Continuous Convolution for Automated Measurement of Sperm Flagella

Quantifying sperm flagellar beating behavior (e.g., beating amplitude, frequency, and wavelength) plays a crucial role in biological research, clinical diagnostics, and the design of sperm-inspired microrobots. However, existing computational methods struggle to accurately and efficiently analyze the highly dynamic, complex, and fine structures of sperm flagella, especially when portions of the flagellum become invisible due to three-dimensional out-of-focus beating. This paper proposes an automated high-throughput tool for quantitative analysis of sperm flagellar beating. The core innovation is continuous convolution (CConv), which adaptively captures the irregular, time-varying patterns of sperm flagella while ensuring continuity in segmentation outputs, even in the presence of locally invisible regions caused by out-of-focus motion. CConv can be integrated into various neural network architectures as a plug-and-play module. Extensive experiments demonstrate that integrating CConv consistently improves the accuracy and continuity of flagella segmentation across different networks. Furthermore, utilizing a curvature-based approach, we quantified key flagellar beating parameters, including length, amplitude, frequency, and wavelength. Applying the high-throughput tool on 1200 sperm revealed that sperm from fertile donors had significantly higher flagellar beating frequency than sperm from infertile patients. The proposed automated tool unlocks high-throughput, quantitative analysis of sperm flagellar beating, showing the potential for applications in reproductive biology and engineering research. The codes and datasets will be released at https://github.com/Goldfish-Yu/CConv.