A Brownian dynamics tumor progression simulator with application to glioblastoma

Agent-based modeling in cancer biomedicine: applications and tools for calibration and validation

Computational models are not just appealing because they can simulate and predict the development of biological phenomena across multiple spatial and temporal scales, but also because they can integrate information from well-established in vitro and in vivo models and test new hypotheses in cancer biomedicine. Agent-based models and simulations are especially interesting candidates among computational modeling procedures in cancer research due to the capability to, for instance, recapitulate the dynamics of neoplasia and tumor - host interactions. Yet, the absence of methods to validate the consistency of the results across scales can hinder adoption by turning fine-tuned models into black boxes. This review compiles relevant literature that explores strategies to leverage high-fidelity simulations of multi-scale, or multi-level, cancer models with a focus on verification approached as simulation calibration. We consolidate our review with an outline of modern approaches for agent-based models' validation and provide an ambitious outlook toward rigorous and reliable calibration.

Connecting Agent-Based Models with High-Dimensional Parameter Spaces to Multidimensional Data Using SMoRe ParS: A Surrogate Modeling Approach

Across a broad range of disciplines, agent-based models (ABMs) are increasingly utilized for replicating, predicting, and understanding complex systems and their emergent behavior. In the biological and biomedical sciences, researchers employ ABMs to elucidate complex cellular and molecular interactions across multiple scales under varying conditions. Data generated at these multiple scales, however, presents a computational challenge for robust analysis with ABMs. Indeed, calibrating ABMs remains an open topic of research due to their own high-dimensional parameter spaces. In response to these challenges, we extend and validate our novel methodology, Surrogate Modeling for Reconstructing Parameter Surfaces (SMoRe ParS), arriving at a computationally efficient framework for connecting high dimensional ABM parameter spaces with multidimensional data. Specifically, we modify SMoRe ParS to initially confine high dimensional ABM parameter spaces using unidimensional data, namely, single time-course information of in vitro cancer cell growth assays. Subsequently, we broaden the scope of our approach to encompass more complex ABMs and constrain parameter spaces using multidimensional data. We explore this extension with in vitro cancer cell inhibition assays involving the chemotherapeutic agent oxaliplatin. For each scenario, we validate and evaluate the effectiveness of our approach by comparing how well ABM simulations match the experimental data when using SMoRe ParS-inferred parameters versus parameters inferred by a commonly used direct method. In so doing, we show that our approach of using an explicitly formulated surrogate model as an interlocutor between the ABM and the experimental data effectively calibrates the ABM parameter space to multidimensional data. Our method thus provides a robust and scalable strategy for leveraging multidimensional data to inform multiscale ABMs and explore the uncertainty in their parameters.

Data-driven spatio-temporal modelling of glioblastoma

Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding glioblastoma, a malignant form of brain cancer. For each approach, we summarize the scope, drawbacks and assets. We highlight the potential clinical applications of each modelling technique and discuss the connections between the mathematical models and the molecular and imaging data used to inform them. By doing so, we aim to prime cancer researchers with current and emerging computational tools for understanding tumour progression. By providing an in-depth picture of the different modelling techniques, we also aim to assist researchers who seek to build and develop their own models and the associated inference frameworks. Our article thus strikes a unique balance. On the one hand, we provide a comprehensive overview of the available modelling techniques and their applications, including key mathematical expressions. On the other hand, the content is accessible to mathematicians and biomedical scientists alike to accommodate the interdisciplinary nature of cancer research.

SMoRe ParS: A novel methodology for bridging modeling modalities and experimental data applied to 3D vascular tumor growth

Multiscale systems biology is having an increasingly powerful impact on our understanding of the interconnected molecular, cellular, and microenvironmental drivers of tumor growth and the effects of novel drugs and drug combinations for cancer therapy. Agent-based models (ABMs) that treat cells as autonomous decision-makers, each with their own intrinsic characteristics, are a natural platform for capturing intratumoral heterogeneity. Agent-based models are also useful for integrating the multiple time and spatial scales associated with vascular tumor growth and response to treatment. Despite all their benefits, the computational costs of solving agent-based models escalate and become prohibitive when simulating millions of cells, making parameter exploration and model parameterization from experimental data very challenging. Moreover, such data are typically limited, coarse-grained and may lack any spatial resolution, compounding these challenges. We address these issues by developing a first-of-its-kind method that leverages explicitly formulated surrogate models (SMs) to bridge the current computational divide between agent-based models and experimental data. In our approach, Surrogate Modeling for Reconstructing Parameter Surfaces (SMoRe ParS), we quantify the uncertainty in the relationship between agent-based model inputs and surrogate model parameters, and between surrogate model parameters and experimental data. In this way, surrogate model parameters serve as intermediaries between agent-based model input and data, making it possible to use them for calibration and uncertainty quantification of agent-based model parameters that map directly onto an experimental data set. We illustrate the functionality and novelty of Surrogate Modeling for Reconstructing Parameter Surfaces by applying it to an agent-based model of 3D vascular tumor growth, and experimental data in the form of tumor volume time-courses. Our method is broadly applicable to situations where preserving underlying mechanistic information is of interest, and where computational complexity and sparse, noisy calibration data hinder model parameterization.

Network Analysis Identifies Phase Transitions for Tumor With Interacting Cells

Metastasis is the process by which cancer cells acquire the capability to leave the primary tumor and travel to distant sites. Recent experiments have suggested that the epithelial–mesenchymal transition can regulate invasion and metastasis. Another possible scenario is the collective motion of cells. Recent studies have also proposed a jamming–unjamming transition for epithelial cells based on physical forces. Here, we assume that there exists a short-range chemical attraction between cancer cells and employ the Brownian dynamics to simulate tumor growth. Applying the network analysis, we suggest three possible phases for a given tumor and study the transition between these phases by adjusting the attraction strength.

Predicting Confined 1D Cell Migration from Parameters Calibrated to a 2D Motor-Clutch Model

Biological tissues contain micrometer-scale gaps and pores, including those found within extracellular matrix fiber networks, between tightly packed cells, and between blood vessels or nerve bundles and their associated basement membranes. These spaces restrict cell motion to a single-spatial dimension (1D), a feature that is not captured in traditional in vitro cell migration assays performed on flat, unconfined two-dimensional (2D) substrates. Mechanical confinement can variably influence cell migration behaviors, and it is presently unclear whether the mechanisms used for migration in 2D unconfined environments are relevant in 1D confined environments. Here, we assessed whether a cell migration simulator and associated parameters previously measured for cells on 2D unconfined compliant hydrogels could predict 1D confined cell migration in microfluidic channels. We manufactured microfluidic devices with narrow channels (60-μm2 rectangular cross-sectional area) and tracked human glioma cells that spontaneously migrated within channels. Cell velocities (vexp = 0.51 ± 0.02 μm min-1) were comparable to brain tumor expansion rates measured in the clinic. Using motor-clutch model parameters estimated from cells on unconfined 2D planar hydrogel substrates, simulations predicted similar migration velocities (vsim = 0.37 ± 0.04 μm min-1) and also predicted the effects of drugs targeting the motor-clutch system or cytoskeletal assembly. These results are consistent with glioma cells utilizing a motor-clutch system to migrate in confined environments.

A simulation algorithm for Brownian dynamics on complex curved surfaces

Brownian dynamics of colloidal particles on complex curved surfaces has found important applications in diverse physical, chemical, and biological processes. However, most Brownian dynamics simulation algorithms focus on relatively simple curved surfaces that can be analytically parameterized. In this work, we develop an algorithm to enable Brownian dynamics simulation on extremely complex curved surfaces. We approximate complex curved surfaces with triangle mesh surfaces and employ a novel scheme to perform particle simulation on these triangle mesh surfaces. Our algorithm computes forces and velocities of particles in global coordinates but updates their positions in local coordinates, which combines the strengths from both global and local simulation schemes. We benchmark the proposed algorithm with theory and then simulate Brownian dynamics of both single and multiple particles on torus and knot surfaces. The results show that our method captures well diffusion, transport, and crystallization of colloidal particles on complex surfaces with nontrivial topology. This study offers an efficient strategy for elucidating the impact of curvature, geometry, and topology on particle dynamics and microstructure formation in complex environments.

Dynamics of 3D carcinoma cell invasion into aligned collagen

Carcinoma cells frequently expand and invade from a confined lesion, or multicellular clusters, into and through the stroma on the path to metastasis, often with an efficiency dictated by the architecture and composition of the microenvironment. Specifically, in desmoplastic carcinomas such as those of the breast, aligned collagen tracks provide contact guidance cues for directed cancer cell invasion. Yet, the evolving dynamics of this process of invasion remains poorly understood, in part due to difficulties in continuously capturing both spatial and temporal heterogeneity and progression to invasion in experimental systems. Therefore, to study the local invasion process from cell dense clusters into aligned collagen architectures found in solid tumors, we developed a novel engineered 3D invasion platform that integrates an aligned collagen matrix with a cell dense tumor-like plug. Using multiphoton microscopy and quantitative analysis of cell motility, we track the invasion of cancer cells from cell-dense bulk clusters into the pre-aligned 3D matrix, and define the temporal evolution of the advancing invasion fronts over several days. This enables us to identify and probe cell dynamics in key regions of interest: behind, at, and beyond the edge of the invading lesion at distinct time points. Analysis of single cell migration identifies significant spatial heterogeneity in migration behavior between cells in the highly cell-dense region behind the leading edge of the invasion front and cells at and beyond the leading edge. Moreover, temporal variations in motility and directionality are also observed between cells within the cell-dense tumor-like plug and the leading invasive edge as its boundary extends into the anisotropic collagen over time. Furthermore, experimental results combined with mathematical modeling demonstrate that in addition to contact guidance, physical crowding of cells is a key regulating factor orchestrating variability in single cell migration during invasion into anisotropic ECM. Thus, our novel platform enables us to capture spatio-temporal dynamics of cell behavior behind, at, and beyond the invasive front and reveals heterogeneous, local interactions that lead to the emergence and maintenance of the advancing front.