We report on the modeling of a photopolymerizable hydrogel and its application as a replacement of the interior of the intervertebral disc (so called Nucleus Pulposus). The hydrogel is initially injected in its liquid form and then photopolymerized via a small catheter. Therefore, also the light necessary for the photopolymerization is constrained to a small light guide to keep the surgical procedure as minimally invasive as possible. Hence, the hydrogel is photopolymerized inside. For applications with restricted physical access and illumination time, such as an Nucleus Pulposus replacement, photopolymerization of volumes with a large volume/illumination-area ratio becomes highly challenging. During polymerization, the material's absorption and scattering coefficients change and directly influence local polymerization rates. By understanding and controlling such polymerization patterns, local material properties can be engineered (e. g. elastic modulus, swelling ratio), to match the set of mechanical requirements for the implant. Thus, it is essential to better understand and model photopolymerization reactions. Experiments were conducted by polymerizing a hydrogel in a column-like volume using an optical fiber for light delivery. Quantitative scattering and absorption values as well as monomer conversion rates of the hydrogel sample were validated using a newly established Monte Carlo model for photopolymerization. The results were used to study and predict 3D polymerization patterns for different illumination configurations. In particular, we show an example of a lumbar intervertebral disc replacement where the jelly core of the intervertebral disc (Nucleus Pulposus) is replaced by an in situ photopolymerized hydrogel. The results provide insights for the development of novel endoscopic light-scattering polymerization probes paving the way for a new generation of implantable hydrogels.