(D-139) A Mathematical Model for Predicting the Spatio-temporal Response of Breast Cancer Cells treated with Doxorubicin

Introduction:: Mathematical modeling has the ability to quantify and predict the spatiotemporal development of tumor growth and response to treatment [1]. Prior investigations in our group have focused on interrogating phenomena of chemoresistance and modeling cell growth on in vitro breast cancer subpopulations exhibiting heterogeneous profiles of treatment response. For example, Yang et al. modeled the growth of MCF7 breast cancer cells treated with various regimens of doxorubicin using a set of ordinary differential equations compartmentalizing colonies into a surviving and irreversibly damaged groups [2]. They used time-resolved fluorescent microscopy to non-invasively track the spatial distribution of cell counts over weeks. Using a similar approach, Liu et al. studied in vitro glioma cell growth and performed predictions of radiotherapy treatment response through a data assimilation pipeline [3]. Frequently applied to weather forecasting [4], and more recently to the planning and optimization of cancer therapies [5,6], data assimilation enables the incorporation of newly-gathered data into the model parametrization to inform and update model predictions. In the present study, we extend the two-subpopulation model developed by Yang et al. to explicitly capture the full heterogeneous spatiotemporal development of in vitro MCF7 cells. Additionally, we implement the data assimilation approach inspired by Liu et al. to provide accurate, short-term predictions of treatment response.


Materials and Methods:: Data acquisition

MCF7 breast cancer cells were seeded onto 96-well plates (initial density: 2000 cells/well). After t_dox = 48 hours, doxorubicin was introduced at different concentrations (10, 20, 35, 50, 75, 100, 125, 150, or 300 nM) for 24 hours. Phase contrast and fluorescent images were then collected every 4 hours for up to 40 days and six replicates were gathered for each dose. Fluorescent images were loaded into MATLAB and pixel cell density maps are created to calibrate a two-phenotype model.



Mathematical model

In the pre-treatment phase, cells (N) are assumed to be phenotypically homogeneous, and obey a standard reaction-diffusion equation characterized by exponential growth with proliferation rate g₀, and diffusion rate D. At t = t_dox, the colony splits into two subpopulations: (i) surviving cells (N_s), with initial fraction f_s and following logistic growth with proliferation rate g_s and carrying capacity θ; and (ii) irreversibly damaged cells (N_d), first proliferating at rate g_d and later decreasing to a death rate k_d, with the difference of the two exponentially decaying at rate γ_d.



Predicting the spatiotemporal development of tumor cell density

Predictions of total cell count and spatial cell distribution are performed through a leave-one out data assimilation pipeline. A training set of five replicates was thus used to calibrate the model. Then, weekly measurements allow for updating short-term predictions on the target left-out replicate. Each week-long segment is predicted through a weighted average of the training model parameters, P_training, with the parameters obtained from the measured data P_measure.


Results, Conclusions, and Discussions:: Results: The model is able to reconstruct spatial tumor growth dynamics in all the experimentally-used drug concentrations with a pixel-based concordance correlation coefficient (CCC) between the model calibration and measured pixel cell count of 0.73 [0.58, 0.85] (median and range). The model also recapitulates the temporal evolution of the total cell count with a CCC between the total model calibration and measured cell count >0.99 [0.88, >0.99]. Moreover, our prediction pipeline allowed the forecast of spatial development patterns with a CCC between model prediction and measured pixel cell count of 0.69 [0.35, 0.79]. The total cell count was predicted with a CCC of 0.97 [0.44, >0.99].



Discussions: A rigorous understanding of chemoresistance through the lens of tumor heterogeneity and its patient-specific nature is crucial to improving the care of breast cancer patients. We have proposed a novel experimental-mathematical pipeline to model and predict the total cell number and spatial distribution of in vitro colonies of MCF7 cells over an extended time frame (up to 6 weeks). This duration is marked by elevated amounts of spatial and temporal heterogeneity generated by the cells’ treatment with doxorubicin. The addition of a spatial component to the model developed by Yang et al. represents significant progress in the effort to gain insights on the heterogeneous aspects of tumors which reduce drug efficacy. Spatially resolving the dynamics enables the capture of response heterogeneities at early times, thereby providing an avenue of investigation for systematically predicting and optimizing treatment protocols in the pre-clinical setting.



Conclusions: We have developed a computational-experimental platform that can efficiently capture and forecast the spatiotemporal development of MCF7 cells exposed to doxorubicin in a controlled in vitro setting. These results represent an important step in the effort of quantifying the relationship between chemoresistance and tumor heterogeneity and their effect on treatment efficacy. We posit that our prediction pipeline can be readily applied to clinical data, allowing the personalized forecasting of spatiotemporal tumor development between patient visits.

Acknowledgements (Optional): :

References (Optional): : < ![if !supportLists] >1. < ![endif] >Yankeelov et al., (2013) Clinically Relevant Modeling of Tumor Growth and Treatment Response. Sci. Transl. Med.5,187ps9-187ps9(2013). DOI:10.1126/scitranslmed.3005686

< ![if !supportLists] >2. < ![endif] >Yang et al., (2022) Mathematical characterization of population dynamics in breast cancer cells treated with doxorubicin. Front. Mol. Biosci. 9:972146. doi: 10.3389/fmolb.2022.972146

< ![if !supportLists] >3. < ![endif] >Liu et al., (2023) A data assimilation framework to predict the response of glioma cells to radiation. Mathematical Biosciences and Engineering, 20(1): 318-336. doi: 10.3934/mbe.2023015

< ![if !supportLists] >4. < ![endif] >Navon et al., (2009) Data Assimilation for Numerical Weather Prediction: A Review. Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications, S. K. Park and L. Xu, Eds. Berlin, Heidelberg: Springer, pp. 21–65. doi: 10.1007/978-3-540-71056-1_2.

< ![if !supportLists] >5. < ![endif] >Zahid et al., (2021) Forecasting Individual Patient Response to Radiation Therapy in Head and Neck Cancer With a Dynamic Carrying Capacity Model. Int. J. Radiat. Oncol. Biol. Phys., vol. 111, no. 3, pp. 693–704, Nov. 2021, doi: 10.1016/j.ijrobp.2021.05.132.

< ![if !supportLists] >6. < ![endif] >Zahid et al., (2021) Dynamics-Adapted Radiotherapy Dose (DARD) for Head and Neck Cancer Radiotherapy Dose Personalization. J. Pers. Med. 2021, 11, 1124. https://doi.org/10.3390/jpm11111124

< ![if !supportLists] >7. < ![endif] >Hu et al., (2022) Live-dead assay on unlabeled cells using phase imaging with computational specificity. Nat Commun 13, 713. https://doi.org/10.1038/s41467-022-28214-x

< ![if !supportLists] >8. < ![endif] >Gutierrez et al., (2021) Multifunctional barcoding with ClonMapper enables high-resolution study of clonal dynamics during tumor evolution and treatment. Nat Cancer 2, 758–772. https://doi.org/10.1038/s43018-021-00222-8