WO2005051233A2

WO2005051233A2 - Computer-aided tissue engineering of a biological body

Info

Publication number: WO2005051233A2
Application number: PCT/US2004/039352
Authority: WO
Inventors: Michael A. Liebschner; Matthew A. Wettergreen; Brandon S. Bucklen; Wei Sun
Original assignee: William Marsh Rice University
Priority date: 2003-11-21
Filing date: 2004-11-22
Publication date: 2005-06-09
Also published as: WO2005051233A3

Abstract

A method for forming an implantable structure. In one embodiment, the method comprises forming an implantable structure, wherein the implantable structure has desired features that correspond to a biological body. The method comprises collecting a set of data describing the biological body and also constructing a model of the body from the set of data, wherein the model comprises features that reflect the desired features. The method further comprises forming a composite structure from the model. In addition, the method comprises forming an implantable structure using the composite structure as a basis such that the implantable structure has features corresponding to the desired features. In an embodiment, the biological body comprises bone.

Description

COMPUTER-AIDED TISSUE ENGINEERING OF A BIOLOGICAL BODY BACKGROUND OF THE INVENTION

Field of the Invention This invention relates to the field of tissue engineering and more specifically to the field of implantable replacements for biological bodies. Background of the Invention There is a strong need for improved tissue engineering processes for fabricating implantable replacements for bone or other tissues in humans and animals. An objective of tissue engineering is to restore tissue function through incorporation of biological materials such as cells, growth factors, and biopolymers. Artificial implants such as metal and plastic have been used in the past as implants to restore damaged areas. The materials comprising the implants are typically selected based on their mechanical and biological compatibility, which may be a factor of anatomic location. One drawback with artificial metal implants is stress shielding. For instance, with hip replacements, the substantial load carried by the stiffer material of the implant (e.g., titanium) may result in reduced deformation of the surrounding bone to below an equilibrium state, which may stimulate osteoclastic bone resorption and eventual implant loosening. Additional drawbacks with artificial implants include ultimate strength, fatigue life, and elasticity. Biocompatible materials have been developed to overcome these problems. However, biocompatible materials typically do not have sufficient mechanical strength or stiffness to mimic bone. Composites have also been developed as implants. Composites can be as simple as the application of peptide sequences onto a carbon-carbon backbone or as complex as developing negative stiffness or "smart" materials. Some bio-composites seek to offer surface modifications or specify binding for a particular application. Other types of composites make use of a biocompatible base material enforced with stronger nodules such as carbon nanotubes. Drawbacks to composites include an increase in the complexity of chemical interactions occurring within the architecture, which makes them more difficult to study and safely apply. Consequently, there is a need for an improved process for creating implants. Other needs include improved methods for creating replacements for biological bodies. BRIEF SUMMARY OF SOME OF THE PREFERRED EMBODIMENTS These and other needs in the art are addressed in one embodiment by a method for forming an implantable structure, wherein the implantable structure has desired features that correspond to a biological body. The method comprises collecting a set of data describing the biological body. The method also comprises constructing a model of the body from the set of data, wherein the model comprises features that reflect the desired features. In addition, the method includes forming a composite structure from the model. The method further includes forming an implantable structure using the composite structure as a basis such that the implantable structure has features corresponding to the desired features. Needs in the art are also addressed by a method for forming an implant having features in common with a biological body. The method comprises forming of the body with a three- dimensional map of values of a desired property. In addition, the method comprises providing a plurality of building blocks, wherein at least one building block approximates an estimated value of the desired property. The method also comprises forming a reconstruction of the body from at least one building block and forming a solid structure based on the reconstruction, wherein the implant comprises the solid structure. In some embodiments, the biological body comprises bone,. In other embodiments, quantitative computed tomography is used to form a three-dimensional model of desired values of the biological body. In further embodiments, the building blocks are part of a permanent implant made of metal, polymers, or other materials. The methods for forming an implantable replacement overcome problems in the art by providing implantable structures that are compatible with the anatomic implant site. For instance, the implantable replacement has biological features that correspond to the biological body to be replaced. In addition, the implantable replacement may have improved longevity. The foregoing has outlined rather broadly the features and technical advantages of the present invention in order that the detailed description of the invention that follows may be better understood. Additional features and advantages of the invention will be described hereinafter that form the subject of the claims of the invention. It should be appreciated by those skilled in the art that the conception and the specific embodiments disclosed may be readily utilized as a basis for modifying or designing other structures for carrying out the same purposes of the present invention. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the spirit and scope of the invention as set forth in the appended claims. BRIEF DESCRIPTION OF THE DRAWINGS For a detailed description of the preferred embodiments of the invention, reference will now be made to the accompanying drawings in which: FIGURES la, lb illustrate stiffness maps with non-uniform density and uniform density, respectively; FIGURE 2 illustrates matching between two dissimilar polyhedra containing a common interface of a split torus; FIGURE 3 illustrates an interface in the shape of a torus; FIGURES 4a-4c illustrate building blocks after a prescribed displacement; FIGURE 5 illustrates a microstructural unit before optimization; FIGURE 6 illustrates the microstructural unit of FIGURE 5 after one optimization iteration for uniaxial compression; FIGURE 7 illustrates a composite structure and a library of building blocks; FIGURE 8 illustrates a boolean difference in shaping a composite structure; FIGURE 9 illustrates a diagram of a lumbar vertebral body; FIGURE 10 illustrates an approximation of half of a human lumbar vertebral body; FIGURE 11 illustrates a building block design where the interfaces are variable and the building block is designed after the interfaces are selected from a library of interfaces; and FIGURE 12 illustrates the concept of connecting the interfaces together in a simplified two- dimensional case. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS In an embodiment, a method for forming an implantable structure includes forming a tissue scaffold and fabricating the implantable structure based upon the tissue scaffold. Forming the tissue scaffold includes obtaining a three-dimensional model (e.g., of a biological body) of assigned data values and designing a composite structure from the model to form the tissue scaffold. Designing a composite structure includes matching building blocks to the assigned values in the model to form the tissue scaffold. In some embodiments, at least a portion of the building blocks may be optimized. In other embodiments, the implantable structure is implanted into an anatomic site as a replacement for the biological body. An implantable structure refers to a solid structure that is suitable for implantation into an anatomic site. In some embodiments, the implantable structure is suitable for implantation into a human or an animal. It is to be understood that the implantable structure is not limited for implantable purposes but can also be suitable for other purposes such as research purposes in a bioreactor setting. The implantable structure may be a replacement for a biological body, an addition to a biological body (e.g., to strengthen the biological body), or an addition to an implant. In some embodiments, the implantable structure approximates features (such as, without limitation, geometry and stiffness values) of the biological body to be added to or replaced. Without limitation, the biological body can be an organ, muscle, ligament, tendon, nerve, cartilage or bone. In an embodiment, the implantable structure is a replacement for bone. For instance, a damaged or missing portion of bone such as a vertebrate may be replaced by the implantable structure. In an embodiment wherein the implantable structure is an addition to an implant, the implantable structure may be attached to the implant before or after implantation of the implant.

The implantable structure may be attached by any suitable process such as fusion (e.g., heat, chemical, and the like), mechanical device (e.g., screws and plates), glues, and any other suitable process. The implantable structure may cover all or a portion of the implant. As an example, the implantable structure may cover a portion of the surface of an existing metal implant. Without being limited by theory, it is believed that surface coating at least a portion of an existing implant (e.g., hip replacement) may allow for better osteointegration of the implant once surgically implanted.

Obtaining a Three-Dimensional Model of a Biological Body In an embodiment, obtaining a three-dimensional model includes obtaining a three- dimensional geometrical model having features related to a biological body. The features include geometry and a set of assigned data values that describe the biological body. In an embodiment, the model has assigned values that approximate similar values of the body. Without limitation, the data can be mechanical properties of the biological body, intrabecular distance, trabecular cross- sectional area, geometric properties of the biological body, morphological characterizations of the biological body, surface-to-volume ratio, bone mineral volume, density, porosity, surface area, trabecular spacing, connectivity, and combinations thereof. Without limitation, examples of mechanical properties include modulus of elasticity, apparent modulus, stiffness, ultimate strength, ultimate stress, energy to failure, bending stiffness, yield point, and combinations thereof. In an embodiment, the three-dimensional geometrical model comprises a three-dimensional stiffness map having stiffness values assigned to locations that approximate similar locations in the biological body. The three-dimensional stiffness map can be obtained by invasive or non-invasive methods that collect spatial data values of the biological body. The invasive methods include removing the biological body and evaluating its tissue and mechanical properties. An example of an invasive technique is a surgical procedure. Evaluating the tissue to obtain the three-dimensional model includes but is not limited to indentation testing, standard tensile or compression testing, quantitative ultrasound analysis, and vibrational analysis. Non-invasive methods include using a template of known values, imaging modalities, or combinations thereof. Without limitation, a template of known values may be a theoretical distribution of known data for the biological body. For instance, the template may be an average of values for a similar biological body. Imaging modalities include without limitation quantitative computed tomography (QCT), x-rays, magnetic resonance imaging (MRI), quantitative ultrasound, and modifications thereof. The x-rays, MRI, and quantitative ultrasound modalities may be used with a template and/or an algebraic reconstruction technique (ART) to provide a three-dimensional model. The imaging modalities allow tissue information to be obtained in real time. The imaging modalities can provide a three-dimensional model having uniform data values or having non-uniform data values. In an embodiment, QCT scans provide a three-dimensional model having non-uniform data values. For instance, QCT scans yield a stiffness map from the non-uniform density values, which refers to each location on the stiffness map having a density value that approximates the density value at a similar three-dimensional location in the biological body. The non-uniform density values are related through regression analysis to the different gray scale values in the CT images, which reflects by itself variations in x-ray attenuation of bone tissue of various density. FIGURE la illustrates a stiffness map with non-uniform density values as produced using a QCT scan. Other embodiments include x-rays, MRI or quantitative ultrasound providing a three-dimensional model having uniform data values. For instance, a stiffness map is provided having an average density value assigned to each location in a dimensional row, wherein the average density value is the density resulting from the imaging modality scan. FIGURE lb illustrates a stiffness map with uniform density as produced using an X-ray scan. QCT involves scanning the biological body and comparing the results to a series of standard liquids or solids in a phantom for which equivalence (e.g., density) has been established. Three-dimensional software provides a three-dimensional model from the results. Without limitation, examples of three-dimensional software include Computer Aided Design (CAD), Finite Element Software, and the like from companies such as SolidWorks and Pro/Engineer for CAD, and ANSYS, Pro/Mechanica and ABAQUS for finite element analysis. The software creates the three-dimensional model by reconstructing the data resulting from the scan into a three-dimensional image of data, segmenting the image to generate surface geometry, and creating a volume of the material to be manipulated by programs such as CAD programs. In some embodiments, mechanical properties can be determined when segmenting the image. To determine the mechanical properties (e.g., bone stiffness) of the biological body from the QCT scan results, QCT absorbance may first be converted into Hounsfeld units. A phantom of several materials of known mineral density may be incorporated into the QCT scan, and a linear regression curve may be established between the given QCT Hounsfeld units and the bone density. By using the calculated bone density in conjunction with previously obtained in vitro relationships (e.g., density related to stiffness), mechanical properties such as modulus of elasticity may be calculated. The QCT scans and software provide a three-dimensional model that defines the biological body, wherein the model has features such as geometry and stiffness values that approximate those of the biological body. In an embodiment wherein the biological body is bone, the three-dimensional model may be a stiffness map. FIGURE la illustrates an example of a stiffness map produced by QCT. X-rays include standard x-ray absorptiometry and dual energy x-ray absorptiometry (DEXA). DEXA involves aiming a x-ray beam with two different energy levels at the biological body and interpolating the differences between the images. In an embodiment, DEXA is used to determine bone mineral density. The bone mineral density can be determined from the absorption of each beam by bone. X-rays may be used with a template, an algebraic reconstruction technique (ART), ultrasound, or combinations thereof to provide a three-dimensional model such as a three- dimensional stiffness map. ART uses multiple projection x-rays to generate a stiffness map of the three-dimensional body. Image registration is first completed to match the x-ray projections to each other. Back calculation of the three-dimensional stiffness map is completed with the resulting correlations between adjacent pixel values contributing to the final value for each location on the stiffness map. In some embodiments, an MRI may be used with a template, ART, ultrasound or combinations thereof to provide a three-dimensional model such as a three-dimensional stiffness map. MRI involves using a magnetic field to create images of the structure of the biological body. Without being limited by theory, the center of every atom of the biological body responds to the magnetic force in characteristic ways, which allows a computer to produce cross-sectional or three- dimensional images of the biological body. In embodiments using a template, the values of a desired template can be combined with the MRI image to provide the three-dimensional model. In embodiments using ART, x-ray images may be used to generate a three-dimensional map of the stiffness values. In some embodiments, less than ten x-ray images are used. The x-ray images are taken from different views of the biological body. ART is then used to generate a three- dimensional approximation of the biological body in terms of overall shape and density distribution. The density values are obtained from conversion of the calibrated image intensity of the x-rays at a specific location to density and subsequently stiffness. If ART is used in combination with MRI or QCT, fewer x-rays may be needed as these imaging modalities provide the overall shape information and base values for the stiffness map. In an embodiment, quantitative ultrasound may be used with a template, ART, ultrasound, or combinations thereof to provide a three-dimensional model. Quantitative ultrasound involves measuring the velocity of sound through the biological body to provide data about the body. In embodiments using a template, the values of a desired template can be combined with the ultrasound results to provide the three-dimensional model. In embodiments using ART and quantitative ultrasound, not limited to the described combination, ART is used to approximate the shape of the biological body, while quantitative ultrasound determines the material properties. The combination provides a three-dimensional representation of geometry and material properties. This type of system is preferably used on long bones. Building Blocks Building blocks can be used to form a composite structure having features that approximate the biological body, using the three-dimensional model as the basis. The building blocks can be selected from a library of shapes or from a library of interfaces. Building blocks refer to shapes having material properties assigned thereto. The building blocks comprise a number of architectures that vary in geometric arrangement of characteristics such as, without limitation, material, porosity, permeability, alignment, anisotropy, and/or surface area. Each building block is surrounded by the same bounding box. A bounding box refers to a theoretical cubic box having equal sides that surrounds a volume. The regulation of the size of the building blocks allows for blocks to be created with a large amount of diversity in the final arrangement of the blocks. FIGURE 2 illustrates examples of two building blocks 5 and 10 connected by an interface 15. Each building block contains a plurality of struts 20, with each end of a strut 20 connected to an interface 15. The building blocks can be any shape such as without limitation elemental shapes such as beams, cylinders, and spheres. In one embodiment, the building blocks are polyhedral. In some embodiments, the shape of each building block may be confined to a volume defined by a cubic bounding box, with each building block having at least one interface on each side of the cube. In an embodiment, the building blocks are selected from a library of shapes that can be used as building blocks. In the library, each building block has at least one mechanical property and at least one deformation pattern assigned to it. Building blocks from the library can be assembled to create a composite structure having features that approximate features of the biological body. In an embodiment, the library has building blocks with a range of mechanical properties. The library of shapes can be assembled by any suitable method. In an embodiment, the library is prepared by the use of computer aided design file databases to create the geometrical shapes of the building blocks. The architecture is first generated via computer aided design. Geometric and morphological characterization is carried out on the architecture using the CAD software. Finite Element Analysis (FEA) is carried out and the mechanical properties of the architecture are determined through an analysis which yields the desired mechanical properties (e.g., stiffness, elastic modulus, yield point, ultimate stress/strength, and the like). In an embodiment, the shapes are confined within a desired volume of a bounding box, preferably within about a 27 mm³ volume, and alternatively between about a 3.38 mm³ volume and about a 125 mm³ volume. It is to be understood that the building blocks are not limited to the shapes of FIGURE 2 but can have any desired shape that fits within the cubic bounding box of desired volume. In an embodiment, each building block will have a common interface. The interface can have any suitable shape such as a torus. In alternative embodiments, at least some of the building blocks do not have common interfaces. FIGURE 3 illustrates an interface 15 in the shape of a torus. Common interfaces 15 in the shape of a torus are illustrated in FIGURE 2. Any suitable three-dimensional modeling program may connect the building blocks to each other by the interfaces. For instance, each block has half of a matching interface that match when connected and thereby connect each block. Determining apparent mechanical properties of each architecture may be accomplished with finite element analysis (FEA), for instance by prescribed linear displacement in a perturbation study through non-linear analysis. Subjecting the building blocks to a prescribed displacement can allow the calculation of mechanical properties. Prescribed linear displacement of a finite strain allows the direct calculation of elastic properties such as stiffness and elastic modulus. It is to be understood that a finite strain refers to a relative deformation of an object independent of the formulation used to calculate strain. Using FEA, the architecture is displaced a specific amount, and the reaction force is calculated on the top nodes of the architecture. The stiffriess is calculated from the reaction force divided by the displacement. Stress is calculated by dividing the reaction force by the cross- sectional area of the top face of the architecture, or the area of the bounding box, whichever is applicable. The elastic modulus is calculated by dividing the stress by the finite strain. The building blocks of FIGURES 4a-4c show an example of the finite element analysis run on architectures by illustrating the displacement patterns of three architectures. In such figures, the ghosted displays of the architectures illustrate the starting shape of each architecture, and the solid architecture illustrates the deformed shape as a result of the displacement in the z-direction. In an embodiment, the library has a range of shapes and mechanical properties. In other embodiments, the library has building blocks that are created to mimic the mechanical properties of the biological body of interest. For instance, in an embodiment wherein the biological body is a vertebral body and the library has blocks to mimic the biological body, a library can be compiled with stiffness values ranging from about 100 MPa to about 2 GPa. The range of values encompasses both bone and implant stiffnesses. By selecting a building block size of 27 mm³ each with total vertebral body dimensions of 48mm x 24 mm x 27 mm, about 1,008 total building blocks may be provided in a library to approximate the vertebral body. In another embodiment, the building blocks are created from a library of interfaces. At least one interface is selected for each side of the building block, providing six total interfaces surrounding the volume of a block as illustrated in FIGURE 11, which shows four of the six interfaces. The interfaces may have a variety of configurations. It is to be understood that the interior architecture of each building block determines its mechanical properties. Therefore, CAD and FEA may be used to design the interior architecture by connecting an interface to another interface of the block with struts within the bounding box. In an embodiment, an iterative algorithm may be used to match the interfaces of each side resulting in an architecture contained within the surrounding bounding box. A simplified case in two-dimensional space is illustrated in FIGURE 12. A connect function may first plot the difference between adjacent interfaces. Then a region growing function may extrude the face of the interfaces towards all other interfaces resulting in an architecture contained within the confines of the block, which connects all the common interfaces. Such region growing function may be subject to user constraint, such as a specific material volume, cross-sectional area, modulus of elasticity, stiffness, connectivity, or spacing. An embodiment includes connecting the dots between adjacent interfaces resulting in parallel pipeds spanning the volume of the cube intersecting each interface at the block face. It is to be understood that the struts can be curved, straight, and the like. In an embodiment, the interface of each side of a building block can be designed as a function of a variety of values. For instance, it can be a function of the average modulus of elasticity between the building block and that of a corresponding building block, the gradient between the building block and that of a corresponding building block, spatial orientation within the building block, the anatomic site of the biological body, porosity, surface area, surface area to volume ratio, spacing, connectivity, or combinations thereof. The mechanical properties of each building block are determined by the struts. For instance, the thickness, spatial orientation, number, cross-sectional area, and connectivity of the struts within the block can determine desired mechanical properties for each building block. Without being limited by theory, by varying the interior architecture of the building blocks through different interfaces, the architecture of the composite structure may resemble the interior physical structure of the biological body. Optimization of the Building Blocks In some embodiments, at least a portion of the building blocks may be optimized to improve post-surgical success. Without being limited by theory, the architecture of the building blocks may be optimized to account for exogenous parameters such as local chemical moieties and pH. Moreover, it is believed that tissue growth may be accentuated through a uniform surface energy distribution. In an embodiment, the architecture is optimized based on mechanotransduction principles. Mechanotransduction, at least with respect to bone, refers to the process whereby mechanical signals are sensed and interpreted in biological terms to effector cells, osteoblasts and osteoclasts, which supply a net change in bone mass. It typically refers to mechanically activated cellular processes responsible for bone growth and remodeling. In an embodiment, mechanotransduction includes, but is not limited to, creating a voxel model of a previous scaffold microstructure obtained through an imaging modality. A voxel model refers to a model generated from discretized object into uniform elements (voxels) that are aligned with the principle coordinates system. Generally, voxel based models contain large numbers of linear finite elements. In contrast, volumetric models contain larger, non-uniform elements that also can have quadratic interpolation points. Examples of voxel models are illustrated in FIGURES 5 and 6. The geometry of the model of FIGURE 5 is altered based on finite element results to distribute the material in such a way to eliminate peak stresses, strains, and/or strain energy densities. Altering the geometry includes moving voxels that are subjected to high stresses to a region containing low stress elements. Finite element results include the determination of the surface energy distribution through prescribed displacement of the elements. FIGURE 6 illustrates the voxel model of FIGURE 5 after an optimization iteration for uniaxial compression. In an embodiment, an iteration involves tabulating finite element results under unit compressive displacement and a fully constrained opposite face. The geometry can be altered, for instance, to reinforce areas of high strain energy and to weaken areas of lower energy to narrow the energy profile (as illustrated in FIGURE 6). Without being limited by theory, it is believed that use of microstructural units such as building blocks supplies biological scalability while maintaining constant material properties. Further, though it is true that apparent mechanical properties may differ from those on the microstructural scale, any shift in the overall size of the building block construct (while keeping relative dimensions consistent) may not affect its overall material response (stress and strain) in contrast to structural properties (load and displacement). It is further believed that an increase or decrease in size may affect the cellular response to the scaffold. Therefore, also without being limited by theory, it is believed that fine tuning of the scaffold's biological response may be conducted by altering its size. A bandwidth may exist in which scaling may not prove biologically favorable, for instance when an interconnected pore structure is not possible. It is further believed that by mixing and matching different microstructural units, increasing some and decreasing or skewing others, a net biological advantage may be achieved. In an alternative embodiment, building blocks may be optimized by a cellular automata standpoint technique. Cellular automata are iterative processes that set simple rules, which result in complex systems. In this embodiment, the voxels would shift based upon a random walk algorithm. Arrangement of Building Blocks into Composite Structure Using building blocks to form the tissue scaffold includes arranging the building blocks into a three-dimensional composite structure, which may represent a reconstruction of the biological body. In an embodiment, the building blocks are arranged in the three-dimensional model to match data values assigned to locations in the model. FIGURE 7 illustrates a non-limiting example by which the building blocks 5 are arranged into a tissue scaffold 30 by using a library of shapes 25. By using a three-dimensional stiffness map generated from an imaging modality and/or template, a building block 5 can be selected from a library of shapes 25 that approximates each corresponding stiffness value. Using CAD, the building blocks 5 can be arranged in series or parallel, which may result in a layered reconstruction (the tissue scaffold 30) of the biological body (e.g., bone). In embodiments wherein a library of interfaces is used to assemble the tissue scaffold, selected interfaces may be arranged in the global three dimensional locations. Matching of the volumetric connections may then occur to form each building block. After arrangement of the building blocks in the proper location, the resulting tissue scaffold provides a general approximation in geometry and designed features of the biological body. In some embodiments, the tissue scaffold is optimized, for instance to provide a continuous boundary. A continuous boundary refers to a matching between adjacent building blocks, which contains complete load transfer through exact material matching. The optimization can be accomplished by suitable programs such as Boolean or cutting functions in solid modeling programs. FIGURES 8a-8d illustrate a non-limiting example of an optimization of a tissue scaffold by use of a boolean difference function. FIGURE 8a illustrates the tissue scaffold prior to optimization, and FIGURE 8b illustrates a complex border to be overlayed on the tissue scaffold, which overlay is illustrated in FIGURE 8c. The program removes the excess material that overlaps outside of the complex border. FIGURE 8d illustrates the optimized tissue scaffold. In some embodiments, a replacement for a biological body is not constructed as a single tissue scaffold but is instead constructed piece-wise as more than one tissue scaffold. For instance, a replacement for a posterior element of a vertebral body is constructed piece-wise. It is to be understood that the posterior element of a vertebral body refers to the region of bone posterior to the vertebral body protecting the spinal cord. Without being limited by theory, the posterior elements may be approximated as a thick shell with a hollow channel running through the center because such elements are similar to cortical bone. In such embodiments, the three-dimensional model may be obtained as noted above. The posterior elements are designed piece-wise, for instance with the posterior elements split axially in order to enclose the spinal cord to ensure protection and to facilitate simpler implantation. Boolean functions can be used to generate the global shape of the posterior elements. After obtaining the tissue scaffolds for the posterior elements, a small channel can be created running through the middle of the posterior elements using a subtractive function. As shown in Figures 8a-8d, a contour (e.g., border, channel) is applied to the desired shape (e.g., cube, posterior element), and the contour is then subtracted from the dominant shape resulting in a complex architecture, which contains both the contour and the original shape. This channel represents the hollow region that exists inside the posterior elements in vivo. The global contour of the vertebral body may also be generated with this negative Boolean process. Fabricating the Implantable Structure In an embodiment, the implantable structure is fabricated using the tissue scaffold as the basis. The implantable structure can be fabricated by casting a mold by any suitable process such as a rapid prototyping process, injection molding, or negative casting. Without limitation, examples of rapid prototyping processes include stereolithography, fused deposition modeling, particle binding, three-dimensional printing (3DP), phase change printer, solid freeform fabrication (SFF), or any stand alone custom-built apparatus for generating three-dimensional objects in a layer-by- layer fashion. The implantable structure may be casted from the mold from biomaterials. The fabricated implantable structure may have about the same complex micro-architecture of the biological body and/or have one or more similar mechanical properties as the biological body. The implantable structure may be fabricated of suitable biomaterials based upon factors such as the anatomical implant site, the fabrication method, patient constraints, available materials, possible processing methods, and the like. Examples of suitable biomaterials include without limitation poly-esters, poly-orthoesters, poly-fumarates, poly-acrylics, poly-methacrylates, hydrogels, shape memory metals, de-mineralized bone matrix, thermoreversible biomaterials, agarose, adsorbed cytokines, growth factors, and combinations thereof. In one embodiment, the mold of the implantable structure is fabricated by stereolithography. In an embodiment, stereolithography includes using a precision laser driven on a plotter that crosslinks a polymer in predetermined arrangements to produce the tissue scaffold in the form of a mold. The polymer may include a suitable photo-crosslinkable polymer. Examples of suitable photo-crosslinkable polymers include without limitation a poly(propylene fumarate), hydrogels, agarose, or any other biomaterial modified with a photo-initiator that initiates crosslinking via UV or any other radiated source. Commercial examples of rapid prototyping are available from Therics Inc., Solid Scape Inc., 3D Systems, ThermoJet, Sanders Prototype, Z-Corp, and Sciperio Inc. Therics Inc. uses a particle binding system with six printheads focused on the eventual goal of printing live cells into the fabricating scaffold. Sciperio Inc. uses a system that is able to print on a complex surface with a variety of materials including fibrin glue, cells and polymers. The machine uses two lasers to guide the printheads to deposit material on an object moving at 10Hz. Solid Scape Inc. produces a machine that generates three-dimensional objects with thermoplastic waxes capable of being removed via heat or organic polymers. 3D Systems offers fused deposition modeling and stereolithography with a number of components, some of which are water soluble. ThermoJet produces a machine that is UV polymerizable. Z-Corp uses a particle binding system with one printhead with material that may be removed via heat or other organic solvents. In an embodiment, the implantable structure is fabricated by fused deposition modeling. Fused deposition modeling typically involves printing the inverse of an object and removing the support material to create a mold of the object. The mold may be a template for injection of the casting material, following removal of the build material. In one embodiment, fused deposition modeling includes a printhead that deposits a thermoplastic material onto a stage of build material in a two-dimensional pattern resulting in a slice of the final geometry of the implantable structure. A second material is printed surrounding the build material, which enables oblique angles. This process is repeated in overlays until a suitable mold of the implantable structure is fabricated. Without limitation, examples of suitable build material include any material that may be removed to provide the mold cavity, which then may be filled with the desired biomaterial. In some embodiments, the build material may be removed. The build material may be removed by any suitable technique such as, without limitation, by using organic chemicals or by melting with high temperature. It is to be understood that incorporating separate rapid prototyped parts into a single mold allows the use of a wide range of materials, while maintaining the resolution required for a bone-like architecture. The PATTERNMASTER from SolidScape is a commercial example of a fused deposition process. It wields two thermoplastic waxes for build and support and several different solvents to remove the reinforcement material. The final object or mold is retrieved by either melting or dissolving the support material with a kerosene based liquid following the build process. In an embodiment, the mold of the implantable structure is fabricated by particle binding. Particle binding involves using a liquid to bind powder particles in an iterative process to produce a mold of the implantable structure. Without limitation, examples of the liquid include adhesive binders, certain fibrin glues, and resins. Examples of suitable bind particles include without limitation starch and demineralized bone matrix. Particle binding involves the deposition of a liquid binder onto a bed of particles. The deposition path is taken from a two-dimensional slice of the object to be printed. Following the deposition of the binder completing one cross-section of the object, the build plate containing the powder moves down an increment equal to the slice height of the cross-sectional slice. Additional powder is coated on top and the process repeats itself, building the object (e.g., mold) in a layer-by-layer fashion. Casting of the mold with biomaterial includes the generation of a negative mold. The negative mold is the encapsulated volume of the desired object surrounded in a removable material. A biomaterial is then delivered into the void space, filling it and taking the shape of the desired object (e.g., implantable structure). Methods for delivery of the biomaterial include without limitation injection of the material via syringe, centrifugal force delivery, or melt casting. The mold is then removed by a variety of methods including, without limitation, melting, burnout, mechanical separation, or solvent dissolution. In an alternative embodiment, a non-porous shell is placed around at least a portion of the surface of the implantable structure. In an embodiment, the non-porous shell is placed around about substantially all of the surface of the implantable structure. Without being limited by theory, the non-porous shell may improve the mechanical stability of the implantable structure and may mitigate fluid leakage. The non-porous shell may comprise any of the biomaterials listed above. The non-porous shell can be placed around the surface of the implantable structure by any suitable method. For instance, the non-porous shell can be placed around the surface by injection molding, negative casting, surface coating, submersion, painting/spraying on the surface, or adsorption. Implanting into an Anatomic Site In an embodiment, the implantable structure is implanted into an anatomic site. Without being limited by theory, to prevent stress shielding and subsequent implant failure, the mechanical properties of the implantable structure may approximate the original biological body properties and may be functionally integrated into the surrounding tissue. The implantable structure may be implanted into the anatomic site by any suitable process. In an embodiment, the implantable structures have a suitable number of attachment sites for attachment of tissue such as muscles, tendons, ligaments, and the like to the implantable structure. The tissue can be attached in any suitable manner that promotes their functional integration. In an embodiment, the attachment sites are suitable for connective tissue to be sutured or tied to the outside of the implantable structure. In some embodiments, tissue glues may be used during the implantation process. For instance, the tissue glues may be used to provide connections between two implantable structure tissue counterparts or to join all the connections that cannot be tied or sutured to the implantable structure. In some embodiments, the tissue glues are fully resorbable. Examples of suitable tissue glues include without limitation fibrin glue, alginate, tissue adhesive, or cyano-acrylate. In an embodiment wherein the biological body is a vertebral body, the implantable structure may be fabricated in more than one part with the posterior elements of the implantable structure matched with the spinal cord to protect and complete load transfer. In one embodiment, the hollow channel present in the posterior elements may be an anatomical attachment point for connecting the two lateral elements. FIGURE 9 illustrates splitting of the vertebrae for implantation of a implantable structure surrounding the spinal cord. By dividing the vertebral body into three portions, the implantation during surgery will be simplified. The spinal cord will be placed in between the two posterior elements which will, in the end, be attached to the vertebral body and themselves, thus protecting the spinal cord. It is to be understood that the invertebral discs above and below the vertebral body may be joined to the surface of the implantable structure with fibrin glue. To further illustrate various illustrative embodiments of the present invention, the following example is provided.

EXAMPLE A model of a vertebral body was generated, which is illustrated as FIGURE 10. A lumbar vertebrae was scanned using a microCT (Scanco, CH) and was reconstructed using ANALYZE 5.0 from AnalyzeDirect to produce a stiffness map. ANALYZE 5.0 is a software package for multidimensional display and processing of biomedical images. Determined stiffness values were grouped into four regions corresponding to four different building blocks, which are illustrated in the library of FIGURE 7. The building blocks were prepared to have a size of 27 mm³ each with dimensions of 48mm x 24 mm x 27 mm. Building blocks were generated via computer aided design. Architectures were based on a system of parallel pipeds arranged in varied geometries. No optimization was completed on this library of shapes. Based upon the generated stiffness map, the building blocks were arranged into their respective locations. About half of the approximated vertebral body was built. A rapid prototyping process using PATTERNMASTER was used to fabricate the replacement. The PATTERNMASTER builds using two thermoplastic waxes, one a support and one a build material. Both waxes can be removed with either heat or organic solvents. The vertebral body was built and the support wax was dissolved using BIOACT. BIOACT is a kerosene based solvent available from Petrofern Inc. Although the present invention and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations may be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims

CLAIMS What is claimed is:

1. A method for forming an implantable structure, wherein the implantable structure has desired features that correspond to a biological body, comprising: a) collecting a set of data describing the biological body; b) constructing a model of the body from the set of data, wherein the model comprises features that reflect the desired features; c) forming a composite structure from the model; and d) forming an implantable structure using the composite structure as a basis such that the implantable structure has features corresponding to the desired features.

2. The method of claim 1, wherein the desired features comprise non-uniform density.

3. The method of claim 1, wherein the desired features comprise uniform density.

4. The method of claim 1, wherein the set of data comprises mechanical properties.

5. The method of claim 1, wherein step a) comprises a non-invasive technique.

6. The method of claim 5, wherein the non-invasive technique comprises a template of known values, an imaging modality, or combinations thereof.

7. The method of claim 1, wherein step a) is accomplished by an imaging modality, wherein the imaging modality comprises quantitative computed tomography, x-rays, magnetic resonance imaging, quantitative ultrasound, or modifications thereof.

8. The method of claim 1, wherein step a) is accomplished by dual energy x-ray absorptiometry.

9. The method of claim 1, wherein step a) is accomplished by standard x-ray absorptiometry.

10. The method of claim 9, wherein step b) is accomplished by an algebraic reconstruction technique.

11. The method of claim 1 , wherein quantitative computed tomography provides the set of data and the model.

12. The method of claim 1, wherein step c) comprises assembling the composite structure from at least one building block.

13. The method of claim 12, wherein the at least one building block is selected from a library of building blocks.

14. The method of claim 13, wherein the library of building blocks represents a range of mechanical property values.

15. The method of claim 13, wherein the library of building blocks have a common interface.

16. The method of claim 12, wherein the at least one building block is created from a library of interfaces.

17. The method of claim 16, wherein the building blocks comprise an interior architecture created to provide the block with a desired value.

18. The method of claim 12, wherein step c) further comprises optimizing at least one of the at least one building block.

19. The method of claim 18, wherein optimizing is accomplished using mechanotransduction.

20. The method of claim 1, wherein step c) comprises assembling the composite structure from a plurality of building blocks, and further wherein two of the building blocks comprise different values.

21. The method of claim 1, wherein step c) further comprises optimizing the composite structure.

22. The method of claim 1 , wherein step d) comprises using a rapid prototyping process.

23. The method of claim 1, wherein step d) further comprises placing a non-porous shell on at least a portion of a surface of the implantable structure.

24. The method of claim 1, wherein the biological body is a bone.

25. The method of claim 1, wherein the biological body is a vertebra.

26. The method of claim 1, further comprising e) implanting the implantable structure.

27. The method of claim 26, wherein implanting comprises replacing the biological body.

28. The method of claim 1 , further comprising e) attaching the implantable structure to an implant.

29. A method for forming an implant having features in common with a biological body, comprising: a) forming of the body a three-dimensional map of values of a desired property; b) providing a plurality of building blocks, wherein at least one building block approximates an estimated value of the desired property; c) forming a reconstruction of the body from at least one building block; and d) forming a solid structure based on the reconstruction, wherein the implant comprises the solid structure.

30. The method of claim 29, wherein the features comprise density.

31. The method of claim 29, wherein step a) comprises a non-invasive technique.

32. The method of claim 31, wherein the non-invasive technique comprises a template of known values, an imaging modality, or combinations thereof.

33. The method of claim 29, wherein step a) is accomplished by an imaging modality, wherein the imaging modality comprises quantitative computed tomography, x-rays, magnetic resonance imaging, or quantitative ultrasound.

34. The method of claim 29, wherein step a) is accomplished by dual energy x-ray absorptiometry.

35. The method of claim 29, wherein step a) is accomplished by quantitative computed tomography.

36. The method of claim 29, wherein the at least one building block is selected from a library of building blocks.

37. The method of claim 36, wherein the library of building blocks have a common interface.

38. The method of claim 29, wherein the at least one building block is created from a library of interfaces.

39. The method of claim 29, further comprising optimizing the at least one building block.

40. The method of claim 39, wherein optimizing is accomplished using mechanotransduction.

41. The method of claim 29, wherein step c) further comprises optimizing the reconstruction.

42. _. The method of claim 29, wherein step d) is accomplished using a rapid prototyping process.

43. The method of claim 29, wherein step d) further comprises placing a non-porous shell on at least a portion of a surface of the implantable structure.

44. The method of claim 29, wherein the biological body is a bone.

45. The method of claim 29, wherein the biological body is a vertebra.

46. The method of claim 29, further comprising e) implanting the implantable structure.

47. The method of claim 46, wherein implanting comprises replacing the biological body.

48. The method of claim 29, further comprising e) attaching the implantable structure to an implant.