started work on introduction and background
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% Packages
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\usepackage{amsmath}
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% biber bibliography
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\usepackage{graphicx}
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\graphicspath{{resources/figures/}}
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\usepackage[style=ieee, backend=biber]{biblatex}
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\addbibresource{../main.bib}
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% university and faculty
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\maketitle
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\include{sections/introduction/introduction}
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\include{sections/introduction}
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\include{sections/background/background}
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\include{sections/background}
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\include{sections/related_work/related_work}
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\include{sections/related_work}
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\include{sections/methodology/methodology}
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\include{sections/methodology}
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\include{sections/results/results}
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\include{sections/results}
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\include{sections/discussion/discussion}
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\include{sections/discussion}
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\include{sections/conclusion/conclusion}
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\include{sections/conclusion}
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\printbibliography
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%! Author = alex
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%! Date = 3/7/25
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\section{Background}\label{sec:background}
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\subsection{Physiological Background}\label{subsec:physiological_background}
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\subsubsection{Menstrual Cycle}\label{subsec:menstrual_cycle}
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The menstrual cycle describes the physiological changes in the female body that prepare it for pregnancy.
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It is divided into two phases: the \textbf{follicular phase} and the \textbf{luteal phase}.
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\\
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During the follicular phase, the ovarian follicles mature, and the endometrium (the inner lining of the uterus) thickens
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in preparation for a potential implantation of a fertilized egg.
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Around day 14 of a typical cycle, ovulation occurs, marking the transition to the luteal phase.
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Ovulation refers to the rupture of the mature ovarian follicle and the release of an egg cell into the fallopian tube.
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Figure\ref{fig:background_basic_female_reproductive_system} illustrates the female reproductive system,
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including the ovaries and the fallopian tubes.
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\\
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\begin{figure}
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\centering
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\includegraphics[width=0.4\textwidth]{background_female_reproductive_organs}
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\caption{The basic female reproductive system\cite{wikimedia_commons_basic_2019}.}
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\label{fig:background_basic_female_reproductive_system}
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\end{figure}
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Ovulation is triggered by a surge in \textbf{luteinizing hormone (LH)}
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and \textbf{follicle-stimulating hormone (FSH)}, following a peak in estradiol levels.
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As ovulation occurs, estradiol levels drop, progesterone levels begin to rise and a slight increase in body temperature
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(typically around 0.5°C) can be observed.
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This marks the beginning of the luteal phase.
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\\
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During the luteal phase, the endometrium thickens further, creating an optimal environment for embryo implantation.
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LH and FSH levels decrease, while progesterone remains elevated to support endometrial maintenance.
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If fertilization does not occur, progesterone levels drop, leading to the shedding of the endometrial lining along
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with the unfertilized egg.
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This process, known as menstruation, marks the beginning of a new cycle.
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\\
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The menstrual cycle typically lasts around 28 days, with ovulation occurring near the midpoint.
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However, variations, particularly in the follicular phase length, are common and can be influenced by factors such as stress, diet, exercise and age\cite{silberstein_physiology_2000}.
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Figure~\ref{fig:background_menstrual_cycle_physiology} provides a detailed overview of the hormonal and physiological changes
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throughout the menstrual cycle.
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\begin{figure}
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\centering
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\includegraphics[width=0.7\textwidth]{background_menstrual_cycle_physiology}
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\caption{Physiological changes during the menstrual cycle\cite{pedroso_menstrual_2022}.}
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\label{fig:background_menstrual_cycle_physiology}
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\end{figure}
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\subsubsection{Fertility Prediction}\label{subsec:fertility_prediction}
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Throughout the menstrual cycle, the chance of fertilization varies significantly.
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An egg cell released from the ovary during ovulation, can be fertilized for up to 24 hours.
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However, since male sperm cells can survive up to 6 days inside the female reproductive tract,
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the fertile window is typically defined as the five days before ovulation until one day after ovulation\cite{dunson_day-specific_1999}.
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Research by \citeauthor{dunson_day-specific_1999} has shown that the highest chance of fertilization is around one day before ovulation,
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as illustrated in Figure~\ref{fig:background_pregnancy_chance}.
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\begin{figure}
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\centering
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\includegraphics[width=0.8\textwidth]{background_pregnancy_chance_over_time}
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\caption{Chance of fertilization depending on the day of the menstrual cycle.
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The highest chance is around one day before ovulation\cite{dunson_day-specific_1999}.}
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\label{fig:background_pregnancy_chance}
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\end{figure}
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It is important to note that fertility prediction is inherently dependent on ovulation prediction.
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Since the probability of conception is tightly linked to ovulation timing, the accuracy of fertility prediction methods
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is constrained by the precision of ovulation detection.
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This relationship underscores the necessity of developing reliable ovulation prediction models,
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as even small inaccuracies can significantly impact fertility assessments.
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\subsubsection{Physiological Signs of Ovulation}\label{subsec:physiological_signs}
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Several physiological signs correlate with ovulation and can be used for prediction.
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As shown in Figure~\ref{fig:background_menstrual_cycle_physiology}, these include hormonal fluctuations (LH and FSH surges) and
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changes in body temperature.
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Additionally, variations in cervical mucus consistency, salivary ferning patterns,
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and electrical resistance of the skin and vaginal mucosa have been observed\cite{silberstein_physiology_2000}.
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Among these, ultrasonography provides the most accurate confirmation of ovulation by detecting follicular changes,
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but it is costly and requires specialized equipment.
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Hormone measurements in urine and blood are widely used and available in at-home test kits,
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but they require frequent testing.
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Temperature-based methods, particularly body temperature tracking, offer a non-invasive alternative by
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detecting the slight temperature rise that follows ovulation.
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Advances in wearable technology have further enabled continuous and automated temperature monitoring,
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improving accessibility and usability\cite{alexander_fertilitatsmonitoring_2014, luo_detection_2020, yu_tracking_2022}.
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\subsection{Technical Background}\label{subsec:technological_background}
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%! Author = alex
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%! Date = 3/7/25
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\section{Background}\label{sec:background}
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\subsection{Menstrual Cycle}\label{subsec:menstrual_cycle}
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The ovulation is defined as the rupture of the ovarian follicle and the release of an egg cell into the fallopian tube.
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There, the egg cell can be fertilized by sperm cells and develop into an embryo\cite{holesh_physiology_2025}.
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This is accompanied by changes in the fluxing gonadotropin-releasing hormone (GnRH), luteinizing hormone (LH),
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and follicle-stimulating hormone (FSH) levels in the blood.
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Additionally, the basal body temperature (BBT) rises by about 0.5 degrees Celsius after ovulation.
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% explain different physiological signs usable for prediction, advantages and disadvantages
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%! Author = alex
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%! Date = 3/6/25
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\section{Methodology}\label{sec:methodology}
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% why did I select tft over other methods -> include examples of time series and why I belief a complex model could help
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% you did I apply it
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% implementation details
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%! Author = alex
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%! Date = 3/6/25
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\section{Methodology}\label{sec:methodology}
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%! Author = alex
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%! Date = 3/6/25
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\section{Related Work}\label{sec:related_work}
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%parts: traditional methods, ml approaches, tft in medical time series or other time series
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%! Author = alex
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%! Date = 3/6/25
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\section{Related Work}\label{sec:related_work}
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