Deformable image registration plays a crucial role in medical imaging by aligning anatomical structures across multiple datasets, essential for accurate diagnosis and treatment planning. However, existing deep learning-based deformable registration models often face challenges ensuring anatomical plausibility, leading to unnatural deformations in critical brain structures. This paper proposes a novel framework integrating Bayesian optimization to address these challenges, focusing on registering 3D point clouds representing brain structures. Our method uses probabilistic modeling to optimize non-rigid transformations, providing smooth and interpretable deformations that align with anatomical constraints. The proposed framework is validated using MRI data from patients diagnosed with hypoxic-ischemic encephalopathy (HIE) due to perinatal asphyxia. These datasets include brain scans taken at multiple time points, enabling the modeling of structural changes over time. By incorporating Bayesian optimization, we enhance the accuracy of the registration process while maintaining anatomical fidelity. Our results demonstrate that the approach provides interpretable, anatomically plausible deformations, outperforming conventional methods in accuracy and reliability. This work offers an improved tool for brain MRI analysis, aiding healthcare professionals in better understanding disease progression and guiding therapeutic interventions.