The post-surgical development of metastases (secondary tumors spread from a primary one) represents the major cause of death from a cancer disease. Mathematical models may have the potential to further assist in estimating metastatic risk, particularly when paired with in vivo tumor data that faithfully represent all stages of disease progression.
In this talk I will first describe a modeling approach that uses data from clinically relevant mouse models of spontaneous metastasis developing after surgical removal of orthotopically implanted primary tumors. Both presurgical (primary tumor) and postsurgical (metastatic) growth was quantified using bioluminescence. The model was able to fit and predict pre-/post-surgical data at the level of the individual as well as the population. Importantly, our approach also enabled retrospective analysis of clinical data describing the probability of metastatic relapse as a function of primary tumor size, where inter-individual variability was quantified by a key parameter of intrinsic metastatic potential. Critically, our analysis identified a highly nonlinear relationship between primary tumor size and postsurgical survival, suggesting possible threshold limits for the utility of tumor size as a predictor of metastatic recurrence.
In the second part of my talk, I will focus on some very intriguing phenomenon concerning systemic interactions between tumors within the organisms, termed “concomitant resistance”, by which, in the presence of two tumors, one inhibits the growth of the other. This has important clinical consequences as it can lead to post-surgery metastatic acceleration. Based on experimental data involving the simultaneous growth of two tumor implants, we will test biological theories underlying this process and establish a biologically relevant and minimally parameterized mathematical model.
These findings represent a novel use of clinically relevant models to assess the impact of surgery on metastatic potential and may guide optimal timing of treatments in neoadjuvant (presurgical) and adjuvant (postsurgical) settings to maximize patient benefit.[-]

In this talk we overview some of the challenges of cardiac modeling and simulation of the electrical depolarization of the heart. In particular, we will present a strategy allowing to avoid the 3D simulation of the thin atria depolarization but only solve an asymptotic consistent model on the mid-surface. In a second part, we present a strategy for estimating a cardiac electrophysiology model from front data measurements using sequential parallel data assimilation strategy.[-]

Cell-extracellular matrix interaction and the mechanical properties of cell nucleus have been demonstrated to play a fundamental role in cell movement across fibre networks and micro-channels and then in the spread of cancer metastases. The lectures will be aimed at presenting several mathematical models dealing with such a problem, starting from modelling cell adhesion mechanics to the inclusion of influence of nucleus stiffness in the motion of cells, through continuum mechanics, kinetic models and individual cell-based models.[-]

​We consider photoacoustic tomography in the presence of approximation and modelling errors. The inverse problem, i.e. estimation of the initial pressure from photoacoustic time-series measured on the boundary of the target, is approached in the framework of Bayesian inverse problems. The posterior distribution is examined in situations in which the forward model contains errors or uncertainties for example due to numerical approximations or uncertainties in the acoustic parameters. Modelling of these errors and its impact on the posterior distribution are investigated.
This is joint work with Teemu Sahlstrm, Jenni Tick and Aki Pulkkinen.[-]

High-fidelity numerical simulation of physical systems modeled by time-dependent partial differential equations (PDEs) has been at the center of many technological advances in the last century. However, for engineering applications such as design, control, optimization, data assimilation, and uncertainty quantification, which require repeated model evaluation over a potentially large number of parameters, or initial conditions, these simulations remain prohibitively expensive, even with state-of-art PDE solvers. The necessity of reducing the overall cost for such downstream applications has led to the development of surrogate models, which captures the core behavior of the target system but at a fraction of the cost. In this context, new advances in machine learning provide a new path for developing surrogates models, particularly when the PDEs are not known and the system is advection-dominated. In a nutshell, we seek to find a data-driven latent representation of the state of the system, and then learn the latent-space dynamics. This allows us to compress the information, and evolve in compressed form, therefore, accelerating the models. In this series of lectures, I will present recent advances in two fronts: deterministic and probabilistic modeling latent representations. In particular, I will introduce the notions of hyper-networks, a neural network that outputs another neural network, and diffusion models, a framework that allows us to represent probability distributions of trajectories directly. I will provide the foundation for such methodologies, how they can be adapted to scientific computing, and which physical properties they need to satisfy. Finally, I will provide several examples of applications to scientific computing.[-]