Genetic algorithm-based optimization of columella shape with FEM surrogate modeling: convergence analysis and application to ossicular chain reconstruction

Ossicular chain reconstruction is a vital surgical approach for restoring hearing in patients with ossicular chain disruption. Despite advancements in prosthetic design, selecting optimal material and geometric configurations remains a challenge due to the complex, nonlinear dynamics of middle ear biomechanics. This study presents a hybrid optimization framework that integrates genetic algorithms (GA) with machine learning-trained finite element (FE) surrogate models to design middle ear columella prostheses with enhanced acoustic performance. Four tympanoplasty models (IIIc, IIIi-M, IVc, IVi-M), based on extended Wullstein classifications, were analyzed using vibroacoustic FE simulations. Surrogate models based on Random Forest regression were trained on 5000 FEM samples per type, capturing key input-output relationships across geometric and material variables. These models enabled over 1000-fold acceleration in optimization time compared to full FEM runs, allowing GA-based design exploration across 40 generations with 200 individuals each. The optimized prosthesis designs favored low-density (1000-1600 kg/m3) and moderately stiff (2-6 MPa) materials, confirming clinical preferences for cartilage. Geometries with smaller cross-sectional areas and tapered shapes consistently improved high-frequency sound transmission. The framework also revealed multimodal design landscapes, underscoring the importance of global search strategies. This work demonstrates a scalable, clinically relevant approach to prosthesis optimization that supports patient-specific customization and efficient design-space exploration, with potential to improve outcomes in otologic surgery.