Traditionally, cancer has been regarded as a disease arising from a single cell undergoing genetic mutations that lead to tumour formation. However, recent research highlights the crucial role of the tumour microenvironment (TME) in influencing the progression of the disease. Understanding and analysing the TME, particularly its mechanical properties, is essential to gaining a deeper insight into cancer biology.

To study these complex interactions, both in vitro and in vivo experimental models are employed. In vitro models provide a controlled environment to simulate tumour behaviour, while in vivo models offer a more realistic approximation of biological processes. Despite their value, experimental approaches face limitations in isolating specific factors and testing hypotheses efficiently.

Computational models offer a complementary solution by replicating experimental conditions and enabling the exploration of individual characteristics of the system. These models can test novel hypotheses and analyse phenomena that may be challenging or impractical to investigate experimentally. However, their effective use requires careful attention to experimental and computational uncertainties, as well as robust calibration processes that integrate experimental data.

Experimental datasets often suffer from heterogeneity and are limited in size due to the high costs and complexity of experiments. Therefore, calibration techniques must be tailored to these common constraints in biomedical engineering laboratories to ensure the reliability and applicability of computational models. Integrating computational and experimental methods holds great promise for advancing our understanding of cancer and developing more effective therapeutic strategies.

In this work, we present a versatile multiphase poroelastic model based on porous media model capable of reproducing tumour evolution [1]. The model represents the extracellular matrix as a solid skeleton, while tumoural and healthy cells, along with interstitial fluid, occupy the pores as fluid components. Additionally, the model incorporates other critical species, such as nutrients and necrotic cells, to provide a comprehensive framework for simulating tumour behaviour. One of the model's key strengths lies in its flexibility, allowing for the simulation of various scenarios. It can easily incorporate additional variables, such as cancer-associated fibroblasts, or evaluate the effects of therapeutic interventions, such as immunotherapy.

To harness the full potential of the information provided by the model, we propose using a global sensitivity analysis based on the Sobol method [2]. This approach identifies the most influential parameters in the computational model, offering valuable insights into which variables or conditions should be prioritized when designing laboratory experiments. However, conducting a global sensitivity analysis requires a large number of computational simulations, which can be resource-intensive. To address this challenge, we propose the use of a Gaussian surrogate model [2]. This surrogate significantly reduces computational cost and runtime, enabling a more efficient exploration of the model's parameter space without compromising accuracy.

Ultimately, we adopt a Bayesian approach to parameterize the proposed computational tumour-growth model for several compelling reasons. First, the model includes uncertain input parameters whose true values are not precisely known. Moreover, these true values may themselves be inherently uncertain, often due to stochasticity in the underlying biological processes [3]. Instead of treating these parameters as fixed values, we represent them as probability distributions to better capture this uncertainty. By embracing a probabilistic framework, we ensure that the inherent uncertainties are systematically incorporated, resulting in a more robust and realistic representation of the system.

The workflow we present enables the measurement of properties that are not easily accessible in laboratory settings, such as the mechanical properties of the tumour microenvironment. Furthermore, if experiments are conducted with patient-specific cells, the model can characterize these properties at an individual level. This personalised data can subsequently be integrated into a more comprehensive, patient-specific model, advancing the potential for tailored therapeutic approaches.

References

[1] Hervas-Raluy, S., Wirthl, B., Guerrero, P. E., Rei, G. R., Nitzler, J., Coronado, E., ... & Wall, W. A. (2023). Tumour growth: An approach to calibrate parameters of a multiphase porous media model based on in vitro observations of Neuroblastoma spheroid growth in a hydrogel microenvironment. Computers in Biology and Medicine, 159, 106895.

[2] Wirthl, B., Brandstaeter, S., Nitzler, J., Schrefler, B. A., & Wall, W. A. (2023). Global sensitivity analysis based on Gaussian‐process metamodelling for complex biomechanical problems. International journal for numerical methods in biomedical engineering, 39(3), e3675.

[3] Dinkel, M., Geitner, C. M., Rei, G. R., Nitzler, J., & Wall, W. A. (2024). Solving Bayesian inverse problems with expensive likelihoods using constrained Gaussian processes and active learning. Inverse Problems, 40(9), 095008.

Acknowledgements

SHR was supported by a Research Fellowship of the Alexander von Humboldt Foundation.