Medical image segmentation is a pivotal task in computer vision, and is essential for applications such as diagnosis, treatment planning, and disease monitoring. Accurate segmentation enables precise delineation of anatomical structures and pathological regions, which is critical for effective clinical decision-making. However, traditional convolutional modules face challenges in capturing complex feature relationships due to their linear nature, and the segmentation results might be discontinuous and inaccurate. To address these issues, we propose U-CKAM, integrating convolutional Kolmogorov-Arnold Network (C-KAN) modules and Markov Random Fields (MRF) modules into the U-KAN model. Specifically, C-KAN modules apply a learnable non-linear activation function to each element before summing them, enhancing the feature extraction capabilities. Additionally, integrating the output of the neural network with the MRF module improves the continuity and accuracy of the segmentation results by modeling spatial dependencies. Extensive experiments on several medical datasets demonstrate that the proposed model performs better in segmentation tasks compared with the original U-KAN model and other U-Net variants. Our study highlights that optimizing convolutional layers and incorporating MRF can effectively improve the accuracy of medical image segmentation.