(B-68) Emulating spatio-temporal dynamics of multi-cellular and multi-scale systems proves challenging with machine learning

Introduction:
High-resolution models are increasingly necessary to capture emergent properties of complex multi-scale biological systems. Agent-based models (ABMs) are rule-based models that simulate multi-cellular systems using individual agents' (cells’) behaviors and interactions, making them well-suited to model emergent dynamics such as the development of biological tissues or the spread of infectious diseases. However, the computational costs of running ABMs for model tuning and analysis can be prohibitive, necessitating the use of statistical emulation (SE) to generate computationally cheaper models. SE is a mapping of model inputs to outputs via statistical machine and deep learning. Here, we explore the use of SE to model the development of tumors using ARCADE, a previously developed ABM with realistic and dynamic vascular networks. Network analysis and average hemodynamics of the vasculature are used as features of the SE model. Results suggest that while temporal information is the most predictive of emergent behavior, most emergent properties are not predictable.






Materials and Methods:

ARCADE simulations

Simulations use the ARCADE framework to characterize a tumor microenvironment [1]. The simulations account for functional coupling across different cell populations and between cells and the surrounding vasculature. This multi-regulatory landscape predicts vascular collapse/remodeling due to tumor growth and necrotic core formation, among other emergent properties, characterizing hallmarks of cancer [2].







Machine learning models

Python package sklearn was used to build machine learning models, which included an elastic net regressor (MLR), support vector regressor (SVR), random forest (RF), and multi-layer perceptron (MLP) [3]. We also create network models using Keras that are tuned to incorporate temporal information [4]. The input features to the machine learning models consist of summaries of the vasculature hemodynamic and graph metrics of the vasculature, including betweenness and closeness, to account for spatial information. The targets for the models were the growth, activity, and symmetry of the colony after two simulated weeks (Figure 1).





Hyperparameter selection and cross-validation

A sobol random search was used to select the tested hyperparameters during cross-validation using the scipy package in Python [5]. Each set of sobol hyperparameters was used to generate an independent model. The model with the best coefficient of determination R²_val across all hyperparameters during 10-fold cross-validation was selected for training and testing evaluation.






Results, Conclusions, and Discussions:Our results indicate that initial topological and hemodynamic vasculature conditions are limited in their utility to predict emergent behavior of in silico tumors. Specifically, vasculature features from the initial timepoint are not predictive of emergent behaviors that take place throughout the simulation. Spatial features, such as the tumor’s center location within the microenvironment, also have little impact on predictive power (Figures 2 and 3).



Features accounting for temporal effects are more predictive of the target behaviors. Similar analyses at timepoints toward the end of the simulation provided better predictive performance. Additionally, models that incorporated temporal data into their training also had increased performance. These findings suggest that incorporating temporal features into machine learning models can improve their predictive performance, which could have important implications for more efficient analysis and prediction of complex systems (Figure 4).



Incorporating time-dependent features into the machine learning models is more effective for predicting emergent behaviors of in silico tumors. Specifically, the analysis revealed that temporal features, such as how the vasculature changes over the course of the simulation, were more predictive of emergent behaviors than initial vasculature or spatial features. Additionally, deep learning networks that incorporated temporal data into their training showed increased predictive performance compared to those that did not. These results highlight the importance of considering time-dependent factors in the modeling and analysis of complex systems.




Acknowledgements (Optional):

References (Optional) :
[1] Yu, J. S., & Bagheri, N. (2020). Agent-based models predict emergent behavior of heterogeneous cell populations in dynamic microenvironments. Frontiers in Bioengineering and Biotechnology, 8, 249.




[2] Fouad, Y. A., & Aanei, C. (2017). Revisiting the hallmarks of cancer. American journal of cancer research, 7(5), 1016.




[3] Pedregosa et al. (2011). Scikit-learn: Machine Learning in Python.




[4] Chollet, F., & others. (2015). Keras. GitHub. Retrieved from https://github.com/fchollet/keras




[5] Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., … SciPy 1.0 Contributors. (2020). SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17, 261–272. https://doi.org/10.1038/s41592-019-0686-2