I. Introduction  
A. Contributions of this Paper  
B. Organization of the Paper  

II. Generative Adversarial Networks  
A. Architecture of GANs  
B. Training of GANs  
C. Objective Function of GANs  

III. Applications of GANs in Biomedical Image Analysis  
A. Image synthesis  
B. Image Segmentation  
C. Image Reconstruction  
D. Image Detection  
E. Image Denoising  

IV. Evaluation Metrics  
A. Inception Score (IS)  
B. Maximum Mean Discrepancy (MMD)  
C. Multi-scale Structural Similarity Index Measure (MS-SSIM)  
D. Fréchet Inception Distance (FID)  
E. Peak signal-to-noise ratio (PSNR)  
F. Dice Score (DS)  
G. Classification Performance Metrics (Precision and Recall)  

V. The Mode Collapse Problem  
B. Identification  
C. Quantification  
D. Solutions to the Problem  

VI. The Non-Convergence Problem  
A. Definition  
B. Identification  
C. Quantification  
D. Solutions to the Problem  

VII. The Instability Problem  
B. Identification  
C. Quantification  
D. Solutions to the Problem  

IX. Challenges and Future Research Directions  
A. The Mode Collapse Problem  
B. The Non-convergence Problem  
C. Instability Problem  
D. Evaluation Metrics  

X. Conclusion