THREE-DIMENSIONAL POROUS STRUCTURES FOR INTERNAL BONE GROWTH AND METHODS FOR PRODUCTION.

Abstract

An orthopedic prosthetic component is provided. The orthopedic prosthetic component comprises a porous three-dimensional structure (100) shaped to be implanted in a patient's body. The porous three-dimensional structure comprises a plurality of unit cells (400). At least one unit cell comprises a first geometric structure having a first geometry and comprising a plurality of first columns (410) and a second geometric structure having a second geometry and comprising a plurality of second columns (420) connected to a number of the plurality of first columns to form the second geometric structure.

Description

THREE-DIMENSIONAL POROUS STRUCTURES FOR INTERNAL BONE GROWTH AND METHODS FOR THEIR PRODUCTION CROSS REFERENCE TO RELATED APPLICATIONS This claims priority to U.S. patent application serial no. 62 / 906,004, filed on September 25, 2019, the description of which is incorporated herein by reference as if set forth herein in its entirety. TECHNICAL FIELD The modalities described in this description are generally directed to porous metallic structures and methods for manufacturing them, and, more specifically, to porous metallic structures in medical devices that have geometric grid configurations suitable to allow precise control of porosity and pore size in a porous metallic structure. BACKGROUND OF THE INVENTION The modalities described in this description are generally directed towards three-dimensional porous structures for internal bone growth and methods for producing such structures. Over the years, there have been many advances in the field of rapid prototyping and additive manufacturing, particularly for the rapid prototyping of items such as prototype parts and mold dies. These advances result in reduced manufacturing costs and time, while simultaneously increasing the accuracy of the finished product, compared to conventional machining processes, such as those where materials (e.g., metal) start as a block of material and are subsequently machined into the finished product. However, the rapid prototyping of three-dimensional structures has primarily focused on increasing the density of rapidly created prototypes. Examples of modern rapid prototyping / additive manufacturing techniques include sheet lamination, adhesive bonding, laser sintering (or selective laser sintering), laser melting (or selective laser sintering), photopolymerization, drop deposition, stereolithography, 3D printing, fused deposition modeling, and 3D graphics. Particularly in the areas of selective laser sintering, selective laser melting, and 3D printing, the improvement in the production of high-density parts has made these techniques useful for precisely designing and producing items such as highly dense metal parts. In recent years, the field of additive manufacturing has focused on creating solutions that provide the mechanical strength, interconnected channel design, porosity, and pore size in porous structures necessary for promoting mammalian cell growth and regeneration. However, current methods and geometries have limited control over pore size distribution, which strongly influences the internal growth behavior of mammalian cells, such as bone cells. Furthermore, current methods and geometries often fall short of producing porous structures with unit cell geometries that simultaneously achieve pore sizes and porosities within the range considered beneficial for internal growth while maintaining structural integrity during the manufacturing process (e.g., 3D printing).As a result, current unit cell geometric structures must have either very large pore sizes or very low porosity. Furthermore, current methods and geometries generally avoid the close correlation between the length and diameter of a selected unit cell column within the structure's geometry and the resulting desired geometric characteristics of the porous structure. Current methods for manufacturing porous metallic materials for bone ingrowth have limited control over pore size distribution, which strongly influences bone ingrowth behavior. Improved simultaneous control of maximum pore size, minimum pore size, and porosity would allow for better bone ingrowth. Additive manufacturing techniques conceptually allow the production of lattice structures with perfect geometric control, but are practically limited by the minimum external column diameter the machine can build and by the requirement that any lattice structure be self-supporting. The minimum column diameter for current 3D printers is approximately 200–250 microns, meaning that many geometric structures must have either very large pore sizes or very low porosity. SUMMARY OF THE INVENTION According to one aspect of the description, an implantable device includes a porous, three-dimensional structure designed to be implanted in a patient's body. The porous, three-dimensional structure includes a plurality of interconnected organic unit cells. Each organic unit cell includes a plurality of external columns and a plurality of internal columns. The respective groups of three external columns intersect to define a respective plurality of external nodes. Each internal column extends from one of the respective external nodes, and the internal columns intersect to define an internal node. The plurality of external nodes includes a first external node defined by the intersection of a first group of three external columns and a second external node defined by the intersection of a second group of three external columns.A shorter path along the columns from the first external node to the second external node includes only three intermediate external nodes out of the plurality of external nodes. An imaginary straight line extends through the first external node and the second external node, and the internal node is offset from this imaginary straight line. In one example, each of the external columns has a constant thickness along its entire length. In another example, each of the internal columns has a constant thickness along its entire length. In another example, at least one of the outer columns is curved along its length. In another example, at least one of the internal columns is curved along its length. In another example, all external columns extend from and to a respective pair of external nodes along their respective lengths, and the lengths of at least some of the external columns are different from each other. In another example, at least one of the outer columns is bent. In another example, all the external columns are substantially straight along their entire respective lengths. In another example, the plurality of external columns includes a longer external column and a shorter external column whose length is not less than approximately 60% of that of the longer external column. In another example, the plurality of external columns includes a longer external column and a shorter external column whose length is not less than approximately 1 / 3 of that of the longer external column. In another example, at least one of the internal columns is bent. In another example, all the internal columns are substantially straight along their entire respective lengths. In another example, the implantable appliance has a porosity between approximately 50% and approximately 75%. In another example, the implantable appliance includes a number of pores defined by the unit cells, respectively, where less than 14.3 percent of the pores have a pore size smaller than 0.1 mm. Fifty percent of the pores may have a pore size ranging from approximately 0.2 mm to approximately 0.7 mm. In another example, the external columns cooperate to define a number of external openings, the internal columns cooperate with a number of the external columns to form a number of internal openings, the porous three-dimensional structure defines window sizes defined as a diameter of a circle positioned at the corresponding external and internal openings, such that each of the columns that defines the external and internal openings, respectively, is positioned on a tangent line of the circle, and the implantable appliance comprises a number of pores defined by the unit cells, respectively, the pores defining a ratio of their respective pore sizes to any of their window sizes that is in the range of 1.00 to 2.90. In another example, the internal node is the only internal node of the porous three-dimensional structure that is internal with respect to the external nodes. In another example, all internal columns intersect at the internal node. In another example, the implantable device comprises an organic rhododic trigonal trapezohedron that has greater ductility than a corresponding geometric rhododic trigonal trapezohedron. In another example, each organic unit cell defines a first half and a second half separated from the first half by a plane that dissects the organic unit cell structure, and for all orientations of the plane, 1) at least some of the external nodes of the first half of the organic unit cell structure are repositioned with respect to the corresponding external nodes of a geometric unit cell structure in a first orientation and 2) at least some of the external nodes of the second half of the organic unit cell structure are repositioned with respect to the corresponding external nodes of the corresponding geometric unit cell structure in the second direction different from the first direction. In another example, an orthopedic implant includes the porous three-dimensional structure and a solid base, where the porous three-dimensional structure is attached to the solid base. According to another aspect of the present description, an implantable device includes a porous three-dimensional structure that is shaped to be implanted in a patient's body. The porous three-dimensional structure includes a plurality of interconnected organic unit cell structures. Each organic unit cell structure includes a plurality of external columns. At least three external columns from the plurality of external columns intersect to define a respective plurality of external nodes. The external columns and nodes combine to substantially define a geometric structure that is within 50% of a geometric rhombic dodecahedron. The external columns have a constant thickness along their entire lengths. The external nodes include a first external node and a second external node opposite the first external node to define a first pair of opposite nodes. The external nodes further include a third external node and a fourth external node opposite the third external node to define a second pair of opposite nodes.The external nodes also include a fifth external node and a sixth external node opposite the fifth external node to define a third pair of opposite nodes. All opposite external nodes are separated from each other by three intermediate external nodes along the shortest path along the external columns. A first imaginary straight line extends through the first external node and the second external node, a second imaginary straight line extends from the third external node to the fourth external node, and a third imaginary straight line extends from the fifth external node to the sixth external node.The first and second imaginary straight lines intersect each other at a first intersection with respect to a selected view of the porous three-dimensional structure, and the third imaginary line intersects the first imaginary straight line at a respective second intersection that is offset from the first intersection with respect to the selected view of the porous three-dimensional structure. In one example, each organic unit cell structure defines a first half and a second half separated from the first half by a plane that bisects the organic unit cell structure. For all orientations of the plane, 1) at least some of the external nodes of the first half of the organic unit cell structure are repositioned with respect to the corresponding external nodes of a geometric unit cell structure in a first orientation, and 2) at least some of the external nodes of the second half of the organic unit cell structure are repositioned with respect to the corresponding external nodes of the corresponding geometric unit cell structure in a second direction different from the first direction. In another example, the external columns define a first geometric structure and the porous three-dimensional structure further includes a plurality of internal columns which, in combination with the external columns, define a plurality of second geometric structures within the first geometry. In another example, the plurality of internal columns consists of four internal columns that intersect each other to define an internal node. In another example, the plurality of internal columns consists of eight internal columns, where the entire plurality of internal columns intersects at least one other internal column. In another example, the implantable device comprises an organic rhombic dodecahedron that has greater ductility than a corresponding geometric rhombic dodecahedron. According to yet another aspect of the present description, an implantable device includes a porous three-dimensional structure designed to be implanted in a patient's body. The porous three-dimensional structure includes a plurality of interconnected unit cells. Each unit cell includes a plurality of columns. At least three columns of the plurality of columns intersect to define a respective plurality of nodes, and at least one of the columns of the plurality of columns is bent along its length between a first node of the plurality of nodes and a second node of the plurality of nodes. In one example, the columns define groups of three columns that intersect each other to define the first node and the second node. According to another aspect, a porous three-dimensional structure is designed to be implanted in a patient's body. The porous three-dimensional structure includes a plurality of interconnected unit cells. Each unit cell includes a plurality of columns. At least three columns of the plurality of columns intersect to define a respective plurality of nodes, and at least one of the columns of the plurality of columns is bent along its length between a first node of the plurality of nodes and a second node of the plurality of nodes. In another example, an orthopedic implant includes the porous three-dimensional structure and a solid base, where the porous three-dimensional structure is attached to the solid base. BRIEF DESCRIPTION OF THE FIGURES For a more complete understanding of the principles described herein, and their advantages, reference is now made to the following descriptions taken in conjunction with the accompanying figures, in which: Figure 1 is a simplified elevation view of an orthopedic prosthetic component; Figure 2 is a simplified perspective view of the orthopedic prosthetic component of Figure 1; Figure 3 is a perspective view of a unit cell of the porous structure of the orthopedic prosthetic component of Figures 1-2; Figure 4 is a perspective view of a geometric structure of the unit cell of Figure 3; Figure 5 is a simplified perspective view of another geometric structure of the unit cell of Figure 3; Figure 6 is a perspective view of another modality of a unit cell of a porous structure for the orthopedic prosthetic component of Figures 1-2; Figure 7 is a simplified perspective view of another geometric structure of the unit cell of Figure 3; Figure 8 illustrates a diagram of the percentage of porosity compared to column length / diameter for various unit cell geometries, according to various modalities; Figure 9 illustrates a diagram of pore size and minimum pore window opening size compared to the percentage of porosity for various unit cell geometries, according to various modalities; Figure 10 illustrates an association of window size with a unit cell structure, according to various modalities; Figure 11 illustrates a workflow for producing a porous three-dimensional structure according to various modalities. Figure 12A is another perspective view of the geometric structure of the unit cell in Figure 4; Figure 12B is a perspective view of an organic structure that is 25% modified with respect to the geometric structure illustrated in Figure 12A; Figure 12C is a perspective view of an organic structure that is 50% modified with respect to the geometric structure illustrated in Figure 12A; Figure 13A is another perspective view of the geometric structure of the unit cell in Figure 3; Figure 13B is a perspective view of an organic structure that is 25% modified with respect to the geometric structure illustrated in Figure 13A, which shows straight outer columns and bent outer columns; Figure 13C is a perspective view of the organic structure of Figure 13B, which shows all straight external columns; Figure 13D is a perspective view of an organic structure that is 50% modified with respect to the geometric structure illustrated in Figure 13A, which shows straight outer columns and bent outer columns; Figure 13E is seen in perspective of the organic structure of Figure 13D, which shows all straight external columns; Figure 14 illustrates a graph representing the percentage of pores as a function of pore diameter for a three-dimensional porous structure having the unit cell geometry illustrated in Figure 13C and a porosity of approximately 55%; and Figure 15 illustrates a graph representing the percentage of pores as a function of pore diameter for a three-dimensional porous structure having the unit cell geometry illustrated in Figure 13C and a porosity of approximately 65%. DETAILED DESCRIPTION OF THE INVENTION This specification describes illustrative modes and applications of the description. However, the description is not limited to these illustrative modes and applications or to the manner in which the illustrative modes and applications operate or are described herein. Furthermore, the Figures may show simplified or partial views, and the dimensions of the elements in the Figures may be exaggerated or otherwise disproportionate. In addition, because the terms "on," "attached to," "connected to," "coupled to," or similar words are used herein, an element (e.g., a material, a layer, a base, etc.) may be on, attached to, connected to, or coupled to another element regardless of whether the element is directly on, attached to, connected to, or coupled to the other element, whether there are one or more intermediate elements between the element and the other element, or whether the two elements are integrated as a single piece.Furthermore, unless the context otherwise indicates, directions (e.g., above, below, top, bottom, side, upward, underneath, over, superior, inferior, horizontal, vertical, x, y, z, etc.), if provided, are relative and are given only as examples and to facilitate illustration and analysis, not as a limitation. Additionally, when a list of items is referenced (e.g., items a, b, c), such reference is intended to include any of the listed items individually, any combination of fewer than all of the listed items, and / or a combination of all the listed items. Section divisions in the specification are for ease of review only and do not limit any combination of the described items. As used in the present description, bonded or union denotes a metal-to-metal bond due to a variety of physicochemical mechanisms including, but not limited to: metallic bonding, electrostatic attraction and / or adhesive forces. Unless otherwise defined, the technical and scientific terms used in connection with the teachings described herein shall have the meanings as commonly understood by those skilled in the art. This description relates to porous three-dimensional metal structures and methods for manufacturing them for medical applications. As described in more detail below, porous metal structures promote hard or soft tissue interlocking between prosthetic components implanted in a patient's body and the surrounding hard or soft tissue. For example, when incorporated into an orthopedic prosthetic component designed for implantation in a patient's body, the porous three-dimensional metal structure can be used to provide a porous outer layer of the orthopedic prosthetic component to form an internal bone growth structure. Alternatively, the porous three-dimensional metal structure can be used as an implant with the structural integrity required to fulfill the intended function of the implant and to provide interconnected porosity for tissue interlocking (e.g.,(internal bone growth) with the surrounding tissue. In various forms, the types of metals that can be used to form porous three-dimensional metallic structures may include, but are not limited to, titanium, titanium alloys, stainless steel, chromium-cobalt alloys, tantalum, or niobium. With reference to Figures 1 and 2, an implantable appliance such as an orthopedic implant or prosthetic component 100 is illustrated. The prosthetic component 100 includes a base 110, a porous three-dimensional structure or layer 120, and a cone or stem 130 extending away from the base 110. In the illustrative embodiment, the porous structure 120 surrounds a portion of the base 110 and a portion of the stem 130. It should be appreciated that the porous structure 120 can be provided as a separate layer from the base 110 and / or the stem 130. The porous structure 120 can also be provided as a coating surrounding the entire base 110 and / or the entire stem 130. As described in more detail later, the porous structure includes a plurality of unit cells that define voids or spaces that allow for internal bone growth, thereby promoting fixation of the prosthetic component. 100 to a patient's bone. The orthopedic implant 100 can be implanted in a tibial bone. For example, the stem 130 can be inserted into the tibial bone, with a flange portion 140 of the implant 100 resting against a proximal portion of the tibial bone. It should be appreciated that the various porous structures described herein can be incorporated into various orthopedic implant designs, including, for example, a tibial prosthetic component or a femoral prosthetic component similar to the tibial and femoral components shown in U.S. Patent No. 8,470,047, which is expressly incorporated herein by reference. The porous structures can also be included in other orthopedic implant designs, including a patellar component shaped to mate with a femoral prosthetic component and prosthetic components for use in hip or shoulder arthroplasty surgery. It should also be noted, for the purposes of the foregoing and what follows, that the 110 base can be any type of structure capable of, for example, contacting, supporting, connecting to, or being attached to components of various types described herein. The 110 base can include, for example, a metallic or non-metallic tray, a metallic or non-metallic base plate, a metallic or non-metallic structure that sits on a tray, and so on. The types of metal that can be used to form the 110 base include, but are not limited to, titanium, titanium alloys, stainless steel, chromium-cobalt alloys, tantalum, or niobium. In the illustrative embodiment, the stem 130 includes a solid region 150, which is coated by a porous region 160 of the porous structure 120. The solid region 150 of the stem 130 is fixed to the base 110 and extends outward from the porous structure 120 such that the porous structure 120 surrounds the region of the stem 130 proximal to the base 110. In other embodiments, the stem 130 may be fixed to the porous structure 120. The types of metal that may be used to form the stem 130 include, but are not limited to, titanium, titanium alloys, stainless steel, chromium-cobalt alloys, tantalum, or niobium. With reference to Figure 4, the porous structure 120 of the implant 100 includes a plurality of connected unit cells, and at least some, up to all, of the unit cells illustratively have the geometric unit cell structure 200 shown in Figure 4. The types of metal that can be used to form the unit cell structures shown include, but are not limited to, titanium, titanium alloys, stainless steel, chromium-cobalt alloys, tantalum, or niobium. As shown in Figure 4, each geometric unit structure includes a plurality of columns 208, which in turn include a plurality of external columns 210. The external columns 210 combine to define a lattice structure. The external columns 210 cooperate to form an external geometric structure 230. In the illustrative modality, the external geometry is a geometric rhombic dodecahedron 215.As described later with respect to Figures 12A-14C, unit cells can include organic structures that differ from geometric structures. In some examples, the organic structures are modified with respect to the geometric structures. As used in this description, the terms substantial, approximately, approximate, words of similar scope and derivatives thereof when used with respect to a size, shape, dimension, direction, orientation or the like include the size, shape, dimension, direction, orientation or the like indicated, as well as a range associated with typical manufacturing tolerances, such as plus and minus 2%. With reference to Figure 4, the external columns 210 further intersect each other to define a plurality of external vertices or external nodes 212. The respective groups of at least three of the external columns 210 intersect each other to define a respective plurality of external nodes 212. For example, each of the external nodes 212 is defined by an intersection of three of the external columns 210. Each of the external columns 210 thus extends from a respective first node of the external nodes 212 to a respective second node of the external nodes 212 along a respective length. Furthermore, each of the plurality of external nodes 212 has a position in three-dimensional space (e.g.,, along an x ​​direction, a y direction and a z direction that are all oriented perpendicular to each other) with respect to the remaining external nodes 212 of the plurality of external nodes 212 that define the nodes 212 of the geometric rhombic dodecahedron 215. When the external columns 210 define the geometric rhombic dodecahedron 215, the columns 210 combine to define fourteen external nodes 212. As shown in Figure 3, the columns 208 include a plurality of external columns 210 and a plurality of internal columns 220. Therefore, each geometric unit cell structure 200 illustrated in Figure 3 includes a plurality of external columns 210 and a plurality of internal columns 220, forming a first geometric structure 230 and a plurality of second geometric structures 240 that are within the first geometric structure 230. In the illustrative form, the first geometric structure 230 comprises the plurality of external columns 210. As described above with respect to Figure 4, the plurality of external columns 210 in Figure 3 cooperate to form a geometric rhombic dodecahedron. Therefore, the first geometric structure 230 defines a geometric rhombic dodecahedron. Internal columns 220 intersect each other to define an internal node 232.In the illustrated mode, all internal columns 220 intersect each other to define the internal node 232. In the illustrated mode, the internal columns 220 intersect each other to define only the single internal node 232 and no other internal nodes. At least some, up to all, of the connected unit cells of the porous structure 120 of the implant 100 may have the unit cell structure 200 shown in Figure 3. Consequently, the unit cell structure 200 defines only a single internal node 232 that is internal with respect to the external nodes 212. Each of the plurality of second geometric structures 240 has an internal volume 250 that is substantially equal to the internal volumes 250 of the other second geometric structures 240. As shown in Figure 5, each second geometric structure 230 is formed by a number of internal columns 220 and a number of external columns 210. Each second geometric structure 230 is illustratively a geometric trigonal trapezohedron. As illustrated in Figure 3, the plurality of second geometric structures 240 within the first geometric structure 230 includes four geometric trigonal trapezohedrons such that the unit cell structure 200 is a geometric rhombic trigonal trapezohedron (GRTT).As will be seen from the description below, a rhombic trigonal trapezohedron (RTT) can be configured as a geometric RTT (GRTT) and alternatively can be configured as an organic RTT (ORTT). It should be noted that each unit cell structure can include other types of secondary geometric structures. For example, as shown in Figure 6, a unit cell structure 300 includes a plurality of external columns 310 and a plurality of internal columns 320, which form a first geometric structure 330 and a plurality of secondary geometric structures 340 that are contained within the first geometric structure 330. In the illustrative form, the first geometric structure 330, like the first geometric structure 230, comprises the plurality of external columns 310 and is a geometric rhombic dodecahedron. The external columns 310 can define constant thicknesses along their entire lengths. Furthermore, the external columns 310 can have equal thicknesses. The internal columns 320 can also define constant thicknesses along their entire lengths.Furthermore, the internal 320 columns can have equal thicknesses. Moreover, the internal 320 columns and the external 310 columns can have equal thicknesses. Alternatively, the internal 320 columns and the external 310 columns can have different thicknesses. In examples where the external 310 columns and the internal 320 columns are cylindrical, the respective thicknesses define the diameters of the external 310 columns and the internal 320 columns, respectively. As shown in Figure 7, each second geometric structure 340 is formed by a number of inner columns 320 and a number of outer columns 310. Each second geometric structure 340 is illustratively a geometric octahedron (e.g., a diamond-shaped structure). As illustrated in Figure 6, the plurality of second geometric structures 340 within the first geometric structure 330 includes six geometric octahedra such that the unit cell structure 300 is a geometric rhombic octahedron (GRO). Within the unit cell structures of the porous three-dimensional structure described above, at least one column of a certain length and diameter within each unit cell can be configured to meet predetermined or desired geometric properties of the unit cell structure. In some examples, at least one column of a certain length and diameter within each unit cell of the MA / t / ZUZZ / U4O I04 The organic structure can be modified with respect to at least one corresponding column of the geometric structure. These geometric properties can be selected from the group consisting of porosity, pore size, minimum window size, and combinations thereof. It was advantageously found that certain geometric structures (described later) of the unit cell structure could optimize one or more of these geometric properties to provide a more robust and homogeneous geometry. The resulting geometry provides enhanced internal bone growth while maintaining the required porous structure stability. With regard to porosity, the porous structure 120 has a porosity of between approximately 50% and approximately 75%. As described above, the term "approximately" refers to a range associated with typical manufacturing tolerances. Thus, a porosity of approximately 50% could be 50% plus or minus a typical manufacturing tolerance such as, for example, 2% (i.e., a range of 48% to 52%). In other configurations, the porosity of the three-dimensional porous structure is between approximately 20% and approximately 95%. Geometrically, the porosity of the unit cell structure depends on the ratio between the column length (a) and the column diameter (d).Figure 8, for example, provides an 800 diagram of the percentage of porosity versus column length / diameter for various unit cell geometries, according to various modalities. As described in the 800 diagram, three particular unit cell geometries / structures were examined, specifically, a geometric rhombic dodecahedron (GRD) (see, e.g., Figure 4), a geometric rhombic dodecahedron provided with four internal columns (GRD+4) (or geometric rhombic trigonal trapezohedron) (see, e.g., Figure 3), and a geometric rhombic dodecahedron provided with eight internal columns (GRD+8) (or geometric rhombic octahedron) (see, e.g., Figure 6).For each of the structures, porosities in various a / da ratios were obtained from a design file for each unit cell structure and the ratio for each unit cell structure was modeled by fitting the data to a fourth-order polynomial equation of the form:. Pürosrcw = 4 « f +- B - (%)' + C > (%-)' + D - (¾ ) + F (1) where A, B, C, D and E are constants. In this comparison, the dimensions of the structure were derived geometrically from the column length and diameter of each unit cell structure. As shown in diagram 800 in Figure 8, the geometric RD structure generally has a higher porosity at a given a / d ratio, which is expected due to its lack of internal columns compared to the geometric RD+4 and RD+8 structures. The porosity for the geometric RD structure is illustrated by line 802. However, this decrease in porosity in the geometric RD+4 and RD+8 structures, illustrated by lines 804 and 806, respectively, allows designs made with them to achieve combinations of relatively lower porosity, smaller pore size, and relatively larger window size at a constant column diameter (fixed by the printer's build resolution) not possible with the geometric RD, as described in more detail later. Now, with reference to Figure 9, a 900 diagram of pore size and minimum pore window size versus porosity percentage is provided for various unit cell geometries / structures, according to various modalities. As in Figure 8, three particular unit cell structures were examined, specifically, a rhombic dodecahedron (GRD) (see, e.g., Figure 4), a geometric rhombic dodecahedron provided with four internal columns (GRD+4) (or geometric rhombic trigonal trapezohedron) (see, e.g., Figure 3), and a geometric rhombic dodecahedron provided with eight internal columns (GRD+8) (or geometric rhombic octahedron) (see, e.g., Figure 6).The pore size of the geometric rhombic dodecahedron, for example, was taken as the equivalent diameter of a sphere within the limited volume of the geometric rhombic dodecahedron unit cell, and the volume was calculated by taking the volume of the geometric rhombic dodecahedron of the column length (a) and subtracting the volume of each column within or limited by the geometric rhombic dodecahedron. The equations provided in this description for calculating the pore size (PS) depend on the column length (a), diameter (d), and porosity (p) in decimal units. The equations are as follows: For the SRD structure: PS = (2) \ X * 'X '· _ x For the SRD+4 structure: PS = [ti — {1 -y}) - (4 - V3 * c3)-0.5- (v - β3- * - 075 * 4 “ - {4-2^2}}] (3) For the SRD+8 structure: PS = [(1- {1 -y}) Y3^3)-.t » c2« {2e - + 4.5c3- {2 λ 2 - Ve}] (4) Line 902 in diagram 900 illustrates the relationship between pore size and porosity percentage for the geometric rhombic dodecahedron (SRD). Line 904 illustrates the relationship between pore size and porosity percentage for the geometric rhombic trigonal trapezohedron (SRD+4), and line 906 illustrates the relationship between pore size and porosity percentage for the geometric rhombic octahedron (SRD+8). As shown in diagram 900 in Figure 9, at lower porosity percentages, the three structures generally provided similar required pore sizes. However, as the determined porosity percentage increases (and assuming the column diameters remain substantially the same), the required pore size in the SRD structure to accommodate the porosity percentage becomes significantly larger than in the other structures. This places more stringent requirements on the SRD structure as the required porosity increases, as the pore size becomes more demanding beyond that effective for internal bone growth. In other words, as the required porosity percentage increases, the SRD structure loses effectiveness, which is particularly noticeable when designing porous three-dimensional structures, such as those described herein. With reference now to Figure 10, each unit cell structure 200 has a plurality of external faces 1002, and the external columns 210 cooperate to define a number of openings 1004 in the external faces 1002. The internal columns 220 of the unit cell structure 200 cooperate with a number of external columns 210 to form a number of internal openings 1006. The minimum window size or aperture of each of the openings 1004, 1006 can be defined as the diameter 1008 of a circle 1010 positioned in the corresponding opening (illustratively, one of the openings 1004 in Figure 10) such that each column 210 (or column 220) lies on a tangent line to the circle 1010. The lengths and diameters of the columns thus determine the size of each of the openings. 1004, 1006 and, by extension, the diameter of the largest sphere that can fit into them.For example, for a given column length, as the column diameter increases, the minimum window opening would decrease. These associations are provided by the following equation, which was used to calculate the minimum window opening for all structures (e.g., SRD, SRD+4, SRD+8, etc.) and generate lines 908, 910, 912 in Figure 9: m - j \ 2 r — r (5) For the purposes of Diagram 900, the minimum window opening is the diameter of the largest circle 1010 that can fit into each opening. In other words, it is the diameter of the inscribed circle and, as such, depends on the column length (a) and diameter (d). The relationship between window size and porosity percentage for various unit cell geometries is shown. Line 908 in Diagram 900 illustrates the relationship between minimum window opening and porosity for the geometric rhombic dodecahedron (GRD). Line 910 illustrates the relationship between minimum window opening and porosity for the geometric rhombic trigonal trapezohedron (GRD+4), and line 912 illustrates the relationship between minimum window opening and porosity for the geometric rhombic octahedron (GRD+8). As shown in diagram 900 in Figure 9, at generally all porosity percentages, there is a generally uniform spacing in the minimum window opening between each unit cell structure. Therefore, regardless of the porosity percentage required for a given three-dimensional porous structure with a substantially constant column diameter, the SRD+8 structure will have a larger minimum window opening than the SRD+4 and SRD structures, and both the SRD+8 and SRD+4 structures will have a larger minimum window opening than the SRD structure, at a given porosity percentage. The results in Figure 9 establish that structures with internal columns, namely SRD+4, and to a lesser extent SRD+8, are advantageous compared to the SRD structure. SRD+4 and SRD+8 allow for a smaller pore size at a given porosity and column diameter. Any apparent advantage of SRD in porosity as a function of the a / d ratio diminishes almost entirely as the required a / d ratio increases. Finally, the SRD+4 and SRD+8 structures (or structures with internal columns) provide the most homogeneous structure by offering a smaller difference between pore size and window size than the SRD structure. In porous structure 120, the ratio of the pore size of a unit cell to any of its corresponding window sizes ranges from 1.50 to 1.60. In other modalities, the ratio can range from 1.00 to 1.10. In still other modalities, the ratio can be from 1.00 to 2.90. As shown in Figure 9, the difference between pore size and window size is substantially smaller for the SRTT structure in Figure 3 and the SRO structure in Figure 6 than for the SRD structure in Figure 4. Consequently, the SRTT structure advantageously provides a more homogeneous structure, with a smaller difference between pore window size and total pore size, especially at high porosity levels, which promotes internal bone growth by providing window sizes that are close in proportion to the pore size.Although only SRTT is referenced in Figure 9, the conclusion would hold for various structures that include internal columns, e.g., structures with internal columns in multiples of four. According to various modalities, an orthopedic implant is provided. The implant may include a three-dimensional porous structure comprising a lattice of connected unit cells, as illustrated, for example, by the unit cell structure in Figures 3-5. The at least one unit cell may comprise a plurality of external columns. The at least one unit cell may further comprise a first geometric structure comprising the plurality of external columns and a second geometric structure that shares a subset of the plurality of external columns of the first geometric structure and has a different geometry from the first geometric structure (see Figures 3 and 6).Furthermore, at least a portion of the subset of the plurality of external columns in the second geometric structure can intersect to form angles substantially equal to the angles formed by intersections of the plurality of external columns of the first geometric structure. As described above, the first geometric structure can be a geometric rhombic dodecahedron, as illustrated, for example, in Figure 4. The second geometric structure can be a geometric trigonal trapezohedron (see Figure 5). The geometric trigonal trapezohedron can be formed by inserting four columns into the first geometric structure, as illustrated, for example, in Figure 3. Furthermore, at least one unit cell can include four geometric trigonal trapezohedral structures within the first geometric structure, as illustrated, for example, in Figure 3. Within the porous three-dimensional structure, at least one column of a certain length and diameter within the lattice can be configured to meet the lattice's predetermined geometric properties. For example, the length and diameter of at least one column of the organic structure can be modified with respect to the length and diameter of at least one column of the geometric structure. As described above, these geometric properties can be selected from the group consisting of porosity, pore size, minimum aperture size, and combinations thereof. For example, the porosity can range from approximately 20% to approximately 95%. It can also range from approximately 35% to approximately 85%. And it can also range from approximately 50% to approximately 75%.Furthermore, the lengths of individual columns can be, for example, approximately 25% to approximately 175% of the average column length of the plurality of columns. As will be described in more detail later, each of the geometric structures described above can be modified to produce an organic structure. In one example, the lengths of individual external columns of each of the geometric structures can also be modified to be, for example, up to approximately 75% to approximately 125% of the average column length of the plurality of external columns of the geometric structures to produce the organic structure.In another example, the lengths of individual external columns of each of the geometric structures can also be modified to be, for example, up to approximately 50% to approximately 150% of the average column length of the plurality of external columns of the geometric structures. According to various modalities, an orthopedic implant is provided. The implant may include a porous three-dimensional structure comprising a plurality of repeating unit cells. Each unit cell may include a base geometric structure and a secondary geometric structure formed from a portion of the base geometric structure and having a geometry different from that of the base geometric structure. Furthermore, for a given porosity of the porous three-dimensional structure, at least one unit cell may have a pore size that differs from the pore size of the average geometric structure of the porous three-dimensional structure and a window size that differs from the window size of the average geometric structure of the porous three-dimensional structure. With reference now to Figures 12A–13E, in general, organic unit cell structures 400 can be modified with respect to the geometric unit cell structures 200 described above. For example, Figures 12A and 13A show the first geometric or external structure 230. Figures 12B–12C and Figures 13B–13E show a first external or organic structure having node positions that differ from those of the corresponding first geometric structure 230. In an example illustrated in Figures 12A, the first geometric structure 230 is illustrated as the geometric rhombic dodecahedron 215 as described above. As illustrated in Figures 12B–C, an organic structure 430 can be configured as an organic rhombic dodecahedron 415 that is modified with respect to the geometric rhombic dodecahedron described above.For example, one or more of the nodes up to all the nodes of the organic structure 430 are repositioned with respect to the corresponding nodes of the geometric structure 230. As shown in Figure 12A, each of the plurality of external nodes 212 has a position in three-dimensional space (e.g., along an x-direction, a y-direction, and a z-direction that are all oriented perpendicular to each other) with respect to the remaining external nodes 212 of the plurality of external nodes 212 that define the external nodes 212 of the geometric rhombic dodecahedron 215. Furthermore, the external nodes 212 include respective pairs of opposite nodes. As an example, the first and second external nodes 212a and 212b of the external nodes 212 define a first pair of opposite external nodes. The nodes of a pair of opposite external nodes can be farther from each other than from any other node. In this sense, none of the external nodes 212 is farther from the first external node 212a than the second external node 212b. Furthermore, none of the external nodes 212 is farther from the second external node 212b than the first external node 212a. Additionally, the nodes of a pair of opposite external nodes can be separated from each other by three intermediate external nodes from the plurality of external nodes 212 along a shortest path along the external columns 210 to and from the nodes of the pair of opposite external nodes.Therefore, the second external node 212b is separated from the first external node 212a by three intermediate external nodes from the plurality of external nodes 212 along a shortest path along the external columns 210 from the first external node 212a to the second external node 212b. That is, when moving along the external columns 210 from the first external node 212a to the second external node 212b along the shortest path, the path includes three intermediate external nodes 217a, 217b, and 217c (it is acknowledged that multiple shortest paths are defined). The third and fourth external nodes 212c and 212d of the external nodes 212 define a second pair of opposite nodes. The fifth and sixth external nodes 212e and 212f of the external nodes 212 define a third pair of opposite nodes. A first imaginary straight line 235 is recognized to extend through the first external node 212a and the second external node 212b. A second imaginary straight line 237 extends through the third external node 212c and the fourth external node 212d. A third imaginary straight line 239 extends through the fifth external node 212e and the sixth external node 212f. The first imaginary straight line 235, the second imaginary straight line 237, and the third imaginary straight line 239 substantially intersect each other at a point of intersection 241. With reference now to Figures 1 and 12B, at least some, and indeed all, of the unit cells of the porous structure 120 of the implant 100 have an organic unit cell structure 400, as shown in Figure 12B. In some instances, the organic unit cell structure 400 is modified from the geometric rhombic dodecahedron 215 illustrated in Figure 4. In other instances, the organic unit cell structure 400 is designed without the aid of a previously designed geometric unit cell structure 200, such as the geometric rhombic dodecahedron described above. Thus, as shown in Figure 12B, each organic unit cell structure includes a plurality of columns 408, which in turn include a plurality of external columns 410. The external columns 410 combine to define a lattice structure.The external columns 410 cooperate to form an organic external structure 430 that is modified with respect to the geometric external structure 230 of Figure 4. In the illustrative mode, the organic external structure 430 is an organic rhombic dodecahedron 415. The external columns 410 can define constant thicknesses. MA / t / ZUZ¿ / U4o I04 along the entire length of their respective lengths. Furthermore, the external columns 410 can have equal thicknesses. The internal columns 420 can also define constant thicknesses along the entire length of their respective lengths. In addition, the internal columns 420 can have equal thicknesses. Furthermore, the internal columns 420 and the external columns 410 can have equal thicknesses. Alternatively, the internal columns 420 and the external columns 410 can have different thicknesses. In examples where the external columns 410 and the internal columns 420 are cylindrical, the respective thicknesses define the diameters of the external columns 410 and the internal columns 420, respectively. The external columns 410 therefore intersect each other to define a plurality of external vertices or external nodes 412. Each of the external nodes 412 is defined by an intersection of three of the external columns 410. Each of the external columns 410 therefore extends from a respective first node of the external nodes 412 to a respective second node of the external nodes 412 along a respective length. When the external columns 410 define the organic rhombic dodecahedron 415, the columns 410 combine to define fourteen external nodes 412. Furthermore, each of the plurality of external nodes 412 has a position in three-dimensional space (e.g., along an x-direction, a y-direction, and a z-direction, all of which are oriented perpendicular to each other) with respect to the remaining external nodes 412 of the plurality of external nodes 412 that define the nodes 412 of the organic rhombic dodecahedron 415. As described above, the position of at least one of the external nodes 412 of the organic rhombic dodecahedron 415, including a plurality of the external nodes 412 up to all the external nodes, is different from the respective at least one external node 212 of the geometric rhombic dodecahedron. With reference to Figure 12B, the external columns 410 and the external nodes 412 combine to substantially define the geometric structure 430, which is within 25% of the geometric rhombic dodecahedron 215. For example, the position of at least one external node 412 of the organic rhombic dodecahedron 415 is up to 25% modified with respect to the position of the corresponding at least one external node 212 of the geometric rhombic dodecahedron 215 shown in Figure 12A.For example, the position of a plurality of external nodes 412 of the organic rhombic dodecahedron 415 is up to 25% modified with respect to the position of the corresponding plurality of external nodes 212 of the geometric rhombic dodecahedron 215. Therefore, the external columns 410 and the external nodes 412 combine to substantially define a geometric structure that is within 25% of the geometric rhombic dodecahedron 215. Furthermore, the position of at least one of the external nodes 412 up to a plurality of external nodes 412 of the organic rhombic dodecahedron 415 illustrated in Figure 12B can be equal to the position of at least one of the corresponding external nodes 212 up to a corresponding plurality of external nodes 212 of the geometric rhombic dodecahedron 215 shown in Figure 12A. The term within, as used in this description, with reference to a percentage includes the percentage stated. The position of the external nodes 412 of the organic rhombic dodecahedron 415 can be expressed by the following equation: MA / t / ZUZ¿ / U4o I 04 Position ntofl.t / icofi.c. .Vt'' ​​= .¥¡ + / Lt: .yi,zij (6) where N identifies a node, i identifies the particular node of the geometry, p is the change in position expressed as a percentage of the position of the node of the geometric structure, yx, yz are positional coordinates of node i of the geometric structure. The modified position of the node of the organic structure 430 may differ from the position of the corresponding node of the geometric structure 230 along one or more up to all of the x direction, the y direction and the z direction. In another embodiment, with reference to Figure 12C, the external columns 410 and the external nodes 412 are combined to substantially define the geometric structure 430 that is within 50% of the geometric rhombic dodecahedron 215. For example, the position of at least one external node 412 of the organic rhombic dodecahedron 415 is up to 50% modified with respect to the position of the corresponding at least one external node 212 of the geometric rhombic dodecahedron 215 shown in Figure 12A. For example, the position of a plurality of external nodes 412 of the organic rhombic dodecahedron 415 is up to 50% modified with respect to the position of the corresponding plurality of external nodes 212 of the geometric rhombic dodecahedron 215. Therefore, the external columns 410 and the external nodes 412 combine to substantially define a geometric structure that is within and includes 50% of the geometric rhombic dodecahedron 215.Furthermore, the position of at least one of the external nodes 412 up to a plurality of the external nodes 412 of the organic rhombic dodecahedron 415 illustrated in Figure 12C may be equal to the position of at least one of the corresponding external nodes 212 up to a corresponding plurality of the external nodes 212 of the geometric rhombic dodecahedron 215 shown in Figure 12A. Therefore, as illustrated in Figures 12A-12C, at least some of the external nodes 412 of the organic rhombic dodecahedron are repositioned with respect to the external nodes 212 of the geometric rhombic dodecahedron 215. Consequently, when a first porous three-dimensional structure including the organic external structure 430 is superimposed on a second porous three-dimensional structure including the geometric structure 230 in the same position and orientation, at least some of the external nodes 412 of the first porous three-dimensional structure are displaced with respect to some of the corresponding nodes 212 of the second porous three-dimensional structure. In some instances, other external nodes 412 of the plurality of external nodes 412 of the first porous three-dimensional structure coincide with other corresponding external nodes 212 of the plurality of nodes 212 of the second porous three-dimensional structure.The organic external structure 430 is in all other respects substantially identical to the geometric external structure 230 except for the repositioned external nodes 412 and the resulting changes to the respective columns 410, as will now be described. For example, the organic external geometry 430 and the resulting porous three-dimensional structure have the same number of columns and nodes, respectively, as the geometric external structure 230 and the resulting porous three-dimensional structure. The porous three-dimensional structure of the organic structure 430 has been found to have a ductility that is greater than the ductility of the porous three-dimensional structure that includes the external geometric structure 230. Furthermore, the porous three-dimensional structure that includes the external organic structure 430 has adequate structural integrity when implanted in human anatomy. In particular, as a result of the repositioned external nodes 412, at least one or more, up to all, of the columns 410 of the organic external structure 430 have at least one geometric property that differs from the corresponding columns 210 of the geometric external structure 230. As described above, the geometric property may include at least one of the length, orientation, and path type (e.g., straight or bent) of the column 210. For example, at least one or more of the external columns 410 that partially define a repositioned external node 412 may be longer or shorter than the corresponding external columns 210 of the corresponding geometric rhombic dodecahedron. In this respect, the external columns 410 extend from and to a respective pair of external nodes 412 along their respective lengths, and the lengths of at least some of the external columns 410 differ from one another.For example, the individual lengths of the 410 external columns can also be modified to be, for example, approximately 75% to approximately 125% of the average column length of the plurality of 410 external columns. Furthermore, the external columns 410 may extend along any suitable path along their length from and to the adjacent nodes 412 that are defined by the external columns 410. For example, one or more of the columns 410 that partially define a repositioned external node 412 may extend along a straight, linear path along their entire respective length, and may have a different orientation from that of the external columns 210 of the corresponding geometric structure 230. Alternatively, at least a portion of at least one or more of the external columns 410 that partially define a repositioned external node 412 may be bent along their length between a respective first external node 412 of the node plurality and a respective second external node 412 of the node plurality.Therefore, at least one bent column 410 intersects two other different pairs of columns 410 to define the respective first and second external nodes 412. In one example, at least a portion of the external column 410 extends along a curved path. Alternatively or additionally, at least a portion of at least one or more of the external columns 410 may be angled and thus bent. It is noticeable that all the external columns 410 illustrated in Figures 12B–12C may be straight (see Figures 13C and 13E). Alternatively, all the external columns 410 may be bent. With continued reference to Figure 12B, the external columns 410 include a longer external column and a shorter external column. None of the external columns 410 extends between respective adjacent external nodes 412 along a path longer than that of the longer external column. Conversely, none of the external columns 410 extends between respective adjacent external nodes 412 along a path shorter than that of the longer external column. When the positions of the external nodes 412 of the organic structure 430 are modified by 25% with respect to the position of the corresponding geometric external structure 230, the length of the shorter external column 410 is not less than approximately 60% of that of the longer external column 410. As illustrated in Figure 12C, the external columns 410 include a longer external column and a shorter external column. None of the external columns 410 extends between respective adjacent external nodes 412 along a path longer than that of the longer external column. Conversely, none of the external columns 410 extends between respective adjacent external nodes 412 along a path shorter than that of the longer external column. When the positions of the external nodes 412 are modified by 50% with respect to the positions of the external nodes 212 of the corresponding geometric external structure 230, the length of the shorter external column 410 is not less than approximately 1 / 3 of that of the longer external column 410. With continued reference to Figures 12B-12C, the external nodes 412 include a first external node 412a and a second external node 412b opposite the first external node 412a to define a first pair of opposite nodes. The external nodes 412 further include a third external node 412c and a fourth external node 412d opposite the third external node 412c to define a second pair of opposite nodes. The external nodes 412 also include a fifth external node 412e and a sixth external node 412f opposite the fifth external node 412e to define a third pair of opposite nodes. As described earlier with respect to Figure 12A, the nodes of a pair of opposite external nodes 412 can be farther from each other than from any other node. In this respect, neither of the external nodes 412 is farther from the first external node 412a than the second external node 412b. Furthermore, neither of the external nodes 412 is farther from the second external node 412b than the first external node 412a. Additionally, the nodes of a pair of opposite external nodes can be separated from each other by three intermediate external nodes from the plurality of external nodes 412 along a shorter path along the external columns 410 to and from the nodes of the pair of opposite external nodes.Therefore, the second external node 412b is separated from the first external node 412a by three intermediate external nodes from the plurality of external nodes 412 along a shortest path along the external columns 410 from the first external node 412a to the second external node 412b. That is, when moving along the external columns 410 from the first external node 412a to the second external node 412b along the shortest path, the path includes three intermediate external nodes 417a, 417b, and 417c (it is acknowledged that multiple shortest paths are defined). A first imaginary straight line 419 extends geometrically to the first external node 412a and the second external node 412b. A second imaginary straight line 421 extends through the third external node 412c and the fourth external node 412d. A third imaginary straight line 423 extends through the fifth external node 412e and the sixth external node 412f. The first and second imaginary straight lines 419 and 421 intersect each other at a first intersection 424a with respect to a selected view of the porous three-dimensional structure. The third straight line 423 intersects the first imaginary straight line 419 at a second intersection that is offset from the first intersection with respect to the selected view of the porous three-dimensional structure.The third imaginary straight line 423 can also intersect with the second imaginary straight line 421 at a third intersection that is offset from either or both of the first and second intersections with respect to the selected view of the porous three-dimensional structure. The organic unit cell structure 400 of Figures 12B-12C can be modified with respect to the geometric unit cell structure 200, such that the external nodes 412 of the organic unit cell structure 400 are repositioned with respect to the corresponding external nodes 212 of the geometric unit cell structure 200 in any suitable direction. Therefore, the external nodes 412 of a first half of the organic unit cell structure 400 can be repositioned with respect to the corresponding external nodes 212 of the geometric unit cell structure 200 in a first direction. The external nodes 412 of a second half of the organic unit cell structure 400 can be repositioned with respect to the corresponding external nodes 212 of the geometric unit cell structure 200 in a second direction different from the first.The first and second directions can be opposite, perpendicular, or oblique to each other. The first and second halves of the organic unit cell structure 400 are separated by a plane that bisects the organic unit cell structure 400. Therefore, in some instances, regardless of the plane's orientation (i.e., for all plane orientations), at least some, up to all, of the external nodes 412 of the first half of the organic unit cell structure 400 are repositioned with respect to the corresponding external nodes 212 of the geometric unit cell structure 200 in different directions, and at least some, up to all, of the external nodes 412 of the second half of the organic unit cell structure 400 are repositioned with respect to the corresponding external nodes 212 of the geometric unit cell structure 200 in different directions. With reference now to Figure 13A, and as described above with respect to Figure 3, the columns 208 include a plurality of external columns 210 that define the first geometric structure 230. The columns 208 further include a plurality of internal columns 220 that, in combination with the external columns 210, form the plurality of second geometric structures 240 that are within the first geometric structure 230. In the illustrative manner, the first geometric structure 230 comprises the plurality of external columns 210. As described above, the plurality of external columns 210 in Figure 3 cooperate to form a geometric rhombic dodecahedron. Therefore, the first geometric structure 230 defines a geometric rhombic dodecahedron. Internal columns 220 intersect each other to define an internal node 232. In particular, all internal columns 220 intersect each other to define internal node 232.Furthermore, each of the internal columns 220 extends from a respective external node 212 to the internal node 232. In the illustrated form, the internal columns 220 intersect each other to define only the unique internal node 232 and no other internal nodes. Therefore, the geometric unit cell 200 defines only a unique internal node 232 that is internal with respect to the external nodes 212. External columns 210 can have constant thicknesses along their entire lengths. Furthermore, external columns 210 can have equal thicknesses. Internal columns 220 can also have constant thicknesses along their entire lengths. In addition, internal columns 220 can have equal thicknesses. Furthermore, internal columns 220 and external columns 210 can have equal thicknesses. Alternatively, internal columns 220 and external columns 210 can have different thicknesses. In examples where external columns 210 and internal columns 220 are cylindrical, their respective thicknesses define the diameters of the external columns 210 and internal columns 220, respectively. As illustrated in Figure 13A, each of the plurality of second geometric structures 240 has an internal volume that is substantially equal to the internal volumes of the other second geometric structures 240. Each second geometric structure 230 is formed by a number of internal columns 220 and a number of external columns 210. Each second geometric structure 230 is illustratively a geometric trigonal trapezohedron. As illustrated in Figure 3, the plurality of second geometric structures 240 within the first geometric structure 230 includes four geometric trigonal trapezohedrons such that the unit cell structure 200 is the geometric rhombic trigonal trapezohedron (GRTT). The first geometric structure 230 includes the first, second, and third pairs of external nodes 212 as described above with respect to Figure 12A. Therefore, the first imaginary straight line 235 extends through the first external node 212a and the second external node 212b. The second imaginary straight line 237 extends through the third external node 212c and the fourth external node 212d. The third imaginary straight line 239 extends through the fifth external node 212e and the sixth external node 212f. The first imaginary straight line 235, the second imaginary straight line 237, and the third imaginary straight line 239 substantially intersect each other at the internal node 232. With reference to Figures 13B-13C, the position of a given external node 412 of the organic rhombic dodecahedron 415 is up to 25% modified with respect to the position of the corresponding external node 212 of the geometric rhombic dodecahedron 215 as described above. In another embodiment illustrated in Figures 13D-13E, the position of a given external node 412 of the organic rhombic dodecahedron 415 is up to 50% modified with respect to the position of the corresponding external node 212 of the geometric rhombic dodecahedron 215 as described above. Furthermore, in both Figures 13B and 13C, the columns 408 of the first organic structure 430 may include a plurality of internal columns 420 which, in combination with the external columns 410, form a plurality of second organic structures 440 which are within the first organic structure 430.The internal columns 420 intersect each other to define an internal node 432 at an intersection of the internal columns. In particular, in the illustrative mode, all the internal columns 420 intersect each other to define the internal node 432. Furthermore, each of the internal columns 420 extends from a different respective node of the plurality of external nodes 412 to the internal node 432. In the illustrated mode, the internal columns 420 intersect each other to define only the unique internal node 432 and no other internal nodes. Therefore, the unit cell structure 400 defines only a unique internal node 432 that is internal with respect to the external nodes 412. In the illustrative form, the first organic structure 430 comprises the plurality of external columns 410. As described above, the plurality of external columns 410 cooperate to form the organic rhombic dodecahedron. Each second organic structure 440 is, for illustrative purposes, an organic trigonal trapezohedron. The plurality of second organic structures 440 within the first organic structure 430 includes four organic trigonal trapezohedrons such that the unit cell structure 400 is an organic rhombic trigonal trapezohedron (ORTT). The organic trigonal trapezohedrons are modified from the geometric trigonal trapezohedrons described above.For example, at least one of the internal node 432 and at least one of the external nodes 412 (including a plurality up to all external nodes 412) are repositioned with respect to at least one of the corresponding internal node and at least one of the corresponding external nodes (including a plurality up to all external nodes) of the geometric trigonal trapezohedrons described above. Therefore, it will be seen that the resulting organic rhombic trigonal trapezohedron is modified with respect to the geometric rhombic trigonal trapezohedron described above.For example, at least one of the internal node 432 and at least one of the external nodes 412 (which include a plurality up to all external nodes 412) are repositioned with respect to at least one of the corresponding internal node and at least one of the external nodes (which include a plurality up to all external nodes) of the geometric rhombic trigonal trapezohedron described above. Every second organic structure 440 is formed by a number of internal columns 420 and a number of external columns 410. Every second organic structure 440 is illustratively an organic trigonal trapezohedron. As described above, the position of at least one or more of the external nodes 412 up to all of the external nodes 412 of the organic structure 430 is modified with respect to the external nodes 212 of the second geometric structure 240. In addition, the position of the internal node 432 of the second organic structure 440 is modified with respect to the position of the internal node 232 of the second geometric structure 240. In an illustrative modality shown in Figures 13B-13C, the position of at least one of the internal node 432 and at least one of the external nodes 412 is modified by up to 25% with respect to the position of the internal node 232 as illustrated in Figure 3B-3C.In another illustrative configuration shown in Figures 13D-13E, the position of at least one of the internal node 432 and at least one of the external nodes 412 is modified by up to 50% with respect to the position of internal node 232, as illustrated in Figures 3B-3C. As described above with respect to Figures 13B-13C, the first organic structure 430 and the internal columns 420 of the second organic structure 440 in Figures 13D-13E intersect to define only the single internal node 432 and no other internal nodes. Therefore, the unit cell structure 400 defines only a single internal node 432, which is internal with respect to the external nodes 412. With continued reference to Figures 13B-13E, the first organic structure 430 includes the first, second, and third pairs of external nodes 412 as described above with respect to Figures 12B-12C. Therefore, the first imaginary straight line 419 extends through the first external node 412a and the second external node 412b. The second imaginary straight line 421 extends through the third external node 412c and the fourth external node 412d. The third imaginary straight line 423 extends through the fifth external node 412e and the sixth external node 412f. At least one or more, up to all, of the first imaginary straight line 419, the second imaginary straight line 421, and the third imaginary straight line 423 are offset from the internal node 232. The organic unit cell structure 400 of Figures 13B-13E can be modified with respect to the geometric unit cell structure 200, such that the external nodes 412 of the organic unit cell structure 400 are repositioned with respect to the corresponding external nodes 212 of the geometric unit cell structure 200 in any suitable direction. Therefore, the external nodes 412 of a first half of the organic unit cell structure 400 can be repositioned with respect to the corresponding external nodes 212 of the geometric unit cell structure 200 in different directions. Similarly, the external nodes 412 of a second half of the organic unit cell structure 400 can be repositioned with respect to the corresponding external nodes 212 of the geometric unit cell structure 200 in different directions.The first and second halves of the organic unit cell structure 400 are separated from each other by a plane that bisects the organic unit cell structure 400, and the internal node 432 lies in the plane. Therefore, in some instances, regardless of the plane's orientation (i.e., for all plane orientations), at least some, up to all, of the external nodes 412 of the first half of the organic unit cell structure 400 are repositioned with respect to the corresponding external nodes 212 of the geometric unit cell structure 200 in different directions, and at least some, up to all, of the external nodes 412 of the second half of the organic unit cell structure 400 are repositioned with respect to the corresponding external nodes 212 of the geometric unit cell structure 200 in different directions. As a result of at least one node of the organic structure 430 being repositioned, at least one or more, up to all, of the internal columns 420 of the organic structure 430 have at least one property that differs from that of the corresponding internal columns 220 of the geometric structure 230. The property may include at least one of the length, orientation, and path type (e.g., straight or bent) of the internal column 420. For example, at least one or more of the internal columns 420 that partially define the repositioned internal node 432 may be longer or shorter than the corresponding internal columns 220 of the corresponding geometric structure 230. In this respect, the internal columns 420 extend from the respective external node 412 to the internal node 432 along their respective lengths, and the lengths of at least some of the internal columns 420 differ from one another.At least one or more up to all of the external columns 410 of the organic external structure 430 also have at least one geometric property that is different from that of the corresponding columns 210 of the geometric external structure 230 as described above with respect to Figures 12B12C. Furthermore, the internal columns 420 shown in Figures 13B-13E can extend along any suitable path along their length from the respective external node 412 to the internal node 432. For example, one or more of the internal columns 420 of the second organic structure 440 can extend along a straight, linear path along their entire respective length, and can have a different orientation from that of the corresponding internal columns 220 of the second geometric structure 240. It is apparent that all the internal columns 420 illustrated in Figures 13B-13E can extend along their respective straight paths from the respective external node 412 to the internal node 432. Alternatively, at least a portion of at least one or more, up to all, of the internal columns 420 can be an internal column bent along its length from the respective external node 412. up to internal node 432.In one example, at least a portion of the internal column 420 may extend along a curved path. Alternatively or additionally, at least a portion of at least one or more of the internal columns 420 may be angled and therefore bent. Alternatively, all of the internal columns 420 may be bent. It has been discovered that the porous three-dimensional structure having the first organic structure 430 and the second organic structure 440 has a ductility that is greater than the ductility of the porous three-dimensional structure that includes the first geometric structure 230 and the second geometric structure 240. In addition, the porous three-dimensional structure that includes the first organic structure 430 and the second organic structure 440 has adequate structural integrity when implanted in a human anatomy. It should be noted that each unit cell structure can include other types of second organic structures. For example, an organic unit cell structure can include a plurality of external columns 410 that define the first organic structure 430 as described above. The modified unit cell structure can further include a plurality of internal columns 420 that, in combination with the external columns 410, define a plurality of second organic or internal structures. Each of the internal organic structures can be configured as a modified octahedron. Thus, in one example, the organic unit cell structure can include eight internal columns 420 as described above with respect to the Figure 6. Accordingly, the plurality of second organic structures within the first organic structure may include six geometric octahedra such that the organic unit cell structure is a modified or organic rhombic octahedron, whereby the position of at least some of the nodes of the first organic structure and at least some nodes of the second organic structure is repositioned with respect to the nodes of the first geometric structure and the nodes of the second geometric structure. In one embodiment, the porous three-dimensional structure having the external organic structure 430 and the internal organic structure 440 has a porosity of approximately 50% to approximately 75%. For example, the porous three-dimensional structure having the external organic structure 430 and the internal organic structure 440 can have a porosity of approximately 55% to approximately 65%. Furthermore, as described above with respect to the external geometric structures 230 and the internal geometric structures 240, the external columns 410 and the internal columns 420 define a plurality of openings in the porous three-dimensional organic structure. Each opening in the plurality of openings has a window size, and the internal volume of each organic structure 430 and 440 has a pore size.As described above, the pore size can be taken as the equivalent diameter of a sphere within the limited volume within the unit cell that has the organic structure 430. With reference to Figure 14, the percentage of pores in the porous three-dimensional structure that includes the unit cells of Figure 13C (e.g., ORTT with all columns 410 and 420 straight and linear), where the porous three-dimensional structure has a porosity of approximately 55%, and the node positions are 25% modified with respect to the GRTT. As illustrated, the percentage of pores in the three-dimensional structure with a pore diameter less than 0.1 mm is less than approximately 14.3 percent. For example, less than approximately two percent of the pores have a pore size smaller than 0.1 mm. Furthermore, Figure 14 illustrates that approximately fifty percent of the pores in the three-dimensional structure have a pore diameter greater than 0.2 mm. For example, approximately fifty percent of the pores in the three-dimensional structure have a pore diameter between approximately 0.2 mm and approximately 0.36 mm. With reference to Figure 15, the percentage of pores in the porous three-dimensional structure that includes the unit cells of Figure 13C (e.g., ORTT with all columns 410 and 420 straight and linear), where the porous three-dimensional structure has a porosity of approximately 65%, and the position of at least one of the nodes is modified by 25% with respect to the GRTT. As described above with respect to Figure 14, the percentage of pores in the three-dimensional structure having a pore diameter less than 0.1 mm is less than approximately 14.3 percent. For example, less than Approximately 1.5 percent of the pores have a pore size smaller than 0.1 mm, as illustrated in Figure 15. Furthermore, Figure 15 illustrates that approximately fifty percent of the pores in the three-dimensional structure have a pore diameter greater than 0.3 mm. For example, approximately fifty percent of the pores in the three-dimensional structure have a pore diameter between approximately 0.3 mm and approximately 0.7 mm. In particular, approximately fifty percent of the pores in the three-dimensional structure have a pore diameter between approximately 0.3 mm and approximately 0.5 mm. It can also be stated from Figures 14-15 that approximately fifty percent of the pores in the three-dimensional structure having ORTT unit cells can have a pore diameter ranging from approximately 0.2 mm to approximately 0.7 mm.For example, approximately fifty percent of the pores in the three-dimensional structure that has ORTT unit cells may have a pore diameter ranging from approximately 0.2 mm to approximately 0.5 mm. Furthermore, as described earlier with respect to geometric structures, the ratio of pore size of organic structures to the window size of each opening in a porous three-dimensional structure can range from 1.00 to 2.90. It is recognized in some examples that at least ninety percent of organic structures have a pore size to window size ratio in the range of 1.00 to 2.90. For example, as described earlier with respect to geometric structures, in one modality, the ratio of pore size of each organic structure to window size of each opening in the organic structure ranges from 1.00 to 1.10. It is recognized in some examples that at least ninety percent of organic structures have a pore size to window size ratio in the range of 1.00 to 2.90.In another example, as described above with respect to the porous three-dimensional structure of geometric unit cells, the ratio of the pore size of an organic unit cell to any of its corresponding window sizes is in the range of 1.50 to 1.60. It is recognized in some examples that at least ninety percent of organic unit cells may have the ratio of pore size to any of their corresponding window sizes in the range of 1.50 to 2.60. With reference again to Figures 12A-13E, methods are generally provided for designing the unit cells described herein, which have one or both of the first and second three-dimensional porous organic structures configured to stimulate internal bone growth when implanted in a human body. The method may include the step of applying a modification factor to a first geometric unit cell design. The first geometric unit cell design includes a number of first columns or outer columns 210, such ML / t / ZUZ¿ / U4o I 04 as three external columns 210, which intersect each other to define a number of first nodes or external nodes 212, wherein each of the first columns 210 has a respective first length, and the first nodes 212 define a first position relative to each other. The respective first lengths of the first columns 210 are all substantially equal to each other in one embodiment. In another embodiment, the respective first lengths of some of the first columns are different from the respective first lengths of at least some other of the first columns 210. The first unit cell layout can be provided in the manner described above. The modification factor can be up to 50%, such as up to 25% in the manner described above.In one example, the application stage can be carried out using a commercially available 3-matic software package from Materialise, headquartered in Leuven, Belgium. The application stage produces a second unit cell design that has 410 second columns or external columns that intersect to define 412 second nodes or external nodes. The number of external nodes 412 is equal to the number of external nodes 212, and the number of external columns 410 is equal to the number of external columns 210. Each of the external columns 410 has a respective first length, and the external nodes 412 define a second relative position with respect to each other that is different from the first relative position. The respective first lengths of at least some of the external columns 410 are different from the respective first lengths of at least some other external columns 410. Furthermore, the respective first lengths of at least some of the external columns 410 are different from the respective first lengths of at least some of the corresponding external columns 210.Alternatively, the organic three-dimensional structures 430 and 440 can be designed without the aid of the previously designed geometric structures 230 and 240, respectively. It is acknowledged that manufacturing tolerances may result in different column lengths. However, different column lengths as described herein refer to different lengths outside of manufacturing tolerances. Once the second unit cell design has been produced, manufacturing instructions can be generated to fabricate the porous three-dimensional structure comprising a plurality of interconnected unit cells, each containing the second unit cell design. The porous three-dimensional structure can be fabricated in place. Alternatively, the manufacturing instructions can be sent to an external manufacturer to fabricate the porous three-dimensional structure. An orthopedic implant is provided according to various modalities. The implant may include a porous three-dimensional structure comprising a plurality of unit cells. Each unit cell may comprise an external geometric structure having a MA / t / ZUZ¿ / U4o I 04 first geometry and comprising a plurality of first columns. Each unit cell may further comprise an internal geometric structure having a second geometry and further comprise a plurality of second columns connected to a portion of the plurality of first columns to form the internal geometric structure within the external geometric structure. According to various modalities, the external geometric structure can be a rhombic dodecahedron. The internal geometric structure can be a trigonal trapezohedron. The trigonal trapezohedron can be formed by inserting four columns into the external geometric structure. Furthermore, at least one unit cell can include four trigonal trapezohedral geometric structures within the external geometric structure. As described above, an orthopedic implant may include a porous three-dimensional structure comprising a plurality of repeating unit cells with unit cell structures. The unit cell structures may define geometric or organic structures. Accordingly, the porous three-dimensional structure may include a plurality of external column groups that define the respective geometric or organic structures. Furthermore, some of the unit cell structures may be surrounded by, or otherwise inwardly arranged with respect to, other unit cell structures within the porous three-dimensional structure of the orthopedic implant.As a result, when unit cell structures combine to define the porous three-dimensional structure, the external columns of certain unit cell structures can define external columns of adjacent unit cell structures. Furthermore, when unit cell structures include internal columns that define secondary geometric or organic structures, it is recognized that the internal columns of certain unit cell structures can define external columns of adjacent unit cell structures. Conversely, the external columns of certain unit cell structures can define internal structures of adjacent unit cell structures.Therefore, any suitable combination of columns in the porous three-dimensional structure of the orthopedic implant can define external columns of the type described herein, regardless of whether other columns are located external to or extend from the external columns. Similarly, any suitable combination of columns in the porous three-dimensional structure of the orthopedic implant can define internal columns of the type described herein, extending from the respective external columns to an internal node. In some examples, the unit cell structures may consist of, or essentially consist of, the external columns that define the external nodes. In other examples, the unit cell structures may consist of, or essentially consist of, the external columns that define the external nodes and the internal columns that define the internal node. Manufacturing processes The porous three-dimensional metallic structures described above can be fabricated using a variety of different additive manufacturing techniques. For example, according to various methods, one way to produce the porous three-dimensional structure 120 involves depositing and scanning successive layers of metallic powders with a beam. The beam (or scanning beam) can be an electron beam. The beam (or scanning beam) can be a laser beam. With regard to the various methods described herein, metal powders can be sintered to form the porous three-dimensional structure. Alternatively, metal powders can be melted to form the porous three-dimensional structure. Successive layers of metal powders can be deposited onto a solid substrate (see above for the description related to the substrate). In various embodiments, the types of metal powders that can be used include, but are not limited to, titanium, titanium alloys, stainless steel, chromium-cobalt alloys, tantalum, or niobium powder. With respect to the various methods described herein, the geometric properties can be selected from the group consisting of porosity, pore size, minimum aperture size, and combinations thereof. Porosity can range from approximately 20% to approximately 95%. Porosity can also range from approximately 40% to approximately 80%. Porosity can also range from approximately 50% to approximately 75%. Furthermore, column lengths can be modified to be approximately 25% to approximately 175% of the average column length of the plurality of columns. The lengths of individual external columns can also be modified to be, for example, approximately 50% to approximately 150% of the average column length of the plurality of external columns.The lengths of individual outer columns can also be modified to be, for example, approximately 75% to approximately 125% of the average column length of the plurality of outer columns. Furthermore, the unit cell can have a smaller pore size than the first pore size of the geometric structure. Additionally, the unit cell can have a larger window size than the window size of each of the plurality of second geometric structures. With respect to the various methods described, the first geometric structure can be a rhombic dodecahedron. Each of the second geometric structures can be a trigonal trapezohedron. The trigonal trapezohedron can be formed by inserting four columns into the first geometric structure. Furthermore, at least one unit cell can include four trigonal trapezohedral geometric structures within the first geometric structure. MA / t / ZUZ¿ / U4o I04 In various embodiments, a method is provided for producing a porous three-dimensional structure. The method comprises applying a stream of metallic particles at a predetermined velocity onto a substrate to form a porous three-dimensional structure comprising a plurality of unit cells and having predetermined geometric properties. Each unit cell comprises a plurality of external columns and a plurality of internal columns. Each unit cell may include a first geometric structure comprising the plurality of external columns and a plurality of second geometric structures formed from the plurality of internal columns within the first geometric structure. In various embodiments, the types of metallic particles that may be used include, but are not limited to, titanium particles, titanium alloys, stainless steel, chromium-cobalt alloys, tantalum, or niobium. The predetermined speed may be a critical speed required for the metal particles to bond upon impact with the base. The critical speed is greater than 340 m / s. The method may also include applying a laser at a predetermined power setting to an area of ​​the base where the stream of metallic particles is impacting. The first geometric structure can be a rhombic dodecahedron. In some embodiments, each of the second geometric structures can be a trigonal trapezohedron. That is, four trigonal trapezohedrons can be formed by inserting four columns into the first geometric structure. In some embodiments, octahedra can be formed, for example, by inserting eight internal columns into a first geometric structure. In this case, six octahedral geometric structures can be provided within the first geometric structure. According to various embodiments, a method is provided for producing a porous three-dimensional structure. The method comprises introducing a continuous feed of metallic wire onto a base surface and applying a beam at a predetermined power setting to an area where the metallic wire contacts the base surface to form a porous three-dimensional structure comprising a plurality of unit cells and having predetermined geometric properties. Each unit cell may comprise a plurality of outer columns and a plurality of inner columns. Each unit cell includes a first geometric structure comprising the plurality of outer columns and a plurality of second geometric structures formed from the plurality of inner columns within the first geometric structure. The beam (or scanning beam) may be an electron beam. The beam (or scanning beam) may be a laser beam.In various forms, the types of metal wire that can be used include, but are not limited to, titanium wire, titanium alloys, stainless steel, chromium and cobalt alloys, tantalum, or niobium. MA / t / ZUZ¿ / U4o I 04 The first geometric structure can be a rhombic dodecahedron. In some variations, each of the second geometric structures can be a trigonal trapezohedron. That is, four trigonal trapezohedrons can be formed by inserting four columns into the first geometric structure. In some variations, octahedra can be formed, for example, by inserting eight internal columns into a first geometric structure. That is, six octahedral geometric structures can be provided within the first geometric structure. According to various embodiments, a method is provided for producing a porous three-dimensional structure. The method comprises introducing a continuous feed of a polymeric material embedded with metallic elements onto a base surface. The method may further comprise applying heat to an area where the polymeric material comes into contact with the base surface to form a porous three-dimensional structure comprising a plurality of unit cells and having predetermined geometric properties. Each unit cell may comprise a plurality of external columns and a plurality of internal columns. Each unit cell includes a first geometric structure comprising the plurality of external columns and a plurality of second geometric structures, formed from a number of the internal columns within the first geometric structure and a number of external columns. The metallic elements may be a metallic powder.In various configurations, the continuous feeding of the polymeric material can be supplied through a heated nozzle, thus eliminating the need to apply heat to the area where the polymeric material comes into contact with the base surface to form the porous three-dimensional structure. In various configurations, the types of metallic elements that can be used to embed the polymeric material may include, but are not limited to, titanium, titanium alloys, stainless steel, chromium-cobalt alloys, tantalum, or niobium. The method may also involve exploring the porous three-dimensional structure with a beam to burn the polymeric material. The beam (or scanning beam) may be an electron beam. The beam (or scanning beam) may be a laser beam. The first geometric structure can be a rhombic dodecahedron. In various configurations, each of the second geometric structures can be a trigonal trapezohedron. That is, four trigonal trapezohedrons can be formed by inserting four columns into the first geometric structure. In various configurations, octahedra can be formed, for example, by inserting eight internal columns into a first geometric structure. That is, six octahedral geometric structures can be provided within the first geometric structure. According to various embodiments, a method is provided for producing a porous three-dimensional structure. The method comprises introducing a metallic suspension through a nozzle onto a base surface to form a porous three-dimensional structure comprising a plurality of unit cells and having predetermined geometric properties. Each unit cell may comprise a plurality of external columns and a plurality of internal columns. Each unit cell may include a first geometric structure comprising the plurality of external columns and a plurality of second geometric structures, formed from a number of the internal columns within the first geometric structure and a number of the external columns. In various embodiments, the nozzle is heated to a temperature required to bond metallic elements of the metallic suspension to the base surface.In various forms, a metal suspension is an aqueous suspension containing metal particles along with one or more additives (liquid or solid) to improve manufacturing process performance or the porous three-dimensional structure. In various forms, a metal suspension is an organic solvent suspension containing metal particles along with one or more additives (liquid or solid) to improve manufacturing process performance or the porous three-dimensional structure. In various forms, the types of metal particles that can be used in a metal suspension include, but are not limited to, titanium particles, titanium alloys, stainless steel, chromium-cobalt alloys, tantalum, or niobium. The first geometric structure can be a rhombic dodecahedron. In some variations, each of the second geometric structures can be a trigonal trapezohedron. That is, four trigonal trapezohedrons can be formed by inserting four columns into the first geometric structure. In various variations, octahedra can be formed, for example, by inserting eight internal columns into a first geometric structure. That is, six octahedral geometric structures can be provided within the first geometric structure. According to various embodiments, a method is provided for producing a porous three-dimensional structure. The method comprises introducing successive layers of molten metal onto a base surface to form a porous three-dimensional structure comprising a plurality of unit cells and having predetermined geometric properties. Each unit cell may comprise a plurality of external columns and a plurality of internal columns. Each unit cell may include a first geometric structure comprising the plurality of external columns and a plurality of second geometric structures, formed from the plurality of internal columns within the first geometric structure and a number of the external columns. Furthermore, the molten metal may be introduced as a continuous stream onto the base surface. The molten metal may also be introduced as a stream of metal droplets. MA / t / ZUZ¿ / U4o I04 discrete casts on the base surface. In various embodiments, the types of cast metals that can be used include, but are not limited to, titanium, titanium alloys, stainless steel, chromium and cobalt alloys, tantalum, or niobium. The first geometric structure can be a rhombic dodecahedron. In various configurations, each of the second geometric structures can be a trigonal trapezohedron. That is, four trigonal trapezohedrons can be formed by inserting four columns into the first geometric structure. In various configurations, octahedra can be formed, for example, by inserting eight internal columns into a first geometric structure. That is, six octahedral geometric structures can be provided within the first geometric structure. According to various embodiments, a method is provided for producing a porous three-dimensional structure. The method comprises applying and photoactivating successive layers of photosensitive polymer embedded with metallic elements onto a base surface to form a porous three-dimensional structure comprising a plurality of unit cells and having predetermined geometric properties. Each unit cell may comprise a plurality of external columns and a plurality of internal columns. Each unit cell may include a first geometric structure comprising the plurality of external columns and a plurality of second geometric structures, formed from the plurality of internal columns within the first geometric structure and a number of the external columns.In various forms, the types of metallic elements that can be used to embed the polymeric material may include, but are not limited to, titanium, titanium alloys, stainless steel, chromium and cobalt alloys, tantalum, or niobium. The first geometric structure can be a rhombic dodecahedron. In some variations, each of the second geometric structures can be a trigonal trapezohedron. That is, four trigonal trapezohedrons can be formed by inserting four columns into the first geometric structure. In some variations, octahedra can be formed, for example, by inserting eight internal columns into a first geometric structure. That is, six octahedral geometric structures can be provided within the first geometric structure. According to various embodiments, a method is provided for producing a porous three-dimensional structure. The method comprises depositing and bonding successive layers of metal powders with a binding material to form a porous three-dimensional structure comprising a plurality of unit cells and having predetermined geometric properties. Each unit cell may comprise a plurality of external columns and a plurality of internal columns. Each unit cell may include a first geometric structure comprising a plurality of MA / t / ZUZ¿ / U4o I 04 external columns and a plurality of second geometric structures, formed from the plurality of internal columns within the first geometric structure and a number of the external columns. In various embodiments, the types of metal powders that may be used include, but are not limited to, titanium, titanium alloys, stainless steel, chromium and cobalt alloys, tantalum, or niobium powder. The method may also include sintering the bonded metal powder with a beam. The beam (or scanning beam) may be an electron beam. The beam (or scanning beam) may be a laser beam. The method may also include melting the bonded metal powder with a beam. The beam (or scanning beam) may be an electron beam. The beam (or scanning beam) may be a laser beam. The first geometric structure can be a rhombic dodecahedron. In some embodiments, each of the second geometric structures can be a trigonal trapezohedron. That is, four trigonal trapezohedrons can be formed by inserting four columns into the first geometric structure. In some embodiments, octahedra can also be formed, for example, by inserting eight internal columns into a first geometric structure. That is, six octahedral geometric structures can be provided within the first geometric structure. According to various embodiments, a method is provided for producing a porous three-dimensional structure. The method comprises depositing droplets of a metallic material onto a base surface and applying heat to an area where the metallic material comes into contact with the base surface to form a porous three-dimensional structure comprising a plurality of unit cells and having predetermined geometric properties. Each unit cell may comprise a plurality of external columns and a plurality of internal columns. Each unit cell may include a first geometric structure comprising the plurality of external columns and a plurality of second geometric structures, formed from the plurality of internal columns within the first geometric structure and a number of the external columns. The beam (or scanning beam) may be an electron beam. The beam (or scanning beam) may be a laser beam.In various forms, the types of metallic materials that can be used include, but are not limited to, titanium, titanium alloys, stainless steel, chromium and cobalt alloys, tantalum, or niobium. The deposited droplets of metallic material may be a metallic suspension embedded with metallic elements. The metallic material may be a metallic powder. The first geometric structure can be a rhombic dodecahedron. In some variations, each of the second geometric structures can be a trigonal trapezohedron. That is, four trigonal trapezohedrons can be formed by inserting four columns into the first geometric structure. In some variations, octahedra can be formed, for example, by inserting eight internal columns into a first geometric structure. That is, six octahedral geometric structures can be provided within the first geometric structure. Although this specification describes specific modes and applications of these, these modes and applications are only illustrative and many variations are possible. Although these teachings are described alongside various modalities, they are not intended to be limited to such modalities. On the contrary, these teachings encompass various alternatives, modifications, and equivalents, as those skilled in the technique will appreciate. Furthermore, in describing various embodiments, the specification may have presented a method and / or process as a particular sequence of steps. However, to the extent that the method or process does not depend on the particular order of the steps set forth in the present description, the method or process should not be limited to the particular sequence of steps described. As a person skilled in the art would appreciate, other sequences of steps may be possible. Therefore, the particular order of the steps set forth in the specification should not be construed as limiting the claims. Moreover, the claims relating to the method and / or process should not be limited to the performance of its steps in the order written, and a person skilled in the art can readily appreciate that the sequences may vary and still remain within the spirit and scope of the various embodiments.

Claims

1. An implantable device, comprising: a porous three-dimensional structure shaped to be implanted in the body of a patient, the porous three-dimensional structure includes a plurality of interconnected organic unit cells, each organic unit cell includes: a plurality of external columns, wherein the respective groups of three external columns intersect to define a respective plurality of external nodes;and a plurality of internal columns, each internal column extending from one of the respective different external nodes, and the internal columns intersecting to define an internal node, wherein the plurality of external nodes includes a first external node defined by the intersection of a first group of three external columns and a second external node defined by the intersection of a second group of three external columns, wherein a shortest path along the columns from the first external node to the second external node includes only three intermediate external nodes from the plurality of external nodes, and wherein an imaginary straight line extends through the first external node and the second external node, and the internal node is offset from the imaginary straight line. 2.- The implantable device according to claim 1, further characterized in that each of the external columns has a constant thickness along its entire length.

3. The implantable device according to claim 1, further characterized in that each of the internal columns has a constant thickness along its entire length. 4.- The implantable device according to claim 1, further characterized in that at least one of the external columns is curved along its length.

5. The implantable device according to claim 1, further characterized in that at least one of the internal columns is curved along its length.

6. The implantable device according to claim 1, further characterized in that all the external columns extend from and to a respective pair of the external nodes along their respective lengths, and the lengths of at least some of the external columns are different from each other.

7. The implantable device according to claim 1, further characterized in that all internal and external columns are substantially straight along their entire lengths. MA / t / ZUZ¿ / U4o I 04 8. The implantable device according to claim 1, further characterized in that it has a porosity between approximately 50% and approximately 75%.

9. The implantable device according to claim 1, further characterized in that it comprises a number of pores defined by the unit cells, respectively, wherein less than 14.3 percent of the pores have a pore size less than 0.1 mm.

10. The implantable device according to claim 9, further characterized in that fifty percent of the pores have a pore size ranging from approximately 0.2 mm to approximately 0.7 mm.

11. The implantable device according to claim 10, further characterized in that the external columns cooperate to define a number of external openings, the internal columns cooperate with a number of the external columns to form a number of internal openings, the three-dimensional porous structure defines window sizes defined as a diameter of a circle positioned at the corresponding external and internal openings, such that each of the columns defining the external and internal openings, respectively, is positioned on a tangent line to the circle, and the implantable device comprises a number of pores defined by the unit cells, respectively, the pores defining a ratio of their respective pore sizes to any of their window sizes that is in the range of 1.00 to 2.

90.

12. The implantable device according to claim 1, further characterized in that the internal node is the only internal node of the porous three-dimensional structure that is internal with respect to the external nodes. 13 - The implantable device according to claim 1, further characterized in that all internal columns intersect at the internal node. 14.- The implantable device according to claim 1, further characterized in that each organic unit cell defines a first half and a second half separated from the first half by a plane bisecting the organic unit cell structure, and for all orientations of the plane, 1) at least some of the external nodes of the first half of the organic unit cell structure are repositioned with respect to the corresponding external nodes of a geometric unit cell structure in a first orientation, and 2) at least some of the external nodes of the second half of the organic unit cell structure are repositioned with respect to the corresponding external nodes of the corresponding geometric unit cell structure in the second direction different from the first direction.

15. The implantable device according to any of the preceding claims, further characterized in that it additionally comprises an organic rhombic trigonal trapezohedron MA / t / ZUZ¿ / U4o I 04 having greater ductility than a corresponding geometric rhombic trigonal trapezohedron.

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