DSpace Collection:https://dspace.lboro.ac.uk/2134/46422017-01-23T12:44:16Z2017-01-23T12:44:16ZMathematical modelling of acetaminophen induced hepatotoxicityReddyhoff, Dennishttps://dspace.lboro.ac.uk/2134/230082016-11-22T14:54:45Z2016-01-01T00:00:00ZTitle: 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.2016-01-01T00:00:00ZThe use of differential equations in optimizationZghier, Abbas K.https://dspace.lboro.ac.uk/2134/220892016-07-25T12:43:39Z1981-01-01T00:00:00ZTitle: 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 optimisationPattison, Rachel L.https://dspace.lboro.ac.uk/2134/220192016-07-19T15:22:16Z2000-01-01T00:00:00ZTitle: 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.2000-01-01T00:00:00ZNumerical and analytical study of the convective Cahn-Hilliard equationAlesemi, Mesharihttps://dspace.lboro.ac.uk/2134/217742016-07-05T10:05:43Z2016-01-01T00:00:00ZTitle: Numerical and analytical study of the convective Cahn-Hilliard equation
Authors: Alesemi, Meshari
Abstract: We consider the convective Cahn-Hilliard equation that is used as a model of coarsening dynamics
in driven systems and that in two spatial dimensions (x; y) has the form
ut + Duux + r2(u u3 + r2u) = 0:
Here t denotes time, u = u(x; y; t) is the order parameter and D is the parameter measuring
the strength of driving. We primarily consider the case of one spatial dimension, when there is
no y-dependence. For the case of no driving, when D = 0, the standard Cahn-Hilliard equation
is recovered, and it is known that solutions to this equation are characterised by an initial
stage of phase separation into regions of one phase surrounded by the other phase (i.e., clusters
or droplets/holes or islands are obtained) followed by the coarsening process, where the
average size of the clusters grows in time and the number of the clusters decreases. Moreover,
two main coarsening mechanisms have been identified in the literature, namely, coarsening due
to volume and translational modes. On the other hand, for the case of strong driving, when
D ! 1, the well-known Kuramoto-Sivashinsky equation is recovered, solutions of which are
characterised by complicated chaotic oscillations in both space and time. The primary aim of
the present thesis is to perform a detailed and systematic investigation of the transitions in the
solutions of the convective Cahn-Hilliard equation for a wide range of parameter values as the
driving-force parameter is increased, and, in particular, to understand in detail how the coarsening
dynamics is affected by driving. We find that one of the coarsening modes is stabilised
at relatively small values of D, and the type of the unstable coarsening mode may change as
D increases. In addition, we find that there may be intervals in the driving-force parameter D
where coarsening is completely stabilised. On the other hand, there may be intervals where twomode
solutions are unstable and the solutions can evolve, for example, into one-droplet/hole
solutions, symmetry-broken two-droplet/hole solutions or time-periodic solutions. We present
detailed stability diagrams for 2-mode solutions in the parameter planes and corroborate our
findings by time-dependent simulations. Finally, we present preliminary results for the case of
the (convective) Cahn-Hilliard equation in two spatial dimensions.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.2016-01-01T00:00:00Z