The phenotypic and genetic variations within tumors are central contributors to tumor heterogeneity and represent a major reason for resistance to chemotherapy, which is a primary cause of treatment failure. However, chemoresistance is often overlooked in mathematical modeling studies conducted on in vivo organisms. Additionally, in vitro studies that examine characteristics of tumor cells typically do not account for the spatial mechanisms underlying chemoresistance. Thus, it is essential to develop spatiotemporal mathematical models that can identify both intra- and inter-tumor heterogeneities to better personalize therapies for individual patients and address chemoresistance. Towards this end, here we present a data assimilation prediction pipeline that employs a mathematical model to analyze and predict the spatiotemporal dynamics of breast cancer cells and their response to chemotherapy in vitro. Our model assumes that the breast cancer cell population can be split into two groups: one that survives treatment, and another that is irreversibly damaged and dies due to the treatment. In this study, model calibration and validation rely on data from MCF7 breast cancer cells, which were cultured in wells and treated with different concentrations of doxorubicin for up to 1000 hours. The wells were monitored through fluorescent microscopy to obtain time-resolved data on cell counts and positions, which were then used to generate pixel-resolved cell density maps. To initiate treatment response predictions, we use a training set and we update our forecasts by assimilating weekly measurements into the model parameterization. Our results show that the proposed spatiotemporal modeling approach successfully recapitulates MCF7 cell dynamics across the entire culture well as evaluated by the total well concordance correlation coefficient, CCCwell = 0.99 [0.88, >0.99] (median and range) and on a local pixel-by-pixel basis, CCCpixel = 0.96 [0.91, >0.99]). Additionally, our proposed data assimilation-prediction pipeline achieved a CCCwell = 0.97 [0.44, >0.99] and a CCCpixel = 0.69 [0.35, 0.79]. Thus, we conclude that our model can capture and forecast the spatiotemporal dynamics of MCF7 cells treated with doxorubicin, and we posit that this approach presents a potential avenue for exploring the in silico improvement of preclinical and clinical treatment plans.