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\title{Advanced 3D Monte Carlo Algorithms for Biophotonic and Medical Applications}

\author{\Large Lewis McMillan\\
\includegraphics[scale=.3]{images/uni.png}\\
This thesis is submitted in partial fulfillment for the degree of \\
PhD\\ 
at the \\
University of St Andrews}

\date{August 2019}
\begin{document}
\frontmatter%make numbers Roman

\maketitle
\loadgeometry{origin}%restore margins to original


\chapter*{Declaration}

\subsection*{Candidate's Declaration}
I, Lewis McMillan, do hereby certify that this thesis, submitted for the degree of PhD, which is approximately 35,670 words in length, has been written by me, and that it is the record of work carried out by me, or principally by myself in collaboration with others as acknowledged, and that it has not been submitted in any previous application for any degree.
\medskip

I was admitted as a research student at the University of St Andrews in September 2015.
I received funding from an organisation or institution and have acknowledged the funder(s) in the full text of my thesis.

\medskip

Date\dotfill \hspace{1cm} Signature of candidate \dotfill

\subsection*{Supervisor's Declaration}

Supervisor's declaration
I hereby certify that the candidate has fulfilled the conditions of the Resolution and Regulations appropriate for the degree of PhD in the University of St Andrews and that the candidate is qualified to submit this thesis in application for that degree.
  
\medskip

Date\dotfill \hspace{1cm} Signature of supervisor \dotfill

\medskip

\indent Date\dotfill \hspace{1cm} Signature of supervisor \dotfill

\subsection*{Permission for publication}

In submitting this thesis to the University of St Andrews we understand that we are giving permission for it to be made available for use in accordance with the regulations of the University Library for the time being in force, subject to any copyright vested in the work not being affected thereby. We also understand, unless exempt by an award of an embargo as requested below, that the title and the abstract will be published, and that a copy of the work may be made and supplied to any bona fide library or research worker, that this thesis will be electronically accessible for personal or research use and that the library has the right to migrate this thesis into new electronic forms as required to ensure continued access to the thesis.
I, Lewis McMillan, confirm that my thesis does not contain any third-party material that requires copyright clearance.
The following is an agreed request by candidate and supervisor regarding the publication of this thesis:

\subsubsection*{Printed Copy}
No embargo on print copy.

\subsubsection*{Electronic Copy}
Embargo on all of electronic copy for a period of 1 year on the following ground(s):
Publication would preclude future publication 
\paragraph*{Supporting statement for electronic embargo request}\hspace*{0pt}\\
I wish to embargo the electronic copy of my thesis, as I intend to publish material based upon content in my thesis.

\subsubsection*{Title and Abstract}
I agree to the title and abstract being published.

\medskip

Date\dotfill \hspace{1cm} Signature of candidate \dotfill

\medskip

Date\dotfill \hspace{1cm} Signature of supervisor \dotfill

\medskip

\indent Date\dotfill \hspace{1cm} Signature of supervisor \dotfill

\section*{Underpinning Research Data or Digital Outputs}

\subsection*{Candidate's declaration}

I, Lewis McMillan, understand that by declaring that I have original research data or digital outputs, I should make every effort in meeting the University's and research funders' requirements on the deposit and sharing of research data or research digital outputs. 

\medskip

Date\dotfill \hspace{1cm} Signature of candidate \dotfill

\subsection*{Permission for publication of underpinning research data or digital outputs}

We understand that for any original research data or digital outputs which are deposited, we are giving permission for them to be made available for use in accordance with the requirements of the University and research funders, for the time being in force.
We also understand that the title and the description will be published, and that the underpinning research data or digital outputs will be electronically accessible for use in accordance with the license specified at the point of deposit, unless exempt by award of an embargo as requested below.
The following is an agreed request by candidate and supervisor regarding the publication of underpinning research data or digital outputs:
Embargo on all of electronic files for a period of 1 year on the following ground(s):
Publication would preclude future publication 

\paragraph*{Permission for publication of underpinning research data or digital outputs}\hspace*{0pt}\\
I wish to embargo the digital outputs, as I intend to publish based upon them.

\medskip

Date\dotfill \hspace{1cm} Signature of candidate \dotfill

\medskip

Date\dotfill \hspace{1cm} Signature of supervisor \dotfill

\medskip

\indent Date\dotfill \hspace{1cm} Signature of supervisor \dotfill

\chapter*{Publications and Presentations}
\subsection*{Publications}
\begin{itemize}

\item ``\textit{Development of a predictive Monte Carlo radiative transfer model for ablative fractional skin laser}'', \textbf{L. McMillan}, P. O'Mahoney, K. Feng, K. Zhou, IRM. Barnard, C. Li, S. Ibbotson, E. Eadie, CTA. Brown, and K. Wood, \textit{Lasers in Surgery and Medicine (in prep)}

\item ``\textit{$\varphi$MC, a phase tracking algorithm for Monte Carlo radiation transfer codes to model light propagation and interference in a turbid media}'', \textbf{L. McMillan}, S. Reidt, C. McNicol, IRM. Barnard, CTA. Brown, MP. MacDonald and K. Wood, \textit{Biomedical Optics Express (in prep)}

\item ``\textit{Quantifying direct DNA damage in the basal layer of skin exposed to UV radiation from sunbeds}'' IRM. Barnard, P. Tierney, CL. Campbell, \textbf{L. McMillan}, H. Moseley, E. Eadie, CTA. Brown, K. Wood, \textit{Photochemistry and photobiology} 94.5 (2018): 1017-1025.

\item ``Could psoralen plus ultraviolet A1 (“PUVA1”) work? Depth penetration achieved by phototherapy lamps'', IRM. Barnard, E. Eadie, \textbf{L. McMillan}, H. Moseley, T. Brown, K. Wood, R. Dawe, \textit{British Journal of Dermatology} (2019)

\end{itemize}

\subsection*{Presentations}

\begin{itemize}
\item ``\textit{Investigating novel cardiovascular disease biomarkers using Monte Carlo simulations}'', British Medical and Lasers Association Conference (BMLA), Darlington, May 2016
\item ``\textit{Recovering fluorescent depth information using Monte Carlo radiative transfer method and Genetic Algorithms}'', British Medical and Lasers Association Conference (BMLA), Manchester, May 2017
\item ``\textit{MCRT in medical physics}'', Invited speaker, St Andrews Monte Carlo Summer School (SAMCSS), St Andrews, August 2017
\item ``\textit{Parallel Computer Simulations of Light-Tissue Interactions for Applications in Medicine, Cosmetics Industry and Biophotonics Research}'', Invited speaker, St Andrews Computer Science School Seminar, St Andrews, April 2019
\item ``\textit{Numerical model of laser tissue ablation and thermal injury}'', British Medical and Lasers Association Conference (BMLA), London, May 2019
\item ``\textit{Medical applications of MCRT}'', Invited speaker, St Andrews Monte Carlo Summer School (SAMCSS), St Andrews, August 2019
\end{itemize}


\subsection*{Posters}

\begin{itemize}
\item ``\textit{Numerical model of laser tissue ablation and thermal injury}'', International Conference of Biophotonics (ICOB), St Andrews, May 2019
\end{itemize}


\subsection*{Awards}

\begin{itemize}
\item British Medical Laser Association (BMLA) Best talk, 2019
\end{itemize}

\subsection*{Summer Schools}

\begin{itemize}
\item Hands-on introduction to HPC, EPCC, Edinburgh 2016
\item Message-passing programming with MPI, EPCC, Edinburgh, 2017
\end{itemize}

\chapter{Abstract}
% Explain MCRT 1 para
% dev of various mcrt codes overview
% then chap by chapter
% \lipsum[1-2]
The Monte Carlo radiation transfer (MCRT) method can simulate the transport of light through turbid media.
MCRT allows the modelling of multiple anisotropic scattering events, as well as a range of microphysics such as polarisation and fluorescence.
This thesis concerns the development of several MCRT algorithms to solve various biophotonic and medically-related problems including modelling of tissue ablation and autofluorescent signals.
An extension of the MCRT method through a theoretical quasi-wave/particle model is also demonstrated, allowing beam shapes with arbitrary phase profiles to be propagated.

Tissue ablation can be used to treat acne scarring, Rhinophyma, and it can also be used to help enhance topical drug delivery.
Currently the depth of ablation is not easily elucidated from a given laser or laser power setting.
Therefore, a numerical tissue ablation model is developed using a combination of MCRT, a heat diffusion model, and a numerical tissue damage model to assess ablation crater depth and thermal damage to the surrounding tissue.

Autofluorescence is the natural fluorescence of biological structures in tissue.
Autofluorescence can be used as a biomarker of several diseases including: cardiovascular diseases, Alzheimers, and diabetes.
However, the origin of the autofluorescence signal is not completely clear.
The effect of tissue optics on the signal, which fluorophores contribute to the signal and by how much, and how different locations on the body can affect the signal are not well understood.
This thesis presents a study of the effect of tissue optics on the autofluorescent signal.
As part of this study, AmoebaMCRT was created to determine the relative concentrations of fluorophores for a given autofluorescent signal.

Finally, we developed an extension to the MCRT method which allows the simulation of quasi-wave/particles.
This method relies on the Huygens-Fresnel principle and the tracking of the phase of each individual photon packet.
The extension, $\varphi$MC, allows the modelling of complex beams that require the wave properties of light such as arbitrary order Bessel beams and Gaussian beams.
We then use $\varphi$MC to predict which beam, Bessel or Gaussian, performs ``better'' in a highly turbid medium.


\chapter{Acknowledgements}
First of all, thank you to my supervisors Dr.~Kenny Wood and Prof.~Tom Brown for allowing me the opportunity to undertake this PhD, and for all their support and encouragement over the course of my thesis.
If it weren't for you both keeping me on the straight and narrow I'm sure I would still be coding instead of writing.
Also, I swear my code is now bug free...
\medskip


Thank you to Isla for answering all my stupid questions over the past three years, and for being a good source of moral support, and good company at conferences.
Also thanks for co-founding, and mostly running, Code \& Cake. I thoroughly enjoyed it, both the baking and the talks.
Finally, thanks for reading over this thesis.
\medskip

Thank you to Sascha, Salvo, Blanca, Faisal, Danni, and Mike for allowing me to collaborate with you, and for your kindness with the time you gave me.
\medskip

Thank you to everyone at Ninewells for making me feel welcome every time I took up space in your research office.
In particular thanks to Luke, Paul, and Ewan for letting me collaborate with you, and for your good company at the conferences we attended together.
\medskip

Thank you to the whole McConnell family; Evelyn, Stevie, and Heather, for welcoming me to stay at your home whilst Kathleen and I were between homes, and for finding accommodation for us both.
I would also like to thank you for everything that you have done for me over these past four years, it has made it so much easier to complete this thesis.
Thank you also to the thesis fairy for the much needed Haribo as I was writing up.
\medskip

A huge thank you to my Mum, Rachel, Eilidh, Allan, Caroline, and Archie, for all the support you have given to me over my last nine years at St Andrews.
All your frequent messages on the family chat have been a source of entertainment and much needed distraction.
I can't begin to list everything you have done for me, but I really appreciate knowing that you are always there for me.
\medskip

Finally, last but certainly not least, to Kathleen.
This thesis would never have been completed if it wasn't for your constant love and support.
Thank you for understanding when I got stressed or chose to work weekends and nights on my PhD, and even on the occasions where I never noticed the time and forgot to meet you.
\noindent Consider reading this as the favour repaid for when I read your \textbf{two} dissertations!

\newpage
\section*{Funding}

This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/K503162/1].

\section*{Research Data/Digital Outputs access statement}


Research data underpinning this thesis are available at TBC
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\begin{center}
    \vspace*{\fill}
    For Lil and Marion.
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\clearpage
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\tableofcontents
\printnoidxglossaries
\newpage

\renewcommand{\cftdotsep}{\cftnodots}%get rid of dots and numbers on LoFs
\cftpagenumbersoff{figure}%ditto

\listoffigures
\addcontentsline{toc}{chapter}{List of Figures}

%arabic numbers
\mainmatter

\include{introduction/intro}
\include{MCRT/mcrt}
\include{ablation/ablation}
\include{bessel/bessel}
\include{fluro/salvo}
\include{conc/conclusion}
\include{appendix/append}

\bibliography{./introduction/intro,./ablation/ablation,./MCRT/mcrt,./bessel/bessel,./fluro/salvo,./conc/conclusion}
\bibliographystyle{unsrt}
\end{document}