Patent Publication Number: US-2020286593-A1

Title: Methods for Developing Porous Implants of Optimal Properties

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Application No. 62/815,256, filed Mar. 7, 2019. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to designing porous implants, and more particularly to systems and methods for developing porous implants of optimal properties. 
     2. Background and Related Art 
     Orthopedic implants are often made porous with a goal of promoting ongrowth of bone to the implant as well as ingrowth of the bone into the porous structure of the implant. Implants are typically manufactured of biocompatible materials. Unfortunately, the majority of manmade materials that are biocompatible and from which implants can be constructed have bulk characteristics that are significantly different from the physical characteristics of bone. 
     Human bones are generally formed of two types of structural bone tissue: cortical bone and trabecular or cancellous bone. Cortical bone generally forms the outer shell of most bones, and is more dense, harder, stronger, and stiffer than trabecular bone. Trabecular bone is typically found at the ends of long bones proximal to joints, as well as in the interior of vertebrae. Trabecular bone is highly vascularized and has a generally porous or spongy structure through which blood vessels pass. Generally, trabecular bone has pores that are on the order of 150 to 650 microns in size. Not all trabecular bone has the same porosity; different bones have different trabecular bone porosity. 
     The physical characteristics of bone are important for physiological purposes related to the growth and formation of bone both originally as well as during the healing process. The cells responsible for bone growth, including osteocytes and osteoblasts, work together to form bone as needed within the body, but will only form bone under proper conditions, including when the cells experience proper loads and stresses, when a network of blood vessels is available to supply needed nutrients, and when gaps to be filled by bone are of a proper size. When proper conditions are not available, bone cannot or will not grow. For example, when bone does not experience loading, it will not grow and can even be resorbed. Additionally, when gaps to be filled are too large or too small, bone cannot bridge the gap and will not grow. 
     In addition to proper physical conditions, bone growth only occurs when certain conditions are met. First, there must be a kernel of living bone to start the process. The living bone supplies the cells necessary for bone growth and formation. Additionally, a cascade of chemical triggers is required for bone to grow. Finally, because bone growth is impeded by the presence of certain materials and/or chemicals, an absence of such materials and chemicals is required for proper bone growth. 
     One example of where it is generally recognized as advantageous to promote bone growth is in the orthopedic implant industry. One goal with many orthopedic implants is for bone growth at the interface to fuse or secure the implant to the bone. For this reason, many orthopedic implants are provided with a porous surface at the bone-implant interface, with the expectation that bone will grow onto and into the porous surface of the implant. Other implants may be provided with one or more cavities or voids to receive bone growth (e.g., a graft window), and during surgery any such cavities or voids may be filled with a material intended to promote bone growth, including morcellized bone graft material. These techniques have been used in implants for years with varying degrees of success, but the success of such devices has been limited by the devices&#39; ongoing failure to provide physical and chemical characteristics most conducive to bone growth. Even when a graft is present in a cavity or void, any bone that does form on or around the device is of lesser quality and quantity. 
     Generally, current implants have one or more characteristics that are not maximally conducive to facilitating bone growth into the implant. For example, some implants may provide a pore size that is generally within a desirable range, but may have a stiffness that is too high to allow bone within the porous structure of the implant to be properly loaded. As a result, the bone will not take advantage of the correct porosity and pore size of such implants, and will grow only minimally, if at all, in the porous structure of such implants. In other implants, the stiffness may be generally within a desirable range, but in order to achieve the desired stiffness, the device manufacturer creates pores that are too large or too small to facilitate proper bone growth. As a result, while the bone cells can be properly loaded, they are unable to grow bone in the available pores. 
     Some manufacturers have used the material polyetheretherketone (PEEK) in orthopedic implants, as PEEK has a bulk stiffness (4 gigapascals (GPa)) that is close to that of bone (0.3 GPa&lt;bone stiffness&lt;4 GPa). Unfortnuately, PEEK is not chemically a bone-friendly material. As a result, when PEEK is used for implants, a fibrous layer is formed by the body around the implant to protect the body from the PEEK, and bone growth does not occur. Other commonly used materials are titanium and tantalum, which are osteoconductive but have a relatively high bulk stiffness (approximately 116 GPa) that shields the bone from appropriate mechanical stimulus necessary for proper bone growth. Stainless steel, another possible implant material, is not very osteoconductive and also has a very high bulk stiffness (approximately 210 GPa). 
     Many currently available implants made of titanium have a stiffness that approaches the stiffness of a block of solid titanium. These devices are typically too stiff even in their porous regions. Additionally, many devices have porous regions contained within a solid surrounding structure that prevents the intervening porous region from being loaded in a way conducive to bone growth. Trabecular metal is one of the least stiff predicate materials that is still more than twice as stiff as the maximum desired stiffness desired to promote bone growth through proper loading. 
     One particular type of implant that is illustrative of the difficulties encountered with predicate devices is an interbody spacer intended for placement between vertebral bodies in spinal fusion procedures. Predicate devices have focused almost exclusively on providing support for the spine, giving little to no attention to promoting or stimulating bone growth. As a result, while such devices may achieve bone on-growth at the surface of the device, such devices do not achieve ingrowth that extends throughout the devices. 
     For example, the TM-S® cervical fusion device and the TM Ardis® interbody system by Zimmer Biomet are made using elemental tantalum (“trabecular metal”) and achieve a pore size on the order of 550 microns. Despite having a pore size that is generally within the desired range, the stiffness of the implant is determined by the size and shape of the material between the pores, and remains at least twice and as much as ten times the desired stiffness. Due to the lack of proper loading, bone does not grow within the Zimmer devices to a significant extent. 
     Similarly, Stryker&#39;s Tritanium® PL posterior lumbar cage has a pore size of 616 microns, only slightly exceeding the desired pore size. Again, however, the device&#39;s stiffness is determined by the size and shape of the material between the pores and at the margins of the device itself. As a result, any bone that does enter the pores of the device cannot be properly loaded, and ingrowth does not occur. The stiffness of the Stryker device may exceed the stiffness of the Zimmer devices. 
     Other devices, such as the 4WEB® Medical Spine Truss system, the K2M Cascadia™ devices, the Titan Endoskeleton® TO device, and the Signus-Mobis® II ST devices all have even larger pore sizes as well as portions of solid non-porous titanium along leading and trailing edges of the devices. Thus, even if portions of such devices have a stiffness that is generally correct, such portions cannot be loaded due to the solid portions of the devices. The lack of loading prevents bone growth in the interior of the devices. Additionally, the large pore sizes (e.g., on the order of greater than 1700 microns) cannot be bridged by bone. 
     Thus, there remains an unmet need in the orthopedic implant industry for implants that provide stiffness and pore sizes that are conducive to bone growth using materials that are also conducive to bone growth. This need is especially felt in the spinal implant industry, for example with respect to interbody spacers. 
     BRIEF SUMMARY OF THE INVENTION 
     Implementation of the invention provides systems, methods (including computer-implemented methods), and non-transitory computer-readable media for causing computer systems to implement methods for developing porous implants of optimal physical properties such as stiffness and porosity. Additionally, implementations of the invention provide implants designed in accordance with the systems and methods disclosed herein. Implementations of the invention address the deficiencies with previous porous implants, providing implants designed to have a stiffness and a porosity (or other physical characteristics) within a desired range to satisfy the design demands to allow the implants to perform a desired function. More specifically, implementations of the invention provide porous implants having desired physical characteristics to provide, for example, conditions conducive to bone ingrowth and ongrowth. 
     According to implementations of the invention, a method for developing a porous implant includes steps of defining a design volume for a porous implant, defining a load to be borne by the design volume of the porous implant, and defining an objective function solution characteristic related to the design volume of the porous implant. The method further includes steps of dividing the load into a plurality of sub-loads and performing an optimization procedure. The optimization procedure includes performing, until all sub-loads have been applied, repeated steps of applying one of the plurality of sub-loads to the material in the design volume, removing material from the design volume such that remaining material within the design volume is capable of bearing one of the plurality of sub-loads and satisfies the objection function solution characteristic, the remaining material defining a void space without material therein, setting the void space as a new design volume for any remaining sub-loads, and setting the new design volume as being full of material. The method further includes a final step of combining the remaining material from each cycle of the optimization as a design of the porous implant. 
     In some implementations, the steps of applying one of the plurality of sub-loads and removing material from the design volume include performing a finite element analysis. In some implementations, the steps of applying one of the plurality of sub-loads and removing material from the design volume include finding a closed form solution. In some implementations, the method is performed on a computer system. 
     In some implementations, the objective function solution characteristic includes maximizing or minimizing a characteristic such as stress, mass, surface area, radiolucency, or stiffness. In some implementations, the repeated steps of the optimization procedure further include dilating the new design volume to create a buffer region to ensure a desired porosity in the boundary between the material from each cycle of the optimization. 
     In some implementations, the method also includes performing a final evaluation and optimization for a different objective function. In some implementations, the different objective function is a function such as weight, porosity, surface area, or stress. In some implementations, the design volume is pre-divided into a plurality of design volumes, each with its own portion of the load to be borne; the method is performed in parallel with respect to each of the plurality of design volumes and portions of the load to be borne. 
     According to further implementations, a computer-implemented method for developing a porous implant includes steps of defining a design volume for a porous implant, defining a load to be borne by the design volume of the porous implant, and defining an objective function solution characteristic related to the design volume of the porous implant. The method further includes using a computing device to divide the load into a plurality of sub-loads and causing the computing device to perform an optimization procedure. The optimization procedure includes performing, until all sub-loads have been applied, repeated steps of applying one of the plurality of sub-loads to the material in the design volume, removing material from the design volume such that remaining material within the design volume is capable of bearing one of the plurality of sub-loads and satisfies the objection function solution characteristic, the remaining material defining a void space without material therein, setting the void space as a new design volume for any remaining sub-loads, and setting the new design volume as being full of material. The method also includes a final step of combining the remaining material from each cycle of the optimization as a design of the porous implant. 
     In some implementations, the steps of applying one of the plurality of sub-loads and removing material from the design volume include performing a finite element analysis. In some implementations, the steps of applying one of the plurality of sub-loads and removing material from the design volume include finding a closed form solution. 
     In some implementations, the objective function solution characteristic includes maximizing or minimizing a characteristic such as stress, mass, surface area, radiolucency, or stiffness. In some implementations, the repeated steps of the optimization procedure further include dilating the new design volume to create a buffer region to ensure a desired porosity in the boundary between the material from each cycle of the optimization. In some implementations, the method further includes performing a final evaluation and optimization for a different objective function such as weight, porosity, surface area, or stress. In some implementations, the design volume is pre-divided into a plurality of design volumes; the method is performed in parallel with respect to each of the plurality of design volumes and portions of the load to be borne. 
     According to additional implementations, a computer-implemented method for developing a porous implant includes steps of defining a design volume for a porous implant, defining a load to be borne by the design volume of the porous implant, and defining an objective function solution characteristic related to the design volume of the porous implant, the objective function solution characteristic including maximizing or minimizing a characteristic such as stress, mass, surface area, radiolucency, or stiffness. The method further includes using a computing device to divide the load into a plurality of sub-loads and causing the computing device to perform an optimization procedure including performing, until all sub-loads have been applied, repeated steps of applying one of the plurality of sub-loads to the material in the design volume, removing material from the design volume such that remaining material within the design volume is capable of bearing one of the plurality of sub-loads and satisfies the objection function solution characteristic, the remaining material defining a void space without material therein, setting the void space as a new design volume for any remaining sub-loads, and setting the new design volume as being full of material. The method also includes a final step of combining the remaining material from each cycle of the optimization as a design of the porous implant. 
     In some implementations, the repeated steps of the optimization procedure further include dilating the new design volume to create a buffer region to ensure a desired porosity in the boundary between the material from each cycle of the optimization. In some implementations, the method further includes performing a final evaluation and optimization for a different objective function such as weight, porosity, surface area, or stress. In some implementations, the design volume is pre-divided into a plurality of design volumes, each with its own portion of the load to be borne; the method is performed in parallel with respect to each of the plurality of design volumes and portions of the load to be borne. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       The objects and features of the present invention will become more fully apparent from the following description and appended claims, taken in conjunction with the accompanying drawings. Understanding that these drawings depict only typical embodiments of the invention and are, therefore, not to be considered limiting of its scope, the invention will be described and explained with additional specificity and detail through the use of the accompanying drawings in which: 
         FIG. 1  shows a representative computer system in which embodiments of the invention may be implemented; 
         FIG. 2  shows a representative networked computer system in which embodiments of the invention may be implemented; 
         FIG. 3  shows steps of a method in accordance with embodiments of the invention; 
         FIG. 4  shows steps of a method in accordance with embodiments of the invention; 
         FIG. 5  illustrates a design space during execution of a method in accordance with certain embodiments of the invention; and 
         FIG. 6  illustrates a design space during execution of a method in accordance with certain embodiments of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     A description of embodiments of the present invention will now be given with reference to the Figures. It is expected that the present invention may take many other forms and shapes, hence the following disclosure is intended to be illustrative and not limiting, and the scope of the invention should be determined by reference to the appended claims. 
     Embodiments of the invention provide systems, methods (including computer-implemented methods), and non-transitory computer-readable media for causing computer systems to implement methods for developing porous implants of optimal physical properties such as stiffness and porosity. Additionally, embodiments of the invention provide implants designed in accordance with the systems and methods disclosed herein. Embodiments of the invention address the deficiencies with previous porous implants, providing implants designed to have a stiffness and a porosity (or other physical characteristics) within a desired range to satisfy the design demands to allow the implants to perform a desired function. More specifically, embodiments of the invention provide porous implants having desired physical characteristics to provide, for example, conditions conducive to bone ingrowth and ongrowth. 
     According to embodiments of the invention, a method for developing a porous implant includes steps of defining a design volume for a porous implant, defining a load to be borne by the design volume of the porous implant, and defining an objective function solution characteristic related to the design volume of the porous implant. The method further includes steps of dividing the load into a plurality of sub-loads and performing an optimization procedure. The optimization procedure includes performing, until all sub-loads have been applied, repeated steps of applying one of the plurality of sub-loads to the material in the design volume, removing material from the design volume such that remaining material within the design volume is capable of bearing one of the plurality of sub-loads and satisfies the objection function solution characteristic, the remaining material defining a void space without material therein, setting the void space as a new design volume for any remaining sub-loads, and setting the new design volume as being full of material. The method further includes a final step of combining the remaining material from each cycle of the optimization as a design of the porous implant. 
     In some embodiments, the steps of applying one of the plurality of sub-loads and removing material from the design volume include performing a finite element analysis. In some embodiments, the steps of applying one of the plurality of sub-loads and removing material from the design volume include finding a closed form solution. In some embodiments, the method is performed on a computer system. 
     In some embodiments, the objective function solution characteristic includes maximizing or minimizing a characteristic such as stress, mass, surface area, radiolucency, or stiffness. In some embodiments, the repeated steps of the optimization procedure further include dilating the new design volume to create a buffer region to ensure a desired porosity in the boundary between the material from each cycle of the optimization. 
     In some embodiments, the method also includes performing a final evaluation and optimization for a different objective function. In some embodiments, the different objective function is a function such as weight, porosity, surface area, or stress. In some embodiments, the design volume is pre-divided into a plurality of design volumes, each with its own portion of the load to be borne; the method is performed in parallel with respect to each of the plurality of design volumes and portions of the load to be borne. 
     According to further embodiments, a computer-implemented method for developing a porous implant includes steps of defining a design volume for a porous implant, defining a load to be borne by the design volume of the porous implant, and defining an objective function solution characteristic related to the design volume of the porous implant. The method further includes using a computing device to divide the load into a plurality of sub-loads and causing the computing device to perform an optimization procedure. The optimization procedure includes performing, until all sub-loads have been applied, repeated steps of applying one of the plurality of sub-loads to the material in the design volume, removing material from the design volume such that remaining material within the design volume is capable of bearing one of the plurality of sub-loads and satisfies the objection function solution characteristic, the remaining material defining a void space without material therein, setting the void space as a new design volume for any remaining sub-loads, and setting the new design volume as being full of material. The method also includes a final step of combining the remaining material from each cycle of the optimization as a design of the porous implant. 
     In some embodiments, the steps of applying one of the plurality of sub-loads and removing material from the design volume include performing a finite element analysis. In some embodiments, the steps of applying one of the plurality of sub-loads and removing material from the design volume include finding a closed form solution. 
     In some embodiments, the objective function solution characteristic includes maximizing or minimizing a characteristic such as stress, mass, surface area, radiolucency, or stiffness. In some embodiments, the repeated steps of the optimization procedure further include dilating the new design volume to create a buffer region to ensure a desired porosity in the boundary between the material from each cycle of the optimization. In some embodiments, the method further includes performing a final evaluation and optimization for a different objective function such as weight, porosity, surface area, or stress. In some embodiments, the design volume is pre-divided into a plurality of design volumes; the method is performed in parallel with respect to each of the plurality of design volumes and portions of the load to be borne. 
     According to additional embodiments, a computer-implemented method for developing a porous implant includes steps of defining a design volume for a porous implant, defining a load to be borne by the design volume of the porous implant, and defining an objective function solution characteristic related to the design volume of the porous implant, the objective function solution characteristic including maximizing or minimizing a characteristic such as stress, mass, surface area, radiolucency, or stiffness. The method further includes using a computing device to divide the load into a plurality of sub-loads and causing the computing device to perform an optimization procedure including performing, until all sub-loads have been applied, repeated steps of applying one of the plurality of sub-loads to the material in the design volume, removing material from the design volume such that remaining material within the design volume is capable of bearing one of the plurality of sub-loads and satisfies the objection function solution characteristic, the remaining material defining a void space without material therein, setting the void space as a new design volume for any remaining sub-loads, and setting the new design volume as being full of material. The method also includes a final step of combining the remaining material from each cycle of the optimization as a design of the porous implant. 
     In some embodiments, the repeated steps of the optimization procedure further include dilating the new design volume to create a buffer region to ensure a desired porosity in the boundary between the material from each cycle of the optimization. In some embodiments, the method further includes performing a final evaluation and optimization for a different objective function such as weight, porosity, surface area, or stress. In some embodiments, the design volume is pre-divided into a plurality of design volumes, each with its own portion of the load to be borne; the method is performed in parallel with respect to each of the plurality of design volumes and portions of the load to be borne. 
       FIG. 1  and the corresponding discussion are intended to provide a general description of a suitable operating environment in which embodiments of the invention may be implemented. One skilled in the art will appreciate that embodiments of the invention may be practiced by one or more computing devices and in a variety of system configurations, including in a networked configuration. However, while the methods and processes of the present invention have proven to be particularly useful in association with a system comprising a general purpose computer, embodiments of the present invention include utilization of the methods and processes in a variety of environments, including embedded systems with general purpose processing units, digital/media signal processors (DSP/MSP), application specific integrated circuits (ASIC), stand alone electronic devices, and other such electronic environments. 
     Embodiments of the present invention embrace one or more computer-readable media, wherein each medium may be configured to include or includes thereon data or computer executable instructions for manipulating data. The computer executable instructions include data structures, objects, programs, routines, or other program modules that may be accessed by a processing system, such as one associated with a general-purpose computer capable of performing various different functions or one associated with a special-purpose computer capable of performing a limited number of functions. Computer executable instructions cause the processing system to perform a particular function or group of functions and are examples of program code means for implementing steps for methods disclosed herein. Furthermore, a particular sequence of the executable instructions provides an example of corresponding acts that may be used to implement such steps. Examples of computer-readable media include random-access memory (“RAM”), read-only memory (“ROM”), programmable read-only memory (“PROM”), erasable programmable read-only memory (“EPROM”), electrically erasable programmable read-only memory (“EEPROM”), compact disk read-only memory (“CD-ROM”), or any other device or component that is capable of providing data or executable instructions that may be accessed by a processing system. While embodiments of the invention embrace the use of all types of computer-readable media, certain embodiments as recited in the claims may be limited to the use of tangible, non-transitory computer-readable media, and the phrases “tangible computer-readable medium” and “non-transitory computer-readable medium” (or plural variations) used herein are intended to exclude transitory propagating signals per se. 
     With reference to  FIG. 1 , a representative system for implementing embodiments of the invention includes computer device  10 , which may be a general-purpose or special-purpose computer or any of a variety of consumer electronic devices. For example, computer device  10  may be a personal computer, a notebook or laptop computer, a netbook, a personal digital assistant (“PDA”) or other hand-held device, a smart phone, a tablet computer, a workstation, a minicomputer, a mainframe, a supercomputer, a multi-processor system, a network computer, a processor-based consumer electronic device, a computer device integrated into another device or vehicle, or the like. 
     Computer device  10  includes system bus  12 , which may be configured to connect various components thereof and enables data to be exchanged between two or more components. System bus  12  may include one of a variety of bus structures including a memory bus or memory controller, a peripheral bus, or a local bus that uses any of a variety of bus architectures. Typical components connected by system bus  12  include processing system  14  and memory  16 . Other components may include one or more mass storage device interfaces  18 , input interfaces  20 , output interfaces  22 , and/or network interfaces  24 , each of which will be discussed below. 
     Processing system  14  includes one or more processors, such as a central processor and optionally one or more other processors designed to perform a particular function or task. It is typically processing system  14  that executes the instructions provided on computer-readable media, such as on memory  16 , a solid state drive, a removable solid state drive, a magnetic hard disk, a removable magnetic disk, a magnetic cassette, an optical disk, or from a communication connection, which may also be viewed as a computer-readable medium. 
     Memory  16  includes one or more computer-readable media that may be configured to include or includes thereon data or instructions for manipulating data, and may be accessed by processing system  14  through system bus  12 . Memory  16  may include, for example, ROM  28 , used to permanently store information, and/or RAM  30 , used to temporarily store information. ROM  28  may include a basic input/output system (“BIOS”) having one or more routines that are used to establish communication, such as during start-up of computer device  10 . RAM  30  may include one or more program modules, such as one or more operating systems, application programs, and/or program data. 
     One or more mass storage device interfaces  18  may be used to connect one or more mass storage devices  26  to system bus  12 . The mass storage devices  26  may be incorporated into or may be peripheral to computer device  10  and allow computer device  10  to retain large amounts of data. Optionally, one or more of the mass storage devices  26  may be removable from computer device  10 . Examples of mass storage devices include solid state drives, hard disk drives, magnetic disk drives, tape drives and optical disk drives. A mass storage device  26  may read from and/or write to solid state memory, a magnetic hard disk, a removable magnetic disk, a magnetic cassette, an optical disk, or another computer-readable medium. Mass storage devices  26  and their corresponding computer-readable media provide nonvolatile storage of data and/or executable instructions that may include one or more program modules such as an operating system, one or more application programs, other program modules, or program data. Such executable instructions are examples of program code means for implementing steps for methods disclosed herein. 
     One or more input interfaces  20  may be employed to enable a user to enter data and/or instructions to computer device  10  through one or more corresponding input devices  32 . Examples of such input devices include a keyboard and alternate input devices, such as a mouse, trackball, light pen, stylus, or other pointing device, a microphone, a joystick, a game pad, a satellite dish, a scanner, a camcorder, a digital camera, and the like. Similarly, examples of input interfaces  20  that may be used to connect the input devices  32  to the system bus  12  include a serial port, a parallel port, a game port, a universal serial bus (“USB”), an integrated circuit, a firewire (IEEE 1394), or another interface. For example, in some embodiments input interface  20  includes an application specific integrated circuit (ASIC) that is designed for a particular application. In a further embodiment, the ASIC is embedded and connects existing circuit building blocks. 
     One or more output interfaces  22  may be employed to connect one or more corresponding output devices  34  to system bus  12 . Examples of output devices include a monitor or display screen, a speaker, a printer, a multi-functional peripheral, and the like. A particular output device  34  may be integrated with or peripheral to computer device  10 . Examples of output interfaces include a video adapter, an audio adapter, a parallel port, and the like. 
     One or more network interfaces  24  enable computer device  10  to exchange information with one or more other local or remote computer devices, illustrated as computer devices  36 , via a network  38  that may include hardwired and/or wireless links. Examples of network interfaces include a network adapter for connection to a local area network (“LAN”) or a modem, wireless link, or other adapter for connection to a wide area network (“WAN”), such as the Internet. The network interface  24  may be incorporated with or peripheral to computer device  10 . In a networked system, accessible program modules or portions thereof may be stored in a remote memory storage device. Furthermore, in a networked system computer device  10  may participate in a distributed computing environment, where functions or tasks are performed by a plurality of networked computer devices. 
     Thus, while those skilled in the art will appreciate that embodiments of the present invention may be practiced in a variety of different environments with many types of system configurations,  FIG. 2  provides a representative networked system configuration that may be used in association with embodiments of the present invention. The representative system of  FIG. 2  includes a computer device, illustrated as client  40 , which is connected to one or more other computer devices (illustrated as client  42  and client  44 ) and one or more peripheral devices  46  across network  38 . While  FIG. 2  illustrates an embodiment that includes a client  40 , two additional clients, client  42  and client  44 , one peripheral device  46  (such as a 3D printer), and optionally a server  48 , which may be a print server, connected to network  38 , alternative embodiments include more or fewer clients, more than one peripheral device, no peripheral devices, no server  48 , and/or more than one server  48  connected to network  38 . Other embodiments of the present invention include local, networked, or peer-to-peer environments where one or more computer devices may be connected to one or more local or remote peripheral devices. Moreover, embodiments in accordance with the present invention also embrace a single electronic consumer device, wireless networked environments, and/or wide area networked environments, such as the Internet. 
     Similarly, embodiments of the invention embrace cloud-based architectures where one or more computer functions are performed by remote computer systems and devices at the request of a local computer device. Thus, returning to  FIG. 2 , the client  40  may be a computer device having a limited set of hardware and/or software resources. Because the client  40  is connected to the network  38 , it may be able to access hardware and/or software resources provided across the network  38  by other computer devices and resources, such as client  42 , client  44 , server  48 , or any other resources. The client  40  may access these resources through an access program, such as a web browser, and the results of any computer functions or resources may be delivered through the access program to the user of the client  40 . In such configurations, the client  40  may be any type of computer device or electronic device discussed above or known to the world of cloud computing, including traditional desktop and laptop computers, smart phones and other smart devices, tablet computers, or any other device able to provide access to remote computing resources through an access program such as a browser. 
       FIG. 3  illustrates an exemplary embodiment of a method, which in exemplary embodiments is a computer-implemented method, for designing an implant in accordance with embodiments of the invention. According to exemplary embodiments of the invention, a method for designing an implant, particularly a porous implant such as an interbody spacer, begins with defining a design space at step  50 . The design space, for example, may be defined by a volume which the implant is intended to occupy or may be defined by a portion of a volume which the implant is intended to occupy (e.g., a portion which is intended to be porous and have certain physical characteristics such as porosity (pore size and spacing), surface area, radiolucency, stress, stiffness, or the like). By way of example,  FIG. 5  shows a conceptual view of a simplified example of a first design space  52  or volume represented as a rectangular volume. An actual design space may have any desirable shape or volume, and may include voids not included in the design space. Accordingly, the first design space  52  should be understood as being illustrated for purposes of discussion only, and not for purpose of limiting the scope of the claims. 
     The design space includes forces expected to be encountered by the implant (or the portion of the implant within the design space or design volume) as well as the material from which the implant is to be made (e.g., titanium, tantalum, titanium alloys, tantalum alloys, and the like). The material of the implant within the design space has bulk material properties that are known and that are taken into account when designing the implant as described herein. 
     The method continues at step  54  with a step of defining a load to be borne by the implant within the design space. By way of example, the load may be an expected load to be borne by the implant or the design volume of the implant. Then, at step  56 , an objective function solution characteristic related to the design volume is defined or assigned to the design space or design volume. By way of example, the objective function characteristic may include maximizing or minimizing one or more characteristics such as stress, mass, radiolucency, surface area, or the like. Other objective functions are possible as desired, either in combination or singly. 
     The method continues as the defined load is divided into sub-loads at step  58 . In some embodiments, the sub-loads are divided into even sub-loads. In other embodiments, the load is divided into uneven sub-loads. In some embodiments, uneven sub-loads may be applied to the design space in any desired order, such as from largest sub-load to smallest sub-load, from smallest sub-load to largest sub-load, or in random order. There is no particular limitation on the manner in which loads are divided or the order in which they are applied to the design space. Components of the original load are optionally held for additional cycles. 
     The method then continues as an optimization procedure is performed by solving the objective function with respect to the partial loads. The optimization procedure proceeds in several steps. First, at step  60 , one of the sub-loads is applied to the material of the design space. Then, at step  62 , material is removed from the design space in a manner to satisfy the objective function. Typically, this involves use of a computer to perform an analysis such as a finite element analysis or deriving a closed form solution. As part of this analysis, it may be necessary, as represented at decision block  64  and step  66 , to add material back to the design space, such as when too much material has been removed at step  62 . Execution proceeds to decision block  68 , where a determination is made as to whether the objective function has been solved. If not, execution loops back to step  62 , otherwise, execution proceeds to  FIG. 4 . 
     When the objective function has been solved, only certain material remains in the design space, and the empty space may be illustrated as voids  70 , as illustrated in the middle of  FIG. 5 . As may be appreciated, the voids  70  shown in  FIG. 5  are not intended to depict any actual solution to any actual objective function, but are intended solely to facilitate the discussion of methods in accordance with embodiments of the invention. As illustrated in  FIG. 4 , execution of the method accordingly proceeds to decision block  72 , where a determination is made as to whether all sub-loads have been applied. If not, the method proceeds to step  74 , where the material removed in the previous steps is identified. Then, at step  76 , the identified removed material is set as a new design space  78 , as also illustrated at the bottom of  FIG. 5 . 
     Once a new design space is defined at step  76 , a determination is made at decision block  80  whether to dilate the new design space  78 . If a determination is made to dilate the new design space, execution proceeds to step  82  for dilation of the new design space  78 . Dilation of the new design space  78  in some embodiments allows determination of contact interactions between the previous solution to the objective function and the new design space  78  (and thus the new solution to the objective function that is to be determined), thus maintaining solution continuity (such as maintaining a desired porosity across the solutions for the various sub-loads). Said differently, dilation of the new design space  78  creates a buffer region between iterative solutions to the various sub-loads to assure that solutions are continuous.  FIG. 6  illustrates how the new design space  78  can be dilated to include a dilated design space  84 . 
     Regardless of whether the new design space  78  is dilated or not at decision block  80  and step  82 , execution of the method now returns to step  60  (in  FIG. 3 ), where another sub-load is applied to the new design space  78  (and/or the dilated design space  84 ), and execution of the method proceeds as described such that a solution to the objective function is determined for the new sub-load. In this fashion, execution of the method loops until it is determined at decision block  72  ( FIG. 4 ) that all sub-loads have been applied and solved, whereupon execution proceeds to step  86 . 
     At step  86 , the solutions to the various sub-loads are combined into a final design result. Then, execution of the method proceeds to decision block  88 , where a determination is made as to whether to optimize an additional objective function. The additional objective function may be any objective function previously discussed, or other objective functions, such as weight, porosity, stress, surface area, or the like. If no other objective functions are to be optimized, execution of the method ends, and the design is complete. Alternatively, if another objective function is to be optimized, then execution proceeds to step  90 , where another objective function can be optimized, using any desirable method, including methods as illustrated in  FIGS. 3-4 . Once the design is finished, the final design can be constructed, such as using a 3-dimensional printer that may be connected to the system (or to another computer system) as a peripheral device or the like. 
     In some embodiments, the design space  52  may be pre-divided allowing for two or more problems to be solved in parallel. In this fashion, the performance of the method to determine the solution and design can be improved. As desired, additional analyses for any of the steps may also be run in parallel to improve system performance or to better utilize system resources. In some embodiments, multiple solutions to the objective function or objective functions may be determined for each sub-load (or for varied application of sub-loads) to determine solutions providing optimal performance characteristics. Accordingly, there is no requirement that embodiments of the invention be limited to finding a single solution to any objective function nor is there any requirement that embodiments of the invention are limited to finding any “best” solution to any particular objective function. 
     The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims, rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.