Closed-loop investigation of the dynamical properties of cardiomyocyte electrophysiology by means of Dynamic clamp and Mathematical modelling

The research field of my PhD concerns mathematical modeling and numerical simulation, applied to the cardiac electrophysiology analysis at a single cell level. This is possible thanks to the development of mathematical descriptions of single cellular components, ionic channels, pumps, exchangers and subcellular compartments. Due to the difficulties of vivo experiments on human cells, most of the measurements are acquired in vitro using animal models (e.g. guinea pig, dog, rabbit). Moreover, to study the cardiac action potential and all its features, it is necessary to acquire more specific knowledge about single ionic currents that contribute to the cardiac activity. Electrophysiological models of the heart have become very accurate in recent years giving rise to extremely complicated systems of differential equations. Although describing the behavior of cardiac cells quite well, the models are computationally demanding for numerical simulations and are very difficult to analyze from a mathematical (dynamical-systems) viewpoint. Simplified mathematical models that capture the underlying dynamics to a certain extent are therefore frequently used. The results presented in this thesis have confirmed that a close integration of computational modeling and experimental recordings in real myocytes, as performed by dynamic clamp, is a useful tool in enhancing our understanding of various components of normal cardiac electrophysiology, but also arrhythmogenic mechanisms in a pathological condition, especially when fully integrated with experimental data.

Bioimaging of animal embryogenesis: mathematical methods and computational algorithms

Some fundamental biological processes such as embryonic development have been preserved during evolution and are common to species belonging to different phylogenetic positions, but are nowadays largely unknown. The understanding of cell morphodynamics leading to the formation of organized spatial distribution of cells such as tissues and organs can be achieved through the reconstruction of cells shape and position during the development of a live animal embryo. We design in this work a chain of image processing methods to automatically segment and track cells nuclei and membranes during the development of a zebrafish embryo, which has been largely validates as model organism to understand vertebrate development, gene function and healingrepair mechanisms in vertebrates. The embryo is previously labeled through the ubiquitous expression of fluorescent proteins addressed to cells nuclei and membranes, and temporal sequences of volumetric images are acquired with laser scanning microscopy. Cells position is detected by processing nuclei images either through the generalized form of the Hough transform or identifying nuclei position with local maxima after a smoothing preprocessing step. Membranes and nuclei shapes are reconstructed by using PDEs based variational techniques such as the Subjective Surfaces and the Chan Vese method. Cells tracking is performed by combining informations previously detected on cells shape and position with biological regularization constraints. Our results are manually validated and reconstruct the formation of zebrafish brain at 7-8 somite stage with all the cells tracked starting from late sphere stage with less than 2% error for at least 6 hours. Our reconstruction opens the way to a systematic investigation of cellular behaviors, of clonal origin and clonal complexity of brain organs, as well as the contribution of cell proliferation modes and cell movements to the formation of local patterns and morphogenetic fields.

Price manipulation: theoretical models and empirical investigation

Understanding why market manipulation is conducted, under which conditions it is the most profitable and investigating the magnitude of these practices are crucial questions for financial regulators. Closing price manipulation induced by derivatives’ expiration is the primary subject of this thesis. The first chapter provides a mathematical framework in continuous time to study the incentive to manipulate a set of securities induced by a derivative position. An agent holding a European-type contingent claim, depending on the price of a basket of underlying securities, is considered. The agent can affect the price of the underlying securities by trading on each of them before expiration. The elements of novelty are at least twofold: (1) a multi-asset market is considered; (2) the problem is solved by means of both classic optimisation and stochastic control techniques. Both linear and option payoffs are considered. In the second chapter an empirical investigation is conducted on the existence of expiration day effects on the UK equity market. Intraday data on FTSE 350 stocks over a six-year period from 2015-2020 are used. The results show that the expiration of index derivatives is associated with a rise in both trading activity and volatility, together with significant price distortions. The expiration of single stock options appears to have little to no impact on the underlying securities. The last chapter examines the existence of patterns in line with closing price manipulation of UK stocks on option expiration days. The main contributions are threefold: (1) this is one of the few empirical studies on manipulation induced by the options market; (2) proprietary equity orderbook and transaction data sets are used to define manipulation proxies, providing a more detailed analysis; (3) the behaviour of proprietary trading firms is studied. Despite the industry concerns, no evidence is found of this type of manipulative behaviour.