Oxygen-Driven Tumour Growth Model: A Pathology-Relevant Mathematical Approach

Geometric analysis enables biological insight from complex non-identifiable models using simple surrogates

An enduring challenge in computational biology is to balance data quality and quantity with model complexity. Tools such as identifiability analysis and information criterion have been developed to harmonise this juxtaposition, yet cannot always resolve the mismatch between available data and the granularity required in mathematical models to answer important biological questions. Often, it is only simple phenomenological models, such as the logistic and Gompertz growth models, that are identifiable from standard experimental measurements. To draw insights from complex, non-identifiable models that incorporate key biological mechanisms of interest, we study the geometry of a map in parameter space from the complex model to a simple, identifiable, surrogate model. By studying how non-identifiable parameters in the complex model quantitatively relate to identifiable parameters in surrogate, we introduce and exploit a layer of interpretation between the set of non-identifiable parameters and the goodness-of-fit metric or likelihood studied in typical identifiability analysis. We demonstrate our approach by analysing a hierarchy of mathematical models for multicellular tumour spheroid growth experiments. Typical data from tumour spheroid experiments are limited and noisy, and corresponding mathematical models are very often made arbitrarily complex. Our geometric approach is able to predict non-identifiabilities, classify non-identifiable parameter spaces into identifiable parameter combinations that relate to features in the data characterised by parameters in a surrogate model, and overall provide additional biological insight from complex non-identifiable models.

Comparison of Burnet's clonal selection theory with tumor cell-clone development

Increasing evidence has shown that Darwin's theory of evolution provides vital insights into the emergence and etiology of different types of cancer. On a microscopic scale, cancer stem cells meet the conditions for the Darwinian process of natural selection. In particular, cancer stem cells undergo cell reproduction characterized by the emergence of heritable variability that promotes replication and cell survival. Methods: Evidence from previous studies was gathered to compare Burnet's clonal selection theory with the tumor evolution theory. Results: The findings show that the Darwinian theory offers a general framework for understanding fundamental aspects of cancer. As fundamental theoretical frameworks, Burnet's clonal selection theory and the tumor evolution theory can be used to explain cancer cell evolution and identify the beneficial adaptations that contribute to cell survival in tissue landscapes and tissue ecosystems. Conclusions: In conclusion, this study shows that both Burnet's clonal selection theory and the tumor evolution theory postulate that cancer cells in tissue ecosystems evolve through reiterative processes, such as clonal expansion, clonal selection, and genetic diversification. Therefore, both theories provide insights into the complexities and dynamics of cancer, including its development and progression. Finally, we take into account the occurrence of biologic variation in both tumor cells and lymphocytes. It is important to note that the presence of lymphocyte variations appears to be advantageous in the framework of tumor defense but also dangerous within the framework of autoimmune disease development.

Systematic Modeling and Design Evaluation of Unperturbed Tumor Dynamics in Xenografts

Xenograft mice are largely used to evaluate the efficacy of oncological drugs during preclinical phases of drug discovery and development. Mathematical models provide a useful tool to quantitatively characterize tumor growth dynamics and also optimize upcoming experiments. To the best of our knowledge, this is the first report where unperturbed growth of a large set of tumor cell lines (n = 28) has been systematically analyzed using a previously proposed model of nonlinear mixed effects (NLME). Exponential growth was identified as the governing mechanism in the majority of the cell lines, with constant rate values ranging from 0.0204 to 0.203 day^-1 No common patterns could be observed across tumor types, highlighting the importance of combining information from different cell lines when evaluating drug activity. Overall, typical model parameters were precisely estimated using designs in which tumor size measurements were taken every 2 days. Moreover, reducing the number of measurements to twice per week, or even once per week for cell lines with low growth rates, showed little impact on parameter precision. However, a sample size of at least 50 mice is needed to accurately characterize parameter variability (i.e., relative S.E. values below 50%). This work illustrates the feasibility of systematically applying NLME models to characterize tumor growth in drug discovery and development, and constitutes a valuable source of data to optimize experimental designs by providing an a priori sampling window and minimizing the number of samples required.

Multiscalar cellular automaton simulates in-vivo tumour-stroma patterns calibrated from in-vitro assay data

BACKGROUND

The tumour stroma -or tumour microenvironment- is an important constituent of solid cancers and it is thought to be one of the main obstacles to quantitative translation of drug activity between the preclinical and clinical phases of drug development. The tumour-stroma relationship has been described as being both pro- and antitumour in multiple studies. However, the causality of this complex biological relationship between the tumour and stroma has not yet been explored in a quantitative manner in complex tumour morphologies.

METHODS

To understand how these stromal and microenvironmental factors contribute to tumour physiology and how oxygen distributes within them, we have developed a lattice-based multiscalar cellular automaton model. This model uses principles of cytokine and oxygen diffusion as well as cell motility and plasticity to describe tumour-stroma landscapes. Furthermore, to calibrate the model, we propose an innovative modelling platform to extract model parameters from multiple in-vitro assays. This platform provides a novel way to extract meta-data that can be used to complement in-vivo studies and can be further applied in other contexts.

RESULTS

Here we show the necessity of the tumour-stroma opposing relationship for the model simulations to successfully describe the in-vivo stromal patterns of the human lung cancer cell lines Calu3 and Calu6, as models of clinical and preclinical tumour-stromal topologies. This is especially relevant to drugs that target the tumour microenvironment, such as antiangiogenics, compounds targeting the hedgehog pathway or immune checkpoint inhibitors, and is potentially a key platform to understand the mechanistic drivers for these drugs.

CONCLUSION

The tumour-stroma automaton model presented here enables the interpretation of complex in-vitro data and uses it to parametrise a model for in-vivo tumour-stromal relationships.