The clinical management of cancer includes the collection of measurements over time to assess tumour growth and treatment response. These longitudinal data contribute to characterise crucial clinical endpoints, such as progression to higher-risk disease and treatment failure. However, many tumours are treated right after diagnosis without collecting longitudinal data, and cancer monitoring protocols may include infrequent measurements. These situations hinder disease prognosis and may lead to treatment excesses and deficiencies, which can respectively affect the patients’ quality of life and life expectancy. To facilitate the estimation of disease dynamics and better guide ensuing clinical decisions in data scarce scenarios, we investigate inverse problems enabling the reconstruction of earlier tumour stages by using a single spatial tumour dataset and a biomathematical model describing disease dynamics [1]. We focus on prostate cancer, for which a single MRI at diagnosis is pivotal to decide whether the patient can benefit from active surveillance or whether treatment is immediately required. We describe tumour dynamics with a phase-field model driven by a generic nutrient that follows reaction-diffusion dynamics. The model is completed with another reaction-diffusion equation for the local production of prostate-specific antigen, which is a key prostate cancer biomarker. By building on our prior analytical results [2] and the classical Landweber scheme, we explore iterative reconstruction algorithms with adaptive step size to enable accurate and fast reconstruction of early states of prostate cancer growth. A simulation study of these algorithms demonstrates high quality in the tumour reconstructions even in scenarios with long time horizons and noisy data [1]. Thus, although further investigation of our methods is required, our reconstructions could potentially enhance the clinical assessment of tumour dynamics with a single imaging dataset (e.g., at diagnosis) and, hence, contribute to more accurate and efficient management of the disease for each patient. REFERENCES [1] Beretta, E., Cavaterra, C., Fornoni, M., Lorenzo, G., & Rocca, E. (2024). arXiv:2409.12844. [2] Beretta, E., Cavaterra, C., Fornoni, M., Lorenzo, G., & Rocca, E. (2024). SIAM Journal on Applied Mathematics, 84(5), 2000-2027.