Remodeling Algorithm Research Articles

Prediction of micro-scale bone adaptation of human trabecular bone under different implanted conditions

Background and objectiveDifferent bone remodeling algorithms are used to predict bone adaptation and to understand how bones respond to the mechanical stimuli altered by implants. This paper introduces a novel micro-scale bone remodeling algorithm, which deviates from conventional methods by focusing on structure-based bone adaptation instead of density-based approaches. MethodsThe proposed model simulated cellular activities such as bone resorption, new bone formation, and maturation of newly formed bone. These activities were assumed to be triggered by mechanical stimuli. Model parameters were evaluated for the 3D geometries of trabecular bone from intact femur developed from micro computed tomography (CT) scan data. Two different hip implants, solid and porous were used, and two different bone remodeling methods were performed using the proposed and conventional methods. ResultsResults showed that micro CT scan-based finite element (FE) models accurately captured the microarchitecture and anisotropy of trabecular bone. The predicted bone resorption rate at the peri-prosthetic regions for the solid and porous implants was in the range of 17–27% and 4.5–7.3%, respectively, for a simulated period of four years. ConclusionsThe results obtained from FE analysis strongly align with clinical findings, confirming the effectiveness of the proposed algorithm. By emphasizing the structural aspect of bone adaptation, the proposed algorithm brings a fresh perspective on bone adaptation at the peri-prosthetic bone. This method can help researchers and clinicians to improve implant designs for better clinical outcomes.

Multi-objective optimization of custom implant abutment design for enhanced bone remodeling in single-crown implants using 3D finite element analysis

The optimal configuration of a customized implant abutment is crucial for bone remodeling and is influenced by various design parameters. This study introduces an optimization process for designing two-piece zirconia dental implant abutments. The aim is to enhance bone remodeling, increase bone density in the peri-implant region, and reduce the risk of late implant failure. A 12-month bone remodeling algorithm subroutine in finite element analysis to optimize three parameters: implant placement depth, abutment taper degree, and gingival height of the titanium base abutment. The response surface analysis shows that implant placement depth and gingival height significantly impact bone density and uniformity. The taper degree has a smaller effect on bone remodeling. The optimization identified optimal values of 1.5 mm for depth, 35° for taper, and 0.5 mm for gingival height. The optimum model significantly increased cortical bone density from 1.2 to 1.937 g/cm3 in 2 months, while the original model reached 1.91 g/cm3 in 11 months. The standard deviation of density showed more uniform bone apposition, with the optimum model showing values 2 to 6 times lower than the original over 12 months. The cancellous bone showed a similar trend. In conclusion, the depth and taper have a significant effect on bone remodeling. This optimized model significantly improves bone density uniformity.

A Soft-Tissue Driven Bone Remodeling Algorithm for Mandibular Residual Ridge Resorption Based on Patient CT Image Data.

The role of the biomechanical stimulation generated from soft tissue has not been well quantified or separated from the self-regulated hard tissue remodeling governed by Wolff's Law. Prosthodontic overdentures, commonly used to restore masticatory functions, can cause localized ischemia and inflammation as they often compress patients' oral mucosa and impede local circulation. This biomechanical stimulus in mucosa is found to accelerate the self-regulated residual ridge resorption (RRR), posing ongoing clinical challenges. Based on the dedicated long-term clinical datasets, this work develops an in-silico framework with a combination of techniques, including advanced image post-processing, patient-specific finite element models and unsupervised machine learning Self-Organizing map algorithm, to identify the soft tissue induced RRR and quantitatively elucidate the governing relationship between the RRR and hydrostatic pressure in mucosa. The proposed governing equation has not only enabled a predictive simulation for RRR as showcased in this study, providing a biomechanical basis for optimizing prosthodontic treatments, but also extended the understanding of the mechanobiological responses in the soft-hard tissue interfaces and the role in bone remodeling.

Evaluating the effect of functionally graded materials on bone remodeling around dental implants

ObjectivesThis study evaluates the potential for osseointegration and remodeling of customized dental implants made from Titanium-Hydroxyapatite Functionally Graded Material (Ti-HAP FGM) with optimized geometry, using the finite element method (FEM). MethodsThe study utilized CT scan images to model and assemble various geometrical designs of dental implants in a mandibular slice. The mechanical properties of Ti-HAP FGMs were computed by varying volume fractions (VF) of hydroxyapatite (0–20%), and a bone remodeling algorithm was used to evaluate the biomechanical characteristics of the ultimate bone configuration in the peri-implant tissue. ResultsThe findings of the FEA reveal that osseointegration improves with changes in the density and mechanical properties of the bone surrounding Ti-HAP implants, which are influenced by the varying VF of hydroxyapatite in the FGM. SignificanceIncreasing the hydroxyapatite fraction improves osseointegration, and appropriate length and diameter selection of Ti-HAP dental implants contribute to their stability and longevity.

410 Improving Patient Outcomes through Design of Biodegradable Implants for Long Bone Fractures

OBJECTIVES/GOALS: Current long bone fracture standard of care uses inert metal intramedullary nails (IMN), 10x stiffer than femur cortex. Consequent “stress-shielding” bone loss sees >5% of patients needing revision surgery. To improve nonunion healing, we develop automated design optimization methods for biodegradable Mg alloy IMNs to control local reloading. METHODS/STUDY POPULATION: Finite element analysis (FEA) is performed on 3D bone-IMN representations to establish this study’s baseline strain states for existing inert IMN geometries within QCT-informed femoral models under simulated biomechanical loading. FEA with Mg alloy properties for same IMN designs simulate transient IMN material loss through discrete time-step models with experimental in vivo Mg corrosion rates and strain-based bone density evolution using remodeling algorithms from literature. Transient stability and strength metrics, fracture zone stress profiles under gradual reloading and manufacturing constraints are formulated through gradient-based sensitivity analysis into a topology optimization framework (TOF) incorporating a reaction-diffusion degradation model to generate IMN topologies. RESULTS/ANTICIPATED RESULTS: TOF designs for Mg alloy IMNs with transient allowable strength constraints, using safety factors to prevent IMN failure, demonstrate higher compliance than standard inert IMNs with mechanical properties closer to native cortical bone. The biodegradation model within the TOF, informed by corrosion behavior from bone-IMN FEA study, predicts how potential design evolutions affect transient strain states of the system. Thus, local fracture region stress states are controlled by the algorithm optimizing for desirable transient stiffness profiles based on a minimum variance objective of fracture zone stress compared to a target bone stress profile. Optimized IMNs with porous, high surface area features achieve 50% decrease in IMN stiffness over 6 months recovery time and complete in vivo degradation in 24 months. DISCUSSION/SIGNIFICANCE: Our TOF reduces “stress-shielding” effects via design for controlled IMN biodegradation to gradually increase fracture zone loading, stimulating remodeling and reducing current risk of post-operative fracture and surgical removal in ~15k cases/yr. in the U.S. In vitro mechanical and in vivo clinical testing is required to validate design results.

The Biomechanical Analysis of Tibial Implants Using Meshless Methods: Stress and Bone Tissue Remodeling Analysis

Total knee arthroplasty (TKA) stands out as one of the most widely employed surgical procedures, establishing itself as the preferred method for addressing advanced osteoarthritis of the knee. However, current knee prostheses require refined design solutions. This research work focuses on a computational analysis of both the mechanical behavior of a knee joint implant and the bone remodeling process in the tibia following implantation. This research study delves into how specific design parameters, particularly the stem geometry, impact the prosthesis’s performance. Utilizing a computed tomography scan of a tibia, various TKA configurations were simulated to conduct analyses employing advanced discretization techniques, such as the finite element method (FEM) and the radial point interpolation method (RPIM). The findings reveal that the introduction of the implant leads to a marginal increase in the stress values within the tibia, accompanied by a reduction in the displacement field values. The insertion of the longest tested implant increased the maximum stress from 5.0705 MPa to 6.1584 MPa, leading to a displacement reduction from 0.016 mm to 0.0142 mm. Finally, by combining the FEM with a bone remodeling algorithm, the bone remodeling process of the tibia due to an implant insertion was simulated.

Mechano-driven intervertebral bone bridging via oriented mechanical stimulus in a twist metamaterial cage: An in silico study

Stiffer cages provide sufficient mechanical support but fail to promote bone ingrowth due to stress shielding. It remains challenging for fusion cage to satisfy both bone bridging and mechanical stability. Here we designed a fusion cage based on twist metamaterial for improved bone ingrowth, and proved its superiority to the conventional diagonal-based cage in silico. The fusion process was numerically reproduced via an injury-induced osteogenesis model and the mechano-driven bone remodeling algorithm, and the outcomes fusion effects were evaluated by the morphological features of the newly-formed bone and the biomechanical behaviors of the bone-cage composite. The twist-based cages exhibited oriented bone formation in the depth direction, in comparison to the diagonal-based cages. The axial stiffness of the bone-cage composites with twist-based cages was notably higher than that with diagonal-based cages; meanwhile, the ranges of motion of the twist-based fusion segment were lower. It was concluded that the twist metamaterial cages led to oriented bone ingrowth, superior mechanical stability of the bone-cage composite, and less detrimental impacts on the adjacent bones. More generally, metamaterials with a tunable displacement mode of struts might provide more design freedom in implant designs to offer customized mechanical stimulus for osseointegration.

Bone remodelling prediction using mechanical stimulus with bone connectivity theory in porous implants

Strain energy density (SED) is considered to be the primary remodelling stimulus influencing the process of bone growth into porous implants. A bone remodelling algorithm incorporating the concept of bone connectivity, that newly formed bone should only grow from existing bone, was developed to provide a more biologically realistic simulation of bone growth. Results showed that the new algorithm prevented the occurrence of unconnected mature bone within porous implants, an unrealistic phenomenon observed using conventional adaptive elasticity theories. The bone connectivity algorithm had minimal effect (0.67% difference) on the final bone density distribution for standard bending and torsional moment cases. For a porous implant model, both algorithms, with and without bone connectivity implementation, reached the same final stiffness, with a difference of less than 0.01%. The bone connectivity algorithm predicted a slower and more gradual bone remodelling process, requiring at least 50% additional time for full remodelling compared to the conventional adaptive elasticity algorithm, which should be accounted for in the planning of rehabilitation strategies. The developed modelling can be employed to improve porous implant designs to achieve better clinical outcomes.

MULTISCALE MECHANOBIOLOGICAL MODELING OF THE CORTICAL/SPONGY INTERFACE USING FINITE ELEMENTS

In this paper, we describe a mathematical model of bone remodeling that integrates the activities of the bone cells and the mechanical behavior of the bone in an intermediate cortical/trabecular zone. This behavior decreases and increases as the bone moves from a dense cortical zone to a less dense porous trabecular zone. The bone remodeling is a combined process of resorption and formation driven primarily by osteoclasts and osteoblasts. The evolution of the bone cell population involves osteoblast-osteoclast signaling, which is mediated by the biological factors and receives a mechanical stimulus assessed at the microscopic scale. Excessive stress on the bone causes microdamage that induces changes in the structural integrity and microarchitecture. This phenomenon explains the attention paid to the mechanical properties of the bone. In this context, numerical simulations were performed in a mechanobiological model, in which different mechanical and biological parameters were considered. A three-dimensional finite-element model of a human proximal femur was generated, and the simulation of the bone remodeling algorithm was implemented. The current work is an exploratory numerical study, and the results obtained reveal the impact of the mechanical properties on the remodeling process of the intermediate bone subjected to cyclic loading, highlighting the effects of the selected parameters for the different remodeling periods.

The effect of early weight-bearing on bone fusion after triple arthrodesis

Triple arthrodesis is an effective method for treating stiff horseshoe feet and severe osteoarthritis. However, it is still a challenge to improve postoperative bone fusion by changing early weight-bearing. This study improved the classical bone remodeling algorithm, established a mathematical relationship between density change rate and mechanical stimulation, and combined it with finite element theory. The proposed algorithm can not only predict the effect of early weight-bearing on triple arthrodesis but also visually demonstrate the change of bone mineral density with time. The analysis results indicated that 2.5% of the initial load was a potential factor leading to bone nonunion, and 50% of the initial load would result in bone resorption. Meanwhile, it was found that 25% of the external load was more conducive to postoperative rehabilitation. The study results have theoretical significance for enhancing the effect of postoperative bone fusion and formulating a more scientific rehabilitation program, thereby supporting patients’ postoperative rehabilitation exercise.

BONE REMODELLING PREDICTION FOR IMPROVED POROUS IMPLANT DESIGN

AbstractObjectivesYoung patients receiving metallic bone implants after surgical resection of bone cancer require implants that last into adulthood, and ideally life-long. Porous implants with similar stiffness to bone can promote bone ingrowth and thus beneficial clinical outcomes. A mechanical remodelling stimulus, strain energy density (SED), is thought to be the primary control variable of the process of bone growth into porous implants. The sequential process of bone growth needs to be taken into account to develop an accurate and validated bone remodelling algorithm, which can be employed to improve porous implant design and achieve better clinical outcomes.MethodsA bone remodelling algorithm was developed, incorporating the concept of bone connectivity (sequential growth of bone from existing bone) to make the algorithm more physiologically relevant. The algorithm includes adaptive elastic modulus based on apparent bone density, using a node-based model to simulate local remodelling variations while alleviating numerical checkerboard problems. Strain energy density (SED) incorporating stress and strain effects in all directions was used as the primary stimulus for bone remodelling. The simulations were developed to run in MATLAB interfacing with the commercial FEA software ABAQUS and Python. The algorithm was applied to predict bone ingrowth into a porous implant for comparison against data from a sheep model.ResultsThe accuracy of the predicted bone remodelling was verified for standard loading cases (bending, torsion) against analytical calculations. Good convergence was achieved. The algorithm predicted good bone remodelling and growth into the investigated porous implant. Using the standard algorithm without connectivity, bone started to remodel at locations unconnected to any bone, which is physiologically implausible. The implementation of bone connectivity ensures the gradual process of bone growth into the implant pores from the sides. The bone connectivity algorithm predicted that the full remodelling required more time (approximately 50% longer), which should be considered when developing post-surgical rehabilitation strategies for patients. Both algorithms with and without bone connectivity implementation converged to same final stiffness (less than 0.01% difference). Almost all nodes reached the same density value, with only a limited number of nodes (less than 1%) in transition areas with a strong density gradient having noticeable differences.ConclusionsAn improved bone remodelling algorithm based on strain energy density that modelled the sequential process of bone growth has been developed and tested. For a porous metallic bone implant the same final bone density distribution as for the original adaptive elasticity theory was predicted, with a slower and more fidelic process of growth from existing surrounding bone into the porous implant.Declaration of Interest(b) declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported:I declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research project.

How to implement constrained mixture growth and remodeling algorithms for soft biological tissues

Biological soft tissues are constantly adapting to their mechanical environment and remodel to restore certain mechanobiological homeostatic conditions. These effects can be modeled using the constrained mixture theory, that assumes degradation of material over time and the gradual replacement of extant material by newly deposited material. While this theory presents an elegant way to grasp phenomena of growth and remodeling in soft biological tissues, implementation difficulties may arise. Therefore, we give a detailed overview of the mathematical description of the constrained mixture theory and its homogenized equivalent, and present practical suggestions to numerically implement the theories. These implementations are thoroughly tested with multiple example growth and remodeling models. Results show a good correspondence between both theories, with the homogenized theory favored in terms of time efficiency. Results of a step time convergence study show the importance of choosing a small enough time step, especially when using the classical theory.

A numerical model for fibril remodeling in articular cartilage

BackgroundCollagen fibrils of articular cartilage have a distinct organization in mature human knee joints. It seems that a mechanobiological process drives the remodeling of newborn collagen fibrils with maturation. Therefore, the goal of the present study was to develop a collagen fibril remodeling algorithm that describes the unique collagen fibril organization in a 3D knee model. MethodA fibril-reinforced, biphasic cartilage model was used with a cuboid and a 3D human knee joint geometries. An isotropic collagen fibril distribution was assigned to the cartilage at the start of the analysis. Each fibril was rotated towards the direction that resulted in a maximum stretch at each time increment of the loading cycle. ResultsThe resulting pattern for the collagen fibrils was compared with split line patterns of porcine knee joint cartilage and also data published in the literature. Fibrils on the articular surface had a radial pattern towards the geometrical centroid of the tibial and femoral cartilage. In the tibiofemoral contact regions of superficial zone, fibrils were oriented circumferentially and randomly. In the porcine samples, the split-line patterns were similar to those obtained theoretically. Depth-wise organization of fibril network was characterized by fibrils perpendicular to the subchondral bone in the deeper layers, and fibrils parallel to the surface of cartilage in the superficial zone. ConclusionsThe maximum stretch criterion, coupled with a biphasic constitutive model, successfully predicted the collagen fibril organization observed in the articular cartilage throughout the depth and on the articular surface.

A bionic topology optimization method with an additional displacement constraint

<abstract><p>Displacement is an important measure of stiffness, and its constraint must be considered in many real engineering designs. However, traditional volume-constrained compliance minimization methods for load-bearing structures do not deal with displacements of practical importance directly. Based on this situation, the paper extends an improved bionic topology optimization method to solve the topology optimization problem with an additional displacement constraint. The updates of density design variables are based on an improved bone remodeling algorithm rather than gradient information employed by traditional methods. An explicit relationship between the threshold in the bone remodeling algorithm and target node displacement is constructed to satisfy displacement constraint. As a result, one will obtain a topology with an optimal cost-weighted sum of stiffness and mass while the target node displacement does not exceed its predefined limit. 2D and 3D examples are given to demonstrate the effectiveness of the proposed method.</p></abstract>

Research on an effective bionic topology optimization method for engineering applications

This article develops a bionic topology optimization method for engineering applications. Unlike traditional density-based methods, the real material density is used as a design variable, and its evolution is controlled by a simpler and improved bone remodelling formula. A calculation method of the threshold value in this formula is given that solves a problem difficult to define in engineering applications. A progressive function is constructed for solving the iterative fluctuation problem. A post-processing method based on the level set method is presented for the jagged boundary problem. Compared with the traditional bone remodelling algorithm, the proposed method has better optimization ability. Some examples prove the feasibility and effectiveness of the method. Moreover, the influence of some key parameters on the optimization is discussed.

Numerical Simulation of Mechanically Adaptive Bone Remodeling Around Teeth and Implants: A Comparison with Clinical Images

The results of numerical simulation of mechanically adaptive bone remodeling have been compared with clinical images. Cone beam computed tomography (CBCT) images of multiple human subjects were superimposed to obtain a continuous bone density spatial distribution map inside the mandible supporting the lateral incisor. Strain energy density in the bone under normal chewing and biting forces was computed using finite element analysis. A bone remodeling algorithm was implemented to compute the bone density distribution at equilibrium. Linear regression analysis was performed between the bone density computed by numerical simulation and that obtained from image analysis, for every trabecular bone element. The results exhibited close agreement with a coefficient of correlation of 0.8499. The bite forces were transmitted through tooth roots to the surrounding bone, thus stimulating high trabecular bone density near the roots. The bending and torsion moments on the sagittal section of the mandible resulted in lower bone density near the center than those towards the edge of the mandible. The results provide a new method to compare the results of adaptive bone remodeling simulation with experimental data, and also provide model parameters to predict the bone density distribution surrounding a dental implant that replaced the tooth.

Application of finite element analysis to tissue differentiation and bone remodelling approaches and their use in design optimization of orthopaedic implants: A review.

Post-operative bone growth and long-term bone adaptation around the orthopaedic implants are simulated using the mechanoregulation based tissue-differentiation and adaptive bone remodelling algorithms, respectively. The primary objective of these algorithms was to assess biomechanical feasibility and reliability of orthopaedic implants. This article aims to offer a comprehensive review of the developments in mathematical models of tissue-differentiation and bone adaptation and their applications in studies involving design optimization of orthopaedic implants over three decades. Despite the different mechanoregulatory models developed, existing literature confirm that none of the models can be highly regarded or completely disregarded over each other. Not much development in mathematical formulations has been observed from the current state of knowledge due to the lack of in vivo studies involving clinically relevant animal models, which further retarded the development of such models to use in translational research at a fast pace. Future investigations involving artificial intelligence (AI), soft-computing techniques and combined tissue-differentiation and bone-adaptation studies involving animal subjects for model verification are needed to formulate more sophisticated mathematical models to enhance the accuracy of pre-clinical testing of orthopaedic implants.

Bone Remodeling Around Solid and Porous Interbody Cages in the Lumbar Spine.

Spinal fusion is an effective surgical treatment for intervertebral disk degeneration. However, the consequences of implantation with interbody cages on load transfer and bone remodeling in the vertebral bodies have scarcely been investigated. Using detailed three-dimensional models of an intact and implanted lumbar spine and the strain energy density based bone remodeling algorithm, this study aimed to investigate the evolutionary changes in distribution of bone density (ρ) around porous and solid interbody cages. Follower load technique and submodeling approach were employed to simulate applied loading conditions on the lumbar spine models. The study determined the relationship between mechanical properties and parametrical characteristics of porous body-centered-cubic (BCC) models, which corroborated well with Gibson-Ashby and exponential regression models. Variations in porosity affected the peri-prosthetic stress distributions and bone remodeling around the cages. In comparison to the solid cage, stresses and strains in the cancellous bone decreased with an increase in cage porosity; whereas the range of motion increased. For the solid cage, increase in bone density of 20-28% was predicted in the L4 inferior and L5 superior regions; whereas the model with 78% porosity exhibited a small 3-5% change in bone density. An overall increase of 9-14% bone density was predicted in the L4 and L5 vertebrae after remodeling for solid interbody cages, which may influence disk degeneration in the adjacent segment. In comparison to the solid cage, an interbody cage with 65-78% porosity could be a viable and promising alternative, provided sufficient mechanical strength is offered.

Symmetry breaking and effects of nutrient walkway in time-dependent bone remodeling incorporating poroelasticity

Bone is an extraordinary biological material that continuously adapts its hierarchical microstructure to respond to static and dynamic loads for offering optimal mechanical features, in terms of stiffness and toughness, across different scales, from the sub-microscopic constituents within osteons—where the cyclic activity of osteoblasts, osteoclasts, and osteocytes redesigns shape and percentage of mineral crystals and collagen fibers—up to the macroscopic level, with growth and remodeling processes that modify the architecture of both compact and porous bone districts. Despite the intrinsic complexity of the bone mechanobiology, involving coupling phenomena of micro-damage, nutrients supply driven by fluid flowing throughout hierarchical networks, and cells turnover, successful models and numerical algorithms have been presented in the literature to predict, at the macroscale, how bone remodels under mechanical stimuli, a fundamental issue in many medical applications such as optimization of femur prostheses and diagnosis of the risk fracture. Within this framework, one of the most classical strategies employed in the studies is the so-called Stanford’s law, which allows uploading the effect of the time-dependent load-induced stress stimulus into a biomechanical model to guess the bone structure evolution. In the present work, we generalize this approach by introducing the bone poroelasticity, thus incorporating in the model the role of the fluid content that, by driving nutrients and contributing to the removal of wastes of bone tissue cells, synergistically interacts with the classical stress fields to change homeostasis states, local saturation conditions, and reorients the bone density rate, in this way affecting growth and remodeling. Through two paradigmatic example applications, i.e. a cylindrical slice with internal prescribed displacements idealizing a tract of femoral diaphysis pushed out by the pressure exerted by a femur prosthesis and a bone element in a form of a bent beam, it is highlighted that the present model is capable to catch more realistically both the transition between spongy and cortical regions and the expected non-symmetrical evolution of bone tissue density in the medium–long term, unpredictable with the standard approach. A real study case of a femur is also considered at the end in order to show the effectiveness of the proposed remodeling algorithm.

A comparative study of bone remodeling around hydroxyapatite-coated and novel radial functionally graded dental implants using finite element simulation

This comparative study simulates bone remodeling outcome around titanium dental implants and compares the final bone configuration with the one around novel implants composed of radial functionally graded materials (FGMs) and the titanium implants with hydroxyapatite (HA) coating. A dental implant system embedded in 3D mandibular bone with masticatory loading was simulated by the finite element method. A bone remodeling algorithm was applied to cancellous and cortical bones. Young's modulus and von Mises stress were obtained to ensure bone homeostasis and evaluate the final bone configuration. Local stress distribution in the bone-implant interface was analyzed before and after bone remodeling. The average final Young's modulus of cancellous bone reached 2.68, 2.49, and 2.32 GPa for the FGM, HA-coated, and the titanium models, respectively. These values for cortical bone were 17.75, 16.86, and 17.20 GPa in the same order. Radial FGM implants generated the highest remodeling stimulus and bone density. Their superiority over the HA-coated models was confirmed by four implant surface stiffness values (10, 20, 30, and 40 GPa). Remodeling increased bone density around the implant, consistent with clinical data and reduced stress concentration in the cortical neck. The stress values were in the safe zone regarding overload-induced bone resorption. The findings of this study were substantiated by clinical images and bone density values from previous literature.