Mathematical modelling and numerical simulation of the morphological development of neurons

BACKGROUND: The morphological development of neurons is a very complex process involving both genetic and environmental components. Mathematical modelling and numerical simulation are valuable tools in helping us unravel particular aspects of how individual neurons grow their characteristic morphologies and eventually form appropriate networks with each other. METHODS: A variety of mathematical models that consider (1) neurite initiation (2) neurite elongation (3) axon pathfinding, and (4) neurite branching and dendritic shape formation are reviewed. The different mathematical techniques employed are also described. RESULTS: Some comparison of modelling results with experimental data is made. A critique of different modelling techniques is given, leading to a proposal for a unified modelling environment for models of neuronal development. CONCLUSION: A unified mathematical and numerical simulation framework should lead to an expansion of work on models of neuronal development, as has occurred with compartmental models of neuronal electrical activity

Modelling and simulation of large-scale complex networks

Real-world large-scale complex networks such as the Internet, social networks and biological networks have increasingly attracted the interest of researchers from many areas. Accurate modelling of the statistical regularities of these large-scale networks is critical to understand their global evolving structures and local dynamical patterns. Traditionally, the Erdos and Renyi random graph model has helped the investigation of various homogeneous networks. During the past decade, a special computational methodology has emerged to study complex networks, the outcome of which is identified by two models: the Watts and Strogatz small-world model and the Barabasi-Albert scale-free model. At the core of the complex network modelling process is the extraction of characteristics of real-world networks. I have developed computer simulation algorithms for study of the properties of current theoretical models as well as for the measurement of two real-world complex networks, which lead to the isolation of three complex network modelling essentials. The main contribution of the thesis is the introduction and study of a new General Two-Stage growth model (GTS Model), which aims to describe and analyze many common-featured real-world complex networks. The tools we use to create the model and later perform many measurements on it consist of computer simulations, numerical analysis and mathematical derivations. In particular, two major cases of this GTS model have been studied. One is named the U-P model, which employs a new functional form of the network growth rule: a linear combination of preferential attachment and uniform attachment. The degree distribution of the model is first studied by computer simulation, while the exact solution is also obtained analytically. Two other important properties of complex networks: the characteristic path length and the clustering coefficient are also extensively investigated, obtaining either analytically derived solutions or numerical results by computer simulations. Furthermore, I demonstrate that the hub-hub interaction behaves in effect as the link between a network's topology and resilience property. The other is called the Hybrid model, which incorporates two stages of growth and studies the transition behaviour between the Erdos and Renyi random graph model and the Barabasi-Albert scale-free model. The Hybrid model is measured by extensive numerical simulations focusing on its degree distribution, characteristic path length and clustering coefficient. Although either of the two cases serves as a new approach to modelling real-world large-scale complex networks, perhaps more importantly, the general two-stage model provides a new theoretical framework for complex network modelling, which can be extended in many ways besides the two studied in this thesis

A Systems Biological Perspective of Cellular Stress-Directed Programmed Cell Death

Each eukaryotic cell of multicellular organisms must be able to maintain its integrity by sensing both external and internal stimuli. The primary goal of the generated response mechanism is to drive back the system to the former or to a new homeostatic state. Moreover, the response has to provide an accurate survival-or-death decision to avoid any “misunderstanding” and its unwanted consequences. New data revealed that a systems-level crosstalk of molecular networks has an essential role in achieving the correct characteristic of the response. Although many molecular components of these processes already have been revealed, several elements and regulatory connections of crosstalk are still missing. These “gaps” of the complex control networks make hardly impossible to present comprehensive models. Therefore we approach the questions from a systems biology aspect by combining the experimental results with the special technique of mathematical modelling. In this short report we discuss some novel and preliminary data gained by this approach on the crosstalk between life and death decisions under cellular stress, to get a systems biological view of these networks

Approximations and their consequences for dynamic modelling of signal transduction pathways

Signal transduction is the process by which the cell converts one kind of signal or stimulus into another. This involves a sequence of biochemical reactions, carried out by proteins. The dynamic response of complex cell signalling networks can be modelled and simulated in the framework of chemical kinetics. The mathematical formulation of chemical kinetics results in a system of coupled differential equations. Simplifications can arise through assumptions and approximations. The paper provides a critical discussion of frequently employed approximations in dynamic modelling of signal transduction pathways. We discuss the requirements for conservation laws, steady state approximations, and the neglect of components. We show how these approximations simplify the mathematical treatment of biochemical networks but we also demonstrate differences between the complete system and its approximations with respect to the transient and steady state behavior

An implicit unsteady hydraulic solver for suspended cuttings transport in managed pressure wells

We present a simulation tool for transient events in complex hydraulic networks. The code includes modelling of the transport of suspended cuttings in near-vertical wells. An unstructured finite volume formulation with implicit time integration has been chosen. The unconditional stability of the integrator makes the method suitable for the simulation of transient events over a wide range of characteristic timescales. It handles both very fast transients (e.g. fluid hammer events) and the long-term evolution of the well (e.g. hole cleaning operations). The software has been developed to address the need of the oil industry for a robust and efficient predictive tool allowing effective well control in managed pressure drilling operations. The physical modelling follows the standard practices accepted by the industry (e.g. mud rheology computations). The mathematical foundation of the algorithm is described followed by validation cases that illustrate its capabilities and accuracy. Finally, a practical industrial application example is provided to demonstrate the real-world performance of the software.Peer ReviewedPostprint (author's final draft

Time domain computational modelling of 1D arterial networks in monochorionic placentas

Published versio

Evolution-based modelling of complex airport networks

Copyright @ 2011 Society for Electronics, Telecommunications, Automation, and InformaticsThis paper presents a time-series model of the United States Airport Network as a directed, weighted network, with the weight representing the total number of passengers flying from an origin to a destination airport, in a two month time period. Six independent networks are built for a given year, in order to capture the seasonal variation of passengers. To explore the evolution of the network over the past two decades, three specific years are investigated: 1990, 2000, and 2010. The results highlight the growth of the network in terms of airports and connections, and suggest a scale-free, small-world topology. In addition, the ranked passenger distribution appears to follow a logarithmic trend, implying high heterogeneity in passengers on different connections.This project was funded by te Brunel Research Support and Development Office