U.S. patent application number 13/391102 was filed with the patent office on 2012-08-23 for porous implant structures.
This patent application is currently assigned to Smith & Nephew, Inc.. Invention is credited to Laura J. Gilmour, Shilesh C. Jani, Ryan L. Landon, Jeffrey Sharp.
Application Number | 20120215310 13/391102 |
Document ID | / |
Family ID | 43607329 |
Filed Date | 2012-08-23 |
United States Patent
Application |
20120215310 |
Kind Code |
A1 |
Sharp; Jeffrey ; et
al. |
August 23, 2012 |
POROUS IMPLANT STRUCTURES
Abstract
Porous biocompatible structures suitable for use as medical
implants and methods for fabricating such structures are disclosed.
The disclosed structures may be fabricated using rapid
manufacturing techniques. The disclosed porous structures has a
plurality of struts and nodes where no more than two struts
intersect one another to form a node. Further, the nodes can be
straight, curved, portions that are curved and/or straight. The
struts and nodes can form cells which can be fused or sintered to
at least one other cell to form a continuous reticulated structure
for improved strength while providing the porosity needed for
tissue and cell in-growth.
Inventors: |
Sharp; Jeffrey; (Salt Lake
City, UT) ; Jani; Shilesh C.; (Memphis, TN) ;
Gilmour; Laura J.; (Alameda, CA) ; Landon; Ryan
L.; (Southaven, MS) |
Assignee: |
Smith & Nephew, Inc.
Memphis
TN
|
Family ID: |
43607329 |
Appl. No.: |
13/391102 |
Filed: |
August 19, 2010 |
PCT Filed: |
August 19, 2010 |
PCT NO: |
PCT/US10/46022 |
371 Date: |
May 2, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61235269 |
Aug 19, 2009 |
|
|
|
Current U.S.
Class: |
623/11.11 ;
29/428 |
Current CPC
Class: |
A61F 2230/0063 20130101;
A61L 24/0036 20130101; A61F 2002/30914 20130101; B33Y 80/00
20141201; A61L 27/56 20130101; Y10T 29/49826 20150115; A61F
2002/30593 20130101; A61F 2002/30962 20130101; B33Y 70/00 20141201;
A61F 2/28 20130101; A61F 2002/3028 20130101; A61F 2002/3092
20130101; B33Y 10/00 20141201 |
Class at
Publication: |
623/11.11 ;
29/428 |
International
Class: |
A61F 2/02 20060101
A61F002/02; B23P 11/00 20060101 B23P011/00 |
Claims
1. A porous structure comprising: a plurality of struts, each strut
comprises: a first end; a second end; and a continuous elongated
body between said first and second ends, said body having a
thickness and a length; and a plurality of nodes, each node
comprises an intersection between one end of a first strut and the
body of a second strut; wherein said porous structure is produced
at least by a rapid manufacturing technologies process.
2. The porous structure of claim 1 wherein the first and second
ends of one or more struts extend between the body of two other
struts.
3. The porous structure of claim 1, wherein the body of one or more
struts comprise a plurality of nodes.
4. The porous structure of claim 1, wherein the cross-section of at
least one end of one or more struts is larger than the
cross-section of a portion of the body of said one or more
struts.
5. The porous structure of claim 1 wherein at least a portion of
the body of one or more struts is curved.
6. The porous structure of claim 1 wherein the plurality of struts
can be sintered, melted, welded, bonded, fused, or otherwise
connected to one another.
7. The porous structure of claim 1 wherein a plurality of the
struts and nodes define at least one fenestration.
8. The porous structure of claim 1 further comprising material
selected from the group consisting of metal, ceramic, metal-ceramic
(cermet), glass, glass-ceramic, polymer, composite and combinations
thereof.
9. The porous structure of claim 8 wherein the metallic material is
selected from the group consisting of titanium, titanium alloy,
zirconium, zirconium alloy, niobium, niobium alloy, tantalum,
tantalum alloy, nickel-chromium (e.g., stainless steel),
cobalt-chromium alloy and combinations thereof.
10. The porous structure of claim 1 wherein the cross section of
one or more struts comprises a polygon.
11. The porous structure of claim 1 wherein at least a portion of
the circumference of the cross-section is curved.
12. A method for fabricating a porous structure comprising the
steps of: creating a model of a porous structure at least in a
computer generated environment, wherein the creation step
comprises: defining one or more struts with a first end, a second
end, and a continuous elongated body between the first and second
ends for each strut, selecting a thickness and length for the body;
and defining at least one node with an intersection between one end
of a first strut and the body of a second strut for each node; and
fabricating the porous structure according to the model by exposing
fusible material to an energy source.
13. The method of claim 12, further comprises the step of defining
the first and second ends of one or more struts to extend between
the body of two other struts.
14. The method of claim 12 further comprises the step of defining
the body of one or more struts to comprise a plurality of
nodes.
15. The method of claim 12 further comprises the step of defining
the cross-section of at least one end of one or more struts to be
larger than the cross-section of a portion of the body of said one
or more struts.
16. The method of claim 12 further comprises the step of defining
at least a portion of the body of one or more struts to be
curved.
17. The method of claim 12 further comprises the step of sintering,
melting, welding, bonding, or fusing a plurality of struts to one
another.
18. The method of claim 12 further comprises the step of defining
at least one fenestration in the porous structure using a plurality
of the struts and nodes.
19. The method of claim 12 wherein the fabricating step further
comprises selecting a material for fabricating the one or more
struts from the group consisting of metal, ceramic, metal-ceramic
(cermet), glass, glass-ceramic, polymer, composite and combinations
thereof.
20. The method of claim 19 further comprises selecting a metallic
material from the group consisting of titanium, titanium alloy,
zirconium, zirconium alloy, niobium, niobium alloy, tantalum,
tantalum alloy, nickel-chromium (e.g., stainless steel),
cobalt-chromium alloy and combinations thereof.
21. The method of claim 12 further comprises the step of defining
the cross section of one or more struts with a polygon.
22. The method of claim 12 further comprises the step of defining
at least a portion the circumference of the cross-section with a
curved portion.
23. A porous structure comprising: at least one cell comprising: a
plurality of sides, each side comprising a polygon, wherein each
leg of the polygon comprises a strut; wherein the strut comprises:
a first end; a second end; and a continuous elongated body between
said first and second ends, said body having a thickness and a
length; and a plurality of nodes, each node comprises an
intersection between one end of a first strut and the body of a
second strut.
24. The porous structure of claim 23 further comprising: a
plurality of cells coupled to one another in a stacked pattern
wherein at least two cells share one side.
25. The porous structure of claim 24 wherein said cell comprises a
hollow interior.
26. The porous structure of claim 23 wherein said porous structure
is manufactured with rapid manufacturing technologies.
Description
[0001] The present application claims the benefit of U.S.
Provisional Patent Application No. 61/235,269, filed Aug. 19, 2009
and entitled "Porous Implant Structures," the disclosure of which
is incorporated by reference herein in its entirety.
FIELD OF INVENTION
[0002] The present invention generally relates to porous structures
suitable for medical implants, and more particularly to porous
structures suitable for medical implants that have improved
combinations of strength, porosity and connectivity and methods for
fabricating such improved porous structures.
BACKGROUND
[0003] Metal foam structures are porous, three-dimensional
structures with a variety of uses, including medical implants.
Metal foam structures are suitable for medical implants,
particularly orthopedic implants, because they have the requisite
strength for weight bearing purposes as well as the porosity to
encourage bone/tissue in-growth. For example, many orthopedic
implants include porous sections that provide a scaffold structure
to encourage bone in-growth during healing and a weight bearing
section intended to render the patient ambulatory more quickly.
[0004] Metal foam structures can be fabricated by a variety of
methods. For example, one such method is mixing a powdered metal
with a pore-forming agent (PFA) and then pressing the mixture into
the desired shape. The PFA is removed using heat in a "burn out"
process. The remaining metal skeleton may then be sintered to form
a porous metal foam structure.
[0005] Another similar conventional method include applying a
binder to polyurethane foam, applying metal powder to the binder,
burning out the polyurethane foam and sintering the metal powder
together to form a "green" part. Binder and metal powder are
re-applied to the green part and the green part is re-sintered
until the green part has the desired strut thickness and porosity.
The green part is then machined to the final shape and
re-sintered.
[0006] While metal foams formed by such conventional methods
provide good porosity, they may not provide sufficient strength to
serve as weight bearing structures in many medical implants.
Further, the processes used to form metal foams may lead to the
formation of undesirable metal compounds in the metal foams by the
reaction between the metal and the PFA. Conventional metal foam
fabrication processes also consume substantial amounts of energy
and may produce noxious fumes.
[0007] Rapid manufacturing technologies (RMT) such as direct metal
fabrication (DMF) and solid free-form fabrication (SFF) have
recently been used to produce metal foam used in medical implants
or portions of medical implants. In general, RMT methods allow for
structures to be built from 3-D CAD models. For example, DMF
techniques produce three-dimensional structures one layer at a time
from a powder which is solidified by irradiating a layer of the
powder with an energy source such as a laser or an electron beam.
The powder is fused, melted or sintered, by the application of the
energy source, which is directed in raster-scan fashion to selected
portions of the powder layer. After fusing a pattern in one power
layer, an additional layer of powder is dispensed, and the process
is repeated with fusion taking place between the layers, until the
desired structure is complete.
[0008] Examples of metal powders reportedly used in such direct
fabrication techniques include two-phase metal powders of the
copper-tin, copper-solder and bronze-nickel systems. The metal
structures formed by DMF may be relatively dense, for example,
having densities of 70% to 80% of a corresponding molded metal
structure, or conversely, may be relatively porous, with porosities
approaching 80% or more.
[0009] While DMF can be used to provide dense structures strong
enough to serve as weight bearing structures in medical implants,
such structures do not have enough porosity to promote tissue and
bone in-growth. Conversely, DMF can be used to provide porous
structures having enough porosity to promote tissue and bone
in-growth, but such porous structures lack the strength needed to
serve as weight bearing structures. Other laser RMT techniques are
similarly deficient for orthopedic implants requiring strength,
porosity and connectivity.
[0010] As a result of the deficiencies of metal foam implants and
implants fabricated using conventional DMF methods, some medical
implants require multiple structures, each designed for one or more
different purposes. For example, because some medical implants
require both a porous structure to promote bone and tissue
in-growth and a weight bearing structure, a porous plug may be
placed in a recess of a solid structure and the two structures may
then be joined by sintering. Obviously, using a single structure
would be preferable to using two distinct structures and sintering
them together.
[0011] In light of the above, there is still a need for porous
implant structures that provide both the required strength and
desired porosity, particularly for various orthopedic applications.
This disclosure provides improved porous structures that have both
the strength suitable for weight bearing structures and the
porosity suitable for tissue in-growth structures and a method for
fabricating such improved porous structures.
SUMMARY OF THE INVENTION
[0012] One objective of the invention is to provide porous
biocompatible structures suitable for use as medical implants that
have improved strength and porosity.
[0013] Another objective of the invention is to provide methods to
fabricate porous biocompatible structures suitable for use as
medical implants that have improved strength and porosity.
[0014] To meet the above objectives, there is provided, in
accordance with one aspect of the invention, there is a porous
structure comprising: a plurality of struts, each strut comprises a
first end, a second end; and a continuous elongated body between
the first and second ends, where the body has a thickness and a
length; and a plurality of nodes, each node comprises an
intersection between one end of a first strut and the body of a
second strut.
[0015] In a preferred embodiment, the first and second ends of one
or more struts extend between the body of two other struts. In
another preferred embodiment, the body of one or more struts
comprise a plurality of nodes.
[0016] In accordance with another aspect of the invention, there is
a porous structure comprising a plurality of struts, wherein one or
more struts comprise a curved portion having a length and
thickness; a plurality of junctions where two of said curved
portions intersect tangentially; and a plurality of modified nodes,
each modified node comprises an opening formed by three or more of
said junctions.
[0017] In a preferred embodiment, the porous structure includes at
least one strut comprising a straight portion having a length and a
thickness. In another preferred embodiment, the porous structure
includes at least one strut having a first end, a second end; and a
continuous elongated body between the first and second ends, where
the body has a thickness and a length; and at least one closed node
comprising an intersection between one end of a first strut and the
body of a second strut, wherein the strut can comprise of a
straight portion, a curved portion, or both.
[0018] In accordance with another aspect of the invention, there
are methods for fabricating a porous structure. One such method
comprises the steps of: creating a model of the porous structure,
the creation step comprises defining a plurality of struts and a
plurality of nodes to form the porous structure and fabricating the
porous structure according to the model by exposing metallic powder
to an energy source. The defining step comprises the steps of
providing a first end, a second end; and a continuous elongated
body between the first and second ends for each strut, selecting a
thickness a length for the body; and providing an intersection
between one end of a first strut and the body of a second strut for
each node.
[0019] In a preferred embodiment, the method includes defining the
first and second ends of one or more struts extend between the body
of two other struts. In another preferred embodiment, defining the
body of one or more struts to comprise a plurality of nodes.
[0020] In accordance with another aspect of the invention, a second
method for fabricating a porous structure comprises the steps of:
creating a model of the porous structure; the creation step
comprises selecting at least one frame shape and size for one or
more cells of the porous structure, where the frame shape comprises
a geometric shape selected from the group consisting of Archimedean
shapes, Platonic shapes, strictly convex polyhedrons, prisms,
anti-prisms and combinations thereof; adding one or more struts to
the frame where the struts comprises a curved portion, said adding
step is performed by inscribing or circumscribing the curved
portion of the one or more struts within or around one or more
faces of the selected shape; selecting a thickness for the frame
and the one or more struts; and fabricating the porous structure
according to the model by exposing metallic powder to an energy
source.
[0021] In a preferred embodiment, the creation step includes the
step of removing a portion of the frame from one or more cells of
the model. In another preferred embodiment, the fabrication step
includes defining N.sub.(1, x) layer-by-layer patterns for the
porous structure based on the selected dimensions, at least one
cell shape and at least one cell size, where N ranges from 1 for
the first layer at a bottom of the porous structure to x for the
top layer at a top of the porous structure; depositing an N.sup.th
layer of powdered biocompatible material; fusing or sintering the
N.sup.th pattern in the deposited N.sup.th layer of powdered
biocompatible material; and repeating the depositing and fusing or
sintering steps for N=1 through N=x.
[0022] In a refinement, the method may further comprise creating a
model of the porous structure wherein, for at least some nodes, no
more than two struts intersect at the same location.
[0023] In another refinement, the method may comprise creating a
model of the porous structure wherein at least one strut or strut
portion is curved.
[0024] The disclosed porous structures may be fabricated using a
rapid manufacturing technologies such as direct metal fabrication
process. The struts can be sintered, melted, welded, bonded, fused,
or otherwise connected to another strut. The struts and nodes can
define a plurality of fenestrations. Further, the struts and nodes
can be fused, melted, welded, bonded, sintered, or otherwise
connected to one another to form a cell, which can be fused,
melted, welded, bonded, sintered, or otherwise connected to other
cells to form a continuous reticulated structure.
[0025] In some refinements, at least one, some, or all struts of a
cell may have a uniform strut diameter. In some refinements, one,
some, or all of the struts of a cell may have a non-uniform strut
diameter. In some refinements, a cell may have combinations of
struts having uniform and non-uniform strut diameters. In some
refinements, at least one, some, or all of the uniform diameter
struts of a cell may or may not share similar, different, or
identical strut diameters, longitudinal shapes, cross-sectional
shapes, sizes, shape profiles, strut thicknesses, material
characteristics, strength profiles, or other properties. In some
refinements, one, some, or all struts within a cell may grow or
shrink in diameter at similar, different, or identical rates along
a predetermined strut length.
[0026] In some refinements, struts within a cell may extend between
two nodes. In a further refinement of this concept, struts may have
varying cross-sectional diameters along a strut length, including a
minimum diameter at a middle portion disposed between the two
nodes. In further refinement of this concept, struts may have two
opposing ends, with each end connected to a node and a middle
portion disposed between the two ends. Struts may flare or taper
outwardly as they extend from the middle portion towards each node
so that a diameter of the middle portion is generally smaller than
a diameter of either or both of the two opposing ends. In some
instances, the struts may flare in a parabolic fluted shape or may
taper frusto-conically.
[0027] In other refinements, at least one, some, or all struts
within a cell are curved. In further refinement of this concept,
one, some, or all of the cells within a porous structure comprise
at least one curved strut. In further refinement of this concept,
all of the struts that make up a porous structure are curved. In
further refinement of this concept, curved struts may form complete
rings or ring segments. The rings or ring segments may be
inter-connected to form open sides or fenestrations of
multiple-sided cells. In some instances, a single ring may form a
shared wall portion which connects two adjacent multiple-sided
cells. In some instances, one or more ring segments alone or in
combination with straight strut portions may form a shared wall
portion which connects two adjacent multiple-sided cells. In still
a further refinement, the number of sides of each cell may range
from about 4 to about 24. More preferably, the number of sides of
each cell may range from about 4 to about 16. One geometry that has
been found to be particularly effective is a dodecahedron or 12
sided cell. However, as explained and illustrated below, the
geometries of the individual cells or the cells of the porous
structure may vary widely and in the geometries may vary randomly
from cell to cell of a porous structure.
[0028] In another refinement, the configurations of the cells,
struts, nodes and/or junctions may vary randomly throughout the
porous structure to more closely simulate natural bone tissue.
[0029] In another refinement, each cell may be multiple-sided and
having an overall shape that may fit within a geometric shape
selected from the group consisting of tetrahedrons, truncated
tetrahedrons, cuboctahedrons, truncated hexahedrons, truncated
octahedrons, rhombicuboctahedrons, truncated cuboctahedrons, snub
hexahedrons, snub cuboctahedrons, icosidodecahedrons, truncated
dodecahedrons, truncated icosahedrons, rhombicosidodecahedrons,
truncated icosidodecahedrons, snub dodecahedrons, snub
icosidodecahedrons, cubes, octahedrons, dodecahedrons,
icosahedrons, prisms, prismatoids, antiprisms, uniform prisms,
right prisms, parallelpipeds, cuboids, polytopes, honeycombs,
square pyramids, pentagonal pyramids, triangular cupolas, square
cupolas, pentagonal cupolas, pentagonal rotundas, elongated
triangular pyramids, elongated square pyramids, elongated
pentagonal pyramids, gyroelongated square pyramids, gyroelongated
pentagonal pyramids, triangular dipyramids, pentagonal dipyramids,
elongated triangular dipyramids, elongated square dipyramids,
elongated pentagonal dipyramids, gyroelongated square dipyramids,
elongated triangular cupolas, elongated square cupolas, elongated
pentagonal cupolas, elongated pentagonal rotundas, gyroelongated
triangular cupolas, gyroelongated square cupolas, gyroelongated
pentagonal cupolas, gyroelongated pentagonal rotundas,
gyrobifastigium, triangular orthobicupolas, square orthobicupolas,
square gyrobicupolas, pentagonal orthobicupolas, pentagonal
gyrobicupolas, pentagonal orthocupolarotundas, pentagonal
gyrocupolarotundas, pentagonal orthobirotundas, elongated
triangular orthobicupolas, elongated triangular gyrobicupolas,
elongated square gyrobicupolas, elongated pentagonal
orthobicupolas, elongated pentagonal gyrobicupolas, elongated
pentagonal orthocupolarotundas, elongated pentagonal
gyrocupolarotundas, elongated pentagonal orthobirotundas, elongated
pentagonal gyrobirotundas, gyroelongated triangular bicupolas,
gyroelongated square bicupolas, gyroelongated pentagonal bicupolas,
gyroelongated pentagonal cupolarotundas, gyroelongated pentagonal
birotundas, augmented triangular prisms, biaugmented triangular
prisms, triaugmented triangular prisms, augmented pentagonal
prisms, biaugmented pentagonal prisms, augmented hexagonal prisms,
parabiaugmented hexagonal prisms, metabiaugmented hexagonal prisms,
triaugmented hexagonal prisms, augmented dodecahedrons,
parabiaugmented dodecahedrons, metabiaugmented dodecahedrons,
triaugmented dodecahedrons, metabidimini shed icosahedrons,
tridiminished icosahedrons, augmented tridiminished icosahedrons,
augmented truncated tetrahedrons, augmented truncated cubes,
biaugmented truncated cubes, augmented truncated dodecahedrons,
parabiaugmented truncated dodecahedrons, metabiaugmented truncated
dodecahedrons, triaugmented truncated dodecahedrons, gyrate
rhombicosidodecahedrons, parabigyrate rhombicosidodecahedrons,
metabigyrate rhombicosidodecahedrons, trigyrate
rhombicosidodecahedrons, diminished rhombicosidodecahedrons,
paragyrate diminished rhombicosidodecahedrons, metagyrate
diminished rhombicosidodecahedrons, bigyrate diminished
rhombicosidodecahedrons, parabidiminished rhombicosidodecahedrons,
metabidiminished rhombicosidodecahedrons, gyrate bidiminished
rhombicosidodecahedrons, and tridimini shed
rhombicosidodecahedrons, snub disphenoids, snub square antiprisms,
sphenocorons, augmented sphenocoronas, sphenomegacorona,
hebesphenomegacorona, disphenocingulum, bilunabirotundas,
triangular hebesphenorotundas, and combinations thereof.
[0030] In another refinement, the powder is selected from the group
consisting of metal, ceramic, metal-ceramic (cermet), glass,
glass-ceramic, polymer, composite and combinations thereof.
[0031] In another refinement, the metallic material is selected
from the group consisting of titanium, titanium alloy, zirconium,
zirconium alloy, niobium, niobium alloy, tantalum, tantalum alloy,
nickel-chromium (e.g., stainless steel), cobalt-chromium alloy and
combinations thereof.
[0032] In another refinement, the porous structure forms at least a
portion of a medical implant, such as an orthopedic implant, dental
implant or vascular implant.
[0033] Porous orthopedic implant structures for cell and tissue
in-growth and weight bearing strength are also disclosed that may
be fabricated using a near-net shape manufacturing process such as
a direct metal fabrication (DMF) process for use with metallic
biomaterials or a stereo-lithography manufacturing process for use
with polymeric biomaterials. In instances where a DMF process is
utilized, a powdered biocompatible material is provided in layers
and individual particles of one layer of powdered biocompatible
material are fused or sintered together one layer at a time.
Exemplary porous structures comprise a plurality of
three-dimensional cells. Each cell comprises a plurality of struts.
Each strut may be sintered or fused to one other strut at a node.
Each node may comprise a junction of not more than two struts. The
struts and nodes of each cell define a plurality of fenestrations.
Each cell comprises from about 4 to about 24 fenestrations. At
least one strut of at least some of the cells are curved. Each cell
may be fused or sintered to at least one other cell to form a
continuous reticulated structure.
[0034] Other advantages and features will be apparent from the
following detailed description when read in conjunction with the
attached drawings. The foregoing has outlined rather broadly the
features and technical advantages of the present invention in order
that the detailed description of the invention that follows may be
better understood. Additional features and advantages of the
invention will be described hereinafter which form the subject of
the claims of the invention. It should be appreciated by those
skilled in the art that the conception and specific embodiment
disclosed may be readily utilized as a basis for modifying or
designing other structures for carrying out the same purposes of
the present invention. It should also be realized by those skilled
in the art that such equivalent constructions do not depart from
the spirit and scope of the invention as set forth in the appended
claims. The novel features which are believed to be characteristic
of the invention, both as to its organization and method of
operation, together with further objects and advantages will be
better understood from the following description when considered in
connection with the accompanying figures. It is to be expressly
understood, however, that each of the figures is provided for the
purpose of illustration and description only and is not intended as
a definition of the limits of the present invention.
BRIEF DESCRIPTION OF THE DRAWINGS
[0035] For a more complete understanding of the present invention,
reference is now made to the following descriptions taken in
conjunction with the accompanying drawing, in which:
[0036] FIGS. 1A-1B illustrate 3-D representations of an example of
the struts at a node in a porous structure of the prior art where
the struts of FIG. 1A have like diameters and the struts of FIG. 1B
have different diameters.
[0037] FIG. 2 is a SEM (Scanning Electron Microscope)
microphotograph of an example of fractured struts of the prior
art.
[0038] FIGS. 3-5 illustrate 3-D representations of one embodiment
of the struts and nodes of the present invention.
[0039] FIGS. 6-8 illustrate 3-D representations of another
embodiment of the struts and nodes of the present invention where
at least some of the struts comprises a smaller cross-sectional
diameter at the body portion of the strut as compared to the
cross-sectional diameter at the node.
[0040] FIGS. 9A and 9B illustrate plan views of the embodiments in
FIGS. 6-8.
[0041] FIGS. 10A-10F illustrate 2-D representations of various
configurations of the frame of struts and nodes in a porous
structure of the prior art.
[0042] FIGS. 11A-11F illustrate 2-D representations of the
corresponding configurations of the frame of struts and nodes of
the prior art in FIGS. 10A-10F modified by one embodiment of the
present invention.
[0043] FIGS. 12A-12D illustrate 3-D representations of exemplary
embodiments of the porous structure of the present invention
comprising one or more frame configurations in FIGS. 11A-11F.
[0044] FIGS. 13A-13M illustrate 2-D representations of various
exemplary configurations of the frame of the two struts of the
present invention forming a node, including frames for struts that
are straight, curved, or a combination of both.
[0045] FIG. 14 illustrates a 2-D representation of an exemplary
embodiment of the porous structure of the present invention
comprising one or more frame configurations in FIGS. 13A-13M.
[0046] FIGS. 15A-15C illustrate 2-D representations of exemplary
configurations of various curved frames and corresponding struts of
the present invention intersecting to form a node.
[0047] FIG. 16 illustrates a 3-D representation of an exemplary
embodiment of the porous structure of the present invention
comprising one or more frame configurations in FIGS. 13A-13M,
including frames for struts that are straight, curved, or a
combination of both.
[0048] FIG. 17 illustrates a 3-D representation of an exemplary
frame for a generally cubical cell of the porous structure of the
present invention.
[0049] FIG. 18 illustrates a 3-D representation of an exemplary
arrangement of frames for cubical cells in FIG. 17.
[0050] FIG. 19 illustrates a 3-D representation of an arrangement
of cubical cells of the porous structure of the prior art.
[0051] FIG. 20 illustrates a 3-D representation of an exemplary
arrangement of cubical cells of the porous structure of the present
invention.
[0052] FIG. 21 illustrates a blown up view of the arrangement in
FIG. 20.
[0053] FIG. 22 illustrates a 3-D representation of an exemplary
frame for a tetrahedron-shaped cell of the porous structure of the
present invention.
[0054] FIG. 23 illustrates a 3-D representation of an exemplary
frame for square-based pyramid cell of the porous structure of the
present invention.
[0055] FIGS. 24A and 24B illustrate various views of 3-D
representations of a conventional cell of the porous structure of
the prior art based on a dodecahedral shape.
[0056] FIGS. 25A and 25B illustrate various views of 3-D
representations of one embodiment of a cell of the porous structure
of the present invention also based on a dodecahedral shape.
[0057] FIGS. 26-28 illustrate 3-D representations of a frame of the
convention cell in FIGS. 24A and 24B modified by one embodiment of
the present invention.
[0058] FIGS. 29A and 29B illustrate 3-D representations of a cell
of the present invention formed from FIGS. 26-28, where FIG. 29B is
a partial view of a 3-D representation of the frame of the
cell.
[0059] FIG. 30 illustrates the frame of FIG. 27 unfolded into a 2-D
representation.
[0060] FIG. 31 illustrates a frame of a truncated tetrahedral cell
unfolded into a 2-D representation.
[0061] FIG. 32 illustrates the frame of FIG. 31 formed with curved
struts according to one embodiment of the present invention.
[0062] FIG. 33 illustrates the frame of a truncated octahedral cell
unfolded into a 2-D representation.
[0063] FIG. 34 illustrates the frame of FIG. 33 formed with curved
struts according to one embodiment of the present invention.
[0064] FIGS. 35A-35E illustrate 2-D representations of examples of
a circle or an ellipse inscribed within various geometric shapes
according to one embodiment of the present invention.
[0065] FIG. 36 illustrates the frame of a truncated tetrahedral
cell unfolded into a 2-D representation with circles circumscribed
around each face of the cell according to one embodiment of the
present invention.
[0066] FIGS. 37A and 37B illustrate various views of 3-D
representations of another embodiment of a cell of the present
invention based on a dodecahedral shape.
[0067] FIG. 38 illustrates a 3-D representation of yet another
embodiment of a cell of the present invention based on a
dodecahedral shape.
[0068] FIGS. 39A-38C illustrate various views of 3-D
representations of yet another embodiment of a cell of the present
invention based on a dodecahedral shape.
[0069] FIG. 40 illustrates a 3-D representation of an exemplary
arrangement of the cells of FIGS. 24 and 25.
[0070] FIGS. 41A and 41B illustrate various views of 3-D
representations of an exemplary arrangement of the cells of FIGS.
24, 25, and 37
[0071] FIG. 42 illustrates a 3-D representation of an exemplary
arrangement of the cells based on a truncated tetrahedral shape
having one or more curved struts.
[0072] FIG. 43 illustrates a 3-D representation of an exemplary
arrangement of the present invention of cells based on truncated
octahedra.
[0073] FIG. 44 illustrates a 3-D representation of an exemplary
arrangement of the present invention of cells based on cubes (light
grey), truncated cuboctahedra (black), and truncated octahedra
(dark grey).
[0074] FIG. 45 illustrates a 3-D representation of an exemplary
arrangement of the present invention of cells based on cuboctahedra
(black), truncated octahedra (dark grey) and truncated tetrahedra
(light grey).
[0075] FIG. 46 illustrates a frame view of the arrangement of FIG.
42.
[0076] FIG. 47 illustrates a frame view of the arrangement of FIG.
43.
[0077] FIGS. 48-50 illustrate 3-D reprsentations of a frame based
an octahedron modified by one embodiment of the present
invention.
[0078] FIGS. 51A and 51B illustrate various views of 3-D
representations of a cell of the present invention formed from the
frames of FIGS. 48-50.
[0079] FIG. 52 illustrates a 3-D representation of a frame based a
truncated tetrahedron.
[0080] FIGS. 53A-53D illustrate various views of 3-D
representations of a cell formed from the frame of FIG. 52 that was
modified by one embodiment of the present invention.
[0081] FIGS. 54A-54E illustrate various views of 3-D
representations of an exemplary arrangement of the cells of FIG.
53.
[0082] FIGS. 55A-55E illustrate 3-D representations of a cell
formed from a frame based on a hexagonal prism that was modified by
one embodiment of the present invention.
[0083] FIGS. 56A-56B and 57A-57B illustrate 3-D representations of
an exemplary arrangement of the cells of FIG. 55.
[0084] FIGS. 58-61 illustrate 3-D representations of frames based
on a dodecahedron modified by various embodiments of the present
invention.
[0085] It should be understood that the drawings are not
necessarily to scale and that the disclosed embodiments are
sometimes illustrated diagrammatically and in partial views. In
certain instances, details which are not necessary for an
understanding of the disclosed methods and apparatuses or which
render other details difficult to perceive may have been omitted.
Also, for simplification purposes, there may be only one exemplary
instance, rather than all, is labeled. It should be understood, of
course, that this disclosure is not limited to the particular
embodiments illustrated herein.
DETAILED DESCRIPTION OF INVENTION
[0086] As discussed above, Rapid Manufacturing Techniques (RMT)
such as Direct Metal Fabrication (DMF) can be used to produce
porous structures for medical implants. However, using DMF or other
RMT to fabricate porous structures can create weak areas between
fenestrations of the three-dimensional porous structure. This is
mostly due to the shapes and configurations of the cells that have
been used in the prior art to form these porous structures. In
particular, fractures typically occur at areas where struts are
connected together at a node. The fractures occur in porous
structures of the prior art because the cross-sectional area of a
strut where it connects to the node is typically less than the
cross-sectional area of the resulting node. The areas where the
struts connect to their node, typically referred to as stress
risers, are common points of structural failure. The pattern of
failure at the stress risers can also occur when the molten phase
of particles does not completely melt and fuse together or when the
surrounding substrate surfaces is too cold, which causes the hot
powdered material to bead up during the DMF process. Regardless of
the exact causes of strut fractures and the resulting poor
performance of porous structures of the prior art, improved porous
structures that can be fabricated using RMT, including DMF, and
other free-form fabrication and near net-shape processes (e.g.,
selective laser sintering, electron beam melting, and
stereo-lithography) are desired.
[0087] FIGS. 1A and 1B provide an illustration of where fractures
may occur. FIGS. 1A-1B illustrate an example of a porous structure
with three or four struts, respectively, connected at a single
node, where the struts of FIG. 1A have the same diameters and the
struts of FIG. 1B have different diameters. Specifically, in FIG.
1A, three struts 102 of generally equal diameters are connected
together at node 104. Three stress risers 106 are created at the
connections between the three struts 102. Because the
cross-sectional diameters of struts 102 at the stress risers 106
are less than the cross-sectional diameter of the node 104, the
stress risers 106 are locations for a typical strut failure. In
FIG. 1B, three smaller struts 108 are connected to a larger strut
110 at a node 112. Three of the four resulting stress risers are
shown at 114, which have substantially smaller cross-sectional
diameters than the node 112. FIG. 2 is a SEM (Scanning Electron
Microscope) microphotograph of a structure 200 fabricated using
RMT, and it shows an example of strut fracture surfaces 202. In
FIG. 2, the sample shown is occluded with build powder 204 in the
areas around the strut fracture surfaces 202.
[0088] Referring to FIGS. 3-5, various embodiments of the present
invention are shown. In FIGS. 3-5, struts 302, 402, and 502 are
connected together at their respective nodes 304, 404, and 504 in
various combinations. Each of nodes 304, 404, and 504 is a
connection between only two struts. For example, in FIG. 5, node
504a comprises a connection between struts 502a and 502b; node 504b
comprises a connection between struts 502b and 502c; and node 504c
comprises a connection between struts 502b and 502d. By reducing
the number of struts 302, 402, and 502 that meet or are connected
at their respective nodes 304, 404, and 504, the diameter or
cross-sectional area where the struts 302, 402, and 502 are
connected is substantially equal to the cross-sectional area at the
respective nodes 304, 404, and 504. Therefore, the effect of the
stress risers (not shown) on the strength of the structure is
lessened in the structures illustrated in FIGS. 3-5. Consequently,
the resulting structures are substantially stronger than the
structures of the prior art illustrated in FIGS. 1A-1B.
[0089] FIGS. 6-8 illustrate alternative embodiments of the porous
structures of the present invention comprising strut and node
combinations where at least some of the struts are characterized by
a smaller cross-sectional diameter at the body of the strut than at
the stress riser. The struts 602, 702, and 802 are characterized by
a fluted or conical shape where each of struts 602, 702, and 802
flares to a wider cross-sectional diameter as the strut approaches
and connects at the respective nodes 604, 704, and 804. The designs
of FIGS. 6-8 illustrate incorporate fluted struts 602, 702, and 802
and non-fluted struts 606, 706, and 806, where both types of struts
are connected at the respective nodes 604, 704, and 804.
[0090] Thus, each of the connections between the fluted struts 602,
702, and 802 and the non-fluted struts 606, 706, and 806 has a
cross-sectional diameter that is essentially equivalent to the
maximum cross-sectional diameter of fluted struts 602, 702, and
802. Accordingly, the effect of the stress risers (not shown) of
the structures are thereby reduced. Referring to FIG. 9A, it is a
plan view of the struts 802 and nodes 804 in FIG. 8. FIG. 9B is a
plan view of an individual node in FIGS. 6-8, which is labeled as
struts 602 and node 604 for demonstrative purposes. Referring to
FIGS. 9A-9B, the fluted struts 602, 802 have a larger or maximum
cross-sectional diameter at the ends 606, 806 that meet at the
nodes 804, 604, and a smaller or minimum cross-sectional diameter
at the middle portions. Thus, the effect of stress risers (not
shown) at the junctions between the struts fluted struts 602, 702,
and 802 and the non-fluted struts 606, 706, and 806 are reduced.
Preferably, only two struts, e.g., 602 and 606, meet any given
node, e.g. 604, for added strength.
[0091] FIGS. 10A-10F illustrate 2-D representations of various
configurations of the frame of the struts and nodes in a porous
structure of the prior art. For simplification purposes, the struts
are not represented in 3-D but rather each strut is represented by
a different line, e.g., its frame, that is either solid, bolded
solid, or dashed lines. This representation is simply exemplary and
not meant to be limiting. In the prior art, it is typical for a
porous structure to have more than two struts meeting at a node
1002, regardless whether the strut may be straight, curved or
irregular. While FIG. 10A may show two struts meeting at a node,
the stress risers of this configuration has the effect of the
stress risers at a node with four struts connecting or intersecting
one another. For example, U.S. Publication Nos. 2006/0147332 and
2010/0010638 show examples of these prior art configurations
employed to form porous structures.
[0092] In contrast, to the prior art configurations of FIGS.
10A-10F, the present invention reduces the effect of the stress
risers at the nodes by ensuring that no more than two struts
intersect at a node. Consequently, some embodiments result in the
diameter or cross-sectional area where the struts intersect being
substantially equal to the cross-sectional area at each node,
thereby reducing the effect of the stress risers on the strength of
the structure. FIGS. 11A-11F illustrate exemplary embodiments of
the present invention for modifying the corresponding
configurations of the prior art to ensure that no more than two
struts intersect at a node. As seen in FIGS. 11A-11F, each of nodes
1102 has only two struts intersecting. For simplification purposes,
only one of the numerous nodes in 11A-11F is labeled with the
number 1102. In particular, the FIGS. 11A-11F show at nodes 1102,
the end of one strut intersect the body of another strut. Further,
the modification of the prior art configurations according to one
embodiment of the present invention forms a modified pore 1104 that
is open in each configuration that provides additional porosity
with added strength, which is a great improvement over the prior
art. FIGS. 12A-12D illustrate 3-D representations of exemplary
embodiments of the porous structure of the present invention formed
with one or more configurations in FIGS. 11A-11F, where the frames,
e.g., lines, have been given a thickness to form struts. In FIGS.
12A-12D, the porous structures have struts 1202 that intersect one
another at nodes 1204 where no more than two nodes intersect at a
node.
[0093] As demonstrated by FIGS. 11A-11F, the conventional nodes
1002 of FIGS. 10A-10F are effectively being "opened" up to ensure
that no more than two struts meet at a node. In addition to
reducing the effect of stress risers at the node, this "opening" up
of the conventional nodes 1002 of FIGS. 10A-10F into nodes 1102 of
FIGS. 11A-11F has the added benefit of reducing heat variations
during the fabrication process. As with any other thermal
processes, being able to control the heat variations, e.g.,
cooling, of the material is important to obtain the desired
material properties.
[0094] Referring to FIGS. 13A-13M, the present invention also
provides for embodiments that reduce the effect of stress risers by
incorporating curved struts into the porous structures. FIGS.
13A-13M illustrate 2-D representations of these various exemplary
configurations of the frame of the two struts of the present
invention forming a node, including frames for struts that are
straight, curved, or a combination of both. As shown, only two
struts intersect each other at the node 1302. At least in FIGS.
13A-13C, the struts intersect one another tangentially at the node
1302, providing increased mechanical strength and bonding. FIG. 14
illustrates 2-D representation of an exemplary embodiment of the
porous structure of the present invention comprising one or more
frame configurations in FIGS. 13A-13M, including frames for struts
that are straight, curved, or a combination of both. As shown by
FIG. 14, no more than two struts, whether curved or straight, meet
at each node. FIGS. 15A-15C illustrate 2-D representations of
exemplary configurations of the present invention of various curved
frames and corresponding struts intersecting to form a node 1502.
In FIGS. 15A-15C, the dashed lines represent the frames 1504 and
the solid lines represent the corresponding struts 1506. As shown,
node 1502a is formed where the circular strut with its center at
1508 tangentially intersect or meet the circular strut with its
center at 1510. The node 1502b is formed where the circular strut
with its center at 1508 tangentially intersect or meet the circular
strut with its center at 1512. Similarly, FIG. 15B shows the
circular strut with its center at 1514 tangentially intersecting
the circular strut with its center at 1516 to form node 1502c.
Likewise, FIG. 15C shows the circular strut with its center at 1518
tangentially intersecting the circular strut with its center at
1520 to form node 1502d. FIG. 16 illustrates a 3-D representation
of an exemplary embodiment of the porous structure of the present
invention comprising one or more frame configurations in FIGS.
13A-13M, including frames for struts that are straight, curved, or
a combination of both.
[0095] FIG. 17 illustrates a 3-D representation of an exemplary
frame for a generally cubical cell 1700 formed by twelve struts
1702 and sixteen nodes 1704. Again, for simplification purposes,
only some of the struts and nodes are labeled. By using sixteen
nodes 1704 that form connections between only two struts 1702 as
opposed to eight nodes that form connections between three struts
as in a conventional cube design (not shown), the cell 1700
provides stronger nodes 1704, and stronger connections between the
struts 1702 and nodes 1704. As a result, this novel configuration
of one embodiment of the present invention avoids variations in
cross-sectional diameters between struts 1702 and nodes 1704. As a
result, the negative effects of stress risers like those shown at
stress risers 106 and 114 in FIGS. 1A-1B on the strength of the
structure are lessened. FIG. 18 illustrates a porous structure 1800
formed from a plurality of connected cells 1802, which are similar
to those shown in FIG. 17. Similarly, FIGS. 19-20 show another
comparison between the arrangement of cells of the prior art in
FIG. 19 and one embodiment of the arrangement of cells of the
present invention in FIG. 20. As previously discussed, by having
more than two struts intersect at a node, the porous structure of
the prior art is weak due to the increased effect of the stress
risers. On the other hand, the arrangement in FIG. 20 of the
present invention provides the requisite porosity with an improved
strength because no more than two struts intersect at a node. In
addition, the arrangement of FIG. 20 has the added benefit of
having more trabecular features, resembling the characteristics of
cancellous bone, unlike the regular prior art configuration.
Moreover, the advantage of looking trabecular while being formed in
a calculated manner provides another benefit to the porous
structures formed in accordance with the invention: a decreased
need for expansive randomization of the porous structure.
Consequently, the arrangement of FIG. 20 resembles the
characteristics of bones more so than the prior art configuration
of FIG. 19. FIG. 21 is a blown up view of the arrangement in FIG.
20 where the dashed lines 2102 represent the frames of the struts
to better show where the struts meet to form a node.
[0096] Similarly, FIG. 22 illustrates another embodiment of a cell
of the present invention. Cell 2200 is based on a
tetrahedron-shaped cell, or a triangular pyramid, where it is
formed using only six struts 2202 and eight nodes 2204. Each node
2204 connects only two struts 2202 together. FIG. 23 illustrates a
similar cell 2300, which is a square-based pyramid. Referring to
FIG. 23, eight struts 2302 and eleven nodes 2304 are used to form
the cell 2300. Other geometrical shapes for cells, such as
dodecahedrons, icosahedrons, octagonal prisms, pentagonal prisms,
cuboids and various random patterns are discussed below. In
addition, FIGS. 17, 18, 22 and 23 illustrate frames of struts that
can be built from these frames where the thickness of each strut
can be selected. As such, the thickness for each strut can be
uniform or vary from one strut to another strut. Further, the
struts can incorporate the fluted struts of FIGS. 6-8. In addition,
the struts do not have to be cylindrical in shape. As further
discussed below, the cross-section of the struts can be rectangular
or square or any other shape, e.g., geometric shape or irregular
shapes, that would be suitable for the application.
[0097] As discussed above with respect to FIGS. 17, 18, 22, and 23,
various cell designs of various shapes can be created using various
techniques discussed above, e.g., DMF. Generally speaking, almost
any three-dimensional multiple-sided design may be employed. For
example, cells with an overall geometric shape such as Archimedean
shapes, Platonic shapes, strictly convex polyhedrons, prisms,
anti-prisms and various combinations thereof are within the
contemplation of the present invention. In other embodiments, the
number of sides of each cell may range from about 4 to about 24.
More preferably, the number of sides of each cell may range from
about 4 to about 16. One geometry that has been found to be
particularly effective is a dodecahedron or 12 sided cell. However,
as explained and illustrated below, the geometries of the
individual cells or the cells of the porous structure may vary
widely and in the geometries may vary randomly from cell to cell of
a porous structure.
[0098] For example, FIGS. 24A and 24B illustrate a conventionally
designed dodecahedral cell 2400 from a prior art porous structure
with each node 2404 being a connection between three struts 2402.
Again, U.S. Publication Nos. 2006/0147332 and 2010/0010638 disclose
examples of porous structures formed from these conventional cells.
A porous structure with a given porosity and having a desired
volume can be formed using a plurality of cells 2400 by attaching
one cell 2400 to another cell 2400 until the desired volume is
achieved. Further, the structures using the prior art cell
configuration may be disadvantageous because they do not resemble
the randomness of native cancellous structures. That is, they do
not adequately resemble the features of trabecular bone. More
importantly, referring to FIGS. 24A and 24B, higher stresses are
placed at each node 2404 because the struts 2402 intersect one
another at 120.degree. angles, thereby increasing stress
concentration factors due to the formation of notches or grooves on
the face of the nodes 2404 and the connection between more than two
struts 2402 at each node 2404.
[0099] FIGS. 25A and 25B illustrate one embodiment of the present
invention that provides a solution to these problems of the prior
art. As shown by FIGS. 25A and 25B, cell 2500 eliminated the
conventional nodes 2404 in FIGS. 24A and 24B by using curved struts
2502 that form a ring or hoop, thereby eliminating the stress
concentration factors caused by these nodes. In addition, cells
2500 replace conventional nodes 2404 in FIGS. 24A and 24B with
modified nodes 2504 that can be open or porous to provide
additional porosity, which is an added benefit for many
applications, such as enhancing tissue/bone ingrowth for
orthopeadic implants. Accordingly, cell 2500 provides additional
strength with increased porosity while the conventional cell 2400
is weaker and less porous.
[0100] FIGS. 26-28 illustrate one embodiment to forming the cell in
FIGS. 25A and 25B. FIG. 26 illustrates a dodecahedral frame 2600
for prior art cells as discussed with respect to FIGS. 24A and 24B.
FIG. 27 illustrates frame 2700 which comprises frame 2800 of FIG.
28 superimposed over the dodecahedral frame 2600 of FIG. 26. FIG.
29A illustrates a cell similar to that of FIGS. 25A and 25B formed
by selecting a thickness for frame 2800. In FIG. 29A, the cell 2900
is constructed from twelve curved struts 2902 that, in this
embodiment, may form a ring, a loop, an annulus, or a hoop. The
curved struts 2902 are joined together at triangular modified nodes
2904 that are more easily seen in FIG. 29B. Referring to FIG. 29B,
the thicker circles represent four of the curved struts 2902 of the
cell 2900 while the thinner circles highlight the modified nodes
2904 formed by struts 2902. Each modified node 2904 includes three
fused connections or sintering junctions 2906 between two different
curved struts 2902. That is, curved struts 2902 tangentially
intersect one another at the respective junction 2906. Depending on
the thickness of each strut 2902, modified node 2904 may also be
porous with openings 2908 disposed between the three junctions 2906
or occluded with no openings disposed between the three junctions
2906. Preferably, modified node 2904 has openings 2908 disposed
between the three junctions 2906 to provide additional porosity in
conjunction with the porosity provided by the fenestrations 2910 of
the curved struts 2902. Referring to FIG. 29B, while the struts
2906 tangentially intersect one another, e.g., their frame
tangentially meet, the struts' thickness may render the individual
junctions 2906 relatively long as indicated by the distance 2912.
These long, generally tangential sintering junctions 2906 provide
increased mechanical strength and bonding.
[0101] Referring to FIG. 30, it depicts an unfolded or flattened
two-dimensional representation of FIG. 27, with conventional frame
3008 and the frame 3010 of cell 2900. As shown by FIG. 30, the
location and number of individual junctions 3006, as compared to
conventional nodes 3004 of the conventional configuration 3008, is
different when using curved struts 3002 provided by the invention.
For example, junctions 3006 are generally located around the center
of the body of curved struts 3002, while conventional nodes 3002 is
located at the end of the conventional struts. In addition, in this
particular embodiment, the number of junctions 3006 where the
curved struts 3002 meet is three times the number of conventional
nodes 3004 where straight struts meet for frame 3008. Accordingly,
the increased number of junctions provide increased mechanical
strength.
[0102] FIGS. 31-34 illustrate how frames for cells based on a
typical polyhedron can be modified with curved struts to form a
cell similar to cell 2900 of FIG. 29. Specifically, FIG. 31
illustrates a frame 3100 of a truncated tetrahedral cell unfolded
into a 2-D representation. In FIG. 32, frame 3202 represents frame
3100 of FIG. 31 as modified by one embodiment the present invention
to be formed with curved struts 3202. Similarly, FIG. 33
illustrates the frame 3300 of a truncated octahedral cell unfolded
into a 2-D representation, and frame 3402 of FIG. 34 represents
frame 3300 of FIG. 31 as modified by one embodiment the present
invention to be formed with curved struts 3402. As discussed above,
e.g., with respect to FIG. 30, the cells formed with frames 3200
and 3400 have increased mechanical strength and porosity over
frames 3100 and 3300, respectively.
[0103] FIGS. 35A-35E illustrate one way of modifying a typical
polyhedron frame with curved struts. According to one embodiment of
the invention, the polyhedron can be modified by inscribing, within
the polyhedron, a circle or other shapes that contain curved
features, such as an ellipse or oblong. Specifically, FIG. 35A is a
circle inscribed within a square, FIG. 35B is a circle inscribed
within a hexagon, FIG. 35C is a circle inscribed within a triangle,
FIG. 35D is a circle inscribed within an octagon, and FIG. 35E is
an oval inscribed within a parallelogram. FIGS. 35A-35E are merely
demonstrative of the different configurations available and are not
intended to limit the scope of the invention.
[0104] FIG. 36 illustrates another way of modifying a typical
polyhedron frame with curved struts. According to another
embodiment of the invention, the polyhedron can be modified by
circumscribing the polyhedron with a circle or other shapes that
contain curved features, such as an ellipse or oblong. FIG. 36
illustrates a frame 3600 of a truncated tetrahedral cell with
circles 3602 circumscribed around each face of the cell. Some or
all portions of frame 3600 may be removed to form a new cell frame
that can be used to fabricate a porous structure according to the
present invention.
[0105] FIGS. 37-39 illustrate embodiments of the present invention
that incorporate both straight and curved struts. Specifically,
FIGS. 37A and 37B illustrate cell 3700 formed from frame 2700 of
FIG. 27, which is a combination of the dodecahedral frame 2600 of
FIG. 26 with frame 2800 of FIG. 28. Cell 3700 has increased
strength due to the addition of the curved struts, which result in
a blending of the stress risers. As shown, cell 3700 has modified
node 3704 comprising a conventional node formed with straight
struts 3702b and a node formed by three junctions of the curved
struts 3702a. FIG. 38 illustrates cell 3800 formed by keeping one
or more conventional nodes 3804 formed by straight struts 3802
while modifying the other struts of the cells with curved struts
3806 to form junctions 3808 and modified nodes 3810. In FIG. 38
some struts are selectively thicker than other struts, depending on
applications.
[0106] Referring to FIG. 38, the cell 3800 has at least one curved
strut 3802, and preferably a plurality of curved struts 3802 that
form modified node 3804a when joined with two other curved struts
3802. In other embodiments, the modified nodes can be formed by
joining together curved struts, curved strut sections, straight
struts, or straight strut sections, or combinations thereof. An
example of a node formed by joining together straight and curved
struts is shown in FIGS. 39A-39C as modified node 3904b. Modified
nodes 3804a are preferably triangular formed by three junctions
3806. Cell 3800 may contain some convention nodes 3808 that join
straight struts 3810 or straight strut sections that may comprise
notches formed by intersecting angles practiced in the prior art.
The modified node 3804a may be porous as discussed previously and
indicated by 3804a or occluded as indicated at 3804b. The occluded
modified nodes 3804b and the porous modified nodes 3804a may be
formed by tangent sintering three or more junctions 3806 between
curved or "ring-like" struts together. Any combination of occluded
nodes 3804b, porous modified nodes 3804a, conventional nodes 3808,
straight struts 3810, curved struts 3802, and portions or segments
thereof may be used in different predetermined or random ways in
order to create stronger, more cancellous-appearing cell structure.
Referring to FIGS. 39A-39C, cell 3900 is an example of such
combination. Cell 3900 has curved struts 3902a that are "ring-like"
and struts 3902b. It also has straight struts 3906 and conventional
nodes 3908. The combination of struts forms porous modified nodes
3904a and occluded modified nodes 3904b.
[0107] Thus, while the cells 3800 within a porous structure may be
homogeneous, they may be arranged in a random and/or predetermined
fashion with respect to each other to more closely resemble the
appearance of cancellous bone. In some instances, it may be
desirable to utilize one or more heterogeneous cell configurations
which may be arranged systematically in predetermined patterns
and/or arranged in random fashion to create a porous structure.
Various arrangements can be designed using computer aided design
(CAD) software or other equivalent software as will be apparent to
those skilled in the art.
[0108] FIGS. 40 and 41 show exemplary configurations of how the
cells 2400, 2900, and 3700 from FIGS. 24, 29, and 37, respectively,
can be combined, e.g., attached, joined, tiled, stacked, or
repeated. Specifically, FIG. 40 illustrates arrangement 4000
comprising cell 2400 and cell 2900 from FIGS. 24 and 29,
respectively. In arrangement 4000, at the face where cell 2400
attaches to cell 2900, conventional nodes 2404 is placed partially
within modified nodes 2904. Accordingly, by using various
combinations of cells 2400 and cells 2900, or other cells formed
according to the present invention, a number of modified nodes 2504
can be selectively occluded completely or partially by matching
conventional nodes with modified nodes. FIGS. 41A and 41B
illustrate arrangement 4100 comprising cells 2400, 2900, and 3700.
Again, FIGS. 40 and 41 are illustrative and do not limit the
combination that can be made with these cells or other cells formed
according to the embodiments of the present invention.
[0109] FIG. 42 illustrates a porous structure 4200 formed by
joining a plurality of cells 4202 together, where the shape of
cells 4202 is based on a truncated tetrahedron. One or more curved
struts 4204 which may or may not form complete rings are inscribed
within, or circumscribed around, each face of the selected
polyhedral shape, which is a truncated tetrahedron in FIG. 42.
Alternatively, the truncated tetrahedron shape or other selected
polyhedral shape may be formed using a large number of short
straight struts to closely approximate truly curved ring struts,
such as the ring struts of cell 2900 in FIG. 29.
[0110] FIGS. 43-45 illustrate 3-D representations of exemplary
arrangements cells formed in accordance with the embodiments of the
present invention. Specifically, FIG. 43 illustrates one way cells
based on truncated octahedra can be stacked to form bitruncated
cubic honeycomb structure 4300, which is by space-filling
tessellation. The cells of structure 4300 in both shades of gray
are truncated octahedra. For simplification purposes, each cell is
not modified with a curved strut but rather the dashed circle
serves to illustrate that one or more faces of one or more
truncated octahedra can be modified according to the embodiments of
the present invention, e.g., curved struts to form porous
structures with increased strength and porosity. Similarly, FIG. 44
illustrates one way, e.g., space-filling tessellation, cells based
on a combination of cubes (light grey), truncated cuboctahedra
(black), and truncated octahedra (dark grey) can be stacked to form
cantitruncated cubic honeycomb structure 4400. Again, it is
understood that the dashed circles represent how one or more
polyhedron of porous structure 4400 can be modified according to
the embodiments of the present invention, e.g., curved struts to
form porous structures with increased strength and porosity.
Likewise, FIG. 45 illustrates one way, e.g., space-filling
tessellation, cells based on a combination of cuboctahedra (black),
truncated octahedra (dark grey) and truncated tetrahedra (light
grey) can be stacked to form truncated alternated cubic honeycomb
structure 4500. Again, it is understood that the dashed circles
represent how one or more polyhedron of structure 4500 can be
modified according to the embodiments of the present invention,
e.g., curved struts to form porous structures with increased
strength and porosity.
[0111] FIG. 46 illustrates a frame view of the bitruncated cubic
honeycomb structure 4300 of FIG. 43. FIG. 47 illustrates a frame
view cantitruncated cubic honeycomb structure 4500 of FIG. 45. As
shown by FIGS. 46 and 47, porous structures formed with polyhedral
are not random, and thus, are not as suitable for implantation
purposes, particularly for bones, because they do not adequately
resemble the features of trabecular bone. On the other hand, as it
can be envisioned that modifying certain or all cells of the frames
in FIGS. 46 and 47 would result in porous structures resembling
trabecular bone.
[0112] When curved struts are employed, at least one curved strut
portion may generally form a portion of a ring which at least
partially inscribes or circumscribes a side of a polyhedron. Such a
polyhedral shape may be any one of isogonal or vertex-transitive,
isotoxal or edge-transitive, isohedral or face-transitive, regular,
quasi-regular, semi-regular, uniform, or noble. Disclosed curved
strut portions may also be at least partially inscribed within or
circumscribed around one or more sides of one or more of the
following Archimedean shapes: truncated tetrahedrons,
cuboctahedrons, truncated cubes (i.e., truncated hexahedrons),
truncated octahedrons, rhombicuboctahedrons (i.e., small
rhombicuboctahedrons), truncated cuboctahedrons (i.e., great
rhombicuboctahedrons), snub cubes (i.e., snub hexahedrons, snub
cuboctahedrons either or both chiral forms), icosidodecahedrons,
truncated dodecahedrons, truncated icosahedrons (i.e., buckyball or
soccer ball-shaped), rhombicosidodecahedrons (i.e., small
rhombicosidodecahedrons), truncated icosidodecahedrons (i.e., great
rhombicosidodecahedrons), snub dodecahedron or snub
icosidodecahedrons (either or both chiral forms). Since Archimedean
shapes are highly symmetric, semi-regular convex polyhedrons
composed of two or more types of regular polygons meeting in
identical vertices, they may generally be categorized as being
easily stackable and arrangeable for use in repeating patterns to
fill up a volumetric space.
[0113] In some embodiments, curved strut portions according to the
invention are provided to form a porous structure, the curved strut
portions generally forming a ring strut portion at least partially
inscribing within or circumscribing around one or more polygonal
sides of one or more Platonic shapes (e.g., tetrahedrons, cubes,
octahedrons, dodecahedrons, and icosahedrons), uniform polyhedrons
(e.g., prisms, prismatoids such as antiprisms, uniform prisms,
right prisms, parallelpipeds, and cuboids), polytopes, polygons,
polyhedrons, polyforms, and/or honeycombs. Examples of antiprisms
include, but are not limited to square antiprisms, octagonal
antiprisms, pentagonal antiprisms, decagonal antiprisms, hexagonal
antiprsims, and dodecagonal antiprisms.
[0114] In yet other embodiments, a porous structure may be formed
from cells comprising the shape of a strictly convex polyhedron,
(e.g., a Johnson shape), wherein curved strut portions generally
form a ring strut portion at least partially inscribed within or
circumscribed around one or more face of the strictly convex
polyhedron, wherein each face of the strictly convex polyhedron is
a regular polygon, and wherein the strictly convex polyhedron is
not uniform (i.e., it is not a Platonic shape, Archimedean shape,
prism, or antiprism). In such embodiments, there is no requirement
that each face of the strictly convex polyhedron must be the same
polygon, or that the same polygons join around each vertex. In some
examples, pyramids, cupolas, and rotunda such as square pyramids,
pentagonal pyramids, triangular cupolas, square cupolas, pentagonal
cupolas, and pentagonal rotunda are contemplated. Moreover,
modified pyramids and dipyramids such as elongated triangular
pyramids (or elongated tetrahedrons), elongated square pyramids (or
augmented cubes), elongated pentagonal pyramids, gyroelongated
square pyramids, gyroelongated pentagonal pyramids (or diminished
icosahedrons), triangular dipyramids, pentagonal dipyramids,
elongated triangular dipyramids, elongated square dipyramids (or
biaugmented cubes), elongated pentagonal dipyramids, gyroelongated
square dipyramids may be employed. Modified cupolas and rotunda
shapes such as elongated triangular cupolas, elongated square
cupolas (diminished rhombicuboctahedrons), elongated pentagonal
cupolas, elongated pentagonal rotunda, gyroelongated triangular
cupolas, gyroelongated square cupolas, gyroelongated pentagonal
cupolas, gyroelongated pentagonal rotunda, gyrobifastigium,
triangular orthobicupolas (gyrate cuboctahedrons), square
orthobicupolas, square gyrobicupolas, pentagonal orthobicupolas,
pentagonal gyrobicupolas, pentagonal orthocupolarotunda, pentagonal
gyrocupolarotunda, pentagonal orthobirotunda (gyrate
icosidodecahedron), elongated triangular orthobicupolas, elongated
triangular gyrobicupolas, elongated square gyrobicupolas (gyrate
rhombicuboctahedrons), elongated pentagonal orthobicupolas,
elongated pentagonal gyrobicupolas, elongated pentagonal
orthocupolarotunda, elongated pentagonal gyrocupolarotunda,
elongated pentagonal orthobirotunda, elongated pentagonal
gyrobirotunda, gyroelongated triangular bicupolas (either or both
chiral forms), gyroelongated square bicupolas (either or both
chiral forms), gyroelongated pentagonal bicupolas (either or both
chiral forms), gyroelongated pentagonal cupolarotunda (either or
both chiral forms), and gyroelongated pentagonal birotunda (either
or both chiral forms) may be utilised. Augmented prisms such as
augmented triangular prisms, biaugmented triangular prisms,
triaugmented triangular prisms, augmented pentagonal prisms,
biaugmented pentagonal prisms, augmented hexagonal prisms,
parabiaugmented hexagonal prisms, metabiaugmented hexagonal prisms,
and triaugmented hexagonal prisms may also be practiced with the
invention. Modified Platonic shapes such as augmented
dodecahedrons, parabiaugmented dodecahedrons, metabiaugmented
dodecahedrons, triaugmented dodecahedrons, metabidiminished
icosahedrons, tridiminished icosahedrons, and augmented
tridiminished icosahedrons may be employed. Moreover, modified
Archimedian shapes such as augmented truncated tetrahedrons,
augmented truncated cubes, biaugmented truncated cubes, augmented
truncated dodecahedrons, parabiaugmented truncated dodecahedrons,
metabiaugmented truncated dodecahedrons, triaugmented truncated
dodecahedrons, gyrate rhombicosidodecahedrons, parabigyrate
rhombicosidodecahedrons, metabigyrate rhombicosidodecahedrons,
trigyrate rhombicosidodecahedrons, diminished
rhombicosidodecahedrons, paragyrate diminished
rhombicosidodecahedrons, metagyrate diminished
rhombicosidodecahedrons, bigyrate diminished
rhombicosidodecahedrons, parabidiminished rhombicosidodecahedrons,
metabidiminished rhombicosidodecahedrons, gyrate bidiminished
rhombicosidodecahedrons, and tridimini shed rhombicosidodecahedrons
are envisaged. Snub disphenoids (Siamese dodecahedrons), snub
square antiprisms, sphenocorona, augmented sphenocorona,
sphenomegacorona, hebesphenomegacorona, disphenocingulum,
bilunabirotunda, and triangular hebesphenorotunda and other
miscellaneous non-uniform convex polyhedron shapes are
contemplated.
[0115] In some embodiments, the average cross section of the cell
fenestrations of the present invention is in the range of 0.01 to
2000 microns. More preferably, the average cross section of the
cell fenestrations is in the range of 50 to 1000 microns. Most
preferably, the average cross section of the cell fenestrations is
in the range of 100 to 500 microns. Cell fenestrations can include,
but are not limited to, (1) any openings created by the struts such
as the open modified pores, e.g., 3804a of FIG. 38 or 1104 of FIGS.
11A-11F, created by the junctions, e.g., 3806 of FIG. 38 or nodes
1102 of FIGS. 11A-11F, or (2) any openings inscribed by the struts
themselves, e.g., 2910 of FIG. 29B. For example, in embodiments
where the cell fenestrations are generally circular, the average
cross section of a fenestration may be the average diameter of that
particular fenestration, and in embodiments where the cell
fenestrations are generally rectangular or square, the average
cross section of a fenestration may be the average distance going
from one side to the opposite side.
[0116] Applying the above principles to other embodiments, FIGS.
51A and 51B illustrate a cell 5100 formed from an octahedron frame
shown in FIG. 48 modified according to one embodiment of the
present invention, shown in FIGS. 49-50. In FIG. 49, frame 4900 is
formed by inscribing circles within the faces of frame 4800 in FIG.
48. In FIG. 50, frame 5000 is formed by removing frame 4800 from
frame 4900 of FIG. 49. As shown in FIG. 49, the frame 5000
generally fits within the octahedron frame 4800. FIGS. 51A and 51B
illustrate the completed cell 5100, which is formed by selecting a
shape and thickness for frame 5000 in FIG. 50. Referring to FIGS.
51A and 51B, cell 5100 generally comprises eight curved struts 5102
that may be provided in the form of rings. The eight curved struts
5102 are connected to one another at twelve different junctions
5106. Six porous modified nodes 5104, each modified node having a
generally rectangular shape are formed by the four different
junctions 5106 and the corresponding struts 5102. As shown by FIGS.
51A and 51B, unlike the curved struts of cell 2500 of FIGS. 25A and
25B, curved struts 5102 have a rectangular or square cross-section
rather than a circular cross-section of cells similar to cells 2500
in FIGS. 25A and 25B. Cells with a rectangular or square
cross-section provide the porous structure with a roughness
different than that of the cells with a circular cross-section. It
is envisioned that struts of other embodiments can have different
shapes for a cross-section. Accordingly, the struts of a cell can
have the same cross-section, the shape of the cross-section of the
struts can be randomly chosen, or the cross-section shape can be
selectively picked to achieve the strength, porosity, and/or
roughness desired.
[0117] As another alternative, FIGS. 53A-53D illustrate yet another
cell 5300 based on a truncated tetrahedron frame shown in FIG. 52
as modified by one embodiment of the present invention. Referring
to FIGS. 53A-53D, the cell 5300 is formed in a similar manner to
cell 5100 of FIGS. 51A and 51B. That is, frame 5200 is inscribed
with circles to form a second frame comprising circular struts, and
frame 5200 is removed leaving behind the circular frame. Cell 5300
is completed by selecting a thickness and shape of the
cross-sectional area for the frame 5300. As discussed above, the
thickness and shape of the cross-section of the struts can be
uniform or it can vary randomly or in a predetermined manner,
including struts with a uniform cross-section or struts that are
fluted. Cell 5300 includes four larger curved struts 5302a that
correspond with the four large hexagonal sides of the truncated
tetrahedral frame 5200 and four smaller curved struts 5202b that
correspond with the four smaller triangular sides of the truncated
tetrahedral frame 5200. Alternative, a cell can be formed by
circumscribing a circle about the large sides 5202 and small sides
5204 of the truncated tetrahedral frame 5200. A 2-D representation
of this alternative embodiment is shown in FIG. 36. While not
expressly shown in the drawings, it is also contemplated that in
some embodiments, combinations of inscribed and circumscribed
curved struts may be employed. As illustrated in FIGS. 53A-53D,
porous triangular modified nodes 5304 are formed between three
junctions 5306 that connect the struts 5202a and 5202b together,
but those skilled in the art will recognize that occluded modified
nodes 3804b as shown in FIG. 38 may also be employed. Also, as
shown in FIGS. 53A-53D, larger curved struts 5302a have a circular
cross-section while smaller curved struts 5302b have a rectangular
cross-section. FIGS. 54A-54E illustrate various angles of a porous
structure formed by stacking cells 5300 of FIG. 53 in one exemplary
manner. It is envisioned that that in some embodiments, cells 5300
of FIG. 53 can be stacked in different manners as known be a person
skilled in the art.
[0118] FIGS. 55A-55E illustrate yet another embodiment where a cell
5500 is based on a hexagonal prism (Prismatic) frame with upper and
lower hexagons and that includes six vertical sides. The six
smaller curved struts 5502a are used for the six sides and larger
upper and lower curved struts 5502b are used for the top and
bottom. In the cell 5500 illustrated in FIGS. 55A-55E, the eight
curved struts 5302a, 5302b are connected by occluded modified nodes
5504 but, it will be apparent to those skilled in the art that
porous modified nodes such as those shown in FIG. 25 may also be
employed. In the particular embodiment shown in FIGS. 55A-55E, the
six smaller curved struts 5502a used for the six sides have a
slightly smaller cross-sectional area than the two larger upper and
lower curved struts 5302b. However, it would be apparent to those
skilled in the art that the struts with uniform or substantially
uniform cross-sectional areas can also be employed without
departing from the scope of this disclosure. FIGS. 56A-56B
illustrate various angles of a porous structure formed by stacking
cells 5500 of FIGS. 55A-55E in one exemplary manner. In FIGS. 56A
and 56B, cells 5500 are placed adjacent to one another to form a
layer 5602 and the layers are placed on top of one another either
in a predetermined or random manner. FIGS. 57A and 57B similarly
show a greater number of cells 5500 stacked in the same manner as
shown in FIGS. 56A and 56B. As seen, cells 5500 are stacked by
layers 5702. It is envisioned that in some embodiments, cells 5500
of FIG. 55 can be stacked in different manners as known to a person
skilled in the art.
[0119] FIGS. 58-61 illustrate dodecahedral frames 5800, 5900, 6000,
and 6100 modified according to another embodiment of the invention.
Instead of using curved struts or struts with curved portions to
eliminate or reduce conventional nodes 5802, 5902, 6002, and 6102,
the particular embodiments of FIGS. 58-61 adjust the conventional
nodes by ensuring at least one of the conventional nodes have no
more than two nodes intersecting at a node as shown by at least
FIGS. 11A-11F. As shown by FIGS. 58-61, frames 5800, 5900, 6000,
and 6100 have at least one modified node 5804, 5904, 6004, and
6104.
[0120] In some embodiment, the configurations of the cells, struts,
nodes and/or junctions may vary randomly throughout the porous
structure to more closely simulate natural bone tissue.
Particularly, the cells formed according to the present invention,
such as the cells illustrated in FIGS. 25A-25B, 29A, 37A-37B, 38,
39A-39C, 42, 51A-51B, 53A-53D, or 55A-55B, can be stacked or
repeated according to the methods outlined in U.S. Application No.
61/260,811, the disclosure of which are incorporated by reference
herein in its entirety. In addition, the methods of U.S.
Application No. 61/260,811 can also be employed to modify
conventional nodes such that no more than two struts intersect at a
node. In yet another embodiment, the porous structure formed
according to the invention can be used in medical implants, such as
an orthopedic implant, dental implant or vascular implant.
[0121] As further discussed in the following paragraphs, the
present disclosure also provides for a method to fabricate the
porous structures described above. Preferably, the improved porous
structures of the present invention is formed by using a free-from
fabrication method, including rapid manufacturing techniques (RMT)
such as direct metal fabrication (DMF). Generally, in free-form
fabrication techniques, the desired structures can be formed
directly from computer controlled databases, which greatly reduces
the time and expense required to fabricate various articles and
structures. Typically in RMT or free-form fabrication employs a
computer-aided machine or apparatus that has an energy source such
as a laser beam to melt or sinter powder to build the structure one
layer at a time according to the model selected in the database of
the computer component of the machine.
[0122] For example, RMT is an additive fabrication technique for
manufacturing objects by sequential delivering energy and/or
material to specified points in space to produce that part.
Particularly, the objects can be produced in a layer-wise fashion
from laser-fusible powders that are dispensed one layer at a time.
The powder is fused, melted, remelted, or sintered, by application
of the laser energy that is directed in raster-scan fashion to
portions of the powder layer corresponding to a cross section of
the object. After fusing the powder on one particular layer, an
additional layer of powder is dispensed, and the process is
repeated until the object is completed.
[0123] Detailed descriptions of selective laser sintering
technology may be found in U.S. Pat. Nos. 4,863,538; 5,017,753;
5,076,869; and 4,944,817, the disclosures of which are incorporated
by reference herein in their entirety. Current practice is to
control the manufacturing process by computer using a mathematical
model created with the aid of a computer. Consequently, RMT such as
selective laser re-melting and sinering technologies have enabled
the direct manufacture of solid or 3-D structures of high
resolution and dimensional accuracy from a variety of
materials.
[0124] In one embodiment of the present invention, the porous
structure is formed from powder that is selected from the group
consisting of metal, ceramic, metal-ceramic (cermet), glass,
glass-ceramic, polymer, composite and combinations thereof. In
another embodiment, metallic powder is used and is selected from
the group consisting of titanium, titanium alloy, zirconium,
zirconium alloy, niobium, niobium alloy, tantalum, tantalum alloy,
nickel-chromium (e.g., stainless steel), cobalt-chromium alloy and
combinations thereof.
[0125] As known by those skilled in the art, creating models of
cells or structures according to the disclosure of the present
invention can be done with computer aided design (CAD) software or
other similar software. In one embodiment, the model is built by
starting with a prior art configuration and modifying the struts
and nodes of the prior art configuration by either (1) adjusting
the number struts that intersect at a node, such as the
configurations in FIGS. 3-8, 11A-11F, 12A-12D, 17-20, or 22-23, or
(2) introduce curved portions to the struts such as the
configurations in FIGS. 13A-13M, 14, 15A-15C, 16, or 58-61. In
another embodiment, curved "ring-like" struts can be added to form
cells illustrated in FIGS. 25A-25B, 29A, 37A-37B, 38, 39A-39C, 42,
51A-51B, 53A-53D, or 55A-55B. Referring to FIG. 26, in one
embodiment, these cells can be formed by starting with a frame 2600
based on a polyhedron, such as a dodecahedron. Referring to FIG.
27, the next step is to inscribe circles within each face of the
frame 2600 to form frame 2700, which is frame 2800 superimposed on
frame 2600. Subsequently, frame 2600 can be removed from frame
2700, leaving only frame 2800. The thickness and shape of the
cross-section of frame 2800 can be selected to form a completed
cell, such as cell 2900 in FIG. 29A. As discussed above, a portion
of the faces of frame 2600 can be inscribed with circles and/or a
portion of frame 2600 can be removed to form, or frame 2600 is not
removed at all. The cells formed by such combinations are
illustrated in FIGS. 37A-37B, 38, and 39A-39C. As shown by FIGS.
48-53 and 55, the same steps can be applied to any type of frames
based on a polyhedron. Also with the aid of computer software,
stacking, tiling or repeating algorithm can be applied to create a
model of a porous structure with the desired dimensions formed from
unit cells or struts and nodes of the present invention. One such
stacking algorithm is space filling tessellation shown by FIGS.
43-45. As mentioned above, the methods disclosed in U.S.
Application No. 61/260,811, which is incorporated by reference
herein in its entirety, can be applied to stack the cells of the
present invention or to form the struts according to the
disclosures of the present invention by controlled
randomization.
[0126] Although the present invention and its advantages have been
described in detail, it should be understood that various changes,
substitutions and alterations can be made herein without departing
from the spirit and scope of the invention as defined by the
appended claims. Moreover, the scope of the present application is
not intended to be limited to the particular embodiments of the
process, machine, manufacture, composition of matter, means,
methods and steps described in the specification. As one of
ordinary skill in the art will readily appreciate from the
disclosure of the present invention, processes, machines,
manufacture, compositions of matter, means, methods, or steps,
presently existing or later to be developed that perform
substantially the same function or achieve substantially the same
result as the corresponding embodiments described herein may be
utilized according to the present invention. Accordingly, the
appended claims are intended to include within their scope such
processes, machines, manufacture, compositions of matter, means,
methods, or steps.
* * * * *