Modeling avascular tumor dynamics and low-intensity ultrasound therapeutics

Resumen

Cancer is a complex process that is influenced by a combination of genetic and environmental factors. It stands as the second leading cause of death globally and constitutes a major public health concern with far-reaching implications for patient outcomes and healthcare costs. Despite the considerable strides that have been made in the diagnosis and research of this disease, our understanding of the mechanisms involved is still incomplete, leaving much to be elucidated. Despite the recent improvement in survival rates, treating cancer remains a challenging endeavor as cancer stem cells are resistant to traditional therapies like chemotherapy or radiotherapy. The role of mechanics has emerged as a critical component in the development of tumors, alongside biochemical studies. Mechanical forces have been identified as both active and passive players in the progression of the disease, regulating a variety of cellular functions, including duplication, motility, growth, reorganization, and remodeling. Therefore, a comprehensive understanding of the interplay between biochemical and mechanical cues in tumor development is criticals for the development of effective strategies for cancer treatment and management. Mechanical therapy is a novel therapeutic approach for cancer treatment that uses mechanotransduction to convert mechanical signals into cellular responses. One of the emerging mechanical treatments is low-intensity ultrasound waves, which is being investigated as a potential target therapy that can complement existing treatments. However, the various configurations used for ultrasound waves result in diverse mechanical and biological effects, which must be carefully considered and optimized to maximize their therapeutic potential. In the current scientific landscape, mathematical oncology is proving to be a promising tool for understanding mechanotransduction, cellular communication, and other complex events that underlie the oncogenic process. In this context, this thesis aims to advance our understanding of cancer by introducing three self-coded numerical models that facilitate the study of tumor behavior through a mechanical perspective. By utilizing these models, the mechanical forces that govern cell fate can be more accurately quantified and characterized, enabling the development of more effective intervention strategies and treatments. Firstly, we study how migration, a process controlled by specific speed, competes with proliferation and possible mutations that give rise to nonhomogeneous volume changes, generating stresses that modify tumor evolution. To unveil the competition, we develop mechanical-growth coupled equations and we solve the system using the Weighted Essentially Non- Oscillatory method in finite differences. Our findings suggest the need to use non-linear flows to limit the propagation velocity. Additionally, if cells are deprived of movement, non-homogeneous growth slows down proliferation while causing instabilities in cell density in a phenomenon known as retrograde diffusion, which is mitigated by the possibility of movement. After studying these phenomena, we investigate the effect of mechanotherapy on tumor dynamics using finite-element models. We first study how ultrasound waves propagate through a spheroid embedded in a culture medium. A Kelvin-Voigt viscoelastic model with different parameters is used to conduct a parametric study of the frequency range (1-20MHz), acoustic pressure (0.1-5kPa), and viscosities (0.05-10Pa · s). The sensitivity analysis suggests that neglecting viscoelasticity can lead to an overestimation of the energy that reaches the tissue, as it fails to account for the dissipation of ultrasound waves caused by the viscosity of the tissue, while high acoustic pressure can lead to irreversible damage or cell death, and low acoustic pressure may not produce the desired therapeutic effects. Selecting the appropriate frequency depends on various factors, such as target tissue geometry, medium properties, and desired intensity. The study concludes that numerical simulations of wave propagations can help determine the optimal mechanical parameters for different cell types and disease states, which can guide the development of safe and effective LIUS treatments for cancer and other diseases. Finally, this thesis proposes a novel quantitative multiscale model that integrates the effects of mechanical waves on tumor development through mechanotransduction. The model is based on coupled stress-growth equations and operates on two main timescales: fast-scale, where the wave propagates and mechanotransduction occurs, and slow-scale, where the tumor grows and adapts to the microenvironment as a poroelastic medium. The hypothesis put forth is that dynamic pressure is more effective in generating a cellular response than static stress, due to the complex mechanisms of stress redistribution involving the cytoskeleton and interstitial fluid flow through pores. Then, this model of mechanotransduction provides a quantitative explanation for the difference in the threshold of dynamic and static stimulation, without the need for ad-hoc relationships. To test the model, we have conducted preliminary experiments with in vitro spheroids and performed a sensitivity analysis of the impact of ultrasound on mechanotransduction. The outcomes demonstrate that the model can accurately reproduce experimental data with a high degree of accuracy, and predict both the growth of the spheroids, as well as the stress and deformation states of the medium and the spheroids. Specifically, our findings suggest that ultrasound generates stress fields that hinder and slow down both the development and migration of the tumor cells. This leads to selective treatment and patterns based on shadow areas of applied stress and cell sensitivity ranges, which alter both gradients of stress and interstitial fluid pressure.