Fig. 1 Simplification of the all-on-4 models consisted in cutting off part of the ascending ramus of the mandible models More about this image found in Simplification of the all-on-4 models consisted in cutting off part of the ...

Fig. 2 The manual refinement in the tetrahedral mesh consisted of adjusting the smallest elements in the regions of interest (i.e., prosthetic components interface, implant–abutment interface, and bone–implant interface) More about this image found in The manual refinement in the tetrahedral mesh consisted of adjusting the sm...

Fig. 3 The static loading of 300 N performed obliquely in the prosthetic bar More about this image found in The static loading of 300 N performed obliquely in the prosthetic bar

Fig. 4 Graphical representations of the von Mises equivalent stress (in MPa) performed at the level of prosthetic components and dental implants More about this image found in Graphical representations of the von Mises equivalent stress (in MPa) perfo...

Fig. 5 Maximum peaks and the pattern of the von Mises equivalent stress distribution in the prosthetic bar of the all-on-4 concept designed with ( a ) tilted standard, ( b ) straight standard, and ( c ) straight short distal implants. The clear area indicates that no mechanical effort was performe... More about this image found in Maximum peaks and the pattern of the von Mises equivalent stress distributi...

Fig. 6 Maximum peaks and the pattern of the von Mises equivalent stress distribution in the distal left bar screws of the all-on-4 concept designed with ( a ) tilted standard, ( b ) straight standard, and ( c ) straight short distal implants. The clear area indicates that no mechanical effort was ... More about this image found in Maximum peaks and the pattern of the von Mises equivalent stress distributi...

Fig. 7 Maximum peaks and the pattern of the von Mises equivalent stress distribution in the distal left abutments of the all-on-4 concept designed with ( a ) tilted standard, ( b ) straight standard, and ( c ) straight short distal implants. The clear area indicates that no mechanical effort was p... More about this image found in Maximum peaks and the pattern of the von Mises equivalent stress distributi...

Fig. 8 Maximum peaks and the pattern of the von Mises equivalent stress distribution in the distal left implants of the ( a )AO4T, ( b ) AO4S, and ( c ) AO4Sh configurations More about this image found in Maximum peaks and the pattern of the von Mises equivalent stress distributi...

Fig. 9 Maximum peaks and the pattern of principal stresses distribution when the ( a ) σ max and ( b ) σ min were applied More about this image found in Maximum peaks and the pattern of principal stresses distribution when the (...

Fig. 10 General displacements of the models ( a ) and bar screws and ( b ) after load application More about this image found in General displacements of the models ( a ) and bar screws and ( b ) after lo...

Fig. 1 FE model of the intact vertebra L3 with: ( a ) random circular structure, ( b ) simulated trabecular structures, ( c ) FE model of the L3 vertebra and fusion cage, for the prediction of osseointegration, and ( d ) flowchart of the DSO-TO based bone remodeling algorithm More about this image found in FE model of the intact vertebra L3 with: ( a ) random circular structure, (...

Fig. 2 Flowchart of the fusion cage design via topology optimization algorithm More about this image found in Flowchart of the fusion cage design via topology optimization algorithm

Fig. 3 Designed relative density distribution of the fusion cages and their corresponding architectures with different views More about this image found in Designed relative density distribution of the fusion cages and their corres...

Fig. 4 ( a ) Simulated load–displacement curves of the fusion cages and ( b ) simulated compliance of the fusion cages under the physiological load cases More about this image found in ( a ) Simulated load–displacement curves of the fusion cages and ( b ) simu...

Fig. 5 ( a ) Schematic diagram of the position of the interested cross section, and the distribution of the von Mises stress on the cross section under the three load cases: ( b ) flexion, ( c ) lateral bending, and ( d ) compression More about this image found in ( a ) Schematic diagram of the position of the interested cross section, an...

Fig. 6 Peak von Mises stress in the fusion cages immediately after surgery under the three load cases More about this image found in Peak von Mises stress in the fusion cages immediately after surgery under t...

Fig. 7 Different views of simulated trabecular structure of the L3 vertebra (cortical bone removed) and the corresponding CT image: ( a ) aerial view, ( b ) frontal view, ( c ) axial view, and ( d ) sagittal view More about this image found in Different views of simulated trabecular structure of the L3 vertebra (corti...