Glioma stem cells (GSCs) are considered a major driver of glioblastoma (GBM) progression and are highly resistant to standard cytotoxic treatments. If outcomes of GBM patients are to be improved, treatments that target GSCs are urgently needed. BMP4 has been shown to drive differentiation of GSCs, increase sensitivity to radiotherapy, slow growth and increase survival times in animal models in a subset of cases. To assess the potential of BMP4 as a differentiation therapy, we develop a mathematical model that describes the growth of a GBM tumor via a hierarchy of GSCs, progenitor cells and terminally differentiated cells. To simulate treatment, we incorporate the differential sensitivity to radiation of these three cellular subpopulations as well as the effects of BMP4 on the abundance of GSCs. We parametrize our model using experimental data from twelve patient-derived GSC lines, on which we measured response to radiotherapy and population growth with and without exposure to BMP4. Cell lines were typically more sensitive to radiotherapy after two days of BMP4 treatment but population growth can either increase or decrease after seven days of exposure to BMP4. To explain this effect in our model we introduce two sensitivities to BMP4: the first describes the effect of BMP4 on GSC self-renewal and the second describes the effect of BMP4 on the proliferative capacity of progenitor cells produced by GSCs. To identify key parameters that drive successful treatment we perform global sensitivity analysis which identifies key parameters for BMP4 efficacy including proliferation rate and self-renewal sensitivity of GSCs. We then compare two treatment schedules: a single dose of BMP4 at resection and continuous delivery of BMP4 from resection till the end of radiotherapy. Due to the short half-life of BMP4 and its synergy with radiotherapy, continuous delivery of BMP4 during radiotherapy is more effective than a single dose prior to radiotherapy. We then perform a series of virtual clinical trials, stratified by tumor proliferation rate and GSC self-renewal sensitivity, which allows us to estimate the probability of observing a successful early-phase clinical trial for various virtual patient cohorts. We find that trials that selected the subset of patients with more proliferative GBMs were more likely to lead to significant improvements in survival. Significance: Targeting glioma stem cells with BMP4 provides a novel opportunity to shift the complex cellular ecosystem of gliomas to enhance treatment efficacy. Mathematical modelling can facilitate optimal patient tumor feature selection when designing successful clinical trials.