DSpace Collection:
https://dspace.lboro.ac.uk/2134/4642
2017-03-28T08:08:56ZMathematical modelling of acetaminophen induced hepatotoxicity
https://dspace.lboro.ac.uk/2134/23008
Title: Mathematical modelling of acetaminophen induced hepatotoxicity
Authors: Reddyhoff, Dennis
Abstract: Acetaminophen, known as paracetamol in the UK and Tylenol in the United States, is a widespread and commonly used painkiller all over the world. Taken in large enough doses, however, it can cause fatal liver damage. In the U.S., 56000 people are admitted to hospital each year due to acetaminophen overdose and its related effects, at great cost to healthcare services.
In this thesis we present a number of different models of acetaminophen metabolism and toxicity. Previously, models of acetaminophen toxicity have been complex and due to this complexity, do not lend themselves well to more advanced mathematical analysis such as the perturbation analysis presented later in this thesis. We begin with a simple model of acetaminophen metabolism, studying a single liver cell and performing numerical and sensitivity analysis to further understand the most important mechanisms and pathways of the model. Through this we identify key parameters that affect the total toxicity in our model. We then proceed to perform singular perturbation analysis, studying the behaviour of the model over different timescales, finding a number of key timescales for the depletion and subsequent recovery of various cofactors as well as critical dose above which we see toxicity occurring. Later in the thesis, this model is used to model metabolism in a spheroid cell culture, examining the difference spatial effects have on metabolism across a 3D cell culture.
We then present a more complex model, examining the difference the addition of an adaptive response to acetaminophen overdose from the Nrf2 signalling pathway, has on our results. We aim to reproduce an unexplained result in the experimental data of our colleagues, and so analyse the steady states of our model when subjected to an infused dose, rather than a bolus one. We identify another critical dose which leads to GSH depletion in the infused dose case and find that Nrf2 adaptation decreases toxicity and model sensitivity. This model is then used as part of a whole-body PBPK model, exploring the effects that the distribution of the drug across the bloodstream and different organs has. We explore the affects of that a delay in up-regulation from the Nrf2 pathway has on the model, and find that with rescaled parameters we can qualitatively reproduce the results of our collaborators.
Finally, we present the results of in vitro work that we have undertaken, the aim of which was to find new parameters for the model in human hepatocytes, rather than from rodent models, and find a new value for a parameter in our model from human cell lines.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.2016-01-01T00:00:00ZLocal spectral asymptotics and heat kernel bounds for Dirac and Laplace operators
https://dspace.lboro.ac.uk/2134/23004
Title: Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators
Authors: Li, Liangpan
Abstract: In this dissertation we study non-negative self-adjoint Laplace type operators acting on smooth sections of a vector bundle. First, we assume base manifolds are compact, boundaryless, and Riemannian. We start from the Fourier integral operator representation of half-wave operators, continue with spectral zeta functions, heat and resolvent trace asymptotic expansions, and end with the quantitative Wodzicki residue method.
In particular, all of the asymptotic coefficients of the microlocalized spectral counting function can be explicitly given and clearly interpreted. With the auxiliary pseudo-differential operators ranging all smooth endomorphisms of the given bundle,
we obtain certain asymptotic estimates about the integral kernel of heat operators.
As applications, we study spectral asymptotics of Dirac type operators such as characterizing those for which the second coefficient vanishes. Next, we assume vector bundles are trivial and base manifolds are Euclidean domains, and study non-negative self-adjoint extensions of the Laplace operator which acts component-wise on compactly supported smooth functions. Using finite propagation speed estimates for wave equations and explicit Fourier Tauberian theorems obtained by Yuri Safarov, we establish the principle of not feeling the boundary estimates for the heat kernel of these operators. In particular, the implied constants are independent of self-adjoint extensions. As a by-product, we affirmatively answer a question about upper estimate for the Neumann heat kernel.
Finally, we study some specific values of the spectral zeta function of two-dimensional Dirichlet Laplacians such as spectral determinant and Casimir energy. For numerical purposes we substantially improve the short-time Dirichlet heat trace asymptotics for polygons. This could be used to measure the spectral determinant and Casimir energy of polygons whenever the first several hundred or one thousand Dirichlet eigenvalues are known with high precision by other means.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.2016-01-01T00:00:00ZThe use of differential equations in optimization
https://dspace.lboro.ac.uk/2134/22089
Title: The use of differential equations in optimization
Authors: Zghier, Abbas K.
Abstract: A new approach for unconstrained optimization of a function f(x)
has been investigated. The method is based on solving the differential
equation dx/dt = ± ∇f(x) which defines orthogonal trajectories in Rⁿ-space.
A number of numerical integration techniques have been used for solving
the above differential equation, the most powerful one which gives rise to
a very efficient optimization algorithm is the generalization of the
Trapezoidal rule. The interaction between the parameters which appear
as a result of using the numerical integration has been investigated.
In the above approach factorization of the positive definite matrix
(θG + λI), allowing some control over the diagonal elements of the matrix.
is presented.
A Liapunov function approach has been used in constructing a number
of different differential equations of the above form. It is well known
that if a Liapunov function which satisfies certain conditions can be
found for a given system of differential equations then the origin of
the system is stable. Pursuing this idea further we constructed a Liapunov
function and then the corresponding differential equation. Application
of this differential equation to the problem of finding a minimum of a
function f is shown to yield a vector that converges to a point where
∇f = 0.
The use of differential equations is also extended to the optimal
control problem. The technique is only applicable to unconstrained optimal
control problems. If a terminal condition and inequality constraints are
presented, the problem should be converted to unconstrained form, e.g. by
the use of penalty functions. The method tends to converge, even from a
poor approximation point to the minimum without using line searches.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.1981-01-01T00:00:00ZSafety system design optimisation
https://dspace.lboro.ac.uk/2134/22019
Title: Safety system design optimisation
Authors: Pattison, Rachel L.
Abstract: This thesis investigates the efficiency of a design optimisation scheme that is
appropriate for systems which require a high likelihood of functioning on demand.
Traditional approaches to the design of safety critical systems follow the preliminary
design, analysis, appraisal and redesign stages until what is regarded as an acceptable
design is achieved. For safety systems whose failure could result in loss of life it is
imperative that the best use of the available resources is made and a system which is
optimal, not just adequate, is produced.
The object of the design optimisation problem is to minimise system unavailability
through manipulation of the design variables, such that limitations placed on them by
constraints are not violated.
Commonly, with mathematical optimisation problem; there will be an explicit
objective function which defines how the characteristic to be minimised is related to
the variables. As regards the safety system problem, an explicit objective function
cannot be formulated, and as such, system performance is assessed using the fault tree
method. By the use of house events a single fault tree is constructed to represent the
failure causes of each potential design to overcome the time consuming task of
constructing a fault tree for each design investigated during the optimisation
procedure. Once the fault tree has been constructed for the design in question it is
converted to a BDD for analysis.
A genetic algorithm is first employed to perform the system optimisation, where the
practicality of this approach is demonstrated initially through application to a High-Integrity
Protection System (HIPS) and subsequently a more complex Firewater
Deluge System (FDS).
An alternative optimisation scheme achieves the final design specification by solving
a sequence of optimisation problems. Each of these problems are defined by
assuming some form of the objective function and specifying a sub-region of the
design space over which this function will be representative of the system
unavailability.
The thesis concludes with attention to various optimisation techniques, which possess
features able to address difficulties in the optimisation of safety critical systems.
Specifically, consideration is given to the use of a statistically designed experiment
and a logical search approach.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.2000-01-01T00:00:00Z