The design of optimized scaffolds for tissue engineering is a key
topic of research, as the complex macro- and micro-architectures
required for a scaffold depend on the mechanical properties and
physical and molecular queues of the surrounding tissue at the
defect site. One way to achieve such hierarchical designs is to create
a library of unit cells (the scaffold is assumed to be a “Lego”
structure), which can be assembled through a specific computational tool [4–6].
In this work, a topological optimization strategy is presented to
find out the best material distribution used for a construct subject
to either a single load or a multiple load distribution, maximizing
its mechanical behavior under tensile and shear stress solicitations.
The proposed topological optimization scheme enables the design
of ideal topological architectures based on existing biologic microCT data for the design of biomimetic scaffolds.
2 Engineering Optimization Schemes
The classical problem in engineering design consists in finding the
optimum geometric configuration of a structure that maximizes a
given cost objective function with boundary conditions and constraints. Structural optimization can be classified as follows [7, 8]:
size optimization, shape optimization, and topological optimization.
In size optimization, only the cross section of a structure is
optimized. A typical size feature of a given structure, such as the
thickness of a beam, is either increased or decreased in order to
improve its performance. In shape optimization, the shape of the
structure is obtained by changing the shape of the used components with other components of different shapes, in order to
improve a desired variable within a system. In topological optimization, the shape and connectivity of the domain are both design
variables.
Topological optimization provides the first design concept of
the structure’s material distribution. Its goal is to minimize the
structure compliance while satisfying the constraints of volume
removal. As the structure compliance is twice the strain energy,
the objective function of minimizing structure compliance is equivalent to minimizing strain energy [9, 10].
In spite of several attempts to define optimized scaffolds [11–
16], there is no work correlating both porosity and mechanical
properties with topological information. Scaffolds must be highly
porous structures but also effective from a mechanical point of view.
This is a complex issue, fundamental for tissue engineering applications and not yet fully addressed. This paper proposes an optimized
strategy to obtain scaffolds with an appropriate topology maximizing both porosity and mechanical behavior. The methodology
proposed in this paper is of simple implementation and does not
require high computational calculation time.
4
Henrique A. Almeida and Paulo J. Ba ´ rtolo
topic of research, as the complex macro- and micro-architectures
required for a scaffold depend on the mechanical properties and
physical and molecular queues of the surrounding tissue at the
defect site. One way to achieve such hierarchical designs is to create
a library of unit cells (the scaffold is assumed to be a “Lego”
structure), which can be assembled through a specific computational tool [4–6].
In this work, a topological optimization strategy is presented to
find out the best material distribution used for a construct subject
to either a single load or a multiple load distribution, maximizing
its mechanical behavior under tensile and shear stress solicitations.
The proposed topological optimization scheme enables the design
of ideal topological architectures based on existing biologic microCT data for the design of biomimetic scaffolds.
2 Engineering Optimization Schemes
The classical problem in engineering design consists in finding the
optimum geometric configuration of a structure that maximizes a
given cost objective function with boundary conditions and constraints. Structural optimization can be classified as follows [7, 8]:
size optimization, shape optimization, and topological optimization.
In size optimization, only the cross section of a structure is
optimized. A typical size feature of a given structure, such as the
thickness of a beam, is either increased or decreased in order to
improve its performance. In shape optimization, the shape of the
structure is obtained by changing the shape of the used components with other components of different shapes, in order to
improve a desired variable within a system. In topological optimization, the shape and connectivity of the domain are both design
variables.
Topological optimization provides the first design concept of
the structure’s material distribution. Its goal is to minimize the
structure compliance while satisfying the constraints of volume
removal. As the structure compliance is twice the strain energy,
the objective function of minimizing structure compliance is equivalent to minimizing strain energy [9, 10].
In spite of several attempts to define optimized scaffolds [11–
16], there is no work correlating both porosity and mechanical
properties with topological information. Scaffolds must be highly
porous structures but also effective from a mechanical point of view.
This is a complex issue, fundamental for tissue engineering applications and not yet fully addressed. This paper proposes an optimized
strategy to obtain scaffolds with an appropriate topology maximizing both porosity and mechanical behavior. The methodology
proposed in this paper is of simple implementation and does not
require high computational calculation time.
4
Henrique A. Almeida and Paulo J. Ba ´ rtolo