Dynamic tomographic imaging can visualize 3D biomechanical systems in action at a very high resolution. Very few imaging techniques make this possible, which makes the modality very desirable for answering questions about the dynamics of biological samples. However, dynamic tomographic imaging of biological samples is complex for three reasons. Firstly obtaining contrast in living soft tissue can be difficult. Secondly, the sample is exposed to ionizing radiation during imaging, which is harmful to live samples. Finally, dynamic tomographic reconstruction is complex, and the approach depends on the dynamics of the object. In this thesis, sperm cells were chosen as the sample of choice because studying their 3D tail-beating pattern is important for understanding factors related to fertility. Furthermore, sperm cells are an excellent object for probing the limits of 3D dynamic imaging systems because they are small, fast-moving and easy to come by. The main results presented are threefold. Firstly, a non-toxic labelling method based on ironoxide nanoparticles was developed for imaging the sperm, and it is shown that labelling with nanoparticles is also practical for dynamic tomographic reconstruction. Secondly, a practical approach to assessing the functional radiation damage caused to living sperm by synchrotron radiation is presented. Finally, a high-level parallel programming approach to tomographic reconstruction was developed, which is hardware-independent and especially well suited for speeding up sparse reconstruction.