PhysiCOOL: A generalized framework for model Calibration and Optimization Of modeLing projects

Abstract

In silico models of biological systems are usually very complex and rely on a large number of parameters describing physical and biological properties that require validation. As such, parameter space exploration is an essential component of computational model development to fully characterize and validate simulation results. Experimental data may also be used to constrain parameter space (or enable model calibration) to enhance the biological relevance of model parameters. One widely used computational platform in the mathematical biology community is PhysiCell, which provides a standardized approach to agent-based models of biological phenomena at different time and spatial scales. Nonetheless, one limitation of PhysiCell is the lack of a generalized approach for parameter space exploration and calibration that can be run without high-performance computing access. Here, we present PhysiCOOL, an open-source Python library tailored to create standardized calibration and optimization routines for PhysiCell models.

Figure 1.

PhysiCOOL’s contributions and advantages to the PhysiCell ecosystem. PhysiCOOL aims to improve the way researchers design and implement their parameter and calibration studies for models written in PhysiCell. To this end, PhysiCOOL introduces new functionalities, such as a configuration file parser that updates configuration files in an error-free and user-friendly manner. PhysiCOOL also enables users to turn models into black-box models, making the optimization pipeline model-agnostic. In addition, it implements a multilevel parameter sweep routine to optimize models using some target data. Lastly, PhysiCOOL facilitates the integration of third-party libraries, which makes PhysiCell more accessible.

Figure 2.

Model and optimization results for the logistic growth example. (a) Growth curves obtained for different parameter sets (carrying capacity, K, and proliferation rate, r). (b) Optimization results after the completion of the first level of the multilevel optimization algorithm. The heatmap shows the difference, as given by the summed squared error, between the target data and the data produced by each cell’s input parameters. (c) Optimization results after seven levels of the multilevel optimization algorithm. Results converged to the parameters that originated the target data.

Figure 3.

Model and optimization results for the chemotaxis example. (a) Initial model configuration design. Cells (represented as grey circles) were placed close to a domain wall and an oxygen source (represented by the blue arrows) was simulated on the opposite wall, creating a chemotactic gradient that cells could follow. This gradient is illustrated by the colour gradient shown in the figure. (b) Expected model results for cells with different migration bias values. High migration bias populations were expected to migrate in a deterministic manner and follow the oxygen gradient, crossing the domain and arriving at the opposite wall. Cell trajectories are shown as grey dashed lines. On the other hand, cells with low migration bias were expected to move randomly and, thus, present low net displacement values. (c) Optimization results after four levels of the multilevel optimization algorithm. Results converged to the parameters that originated the target data. The colourmap was updated for each level, describing the minimum and maximum error values at the current level.