Research interest
Our projects focus on building hybrid models that combine reaction-diffusion equations, stochastic vertex models, and multiscale simulations. We aim to explore how parameters such as friction coefficients and E-cadherin dysfunction influence cellular processes like tissue behavior and early cancer invasion dynamics. By integrating computational physics and biology, we strive to uncover complex biological systems and drive innovation in research.
Ongoing work continues to refine these models, especially in cancer dynamics. Vertex models are critical for understanding tissue mechanics, cell packing, and how these disruptions relate to disease, offering new insights into tissue-level dynamics.
ABOUT ME
I did my thesis with an excellent project grant of Junta de Andalucia, from 2005-2010 working on the analysis of some qualitative aspects of partial differential equations arising in developmental biology and quantum mechanics, in particular, properties of the solutions concerning diffusion, dispersion and dissipation.
Continuing with my applied mathematics motivation, I joined to The Computational and Mathematical Biology group at the Centre de Recerca Matematica (CRM) under the supervision of Tomás Alarcón, as a postdoc for 2 years and 6 months modelling cancer behaviour. I worked on stochastic multi-scale modelling of biological systems and mathematical modelling of the cell-cycl. During this position I get a visitor position during 3 in OCCAM centre in Oxford where I collaborated with Helen Byrne and Philip K. Maini, working on stochastic models of the competition between resource-limited cell populations with different response strategies and we have been developing multi-scale models of tumour growth and tumour-induced angiogenesis, cancer cells is coupled to models of intracellular processes and to the vascular network through the distribution of oxygen and the development of numerical methods for their simulation and analysis.
From July 2013 until August 2018, I have been a Postdoctoral Research Associated in Mathematical Biology in the mathematical department of University College London (UK) working with Prof Karen Page (UCL Mathematics) and Dr James Briscoe (Francis Crick Institute, Developmental Dynamics Laboratory) on mathematical modelling of the development of the neural tube in the vertebrate embryo. We have worked in modelling the spatial patterning of the neural tube using a computational 3D model, and how patterning is coordinated with growth and for developing an in silico neural tube though stochastic models.
From September 2018, I work in the Mathematic department of Universidad Carlos III as an Assistant Professor and, I’m a member of the Interdisciplinary Group of Complex System (GISC). Since May 2022, I am a “Profesora titular de Universidades” (Assistant professor).