Pilocytic astrocytoma (PA) is the most common brain tumor in children. This tumor is usually benign and has a good prognosis. Total resection is the treatment of choice and will cure the majority of patients. However, often only partial resection is possible due to the location of the tumor. In that case, spontaneous regression, regrowth, or progression to a more aggressive form have been observed. The dependency between the residual tumor size and spontaneous regression is not understood yet. Therefore, the prognosis is largely unpredictable and there is controversy regarding the management of patients for whom complete resection cannot be achieved. Strategies span from pure observation (wait and see) to combinations of surgery, adjuvant chemotherapy, and radiotherapy. Here, we introduce a mathematical model to investigate the growth and progression behavior of PA. In particular, we propose a Markov chain model incorporating cell proliferation and death as well as mutations. Our model analysis shows that the tumor behavior after partial resection is essentially determined by a risk coefficient γ, which can be deduced from epidemiological data about PA. Our results quantitatively predict the regression probability of a partially resected benign PA given the residual tumor size and lead to the hypothesis that this dependency is linear, implying that removing any amount of tumor mass will improve prognosis. This finding stands in contrast to diffuse malignant glioma where an extent of resection threshold has been experimentally shown, below which no benefit for survival is expected. These results have important implications for future therapeutic studies in PA that should include residual tumor volume as a prognostic factor.

Pilocytic astrocytoma (PA) is the most common brain tumor in children. This tumor is usually benign and has a good prognosis. Total resection is the treatment of choice and will cure the majority of patients. However, often only partial resection is possible due to the location of the tumor. In that case, spontaneous regression, regrowth, or progression to a more aggressive form have been observed. The dependency between the residual tumor size and spontaneous regression is not understood yet. Therefore, the prognosis is largely unpredictable and there is controversy regarding the management of patients for whom complete resection cannot be achieved. Strategies span from pure observation (wait and see) to combinations of surgery, adjuvant chemotherapy, and radiotherapy. Here, we introduce a mathematical model to investigate the growth and progression behavior of PA. In particular, we propose a Markov chain model incorporating cell proliferation and death as well as mutations. Our model analysis shows that the tumor behavior after partial resection is essentially determined by a risk coefficient γ, which can be deduced from epidemiological data about PA. Our results quantitatively predict the regression probability of a partially resected benign PA given the residual tumor size and lead to the hypothesis that this dependency is linear, implying that removing any amount of tumor mass will improve prognosis. This finding stands in contrast to diffuse malignant glioma where an extent of resection threshold has been experimentally shown, below which no benefit for survival is expected. These results have important implications for future therapeutic studies in PA that should include residual tumor volume as a prognostic factor.