**1. Introduction**

The healthcare sector must continually deal with aspects of economic nature: the minimization of both the surgical timing and the complete recovery of the patient represents one of the primary objectives in this regard. This goal has led to continuous progress and innovations with the clear aim of obtaining highly performing implants for the individual patient. In light of this, one of the most important challenges involving the field of medicine is represented by the manufacture of highly customized prosthetic implants able to restore to the patient both the functionality and the natural conformation of the damaged part [1]. The need to perfectly reproduce the bone conformation of the reference patient requires a reliable procedure based on certified protocols that guarantees the perfect fitting between the prosthetic implant and the host area to be healed [2].

**Citation:** Palumbo, G.; Ambrogio, G.; Crovace, A.; Piccininni, A.; Cusanno, A.; Guglielmi, P.; De Napoli, L.; Serratore, G. A Structured Approach for the Design and Manufacturing of Titanium Cranial Prostheses via Sheet Metal Forming. *Metals* **2022**, *12*, 293. https://doi.org/10.3390/ met12020293

Academic Editor: Mieczyslaw Jurczyk

Received: 30 December 2021 Accepted: 1 February 2022 Published: 8 February 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

In this scenario, all the aspects involved are equally essential, starting from the appropriate choice of the prosthesis material, passing through the acquisition and manipulation of the damaged area geometry, up to the most appropriate manufacturing technology. With reference to the fabrication of cranial prostheses, there are several proofs of the importance deriving from the use of different Computer Aided Design (CAD) and advanced production platforms [3]. In fact, CAD tools combined with advanced patient scanning techniques have drastically transformed the process of designing prosthetic devices, effectively replacing the more traditional manual approaches based on cast and invasive techniques. In addition, these methods have made it possible to reduce costs and response times [4,5]. Moreover, typical materials adopted for biomedical applications must meet different requirements such as: (i) a certain chemical composition to avoid adverse tissue reactions, (ii) excellent resistance to degradation in the case of permanent prostheses, (iii) load-bearing capacities, (iv) capability to absorb the impacts and (v) good wear resistance for prostheses involved in reciprocal sliding [6].

In this context, metallic materials such as titanium (Ti) alloys, thanks to their capability to fully match the above-mentioned requirements, appear to be promising candidates. Such alloys, in fact, are constantly growing in terms of use in the biomedical field [7] due to their high biocompatibility, excellent resistance characteristics coupled with an appropriate elastic modulus, as well as a high resistance to corrosion (even if compared to the performing chromium-cobalt alloys) [8,9]. The best fitting between the patient's anatomy and the geometry of the prosthesis, as well as required by aesthetic aspects, is motivated by the need to minimize the risk of infection due to micromotions between the implant and the surrounding bone [10].

For all these aspects, in addition to motivating the manufacture of complex shapes (e.g., very small radii, complex profiles and, in some cases, the presence of undercuts), customized prostheses require prohibitive tolerances for most of the manufacturing processes. Innovative processes, such as Single Point Incremental Forming (SPIF) and Superplastic Forming (SPF) can be considered as viable solutions. In fact, as demonstrated in previous studies, titanium custom prostheses can be successfully manufactured by both SPF and SPIF [11,12].

During the SPF process a metal sheet is plastically deformed at a high temperature by means of a pressurized gas. Specifically, this type of manufacturing process is intended for materials capable of emphasizing their deformation properties under appropriate operating conditions both in terms of temperature and strain rate [8]. Furthermore, SPF is a costeffective method of producing a small to medium number of complex parts obtained with expensive materials and low formability at room temperature [13]. The process can be made more competitive by adopting less expensive tools (for example ceramic dies). The process temperature and gas pressure must be suitably selected according to the geometry and the material. For this scope, a numerical/experimental approach is fundamental during the whole design process. In fact, to obtain a sound complex component, an optimized manufacturing process involves a Finite Element (FE) modelling capable to correctly predict the alloy behaviour [14–16].

SPIF is based on the idea to apply a plastic deformation on a flat sheet, clamped at its periphery, by a rotating tool which describes concentric and decreasing spirals reproducing the 3D profile of the desired geometry. In this way, the material is incrementally stretched, up to reach the final shape [17]. Additionally, in this case the process design is a critical issue since the quality of the results, in terms of minimum thickness and accuracy, are strongly affected by the tool trajectory: parameters such as tool pitch (p), wall inclination angle (α), or the 3D shape positioning with respect to the flat surface need to be properly calibrated in order to optimize the quality of the formed part [18]. For this reason, when a complex profile has to be manufactured, a numerical/experimental approach is suitable for calibrating the above-mentioned parameters. Nevertheless, SPIF is a really cheap technology for producing small batch and, mainly, single part such as in custom made

prosthesis application since it does not require any additional dedicated equipment but only general-purpose tool and clamping frame [19]. ‐

The aim of the present work is to provide an effective methodology for the design and subsequent fabrication of a customized cranial prosthesis in Ti6Al4V-ELI, validated by means of in vivo tests. In particular, a numerical/experimental design method was proposed for two different innovative sheet metal forming processes (SPF and SPIF) aimed to the fabrication of the prosthetic implants. ‐

The Computed Tomography (CT) scan images were used to generate a three-dimensional model of the sheep's damaged skull. Such geometrical acquired data were properly modified via CAD and allowed to obtain the target geometry on which the study was based. For both investigated manufacturing processes, a Finite Element approach was used to: (i) design the gas pressure (for the SPF process); (ii) define the tool trajectory (for the SPIF process). The post forming characteristics, such as thickness distributions and the shape accuracy of the prostheses, were also evaluated. Finally, the in vivo response of the prostheses manufactured using both the processes was assessed by means of histological analyses on tissues extracted after 3 and 6 months from 16 sheep in which they were implanted. ‐

#### **2. Materials and Methods**
