# Topology Optimization of Biomedical Wrist Orthosis Using Tough Photopolymer Resin

David Bassir, Sofiane Guessasma, Nadhir Lebaal, Gauthier Brunel, Axel Choquet, Haochen Chang

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## To cite this version:

David Bassir, Sofiane Guessasma, Nadhir Lebaal, Gauthier Brunel, Axel Choquet, et al., Topology Optimization of Biomedical Wrist Orthosis Using Tough Photopolymer Resin. E3S Web of Conferences, 2025, 6th International Conference on Multidisciplinary Design Optimization and Applications (MDOA 2024) Paris, France, October 16-19, 2024, 631, pp.02003. 10.1051/e3sconf/202563102003 . hal-05119515

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# Topology Optimization of Biomedical Wrist Orthosis Using Tough Photopolymer Resin

David Bassir<sup>1,2,a)</sup>, Sofiane Guessasma<sup>3,b)</sup>, Nadhir Lebaal<sup>4,c)</sup>, Gauthier Brunel<sup>2,d)</sup>, Axel Choquet<sup>2,e)</sup>, François Gleyzon<sup>2,f)</sup>, Haochen Chang<sup>2,g)</sup>

**Abstract** : This paper presents a study case on the structural topology optimization of biomedical wrist orthosis. The manufacturing process integrates photosensitive resign that enables production of geometries that are both impact-resistant and exhibit a smooth, refined surface finishing which is essential for biomedical applications. The 3D printing is based on Digital Light Processing (DLP). Based on extensive biomechanical studies for accurate simulation parameters, four loading cases were defined for topology optimization. Maximum stresses and displacements were considered at upper limits for the optimization problem with weight reduction.

## TOPOLOGY OPTIMIZATION OF BIOMEDICAL DEVICES

Topology optimization [1], [2], a key technique in geometric engineering, is rapidly advancing applications in the medical and biomedical sectors. Far from being purely academic, it is transforming healthcare. Recent breakthroughs in computational methods have revolutionized prosthetics and orthopedics, greatly improving mobility and quality of life for individuals facing physical challenges (Figure 1). Moreover, topology optimization plays a crucial role in the development of innovative medical devices from implants to surgical tools enhancing their performance and biocompatibility. By carefully balancing complex factors like material selection, this approach ensures that biomedical devices integrate smoothly with biological systems. In the following, we focus on the optimization of a wrist orthosis component using photosensitive resign for the 3D manufacturing [3].

<figure><img src="image_3.png" /><figcaption>Figure 1: Hand-Feet-Neck biomedical orthosis.</figcaption></figure>

A standardized workflow was implemented to integrate experimental procedures aimed at establishing the material properties required for Computer-Aided Design (CAD) and Finite Element Analysis (FEA). The primary application

<footnote n="1"><sup>1</sup> Smart Structural Health Monitoring and Control Laboratory, DGUT-CNAM, Dongguan University of Technology, China</footnote>

<footnote n="2"><sup>2</sup> IRAMAT UMR CNRS 7065, UTBM, Rue du Chateau, 90010 Belfort Cedex, France</footnote>

<footnote n="2"><sup>2</sup> INRA, BIA, rue de la géraudière, 44316 Nantes, France</footnote>

<footnote n="3"><sup>3</sup> ICB-COMM, Université de Technologie de Belfort-Montbéliard, France</footnote>

<footnote>Corresponding author: a) david.bassir@utbm.fr;</footnote>

<footnote>b) sofiane.guessasma@inra.fr; c) nadhir.lebaal@utbm.fr;</footnote>

<footnote>d) gauthier.brunel@utbm.fr; e) axel.choquet@utbm.fr; f) francois.gleyz@utbm.fr; g) haochen.chang@utbm.fr</footnote>
domain encompassed prosthetics and orthoses, with the objective of addressing a variety of anatomical regions for reconstructive and supportive purposes.

For the fabrication process, Digital Light Processing [4] was selected as the 3D printing technology of choice. The printer, featuring a build platform with dimensions of 30 cm × 30 cm, operates with high precision (~50 µm), utilizing a photosensitive resin. This configuration enables the production of geometries that are both impact-resistant and exhibit a smooth, refined surface finish, which is essential for biomedical applications.

Material characterization was conducted using tensile testing on three distinct specimen orientations: lateral (LA), longitudinal (NO), and thickness (LG). These orientations were specifically chosen to assess anisotropic material behavior resulting from the layer-by-layer nature of additive manufacturing. The experimental setup aimed to replicate diverse loading conditions to simulate real-world biomechanical scenarios.

The calculated mean values of Poisson's ratio (v) for each printing orientation with the standard deviation were as follows:
LA: 0.410 ± 0.137 ; NO: 0.288 ± 0.113 ; LG: 0.381 ± 0.143. These findings indicate that the LA orientation exhibits the highest average Poisson's ratio, signifying a greater transverse strain relative to axial strain under tensile loading. In contrast, the NO orientation demonstrated the lowest average value, reflecting reduced transverse deformation.

Furthermore, the Young's modulus (E) was determined from the stress-strain responses for each printing direction: LA: 18.63 Mpa ; LG: 22.19 Mpa ; NO: 17.99 Mpa. Although slight variations were observed (approximately 10 MPa), the results remained within acceptable experimental uncertainty. The LG orientation exhibited the highest modulus, suggesting superior stiffness. These directional differences will be incorporated into the calculation of the orthosis' safety factor during subsequent design stages.

Potential sources of variability, including minor manufacturing inconsistencies and specimen-specific anomalies, were documented as part of the experimental record. In addition, microscopic post-test analysis provided further insights into the fracture mechanisms and surface morphology, which will be instrumental for refining material models used in FEA simulations.

## BOUNDARY AND LOADING CONDITIONS

Boundary conditions play a critical role in FEM simulations conducted in this study. These constraints include fixed supports that restrict specific degrees of freedom and carefully defined loading scenarios, both of which are essential to achieve accurate and reliable results in topology optimization. The application of realistic physiological loads ensures that the simulations reflect patient-specific use cases. Furthermore, standardized angular values for wrist and forearm movements, derived from validated medical references, are incorporated into the models (Figure 2). These angles facilitate the simulation of functional motion and support kinesthetic analysis of bone displacement under dynamic loading conditions.

<figure><img src="image_4.png" /><figcaption>Figure 2: Boundary conditions illustrating Flexion-Extension (FE) and Radial-Ulnar Deviation (RUD) movements. Left: sagittal view showing flexion and extension. Right: palmar view depicting ulnar and radial deviation. Red arrows indicate applied loading directions, while blue arcs represent joint rotational movements [5].</figcaption></figure>
Forces and moments generated by wrist flexors, extensors, and deviators were systematically defined to establish accurate simulation parameters. Based on extensive biomechanical studies, typical flexion activities produce maximum forces approaching 30N. Relevant table (1) and figures (2 and 3) present detailed distributions of forces and corresponding moments, emphasizing the necessity of precise loading conditions for both orthosis design and simulation reliability. In this study, these datasets were directly used to assign boundary and loading conditions within the simulation environment, ensuring realistic replication of physiological stresses.

<table><caption>Table 1: Maximum force for the wrist summarized from literature [6], [7].</caption><thead><tr><td>Movement</td><td>Maximum force [N]</td></tr></thead><tbody><tr><td>Flexion</td><td>30</td></tr><tr><td>Extension</td><td>25</td></tr><tr><td>Radial deviation</td><td>30</td></tr><tr><td>Ulnar deviation</td><td>30</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Figure 3: Applied force flexion.</figcaption></figure>

MULTIPLE LOAD OPTIMIZATION

All four primary wrist motions, flexion, extension, ulnar deviation, and radial deviation were integrated into the computational analyses, each contributing critically based on insights from preliminary research. The primary objective of the optimization process was to minimize structural compliance while applying constraints on either mass or volume; notably, both approaches produced comparable outcomes during validation tests. Exclusion zones were strategically defined to encompass the peripheral regions of the geometry, thereby preserving essential anatomical features throughout the optimization procedure. Additionally, the material retention parameter, varying between 0 and 1, was carefully adjusted to reduce discontinuities and prevent the formation of isolated or floating elements in the final optimized design.

To address diverse load cases efficiently, topology optimization was consolidated across all four movements rather than conducting separate optimizations for each (Equation 1). This holistic approach sought to find an optimal geometry that balanced performance across all scenarios, enhancing robustness and durability of the orthosis. Equal weighting was applied to each movement during the density- based optimization problem.

$$ \left\{ \begin{array}{l} \text{Objective for Multi-loading cases : Min (Weight)} \\ \quad \text{Max Stress} < \text{Stress Limit} \\ \quad \text{Max Deflexion} < \text{Deflexion limit} \\ \quad \text{Weight retained } \alpha \text{ in term of %} \\ \text{Parameters are densities at each FE} \end{array} \right. \qquad (1) $$

Here, $\alpha$ represents the percentage of retained material, tested across different values to strike the optimal balance between mass reduction and stress distribution. Consistent mesh quality was maintained throughout all simulations, previously validated through convergence studies. Uniformity in material properties and boundary conditions across simulations ensured reliable comparability of results. Systematically adjusting the mass parameter allowed for exploration of diverse geometries, identifying configurations that best met performance and stability criteria. Five different topology optimizations were conducted for different value of $\alpha$ in [30%; 100%].
RESULTS

For this section, Python plots were generated to summarize the stress and displacement results across the four considered cases. It is noteworthy that stress significantly increases for the geometry at $\alpha = 40\%$ (Figure 4), potentially due to a mesh error (it is therefore not a value to account for). Moreover, the simulations exhibited variability in their outcomes despite identical initial conditions, highlighting potential robustness challenges within the ANSYS topology optimization process.

<figure><img src="image_6.png" /><figcaption>Figure 4: (a) Maximum equivalent constraints [MPa], (b) Maximum displacement measured [mm].</figcaption></figure>

Regarding displacements, they consistently escalate across simulations, following a predictable trend. Notably, around $\alpha = 50\%$ (Figure 5), displacements show a pronounced increase, nearly doubling those observed in the baseline geometry ($\alpha = 100\%$). These observations underscore the dynamic nature of topology optimization outcomes, influencing both stress distribution and displacement characteristics under varying mass retention scenarios.

<figure><img src="image_7.png" /><figcaption>Figure 5: Topology optimization results.</figcaption></figure>
CONCLUSION

In summary, the topology optimization studies have identified distinct trends correlating stress constraints and displacement responses with retained mass. Notably, marked variations emerge near the 50% retention level, suggesting this as an optimal point for geometry selection. While displacements increase substantially beyond this threshold, stress levels remain within the elastic range defined by tensile testing. Overall, this investigation establishes a robust foundation for the topology optimization of a wrist orthosis and offers a platform for future work focused on detailed characterization of its material properties and mechanical performance.

REFERENCES

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[6] Anabela Faria, 'Additive Manufacturing of Custom-Fit Orthoses for the Upper Limb'.

[7] D. Popescu, F. Baciu, D. Vlăsceanu, R. Marinescu, and D. Lăptoiu, 'Investigations on the Fatigue Behavior of 3D-Printed and Thermoformed Polylactic Acid Wrist-Hand Orthoses', *Polymers*, vol. 15, no. 12, p. 2737, Jun. 2023, doi: 10.3390/polym15122737.