Computer Simulation-Based Multi-Objective Optimisation of Additively Manufactured Cranial Implants

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper aims to optimize cranial implants using a combination of computer simulation tools and multi-objective optimization techniques. It is motivated by the need for custom implants that improve both aesthetic and functional outcomes for patients with cranial defects. The focus is on optimizing the gyroid architecture of implants to balance mechanical and biological properties.

The study employs a detailed parametric modeling approach using the gyroid TPMS (Triply Periodic Minimal Surfaces) architecture. The main parameters varied are cell size, isovalue, and shape factor. The optimization process uses computational tools like CAD, FEM, and CFD to model and simulate the relationship between these parameters and the desired properties: surface area, permeability, porosity, and Young's modulus. The NSGA-II algorithm is utilized for multi-objective optimization, targeting the surface area and permeability while adhering to constraints on porosity and elasticity.

- The gyroid architecture, with its intricate structure, shows promise for cranial implants due to its favorable mechanical properties and ability to promote biological integration.

- The use of computer simulations to derive regression models effectively links design parameters to performance outcomes.

- The optimization process identifies a Pareto set of solutions, from which the most suitable implant design can be selected based on specific application requirements.

- An additively manufactured prototype implant validated the proposed approach, showcasing the practical applicability of the research.

 

The paper covers a broad spectrum from theoretical modeling to practical validation, providing a robust framework for implant optimization.

The research objectives are clearly stated, and the methodology is well-detailed, facilitating reproducibility and understanding.

Areas for Improvement:

- While the paper includes a prototype validation, more extensive in vivo or clinical trials could strengthen the conclusions.

- The discussion on material selection could be expanded to include more detail on why specific materials were chosen for the prototype and how they compare to alternatives.

- The effects in the long run must be discussed. The paper does not address this aspect related to the interaction between bone-graft evolving over time (see, e.g., [1,2]).

- Providing more detailed analysis and discussion of the simulation results and their implications for real-world applications would enhance the paper's impact.

- Some similar approaches already present in the literature must be recalled and compared with (see, e.g., [3]). 

The paper presents a well-executed study on optimizing cranial implants using computational simulations and multi-objective optimization. The findings indicate that gyroid TPMS structures are promising for this application, and the methodology offers a valuable tool for designing custom implants. Future work could focus on broader validation and exploring additional materials to further refine the implant designs.

[1] Giorgio, I., Dell'Isola, F., Andreaus, U., & Misra, A. (2023). An orthotropic continuum model with substructure evolution for describing bone remodeling: an interpretation of the primary mechanism behind Wolff’s law. Biomechanics and Modeling in Mechanobiology, 22(6), 2135-2152.

[2] Grillo, A., & Di Stefano, S. (2023). An a posteriori approach to the mechanics of volumetric growth. Mathematics and Mechanics of Complex Systems, 11(1), 57-86.

[3] Nowak, M., Sokołowski, J., & Żochowski, A. (2020). Biomimetic approach to compliance optimization and multiple load cases. Journal of Optimization Theory and Applications, 184(1), 210-225.

Comments on the Quality of English Language

Moderate editing of the English language is required.

Author Response

Comments 1: While the paper includes a prototype validation, more extensive in vivo or clinical trials could strengthen the conclusions.

Response 1: We fully agree with the suggestion. It was incorporated in the discussion as a future development of the work.

Comments 2: The discussion on material selection could be expanded to include more detail on why specific materials were chosen for the prototype and how they compare to alternatives.

Response 2: A paragraph was added at the “2.4 Computing the Young modulus” subsection, justifying the selection of PEEK.

Comments 3: The effects in the long run must be discussed. The paper does not address this aspect related to the interaction between bone-graft evolving over time (see, e.g., [1,2]).

Response 3: It was also incorporated, as a future work, in the discussion. References were added.

Comments 4: Providing more detailed analysis and discussion of the simulation results and their implications for real-world applications would enhance the paper’s impact.

Response 4: A paragraph was added at subsection “3.2 Regression models” discussing the obtained models.

Comments 5: Some similar approaches already present in the literature must be recalled and compared with (see, e.g., [3]).

Response 5: A paragraph was inserted at the end of subsection “3.3 Optimisation restuls” addressing this issue. Proper references (including [3]) were added.

Reviewer 2 Report

Comments and Suggestions for Authors

 

The paper presents a design approach for the optimization of the unit cell of cranial implants manufactured via additive manufacturing. First, the mathematical definition of the TPMS cell is presented with all the parameters adopted for its design, secondly some configurations of these unit cells are investigated via FEM and CFD to assess their mechanical performance and biocompatibility. Finally, a genetic algorithm is applied to find the best configuration of the design parameters.

The paper has a good introduction with a deep analysis of the state of art, followed by a materials and method section. The results are presented in a clear way. References are up to date and the English language is fine.

Some minor points must be considered before publication:

1.     Lines 196-200: For compression test on scaffold structures, a friction coefficient of 0.1 was adopted from literature (ref 53). In that reference the compression test was performed on Ti6Al4V; hence, are the adopted boundary conditions still valid for PEEK. Have you performed some experimental compression test to verify if the predictions from the FEM are accurate?

2.     Line 204: Was the PEEK modelled as a lunear elastic material? Why don’t you take into account the plastic behaviour of the material?

3.     Line 264: Can you cite some work in literature that report the correct porosity range for bone formation and integration?

4.     Lines 370 and 376: are these lines repeated?

 

For all the previous reasons, the reviewer recommends minor amendments of paper for publication in Technologies.

Author Response

Comments 1: Lines 196-200: For compression test on scaffold structures, a friction coefficient of 0.1 was adopted from literature (ref 53). In that reference the compression test was performed on Ti6Al4V; hence, are the adopted boundary conditions still valid for PEEK. Have you performed some experimental compression test to verify if the predictions from the FEM are accurate?

Response 1: This value was selected because it corresponds to the range reported for the coefficient of friction of PEEK under lubrication, which is done to decrease the effect of the forces in the transverse direction. This explanation, with proper references, was included in subsection “2.4 Computing the Young modulus”.

Comments 2: Line 204: Was the PEEK modelled as a linear elastic material? Why don’t you take into account the plastic behaviour of the material?

Response 2: In this specific simulation, the plastic behaviour of PEEK was not considered due to several key factors: the applied loads were within the yield strength of PEEK, which guarantees linear elastic behaviour, as PEEK has a high yield strength, the induced stresses do not reach the yield point. The main objective was to analyse the initial structural response of the gyroid TPMS scaffold under the given loading conditions, focusing on the linear elastic behaviour to obtain valuable information on stress distribution and deformation without the additional complexity of plastic deformation. In addition, linear elastic analysis is less computationally intensive, allowing faster iterations for preliminary design and optimisation. This simulation serves as a preliminary evaluation, in the future a more detailed analysis incorporating plastic behaviour may be considered.

Comments 3: Line 264: Can you cite some work in literature that report the correct porosity range for bone formation and integration?

Response 3: References were added for supporting the selected range.

Comments 4: Lines 370 and 376: are these lines repeated?

Response 4: The repeated sentence was removed.