Mathematical Modeling and Statistical Analysis of Deep Learning Techniques for Brain Tumor Segmentation using MRI Scans

Abstract

This study presents a mathematical and statistical framework for analyzing the performance of deep learning models applied to brain tumor segmentation using MRI scans. Models such as 3D U-Net, PSPNet, DeepLabV3, and ResNet50 are evaluated using quantitative metrics, including the Dice coefficient, Hausdorff distance, sensitivity, specificity, and false positive/negative rates. The segmentation process is modeled mathematically to assess the accuracy and precision of tumor boundary delineation. Among the models, 3D U-Net demonstrates superior performance in boundary demarcation and overall segmentation accuracy, achieving the lowest Hausdorff distance and a high Dice coefficient.Computational analysis includes model parameters, training time, and GPU memory usage, emphasizing the feasibility of deploying these models in clinical settings with resource constraints. Statistical measures such as sensitivity, specificity, and false positive rates further validate the diagnostic capabilities of the models. The results reveal that the 3D U-Net model provides the best trade-off between computational efficiency and segmentation accuracy, making it a viable choice for neuro-oncology applications. The findings underscore the importance of leveraging mathematical models and statistical analyses to enhance early tumor detection, optimize treatment planning, and improve patient outcomes. This study concludes that integrating these models into clinical workflows offers significant potential to transform brain tumor diagnostics, particularly in resource-limited settings.