The incidence of advanced renal cell carcinoma(RCC) has been rising, presenting significant challenges due to the limited efficacy and severe side effects of traditional radiotherapy and chemotherapy. While combination immunotherapies show promise, optimizing treatment strategies remains difficult due to individual heterogeneity. To address this, we developed a Quantitative Cancer-Immunity Cycle (QCIC) model that integrates ordinary differential equations with stochastic modelling to quantitatively characterize and predict tumor evolution in patients with advanced RCC. By systematically integrating quantitative systems pharmacology principles with biological mechanistic knowledge, we constructed a virtual patient cohort and calibrated the model parameters using clinical immunohistochemistry data to ensure biological validity. To enhance predictive performance, we coupled the model with pharmacokinetic equations and defined the Tumor Response Index (TRI) as a quantitative metric of efficacy. Systematic analysis of the QCIC model allowed us to determine an optimal treatment regimen for the combination of bevacizumab and atezolizumab and identify tumor biomarkers with clinical predictive value. This study provides a theoretical framework and methodological support for precision medicine in the treatment of advanced RCC.
Understanding the interactions between cells and the extracellular matrix (ECM) during collective cell invasion is crucial for advancements in tissue engineering, cancer therapies, and regenerative medicine. This study focuses on the roles of contact guidance and ECM remodelling in directing cell behaviour, with a particular emphasis on exploring how differences in cell phenotype impact collective cell invasion. We present a computationally tractable two-dimensional hybrid model of collective cell migration within the ECM, where cells are modelled as individual entities and collagen fibres as a continuous tensorial field. Our model incorporates random motility, contact guidance, cell-cell adhesion, volume filling, and the dynamic remodelling of collagen fibres through cellular secretion and degradation. Through a comprehensive parameter sweep, we provide valuable insights into how differences in the cell phenotype, in terms of the ability of the cell to migrate, secrete, degrade, and respond to contact guidance cues from the ECM, impacts the characteristics of collective cell invasion.
We propose a mathematical kinetic framework to investigate interactions between tumor cells and the immune system, focusing on the spatial dynamics of tumor progression and immune responses. We develop two kinetic models: one describes a conservative scenario where immune cells switch between active and passive states without proliferation, while the other incorporates immune cell proliferation and apoptosis. By considering specific assumptions about the microscopic processes, we derive macroscopic systems featuring linear diffusion, nonlinear cross-diffusion, and nonlinear self-diffusion. Our analysis provides insights into equilibrium configurations and stability, revealing clear correspondences among the macroscopic models derived from the same kinetic framework. Using dynamical systems theory, we examine the stability of equilibrium states and conduct numerical simulations to validate our findings. These results highlight the significance of spatial interactions in tumor-immune dynamics, paving the way for a structured exploration of therapeutic strategies and further investigations into immune responses in various pathological contexts.
A general model is presented for coupling of high-Q whispering-gallery modes in optical microsphere resonators with coupler devices that possess a discrete and continuous spectrum of propagating modes. By contrast to conventional high-Q optical cavities, in microspheres the independence of high intrinsic quality-factor and controllable parameters of coupling via an evanescent field offer a variety of regimes similar to those that are already available in rf devices. The theory is applied to data reported earlier on different types of couplers to microsphere resonators and is complemented by the experimental demonstration of enhanced coupling efficiency (∼80%) and variable loading regimes with Q>108 fused-silica microspheres.