Transmural propagation of the action potential in mammalian hearts: marrying experimental and theoretical studies
Abstract
Transmural propagation is a little studied feature of mammalian electrophysiology, this talk reviews our experimental work using different optical techniques to characterise this mode
of conduction under physiological and pathophysiological conditions.
What can we reconstruct about neural organization from time series of electrophysiological recordings?
Abstract
We will discuss how the analysis of a stochastic mean-field model for
synaptic activity can be used to reconstruct some parameters about
neuronal networks. The method is based on a non-standard analysis of the
Fokker-Planck equation and the asymptotic computation of the spectrum for
the nonself-adjoint operator. Applications concern Up- and Down- states
and bursting activity in neuronal networks.
oxDNA: A coarse-grained approach to model DNA
Abstract
Simulating the long time and length scales associated with DNA self-assembly
and DNA nanotechnology is not currently feasible with models at an atomic level
of detail. We, therefore, developed oxDNA a coarse-grained representation of
DNA that aims to capture the fundamental structural, thermodynamic and
mechanical properties of double-stranded and single-stranded DNA, which we have
subsequently applied to study a wide variety of DNA biophysical properties and
DNA nanotechnological systems.
Mathematical modelling of breast cancer for personalised therapy
Abstract
Ductal carcinoma is one of the most common cancers among women, and the main cause of death is the formation of metastases. The development of metastases is caused by cancer cells that migrate from the primary tumour site (the mammary duct) through the blood vessels and extravasating they initiate metastasis. In my talk, I present a multi-compartment mathematical model which mimics the dynamics of tumoural cells in the mammary duct, in the circulatory system and in the bone. Using a branching process approach, the model describes the relation between the survival times and the four markers mainly involved in metastatic breast cancer (EPCAM, CD47, CD44 and MET). In particular, the model takes into account the gene expression profile of circulating tumour cells to predict personalised survival probability. Gene expression data of metastatic breast cancer have been used to validate the model. The administration of drugs as bisphosphonates is also included in order to analyse the dynamic changes induced by the therapy.
Stochastic and deterministic processes are merged together to describe cancer progression and obtain personalised survival analysis based on the gene expression levels of each patient. The main aim of the talk is showing that Mathematics can have a strong impact in speeding cancer research, predicting survival probability and selecting the best cancer treatment.