April 2005, pp 387-397
[21] Abdel-Malek K, Yeh H. J, “Determining intersection curves between
surfaces of two solids”, Computer-Aided Design, Vol 28, 1996:539-549
[5]
Wang, F., Shor, L., Darling, A., Khalil, S., Sun, W., Güçeri, S. and Lau,
A., “Precision Extruding Deposition and Characterization of Cellualr
Poly-e-Caprolactone Tissue Scaffolds”, Rapid Prototyping Journal, Vol.
10, Issue 1, 2004. pp. 42-49.
[6]
Linda G. Griffith, Gail Naughton, “Tissue Engineering-Current
Challenges and Expanding Opportunities”, Science, Vol 295, Feb
8,2002
[7]
Wei Sun, Lallavi Lal, “Recent Development on Computer Aided Tissue
Engineering –a Review”, Journal of Computer Methods and Programs in
Biomedicine. Vol 67, 2002, 85-103
[8]
W. Sun, F. Lin, X. Hu, “Computer-aided Design and Modeling of
Composite Unit Cells”, Journal of Composites Sciences and Technology,
Vol 61, 2001, 289-299.
[9]
E. Sachlos, J.T. Czernuszka, “Making Tissue Engineering Scaffolds
Work. Review on the Application of Solid Freeform Fabrication.”
Journal of European Cells and Materials, Vol 5, 2003: 29-40
[18] W.P Wang, K.K. Wang, “Geometric modeling for swept volume of moving
solids”, IEEE Computer Graphics and Application, Vol 6, 1986:8-17
[19] Andrew S. Winter and Min Chen, “Image-Swept Volumes”, Eurographics,
V21, 2002
[22]
Abdel-Malek K, Yeh H. J, “Geometric representation of the swept
volume using Jocobian rank-deficiency conditions”, Computer-Aided
Design, Vol 29, 1997: 457-468
[10] Hsu YY, Gresser JD, Trantolo DJ, Lyons CM, Gangadharam PRJ, Wise
DL ,”Effect of polymer foam morphology and density on kinetics of in
vitro controlled release of isoniazid from compressed foam matrices”,
Journal of Biomedical Materials Science, Vol. 35: 107-116.
[11] Cima LG, Vacanti JP, Vacanti C, Inger D, Mooney D, Langer R. ”Tissue
engineering by cell transplantation using degradable polymer substrates”.
Journal of Biomechanical Engineering , Vol 113, 1991: 143-151.
[12]
Chihchen Chen, Danny Hirdes, Albert Folch, “Gray-scale
photolithography using microfluidic photomasks”, Proceedings of
National Academy of Sciences of the United States of America, Vol 100,
2003: 1499-1504
[13] Langer R, Vacanti JP, “Tissue engineering”. Science Vol 260, 1993: 920926.
[14] Bredt JF, Sach E, Brancazio D, Cima M, Curodeau A, Fan T ,”Three
dimensional printing system”, US Patent 5807437,1998.
5
Copyright © #### by ASME