Modern medicine has given us effective tools to treat some of the most significant and burdensome diseases. At the same time, it is becoming consistently more challenging and more expensive to develop new therapeutics. A key factor in this trend is that we simply don't understand the underlying biology of disease, and which interventions might meaningfully modulate clinical outcomes and in which patients. To achieve this goal, we are bringing together large amounts of high content data, taken both from humans and from human-derived cellular systems generated in our own lab. Those are then used to learn a meaningful representation of biological states via cutting edge machine learning methods, which enable us to make predictions about novel targets, coherent patient segments, and the clinical effect of molecules. Our ultimate goal is to develop a new approach to drug development that uses high-quality data and ML models to design novel, safe, and effective therapies that help more people, faster, and at a lower cost. 

Mathematical and computational techniques can improve our understanding of diseases. In this talk, I’ll present ways in which data from cancer patients can be combined with mathematical modelling and used to improve cancer treatments.

Given the variability in individual responses to cancer treatments, agent-based modelling has been a useful technique for accurately capturing cellular behaviours that may lead to stochasticity in patient outcomes. Using a hybrid agent-based model and partial differential equation system, we developed a model for brain cancer (glioblastoma) growth informed by ex-vivo patient samples. Extending the model to capture patient treatment with an oncolytic virus rQNestin, we used our model to propose reasons for treatment failure, which was later confirmed with further patient samples. More recently, we extended this model to investigate the effectiveness of combination treatments (chemotherapy, virotherapy and immunotherapy) informed by individual patient imaging mass cytometry.

This talk hopes to provide examples of ways mathematical and computational modelling can be used to run “virtual” clinical trials with the goal of obtaining more effective treatments for diseases.  

Many natural and social phenomena involve individual agents coming together to create group dynamics, whether the agents are drivers in a traffic jam, cells in a developing tissue, or locusts in a swarm. Here I will focus on two examples of such emergent behavior in biology, specifically cell interactions during pattern formation in zebrafish skin and gametophyte development in ferns. Different modeling approaches provide complementary insights into these systems and face different challenges. For example, vertex-based models describe cell shape, while more efficient agent-based models treat cells as particles. Continuum models, which track the evolution of cell densities, are more amenable to analysis, but it is often difficult to relate their few parameters to specific cell interactions. In this talk, I will overview our models of cell behavior in biological patterns and discuss our ongoing work on quantitatively relating different types of models using topological data analysis and data-driven techniques.

Complex dynamics underlying industrial manufacturing depend in part on
multiphase multiphysics, in which fluids and materials interact across
orders of magnitude variations in time and space. In this talk, we will
discuss the development and application of a host of numerical methods for
these problems, including Level Set Methods, Voronoi Implicit Interface
Methods, implicit adaptive representations, and multiphase discontinuous
Galerkin Methods.  Applications for industrial problems will include modeling
how foams evolve, how electro-fluid jetting devices work, and
the physics and dynamics of rotary bell spray painting across the automotive
industry.