Artificial intelligence-based method for the design of a bone implant

Abstract

A method implemented on a computer system, the method comprising the following steps: receiving one or more parameters of a bone in which an implant is to be placed, generating an input to an artificial neural network (ANN)- based optimization framework based at least in part on the one or more parameters, and receiving, based at least in part on the input, an output of the ANN-based optimization framework indicating a relative density and a topology for a triply periodic minimal surface (TPMS) architecture for the implant.

Description

CROSS-REFERENCES TO RELATED APPLICATIONS

[0002] This application claims the benefit of U.S. Provisional Patent Application No. 63 / 559,643, filed February 29, 2024, the entire contents of which are hereby incorporated by reference for all purposes in its entirety.BACKGROUND OF THE INVENTION

[0003] Inspired by nature, architected metamaterials have been designed and then become a topic of intensive research. Among them, a triply periodic minimal surface (TPMS) architecture is considered one of the best, with unique topologies constructed by interconnecting bi-continuous phases, such as solid and void, repeating themselves in space and exhibiting the locally zero-mean curvature that significantly reduces the high-stress concentration in materials, especially for the bone implants. Also, the TPMS architecture possesses a topology-driven property, an extremely high surface-to-volume ratio, and the very high strength-to-weight ratio but is simple to be fabricated by additive manufacturing. As a result, TPMS architectures have been found in a broad range of advanced, innovative applications such as in space flight safety systems. BRIEF SUMMARY OF THE INVENTION

[0004] Embodiments of the disclosure relate to a method implemented on a computer system that involves receiving one or more parameters of a bone, including stiffness, mass density, strength, and so on in which an implant is to be placed, generating an input to an artificial neural network (ANN)-based optimization framework based at least in part on the one or more conditions, and receiving, based at least in part on the input, an output of the framework indicating a relative density and a topology for a triply periodic minimal surface (TPMS) architecture for the implant.

[0005] In an example, a computer system includes one or more data processors and one or more memory devices storing computer-readable instructions that, upon execution by the one or more data processors, configure the computer system to: receive one or more parameters of a bone, including stiffness, mass density, strength, and so on in which an implant is to be placed; generate an input to an artificial neural network (ANN)-based optimization framework based at least in part on the one or more parameters; and receive, based at least in part on the input, an output of the ANN-based optimization framework indicating a relative density and a topology for a triply periodic minimal surface (TPMS) architecture for the implant.

[0006] In an example, a non-transitory computer readable storage medium, stores instructions that upon execution by one or more data processors of a computer system, configure the computer system to: receive one or more parameters of a bone in which an implant is to be placed; generate an input to an artificial neural network (ANN)-based optimization framework based at least in part on the one or more parameters; and receive, based at least in part on the input, an output of the ANN-based optimization framework indicating a relative density and a topology for a triply periodic minimal surface (TPMS) architecture for the implant. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Various embodiments in accordance with the present disclosure will be described with reference to the drawings, in which:

[0008] FIG. 1 illustrates a schematic demonstration of unit cells of solid and sheet-typed triply periodic minimal surface scaffolds;

[0009] FIG. 2 illustrates an example of a biomedical application of a bone implant with a gyroid scaffold;

[0010] FIG. 3 illustrates an example flow of a deep artificial neural network mode-based optimization framework for bone implants with triply periodic miniml surface architectures;

[0011] FIG. 4 illustrates example printed cubic samples of triply periodic minimal surfaces with a primitive sample undergoing a compressive test;

[0012] FIG. 5 illustrates a comparison between a deep artificial neural network-based optimization framework and a numerical model in terms of effective stress-strain responses of sheet-based titanium triply periodic minimal surfaces subjected to tensile load;

[0013] FIG. 6 illustrates a comparison between an original artificial neural network (ANN) model-based optimization and an improved deep ANN model-based optimization in aspects of mean square errors (MSE) and stress-strain response of sheet diamond scaffold where (a): MSE of original ANN-based optimization, (b): MSE of improved ANN-based optimization, (c): Stress-strain response based on original ANN-based optimization;

[0014] FIG. 7 illustrates a comparison between an improved deep artificial neural network -based optimization framework and experiment in terms of normalized Young’s modulus of sheet triply periodic minimal surfaces;

[0015] FIG. 8 illustrates a comparison between an artificial neural network-based optimization framework, a numerical model, and an experiment of trabecular bone in terms of the effective tensile stress-strain responses of triply periodic minimal surface-based implants under the same yield strength where (a): Sheet Gyroid implant, (b): Sheet Primitive implant, (c): Sheet Diamond implant, (d): Sheet IWP implant;

[0016] FIG. 9 illustrates relative density based on the ratio of tensile yield strength of triply periodic minimal surface architectures to that of bones using an improved deep artificial neural network model-based optimization where (a): Trabecular bone, (b): Cortical bone;

[0017] FIG. 10 illustrates spatial anisotropy of effective Young’s modulus in GPa versus orientation;

[0018] FIG. 11 illustrates tensile stress-strain relation of an implant with sheet triply periodic minimal surfaces having the same weight as that of the trabecular bone and cortical bone obtained from an optimization framework;

[0019] FIG. 12 illustrates an influence of the ratio of a triply period minimal surface-based titanium implant weight to bone weight on a yield strength per weight;

[0020] FIG. 13 illustrates an optimization-based prediction of stress-strain response of titanium triply periodic minimal surface implants, cortical bone, and trabecular bone subjected to the same elastic Young’s modulus where (a): as that of trabecular bone, (b): as that of cortical bone;

[0021] FIG. 14 illustrates spatial anisotropic surface of Young’s modulus of triply periodic minimal surface implants against an orientation, having the same Young’s modulus as that of the cortical bone and the trabecular bone generated by an optimization framework;

[0022] FIG. 15 illustrates long-frequency longitudinal impact phase wave velocity propagating in a titanium implant with sheet-typed triply periodic minimal surfaces having the same tensile yield strength as that of (a) the cortical bone and (b) the trabecular bone;

[0023] FIG. 16 illustrates directional buckling resistance stress of sheet triply periodic minimal surfaces implant cantilever beam having a similar yield strength as that of (a) cortical bone and (b) trabecular bone; and

[0024] FIG. 17 is an illustrative architecture of a computing system implemented as some embodiments of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0025] Triply periodic minimal surface (TPMS) architectures have been experimentally fabricated and used to absorb the sound in the upper midrange frequency, medical porous implants, etc. By having the unique properties of a reduced high-stress concentration, a high surface-to-volume ratio, and a high strength-to-weight ratio, TPMSs offer ideal conditions for bone ingrowth and proliferation while the architected porosity allows tuning of the implant stiffness to fit that of bone tissue and optimizes the fluid flow for better delivery of nutrients. As a result, TPMS architectures may be valuable for making bone implants.

[0026] The present disclosure provides techniques for using improved artificial intelligence-powered optimization models, such as artificial neural networks (ANNs), to determine an ultimate titanium bone implant with TPMS architectures. ANNs are conceptually inspired by the biological human brain, with its first version implementing a computational model for node networks, like that of the human brain neural network. With ever-increasing computer power over the last few decades, the ANN has been utilized in applications in daily life owing to its capability to learn and model nonlinear processes. ANNs provide accurate outputs, such as system identification and control, game, three-dimensional (3D) reconstruction, internet, medicine, construction, banking system, etc. Improved ANNs are described herein as a primary example, although other types of artifical intelligence models (including other types of neural networks) may be possible.

[0027] A bone implant can be constructed using TPMS architectures, and embodiments of the present disclosure introduce a novel deep artificial neural network-powered optimization framework to determine the topology and relative density of ultimate titanium bone implants with TPMSs subjected to given criteria, such as the yield strength, stiffness, and weight, but not limited to, fitted with that of cortical and trabecular bones. The bone implant with TPMS architectures can also possess the capability to reduce a stress shielding effect as well as bone resorption. In addition, bone ingrowth depth can improve the stiffness and yield strength of a TPMS implant-bone tissue composite in a nonlinear pattern. A gyroid-based implant can display a similar internal structure to human bone. Using the finite element method, the biomechanical properties of porous TPMS meniscal implants can reduce the compressive and shearing stresses on the articular cartilage compared to solid meniscal implants. 

[0028] To make a high-quality titanium implant and protect the contacting bone tissue, criteria need to be considered. For instance, a significant difference in the stiffness between the implant and bone can result in the stress shielding effect at the implantation site, causing bone degradation and requiring revision of the surgery. As such, the implant is to have the same (or a substantially similar) stiffness as the bone. It may be challenging and expensive for an experiment or numerical model to obey such conditions or criteria. Embodiments described herein introduce a novel, flexible, and efficient optimization framework using an improved deep ANN framework to accurately determine a titanium bone implant with TPMS architectures subjected to the parameters of the bone, including, but not limited to, the same stiffness, yield strength, and weight, at a low computational cost. The objective of the optimization process is to point out the relative density and topology of TPMSs for constructing the most suitable titanium bone implant. Afterward, the directional mechanical performances of the implant under a criterion, including the buckling resistance and impact phase wave propagation property based on the optimization framework, are explored. 

[0029] In general, the parameters of a bone in which an implant is to be placed can be received and used as input data for the ANN-based optimization framework. The ANN-based optimization framework receives the input and generates an output, which indicates a relative density and a topology for a TPMS architecture for the ultimate implant.

[0030] FIG. 1 illustrates unit cells of solid and sheet-typed TPMS scaffolds. The unit cells include I-graph and wrapped package-graph (IWP), gyroid, diamond, and primitive architectures. The relative density (Rd) for each of the unit cells in the xyz-coordinate system is 0.3. The architected unit cells are assumed to have a cubic shape with a height, a width, and a depth all equal to , generated by an MSLattice method. To extract the mechanical property of TPMS-based bone implant, the 3D FEM simulation for unit cells representing the mechanical behavior for the whole structure is implemented by commercial software Abaqus, using the periodic boundary condition given as:, (1)where is the edge length of the unit cell in the direction ; is the component of the position vector; is the unit vector in the direction ; is the applied strain; is the cell boundary, and is the surface traction normal to . The homogenization can be performed by commercial software MATLAB using the simulation data obtained from 3D FEM simulation to compute the effective value , including the effective axial stress, effective shear stress, effective axial strain, effective shear strain, or so on, expressed as: (2) where term stands for differential volume element and, stands for either the stress or strain components of the stress or strain tensors in ; represents element number; is total element number; is node number in the element with volume ; and is total node number in the element. The spatial surface of the anisotropy of effective Young’s modulus versus the orientation of the TPMS architectures exhibiting the cubic symmetry, can be expressed as: (3)where notations , , and are the directional cosines of the angle between the spatial position vectors of the effective value and axes of -coordinate system; , , and are elements of the elastic compliance matrix in Voigt form. When the TPMS architectures are used to be bone implants, their shape is commonly in beam shape, with one example depicted in FIG. 2. Specifically, the bone implant in FIG. 2 is a gyroid scaffold.

[0031] During daily activity of the host bone, the implant can be subjected to many types of loads, including impact, dynamic and static multidirectional loads, and so on. Thus, the directional mechanical performance of the implant in terms of buckling resistance stress and impact wave propagation velocity can be explored. In an example, the implant beam has a dimension with a length l=100 mm, width b=5mm, and height h=5mm, constructed by several TPMS unit cells connecting to each other. It can be assumed that the orientation of the unit cells is adjustable with respect to the direction of applied load or wave propagation. The mechanical properties of the implant beam, including effective Young’s modulus, effective shear modulus, and effective Poisson’s ratio are extracted from the outcome of the optimization framework. When the implant beam is impacted by an external load, the induced in-plane longitudinal long-frequency phase wave propagates through the beam, with the velocity expressed as: (4)where the values of the constant are , and . Due to the cubic symmetry behavior of TPMS structures, the relationship of constants can be rewritten as and . The stress for the onset of the buckling is calculated based on the mathematical equation of the internal bending moment of the implant beam subjected to the uniaxial compression force at the one end, with the general solution for transverse displacement, with considering the orientation expressed as: (5)where coefficients and are chosen following the boundary condition. For example, when the implant is subjected to the pinned-pinned boundary condition, it is inserted to Eq. (5), and the buckling force of the implant beam is determined based on the appropriate correlation between coefficients and , obtained as: (6)where is the buckling mode shape, and the buckling resistance stress is then inferred from Eq. (6) as .

[0032] The optimization framework that uses a deep ANN model can accurately search for optimal bone implants with TPMS architectures based on given criteria and bone parameters. Components of the deep ANN model include multilayers, with each containing an artificial neuron consisting of input data, a bias (or threshold), weight, and an output, connecting to another for transmitting the digital signal. In the ANN framework-based optimization, the mean square error, used to measure the accuracy of the method is evaluated by the outcome and real dataset, given as: (7)where notations , , and are pair number, trained outcome of neuron , and real output, respectively. Once the value achieves the convergence, the training process is complete. During attaining the convergence, the weight and bias value are updated through the digital signal transmitting from one neuron to another, to minimize the value of by using the gradient descent given as: and (8) where notation is gradient descent associated with hidden layer for neutron and incoming neutron ; is bias delta for neutron in layer ; is learning rate, which can be selected as 0.01; is weight in hidden layer for neutron and incoming neutron , is bias for neutron in layer . When the computation of the weight and bias is complete, the output value is evaluated as: for (9)where term is an activation function. The loops with multiple conditions inserted in the ANN algorithm help to remove the uncertain, inconsistent, and unexpected outcomes of the original ANN framework developed in MATLAB at the fixed configuration, and then produce a desired outcome. In the improved deep ANN framework, a maximum percent tolerance value () associated with a change of the ANN configuration, including neuron number and hidden layer as well as bias and weight, is calculated until is below the given value , with the definition of as: (10)

[0033] In the equation, the term is a selection of a maximum value among components of matrix ; is an absolute operator; and are ANN-produced outcomes and real dataset, respectively. Upon the satisfaction of the inequality condition , the deep ANN model can generate an accurate outcome. One of the mathematical concepts in the optimization algorithm is a computation of the minimal value upon the given criteria, and subsequently prints out the corresponding relative density in MATLAB, given as: (11)where the notation stands for the matrix of the ANN outcome data; is a component of corresponding to the minimal value of ; and is the given value of the criteria, such as the stiffness, the yield strength, the weight, and so on. When the condition is established and the criteria for the bone implant are provided, the optimization framework can determine the relative density of the most ideal implant, with the flow chart of improved deep ANN-based optimization conceptually depicted in FIG. 3.

[0034] Afterward, the spatial surface of anisotropy of Young’s modulus of each TPMS-based implant against orientation is generated and then compared to that of bone to find the best TPMS topology for the implant. The data used to train the deep ANN model in the optimization technique is obtained from the numerical homogenization, with only ten scaffolds corresponding to ten relative densities ranging average from 0.1 to 0.55 for each topology.

[0035] In an experiment, cubic samples of a sheet-based TPMS architecture having relative densities of 0.3 and 0.4, and a dimension of 30mm x 30mm x 30mm were additively 3D printed by Ultimaker Pro 5 with a fine printing quality using the base material of yellow Polylactic acid (PLA). Examples of printed samples with Rd=0.4 are shown in FIG. 4.

[0036] A compressive test for the samples and dense cube of polylactic acid (PLA) material with a dimension of 1cm x 1cm x 1cm was performed by 50kN-INSTRON testing machine at room temperature to generate a stress-strain response where the strain control mode was applied with a displacement increase rate of 0.2 mm / min set as depicted in FIG. 4. The outcome of the compressive test in terms of stress-strain response was then used to compute the effective Young’s modulus of the sample, which was subsequently used to validate the accuracy of predictions by the deep ANN model used in the optimization. The testing results show the Young’s modulus of the dense base PLA material measured approximately 2.3 and the Poisson’s ratio is adopted as 0.35.

[0037] The soundness of the prediction capability of the improved deep ANN-based optimization framework can be validated numerically and experimentally. In addition, the optimization outcome based on criteria, including the stiffness, the yield strength, and the weight to determine the relative density and topology for the most ideal titanium bone implant with TPMSs can be expressed. Maximum percent difference is defined as the absolute ratio of subtraction of two values to the highest value between them, all multiplied by one hundred. The normalized mechanical value is a ratio of the effective mechanical value of architected material obtained from ANN-based optimization framework to the mechanical value of the dense base material. In all training process, value of is set below seven. In all simulations, the titanium base material with the adopted Young’s modulus of one-hundred four GPa, Poisson’s ratio of 0.3, and experimental stress-strain curve is used.

[0038] FIG. 5 shows a comparison between the improved deep ANN-based optimization framework and a numerical model in terms of effective stress-strain responses of sheet-based titanium TPMS architectures, including IWP, primitive, gyroid, and diamond subjected to tensile load. The numerical model-generated data used does not belong to training samples.

[0039] FIG. 5 shows a substantial fit between the numerical model and deep ANN-based optimization framework in aspects of curve trend and magnitude of the effective stress-strain response, with maximum percent difference being approximately 3%. This displays the accurate prediction capability of the framework regardless of the topology. In addition, it may take longer than three days to numerically obtain the data to train the ANN model in the optimization technique while taking only two minutes for deep ANN model to comprehend and produce the accurate mechanical responses at almost any point of relative density after the training, displaying thousands of times faster than the numerical model or experiment. Furthermore, the ANN-based optimization can be handled by a regular computer with random access memory (RAM) of sixteen GB with the abovementioned time and capability, while it is expensive for the experimental work to produce similar results, demonstrating it as a low financial cost model compared with the experiment. In order to access the improvement of the improved ANN optimization compared with that based on the original ANN model developed by MATLAB, the mean square errors obtained from the original ANN model-based optimization and improved ANN model-based optimization, and the stress-strain response based on the original ANN model-based optimization are illustrated in FIG. 6. (a) shows the mean square error of the original ANN-based optimization; (b) shows the mean square error of the improved ANN-based optimization; and (c) shows the stress-strain response based on the original ANN-based optimization.

[0040] FIG. 6 indicates that the value of the mean square error in the original ANN-based optimization framework is 0.01 which is times higher than that of the improved ANN-based optimization framework. This shows a significant improvement of prediction with the improved ANN-based optimization framework. In terms of stress-strain response, the original ANN optimization framework produces the mechanical response having a large mismatch to that of the numerical model, with data laying clearly outside the curve produced by the numerical model while the improved deep ANN-based optimization framework generates mechanical responses almost exactly laying on the curve of the numerical model (see FIG. 5(d)).

[0041] To further verify the accuracy of the optimization framework, its normalized Young’s modulus of sheet TPMS architectures with relative densities of 0.3 and 0.4 is compared to that of the experiment under the same conditions, depicted in FIG. 7. There is an agreement between the optimization framework and the experiment in terms of normalized Young’s modulus, with a maximum percent difference being approximately 16.5 % found for the case of Primitive scaffold with Rd=0.3. One of the main reasons for the observed difference may be due to the unavoidable defect in samples additively printed by a 3D printer. In addition, the difference may also be due to the difference in applying the boundary condition. In the numerical simulation, the periodic boundary condition is applied on the unit cell, which helps it represent the infinity number of unit cells in the whole structure, but in the experiment, the number of unit cells is limited and equal to nine.

[0042] FIG. 8 depicts the effective tensile stress-strain responses of titanium implants with TPMSs under the same yield strength attained by the ANN-based optimization framework, numerical model, and experimental result of trabecular bone. It is noted that the numerical data presented does not belong to the training samples for the ANN framework. The yield strength of trabecular bone is selected as 32 MPa at the elastic limit following the work. FIG. 8 shows the agreement between the optimization approach and the numerical model in terms of the curve trend of stress-strain relation and the magnitude of stress upon the requirement of the same yield strength as that of bone, proving the capability of the ANN optimization to quickly and accurately predict the relative density based on given criteria, beyond the capability of either the numerical model or the experiment. What is more, in all cases, the elastic stiffness of titanium implant is observed higher than that of trabecular bone when they all have the same yield strength. Indeed, under the same yield strength, the stiffness of the titanium implant with gyroid, primitive, diamond, and IWP is 1.5, 1.1, 1.7, and 1.3 times higher than that of the trabecular bone, respectively.

[0043] It may be relevant to accurately determine the relative density and topology of architected materials for the best bone implant when the value of implant’s yield strength compared to that of bone is given. When the yield strength of the titanium TPMS implant is from one to two times higher than that of cortical and trabecular bones, the resultant relative density is indicated by the improved deep ANN-based optimization, with the relationship illustrated in FIG. 9. (a) is the relative density based on the ratio of tensile yield strength of TPMS architectures to that of trabecular bone using the improved ANN model-based optimization and (b) is the relative density based on the ratio of tensile yield strength of TPMS architectures to that of cortical bone using the improved ANN model-based optimization.

[0044] In FIG. 9, notations and are the yield strength of trabecular bone, cortical bone, and titanium TPMS-based implant, respectively. It is obvious that increasing the yield strength of the bone implant leads to a rise of the relative density of the implant in a nonlinear pattern. For example, in the implant with the gyroid scaffold, when the ratio increases from one to two, the relative density nonlinearly rises from 0.12 to 0.2 for the trabecular bone’s implant and from 0.36 to 0.56 for the cortical bone implant. In addition, under the same relative density, the implants with IWP and gyroid scaffolds are found to possess the highest and lowest yield strength, respectively among the considered sheet-typed architectures.

[0045] In order to understand which TPMS topology possesses the most similar directional mechanical behaviour to that of bone, the spatial surface of anisotropy of effective Young’s modulus versus the orientation of the sheet and solid-typed TPMSs with a relative density of 0.33 and cortical bone is illustrated in FIG. 10. The selected sheet and solid-typed TPMSs with a relative density of 0.33 possess an average yield strength almost equal to that of cortical bone, computed based on the deep ANN-based optimization framework where the training data is obtained from numerical data. From (j) and (k), the anisotropy surface of bone is seen as smooth and less spatially distorted, proving a less extreme anisotropy of the bone. The small spatial anisotropy or having a similar spatial anisotropy to that of bone can be relevant for the implant so that the mismatch in the stiffnesses of the bone and implant can be removed and the stress-shielding effect in the implantation area, which causes the bone resorption, can be avoided. Hence, according to FIG. 10, the implant with a gyroid scaffold exhibits the most mechanically compatible with the bone in terms of Young’s modulus compared to other considered sheet and solid TPMSs where the gyroid’s anisotropy is seen as the least extreme, reflecting the fact that sheet gyroid topology is the best candidate to construct the bone implant among the considered TPMSs, due to its topology.

[0046] FIG. 11 shows the tensile stress-strain relation of a titanium implant with sheet TPMSs obtained by the optimization framework, cortical bone, and trabecular bone, all having the same weight. The average mass density of bone tissue adopted is 1990 . FIG. 11 shows that, under the same weight, the implant exhibits a higher yield strength compared to that of cortical or trabecular bones. Specifically, the yield strength of a titanium implant with sheet gyroid, sheet primitive, sheet IWP, and sheet diamond is 0.21 GPa, 0.222 GPa, 0.265 GPa, and 0.22 GPa while the yield strengths of trabecular bone and cortical bone are 0.032 GPa, and 0.15 GPa, respectively. This reflects the fact that titanium implants with TPMSs are satisfactory candidates for bone implants when they are considered for the same weight as that of bone. In addition, from the response curve, the stiffness of the titanium implant is observed almost close to that of the cortical bone, but much higher than that of the trabecular bone, further showing the ideal characteristic for the titanium bone implant with TPMSs.

[0047] In medical applications, the corelative weight between the bone and the implant can be a relevant factor that significantly affects the balance of the human body and influences the daily activity of the host. In some locations, such as the spine and the jawbone, the varying weight of the implant exposes a minor effect on the balance of the body. A benefit in terms of the yield strength-to-weight ratio is added if the implant weight is a little less than the bone weight. Hence, the influence of the ratio of implant weight to bone weight on the yield strength per weight in a unit volume of one cm3 using the optimization framework is illustrated in FIG. 12. The notation RYw is the yield strength per weight in one cm3 for either the implant or the bone, and the weight ratio is the ratio of the implant weight to bone weight. FIG. 12 indicates that the yield strength per weight of titanium implant with TPMSs decreases with a drop of weight ratio in a nonlinear pattern. More particularly, the results find that even though the implant weight is as low as 90% of the bone, the yield strength of titanium TPMS implant is still much higher than either cortical or trabecular bones. In particular, at =0.9 or the weight of the implant is 90% that of bone, the yield strength of the sheet TPMS implant with gyroid, primitive, diamond, and IWP in a volume of 1 cm3 is 1.3, 1.36, 1.41, and 1.7 times higher than cortical bone, respectively, and 6.12, 6.3, 6.6, and 8 times higher than trabecular bone, respectively.

[0048] As discussed, the mismatch between bone and implant in terms of elastic stiffness leads to a stress shielding effect, causing the bone rupture so that the criterion of the same stiffness for bone and implant is vital. FIG. 13 demonstrates the optimization-based prediction of the stress-strain response of titanium TPMS implants, cortical bone, and trabecular bone subjected to a criterion as the same elastic Young’s modulus. the Young’s modulus of cortical and trabecular bones is estimated as 3.2 GPa and 1.89 GPa, respectively. The distribution of data based on the optimization framework fits well with that of the two bones in the elastic regime, proving that the framework can learn and indicate accurately the relative density when the same elastic stiffness of the host bone is required for the implant. Such attained capability is beyond that of either the numerical model or experiment to handle, showing another ability of the optimization framework for finding the ultimate bone implant. Moreover, FIG. 13 indicates that, under the same stiffness, the yield strength of implants is higher than that of cortical bone, and a little lower than that of trabecular bone, which can be addressed when selecting the titanium implant upon a proper bone type.

[0049] In order to observe the spatial mechanical behaviour of implants, the 3D anisotropic surface of Young’s modulus of TPMS implants having almost the same Young’s modulus as that of the cortical bone and the trabecular bone generated by the ANN-based optimization framework is shown in FIG. 14. Overall, under the same stiffness, the implants with gyroid and IWP are the most suitable ones for cortical and trabecular bones, respectively, due to a less distorted spatial profile against the orientation, similar to that of the bone (see FIG. 10(j)). The anisotropic similarity between the bone and implant can be relevant because that can remove the spatial mismatch in the stiffness under multidirectional loads, leading to the removal of the stress shielding effect or bone degradation, and then avoiding the surgery revision.

[0050] FIG. 15 shows longitudinal long-frequency in-plane impact phase wave velocity propagating in m / s in the sheet-type TPMS implants having the same tensile yield strength as that of the (a) cortical bone and (b) trabecular bone. The in-plane impact wave propagation in the implant is directionally different among the titanium TPMS implants, with each architected implant possessing a distinct directional phase wave profile. Faster wave propagation carries higher adverse energy or more destruction for implant as well as surrounding bone tissue. Averagely, the impact phase wave propagating in gyroid-based titanium implant is found to be the second lowest one among others, together with the least distorted directional profile, all proving that the sheet gyroid architecture is an ideal candidate for the bone implant. For example, the impact wave velocity propagating in the implant with gyroid, primitive, diamond, and IWP, having the same yield strength as that of cortical bone, along the uniaxial direction of the unit cell is 3159 m / s, 2708 m / s, 3243 m / s, and 3242 m / s, respectively.

[0051] The mechanical performance of a titanium TPMS implant with the cantilever-beam form in terms of directional buckling resistance stress, having almost the same yield strength as that of the (a) cortical bone and (b) trabecular bone is shown in FIG. 16. In general, the titanium implant with gyroid TPMSs resists the buckling more uniformly along the orientation compared to the other implants, reflecting through the least distorted profile of directional buckling resistance stress. In particular, the gyroid-based cortical implant beam possesses the highest buckling resistance stress with the least distorted profile of buckling resistance stress versus the orientation. In this regard, the buckling stress of implant beam with sheet gyroid, sheet primitive, sheet IWP, and sheet diamond having the same tensile yield strength as that of cortical bone is 8.26 GPa, 5.6 GPa, 7.1 GPa, and 8.1 GPa, respectively. Furthermore, although a gyroid-based implant does not possess the highest buckling resistance capability, its profile is still the least distorted compared with other TPMS-based implants and similar to bone (see FIG. 10(k)), making it the most ideal candidate for the bone implant. Although, the primitive implant demonstrates the highest buckling resistance in the diagonal direction through the origin, it resists weakest in the axial direction compared with other directions, demonstrating that the primitive scaffold is less appropriate to be a bone implant compared to the gyroid scaffold.

[0052] In the present disclosure, a novel optimization framework powered by an improved deep ANN model inserted by a loop with multiple conditions is presented to seek the ultimate bone implant with TPMS architectures, including sheet and solid-typed gyroid, primitive, diamond, and IWP, upon given criteria, such as the yield strength, stiffness, and weight. The soundness of the framework is numerically and experimentally verified, with a good agreement with the numerical model found being a maximum of 3% difference and agreement with the experiment being a maximum of 16.5% difference. The results based on the optimization framework found that:

[0053] (i) The introduced optimization framework can determine the relative density and topology upon the given criteria, which is beyond the capability of numerical model or experiment. The optimization framework is thousands of times faster than either numerical model or experiment, but low cost, and has the ability to explore the mechanical behaviour of the TPMS implant at almost any point of relative density regardless of the topology.

[0054] (ii) A titanium bone implant with a gyroid scaffold is the most ideal candidate among TPMSs for constructing the bone implant due to its similar anisotropic surface as the bone.

[0055] (iii) Under the same yield strength, for example, as that of the trabecular bone, the relative density of sheet-typed TPMSs, including gyroid, primitive, IWP, and diamond is determined as 0.12, 0.123, 0.092, and 0.103, respectively, and the elastic stiffness of the titanium implant is found to be higher than that of trabecular bone.

[0056] (iv) For the criterion of having the same weight as that of trabecular or cortical bones, the relative density of sheet-typed TPMSs, including gyroid, primitive, IWP, and diamond is determined as 0.442, and the elastic stiffness of the TPMS implant is higher than that of trabecular bone, and close to that of cortical bone.

[0057] (v) For the criterion of having the same elastic stiffness, for example as that of cortical bone, the relative density of sheet-typed TPMSs, including gyroid, primitive, diamond, and IWP is found to be 0.556, 0.55, 0.543, and 0.52, respectively, and the implant yield strength is higher than that of cortical bone, and a little bit lower than that of trabecular bone.

[0058] (vi) The yield strength per weight of a titanium implant with TPMSs nonlinearly drops with a reduction of weight ratio in a nonlinear pattern. Although the weight of the implant is 90% of the bone, the yield strength of the TPMS implant is found still higher than either cortical or trabecular bones.

[0059] (vii) Rising the yield strength of titanium bone implant with TPMSs results in an increase in the relative density of the implant in a nonlinear pattern.

[0060] (viii) The directional impact wave propagating in titanium implants is different among constituent TPMS architectures. The phase wave propagating in a gyroid-based titanium implant is found to be the second lowest one among others, with the least distorted directional velocity profile, reflecting it as an ideal candidate for the bone implant.

[0061] (ix) The titanium implant beam with gyroid scaffolds resists the buckling uniformly along the direction compared with others, making it the ultimate bone implant candidate.

[0062] FIG. 17 is an illustrative architecture of a computing environment 1700 implemented as some embodiments of the present invention. The computing environment 1700 can be used to implement the ANNs and related methods described herein above. The computing environment 1700 is only one example of a suitable computing system and is not intended to suggest any limitation as to the scope of use or functionality of the present invention. Also, computing environment 1700 should not be interpreted as having any dependency or requirement relating to any one or combination of components illustrated in computing environment 1700.

[0063] As shown in FIG. 17, computing environment 1700 includes a computer system 1705. The computer system 1705 can be resident on a network infrastructure such as within a cloud environment or may be a separate independent computing device (e.g., a computing device of a service provider). The computer system 1705 may include a bus 1710, processor 1715, a storage device 1720, a system memory (hardware device) 1725, one or more input devices 1730, one or more output devices 1735, and a communication interface 1740.

[0064] The bus 1710 permits communication among the components of computer system 1705. For example, bus 1710 may be any of several types of bus structures including a memory bus or memory controller, a peripheral bus, and a local bus using any of a variety of bus architectures to provide one or more wired or wireless communication links or paths for transferring data and / or power to, from, or between various other components of computer system 1705.

[0065] The processor 1715 may be one or more processors, microprocessors, or specialized dedicated processors that include processing circuitry operative to interpret and execute computer readable program instructions, such as program instructions for controlling the operation and performance of one or more of the various other components of computer system 1705 for implementing the functionality, steps, and / or performance of the present invention. In certain embodiments, processor 1715 interprets and executes the processes, steps, functions, and / or operations of the present disclosure, which may be operatively implemented by the computer readable program instructions. For example, processor 1715 can receive data from synchronous machines, input the data into a real-time power grid model, generate bus inertia, and cause at least one action to be implemented based on the bus inertia. In embodiments, the information obtained or generated by the processor 1715, e.g., bus inertia, bus group coherency, etc., can be stored in the storage device 1720.

[0066] The storage device 1720 may include removable / non-removable, volatile / non-volatile computer readable media, such as, but not limited to, non-transitory machine readable storage medium such as magnetic and / or optical recording media and their corresponding drives. The drives and their associated computer readable media provide for storage of computer readable program instructions, data structures, program modules and other data for operation of computer system 1705 in accordance with the different aspects of the present invention. In embodiments, storage device 1720 may store operating system 1745, application programs 1750, and program data 1755 in accordance with aspects of the present invention.

[0067] The system memory 1725 may include one or more storage mediums, including for example, non-transitory machine readable storage medium such as flash memory, permanent memory such as read-only memory (“ROM”), semi-permanent memory such as random access memory (“RAM”), any other suitable type of non-transitory storage component, or any combination thereof. In some embodiments, an input / output system 1760 (BIOS) including the basic routines that help to transfer information between the various other components of computer system 1705, such as during start-up, may be stored in the ROM. Additionally, data and / or program modules 1765, such as at least a portion of operating system 1745, program modules, application programs 1750, and / or program data 1755, that are accessible to and / or presently being operated on by processor 1715, may be contained in the RAM. In embodiments, the program modules 1765 and / or application programs 1750 can comprise, for example, a processing tool to identify optimal locations to place PMUs, etc.

[0068] The one or more input devices 1730 may include one or more mechanisms that permit an operator to input information to computer system 1705, including, but not limited to, a touch pad, dial, click wheel, scroll wheel, touch screen, one or more buttons (e.g., a keyboard), mouse, game controller, track ball, microphone, camera, proximity sensor, light detector, motion sensors, biometric sensor, and combinations thereof. The one or more output devices 1735 may include one or more mechanisms that output information to an operator, such as, but not limited to, audio speakers, headphones, audio line-outs, visual displays, antennas, infrared ports, tactile feedback, printers, or combinations thereof.

[0069] The communication interface 1740 may include any transceiver-like mechanism (e.g., a network interface, a network adapter, a modem, or combinations thereof) that enables computer system 1705 to communicate with remote devices or systems, such as a mobile device or other computing devices such as, for example, a server in a networked environment, e.g., cloud environment. For example, computer system 1705 may be connected to remote devices or systems via one or more local area networks (LAN) and / or one or more wide area networks (WAN) using communication interface 1740.

[0070] As discussed herein, computing environment 1700 may be configured to determine a relative density and topology for TPMSs of a bone implant. In particular, computer system 1705 may perform tasks (e.g., process, steps, methods and / or functionality) in response to processor 1715 executing program instructions contained in non-transitory machine readable storage medium, such as a system memory 1725. The program instructions may be read into system memory 1725 from another computer readable medium (e.g., non-transitory machine readable storage medium), such as data storage device 1720, or from another device via the communication interface 1740 or server within or outside of a cloud environment. In embodiments, an operator may interact with computer system 1705 via the one or more input devices 1730 and / or the one or more output devices 1735 to facilitate performance of the tasks and / or realize the end results of such tasks in accordance with aspects of the present invention. In additional or alternative embodiments, hardwired circuitry may be used in place of or in combination with the program instructions to implement the tasks, e.g., steps, methods and / or functionality, consistent with the different aspects of the present invention. Thus, the steps, methods and / or functionality disclosed herein can be implemented in any combination of hardware circuitry and software.

[0071] In the preceding description, various embodiments have been described. For purposes of explanation, specific configurations and details have been set forth in order to provide a thorough understanding of the embodiments. However, it will also be apparent to one skilled in the art that the embodiments may be practiced without the specific details. Furthermore, well-known features may have been omitted or simplified in order not to obscure the embodiment being described.

[0072] Some embodiments of the present disclosure include a system including one or more data processors. In some embodiments, the system includes a non-transitory computer readable storage medium containing instructions which, when executed on the one or more data processors, cause the one or more data processors to perform part or all of one or more methods and / or part or all of one or more processes and workflows disclosed herein. Some embodiments of the present disclosure include a computer-program product tangibly embodied in a non-transitory machine-readable storage medium, including instructions configured to cause one or more data processors to perform part or all of one or more methods and / or part or all of one or more processes disclosed herein.

[0073] The terms and expressions which have been employed are used as terms of description and not of limitation, and there is no intention in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the invention claimed. Thus, it should be understood that although the present invention as claimed has been specifically disclosed by embodiments and optional features, modification and variation of the concepts herein disclosed may be resorted to by those skilled in the art, and that such modifications and variations are considered to be within the scope of this invention as defined by the appended claims.

[0074] The description provides preferred exemplary embodiments only, and is not intended to limit the scope, applicability or configuration of the disclosure. Rather, the ensuing description of the preferred exemplary embodiments will provide those skilled in the art with an enabling description for implementing various embodiments. It is understood that various changes may be made in the function and arrangement of elements without departing from the spirit and scope as set forth in the appended claims.

[0075] Specific details are given in the description to provide a thorough understanding of the embodiments. However, it will be understood that the embodiments may be practiced without these specific details. For example, specific computational models, systems, networks, processes, and other components may be shown as components in block diagram form in order not to obscure the embodiments in unnecessary detail. In other instances, well-known circuits, processes, algorithms, structures, and techniques may be shown without unnecessary detail in order to avoid obscuring the embodiments.

Claims

1. A method implemented on a computer system, the method comprising:receiving one or more parameters of a bone in which an implant is to be placed;generating an input to an artificial neural network (ANN)-based optimization framework based at least in part on the one or more parameters; and receiving, based at least in part on the input, an output of the ANN-based optimization framework indicating a relative density and a topology for a triply periodic minimal surface (TPMS) architecture for the implant. 2. The method of claim 1, wherein the one or more parameters comprise a stiffness of the bone, a yield strength of the bone, and a weight of the bone. 3. The method of claim 1, wherein the TPMS architecture comprises a solid or sheet-typed I-graph and wrapped package-graph (IWP) scaffold, a gyroid scaffold, a primitive scaffold, or a diamond scaffold. 4. The method of claim 1, further comprising:determining, based at least in part on the output of the ANN-based optimization framework, at least one mechanical property of the implant; anddetermining, based on the at least one mechanical property of the implant, a buckling resistance or an impact phase wave propagation of the implant. 5. The method of claim 1, wherein the ANN-based optimization framework comprises a plurality of multilayers, wherein each multilayer of the plurality of multilayers includes:an artificial neuron configured to receive input data;a threshold for determining a result;a weight to be applied to the input data in determining the result; anda connection to another multilayer of the plurality of multilayers for transmitting the result. 6. The method of claim 1, further comprising:determining the output by determining that a maximum percent tolerance value associated with a change of the ANN-based optimization framework is below a threshold value, wherein the change of the ANN-based optimization framework comprises at least one of a neuron number, a hidden layer, a bias, or a weight. 7. The method of claim 1, further comprising:determining, based at least in part on the output, a spatial surface of anisotropy of Young’s modulus for the TPMS architecture against orientation of the implant. 8. A computer system comprising:one or more data processors; andone or more memory devices storing computer-readable instructions that, upon execution by the one or more data processors, configure the computer system to:receive one or more parameters of a bone in which an implant is to be placed;generate an input to an artificial neural network (ANN)-based optimization framework based at least in part on the one or more parameters; andreceive, based at least in part on the input, an output of the ANN-based optimization framework indicating a relative density and a topology for a triply periodic minimal surface (TPMS) architecture for the implant. 9. The computer system of claim 8, wherein the one or more parameters comprise a stiffness of the bone, a yield strength of the bone, and a weight of the bone. 10. The computer system of claim 8, wherein the TPMS architecture comprises a solid or sheet-typed I-graph and wrapped package-graph (IWP) scaffold, a gyroid scaffold, a primitive scaffold, or a diamond scaffold. 11. The computer system of claim 8, wherein the one or more memory devices further store computer-readable instructions that, upon execution by the one or more data processors, configure the computer system to:determine, based at least in part on the output of the ANN-based optimization framework, at least one, mechanical property of the implant; anddetermine, based on the at least one mechanical property of the implant, a buckling resistance or an impact wave propagation of the implant. 12. The computer system of claim 8, wherein the ANN-based optimization framework comprises a plurality of multilayers, wherein each multilayer of the plurality of multilayers includes:an artificial neuron configured to receive input data;a threshold for determining a result;a weight to be applied to the input data in determining the result; anda connection to another multilayer of the plurality of multilayers for transmitting the result. 13. The computer system of claim 8, wherein the one or more memory devices further store computer-readable instructions that, upon execution by the one or more data processors, configure the computer system to:determine the output by determining that a maximum percent tolerance value associated with a change of the ANN-based optimization framework is below a threshold value, wherein the change of the ANN-based optimization framework comprises at least one of a neuron number, a hidden layer, a bias, or a weight. 14. The computer system of claim 8, wherein the one or more memory devices further store computer-readable instructions that, upon execution by the one or more data processors, configure the computer system to:determine, based at least in part on the output, a spatial surface of anisotropy of Young’s modulus for the TPMS architecture against orientation of the implant. 15. A non-transitory computer readable storage medium, storing instructions that upon execution by one or more data processors of a computer system, configure the computer system to:receive one or more parameters of a bone in which an implant is to be placed;generate an input to an artificial neural network (ANN)-based optimization framework based at least in part on the one or more parameters; andreceive, based at least in part on the input, an output of the ANN-based optimization framework indicating a relative density and a topology for a triply periodic minimal surface (TPMS) architecture for the implant. 16. The non-transitory computer readable storage medium of claim 15, wherein the one or more parameters comprise a stiffness of the bone, a yield strength of the bone, and a weight of the bone. 17. The non-transitory computer readable storage medium of claim 15, wherein the TPMS architecture comprises a solid or sheet-typed I-graph and wrapped package-graph (IWP) scaffold, a gyroid scaffold, a primitive scaffold, or a diamond scaffold. 18. The non-transitory computer readable storage medium of claim 15, further storing instructions that upon execution by one or more data processors of a computer system, configure the computer system to:determine, based at least in part on the output of the ANN-based optimization framework, at least one mechanical property of the implant; anddetermine, based on the at least one mechanical property of the implant, a buckling resistance or an impact phase wave propagation of the implant. 19. The non-transitory computer readable storage medium of claim 15, wherein the ANN-based optimization framework comprises a plurality of multilayers, wherein each multilayer of the plurality of multilayers including:an artificial neuron configured to receive input data;a threshold for determining a result;a weight to be applied to the input data in determining the result; anda connection to another multilayer of the plurality of multilayers for transmitting the result. 20. The non-transitory computer readable storage medium of claim 15, further storing instructions that upon execution by one or more data processors of a computer system, configure the computer system to:determine the output by determining that a maximum percent tolerance value associated with a change of the ANN-based optimization framework is below a threshold value, wherein the change of the ANN-based optimization framework comprises at least one of a neuron number, a hidden layer, a bias, or a weight.  

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