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\subsection{Physiological Background}\label{subsec:physiological_background}
\subsubsection{Menstrual Cycle}\label{subsec:menstrual_cycle}
The menstrual cycle describes the physiological changes in the female body that prepare it for pregnancy.
It is divided into two phases: the \textbf{follicular phase} and the \textbf{luteal phase}.
\\
During the follicular phase, the ovarian follicles mature, and the endometrium (the inner lining of the uterus) thickens
in preparation for a potential implantation of a fertilized egg.
Around day 14 of a typical cycle, ovulation occurs, marking the transition to the luteal phase.
Ovulation refers to the rupture of the mature ovarian follicle and the release of an egg cell into the fallopian tube.
The menstrual cycle consists of physiological changes preparing the female body for potential pregnancy,
typically spanning around 28 days but varying considerably among individuals.
It includes two main phases: the follicular phase, beginning with menstruation, and the luteal phase, following ovulation.
Ovulation is triggered by a surge in \textbf{luteinizing hormone (LH)}
and \textbf{follicle-stimulating hormone (FSH)}, following a peak in estradiol levels.
As ovulation occurs, estradiol levels drop, progesterone levels begin to rise and a slight increase in body temperature
(typically around 0.5°C) can be observed.
This marks the beginning of the luteal phase.
During the follicular phase, ovarian follicles mature under the influence of rising estradiol levels, thickening the uterine lining (endometrium).
Around mid-cycle, a surge of luteinizing hormone (LH) and follicle-stimulating hormone (FSH), triggered by peak estradiol,
induces ovulation—the release of a mature egg into the fallopian tube.
During the luteal phase, the endometrium thickens further, creating an optimal environment for embryo implantation.
LH and FSH levels decrease, while progesterone remains elevated to support endometrial maintenance.
If fertilization does not occur, progesterone levels drop, leading to the shedding of the endometrial lining along
with the unfertilized egg.
This process, known as menstruation, marks the beginning of a new cycle.
After ovulation, the luteal phase begins.
Progesterone increases substantially, maintaining endometrial thickness for potential embryo implantation.
In parallel, a subtle rise in body temperature (~0.5°C) occurs due to progesterone elevation.
If fertilization does not happen, progesterone and temperature decline back to baseline levels, resulting in menstruation and initiating a new cycle.
\begin{figure}[htbp]
\centering
@@ -36,27 +29,23 @@ This process, known as menstruation, marks the beginning of a new cycle.
\label{fig:background_menstrual_cycle_physiology}
\end{figure}
The menstrual cycle typically lasts around 28 days, with ovulation occurring near the midpoint.
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}.
Figure~\ref{fig:background_menstrual_cycle_physiology} provides a detailed overview of the hormonal and physiological changes throughout the menstrual cycle.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.9\textwidth]{resources/figures/background/background_labeled_cycle}
\caption{Body core temperature curve across a menstrual cycle. The red line represents a locally smoothed temperature trend.
Menstruation, ovulation, and the fertile phase are indicated in red, blue, and green, respectively.}
Menstruation, ovulation, and the fertile window are indicated in red, blue, and green, respectively.}
\label{fig:background_labeled_cycle}
\end{figure}
Figure~\ref{fig:background_menstrual_cycle_physiology} illustrates these physiological changes, highlighting hormonal fluctuations and temperature shifts around ovulation.
The menstrual cycle length varies significantly, influenced by factors such as stress, age, diet, and exercise~\cite{silberstein_physiology_2000}.
Figure~\ref{fig:background_labeled_cycle} shows the temperature curve over the course of a menstrual cycle with the
menstruation, fertile phase and ovulation marked.
menstruation, fertile window and ovulation marked.
It starts with a menstruation and ends just before the next menstruation.
The follicular phase starts at the beginning and goes on until the ovulation.
The luteal phase begins at the ovulation and continues until the next menstruation.
Not every cycle results in ovulation—a phenomenon known as anovulation—which leads to a monophasic temperature pattern.
Anovulation can have various causes, including hormonal imbalances, stress, or underlying health conditions~\cite{rosenfield_adolescent_2013}.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.9\textwidth]{resources/figures/background/background_anovulatory_cycle}
@@ -65,25 +54,28 @@ Anovulation can have various causes, including hormonal imbalances, stress, or u
\end{figure}
Anovulation is reflected in temperature data as either an absence of a clear temperature rise or a rise
that is insufficient in magnitude or duration to be considered a reliable indicator of ovulation.
Distinguishing between ovulatory and anovulatory cycles is challenging, as the only definitive confirmation of
successful ovulation in a clinical sense is a positive pregnancy test.
While many cycles exhibit a characteristic biphasic pattern, deviations from this norm are common.
Some remain monophasic, which might be an indication for an anovulatory cycle, which is a menstrual cycle, where no ovulation occurs.
Anovulation can have various causes, including hormonal imbalances, stress, or underlying health conditions~\cite{rosenfield_adolescent_2013}.
Monophasic cycles with a confirmed ovulation event have been observed, so there seems to be no clear indication that it is a direct cause of anovulation~\cite{moghissi_accuracy_1976}.
Thus, distinguishing between ovulatory and anovulatory cycles is challenging, as the only definitive confirmation of
successful ovulation in a clinical sense is a pregnancy.
Even ultrasound imaging can only confirm that an egg was released from its follicle—not whether it was successfully implanted or fertilized.
Figure~\ref{fig:background_anovulation} shows a cycle that does not have an ovulation, and thus no resulting temperature rise.
Figure~\ref{fig:background_anovulation} shows a cycle with a monophasic temperature pattern.
To illustrate the diversity of real-world menstrual cycles, Figures~\ref{fig:background_long_cycle} and~\ref{fig:background_short_cycle}
show examples of cycles that are significantly longer or shorter than a normative 28-day cycle.
\citeauthor{bull_real-world_2019} have done an extensive study on cycle variability,
highlighting that women frequently deviate from the normative cycle, especially with age\cite{bull_real-world_2019}.
\begin{figure}[htb]
\begin{figure}[htbp]
\centering
\includegraphics[width=0.9\textwidth]{resources/figures/background/background_long_cycle}
\caption{Example of a long cycle with a length of 111 days}
\label{fig:background_long_cycle}
\end{figure}
\begin{figure}[htb]
\begin{figure}[htbp]
\centering
\includegraphics[width=0.9\textwidth]{resources/figures/background/background_short_cycle}
\caption{Example of a short cycle with a length of 22 days}
@@ -93,36 +85,28 @@ show examples of cycles that are significantly longer or shorter than a normativ
These irregularities appear not only on a per-cycle basis, but also across time within the same individual.
Figures~\ref{fig:background_irregular_cycles} and~\ref{fig:background_regular_cycles}
show examples of a woman with an irregular and a regular menstrual cycle pattern, respectively.
Raw body core temperature readings are shown in light blue, with a red line indicating smoothing by local regression.
Vertical dotted black lines mark the beginning of each cycle.
The irregular example highlights how multiple parameters can vary between individuals:
cycle length, timing of ovulation, temperature shift magnitude between phases, and intra-phase temperature variability.
This multidimensional variability underscores the need for adaptive, data-driven models capable of learning personalized patterns---
rather than relying on population-wide assumptions.
For a regular cycle pattern, sophisticated analysis or predictions are often not necessary, as the last ovulation day
can reliably be used as the next.
\begin{figure}[htb]
\begin{figure}[htbp]
\centering
\includegraphics[width=0.9\textwidth]{resources/figures/background/background_irregular_cycle_example}
\caption{Example of a woman with irregular menstrual rhythm}
\caption{Example of a woman with irregular menstrual rhythm. The dashed vertical lines indicate the ends of each cycle.}
\label{fig:background_irregular_cycles}
\end{figure}
\begin{figure}[htbp]
\centering
\includegraphics[width=0.9\textwidth]{resources/figures/background/background_regular_cycle_example}
\caption{Example of a woman with regular menstrual rhythm}
\caption{Example of a woman with regular menstrual rhythm. The dashed vertical lines indicate the ends of each cycle.}
\label{fig:background_regular_cycles}
\end{figure}
\subsubsection{Fertility Prediction}\label{subsubsec:fertility_prediction}
Throughout the menstrual cycle, the chance of fertilization varies significantly.
An egg cell released from the ovary during ovulation, can be fertilized for up to 24 hours.
However, since male sperm cells can survive up to 6 days inside the female reproductive tract,
the fertile window is typically defined as the five days before ovulation until one day after ovulation~\cite{dunson_day-specific_1999}.
Research by~\citeauthor{dunson_day-specific_1999} has shown that the highest chance of fertilization is around one day before ovulation,
as illustrated in Figure~\ref{fig:background_pregnancy_chance}.
Fertility varies throughout the menstrual cycle, centered around the ovulation event.
An egg remains viable for about 24 hours post-ovulation, while sperm can survive up to 6 days in a woman's reproductive tract,
thus the fertile period extends to approximately five days prior to ovulation~\cite{dunson_day-specific_1999}.
Consequently, the whole fertile window generally spans six days: five days preceding ovulation and one day after.
\begin{figure}[htbp]
\centering
@@ -132,11 +116,30 @@ as illustrated in Figure~\ref{fig:background_pregnancy_chance}.
\label{fig:background_pregnancy_chance}
\end{figure}
It is important to note that fertility prediction is inherently dependent on ovulation prediction.
Since the probability of conception is tightly linked to ovulation timing, the accuracy of fertility prediction methods
is constrained by the precision of ovulation detection.
This relationship underscores the necessity of developing reliable ovulation prediction models,
as even small inaccuracies can significantly impact fertility assessments.
Figure~\ref{fig:background_pregnancy_chance} demonstrates the probability of fertilization peaking one day before ovulation, emphasizing the critical timing for fertility prediction.
Fertility prediction fundamentally depends on accurate ovulation timing.
However, since the goal is to identify the fertile window before ovulation occurs, detection must be early and precise.
For individuals trying to conceive or avoid pregnancy, knowing the window of fertility is more actionable than identifying the ovulation event itself.
\subsubsection{Practical Use Cases}\label{subsubsec:practical_use_cases}
In this study, we will focus on \emph{natural family planning} (NFP), which includes preventing and achieving pregnancy.
Individuals aiming to avoid pregnancy identify fertile days to abstain from intercourse,
whereas those seeking pregnancy aim to focus intercourse around days with the highest fertility probability.
Both use cases revolve around accurately predicting ovulation.
However, the implications of prediction errors differ significantly.
A false-positive prediction indicates high fertility despite actual fertility being low or nonexistent,
whereas a false-negative prediction implies low fertility when fertility is actually high.
For women aiming to avoid pregnancy, minimizing false-negative predictions is crucial due to the risk of unintended pregnancy.
Although false-positives may lead to unnecessary abstinence, this outcome is generally considered less severe.
Consequently, prediction algorithms should be conservative, erring on the side of higher fertility estimates to prioritize safety.
Conversely, for women aiming to conceive, false-positive predictions could misdirect efforts toward incorrect cycle days,
causing frustration or delays.
False-negatives have fewer negative consequences.
Therefore, algorithms for this group should prefer cautious fertility estimates, reducing the risk of misdirected effort.
\subsubsection{Physiological Signs of Ovulation}\label{subsubsec:physiological_signs}
Several physiological signs correlate with ovulation and can be used for prediction.
@@ -154,26 +157,7 @@ detecting the slight temperature rise that follows ovulation.
Advances in wearable technology have further enabled continuous and automated temperature monitoring,
improving accessibility and usability~\cite{alexander_fertilitatsmonitoring_2014, luo_detection_2020, yu_tracking_2022}.
\subsubsection{Use Cases of Fertility Prediction}\label{subsubsec:use_cases_of_ovulation_prediction}
The prediction of ovulation and corresponding fertility within a menstrual cycle serves two distinct use cases.
Specifically, we will focus on \emph{natural family planning} (NFP), which includes preventing and achieving pregnancy.
Individuals aiming to avoid pregnancy identify fertile days to abstain from intercourse,
whereas those seeking pregnancy aim to focus intercourse around days with the highest fertility probability.
Both use cases revolve around accurately predicting ovulation.
However, the implications of prediction errors differ significantly.
A false-positive prediction indicates high fertility despite actual fertility being low or nonexistent,
whereas a false-negative prediction implies low fertility when fertility is actually high.
For women aiming to avoid pregnancy, minimizing false-negative predictions is crucial due to the risk of unintended pregnancy.
Although false-positives may lead to unnecessary abstinence, this outcome is generally considered less severe.
Consequently, prediction algorithms should be conservative, erring on the side of higher fertility estimates to prioritize safety.
Conversely, for women aiming to conceive, false-positive predictions could misdirect efforts toward incorrect cycle days,
causing frustration or delays.
False-negatives have fewer negative consequences.
Therefore, algorithms for this group should prefer cautious fertility estimates,
reducing the risk of misdirected effort.
Among the available methods, temperature-based monitoring, especially when automated and continuous, offers a promising avenue for large-scale cycle analysis.
\subsection{Data Source and Characteristics}\label{subsec:data_background}
This study is based on a dataset collected from users of the \emph{OvulaRing}~\cite{noauthor_ovularing_nodate},
@@ -202,14 +186,15 @@ Therefore, all user-entered cycle starts undergo manual review to reduce annotat
In addition to temperature measurements, the database includes contextual metadata such as age, height, weight, and optional user-entered markers.
These markers provide further physiological context and may include information about intermediate bleeding, sexual intercourse, or positive pregnancy tests.
At the time of writing, the dataset contains approximately 65{,}000 annotated cycles, comprising more than 350 million individual temperature measurements.
At the time of writing, the dataset contains approximately 65{,}000 annotated cycles,
comprising more than 350 million individual temperature measurements~\footnote{This is the largest dataset of continuous body core temperature data used in any study so far.}.
\subsubsection{Dataset Summary}
For the present study, the dataset was reduced to approximately 40{,}000 cycles after filtering out entries that were incomplete,
contained hardware-related anomalies, or fell outside a reasonable cycle length range.
Very short cycles typically result from incorrect cycle start entries or premature termination of temperature recordings.
Extremely long cycles are often due to data entry errors or pregnancy-related recordings,
Cycles shorter than 10 days typically result from incorrect cycle start entries or premature termination of temperature recordings.
Long cycles, longer than 150 days, are often due to data entry errors or pregnancy-related recordings,
where the sensor was worn continuously throughout gestation—sometimes producing sequences up to nine months long.
While such cases may still contain useful information, they were excluded from this analysis to avoid complications in preprocessing and labeling.
@@ -222,16 +207,18 @@ The median number of cycles per user is 4 (IQR: 2--8) and the median cycle lengt
The average data density—defined as the fraction of available measurements out of the theoretical maximum of 288 measurements per day—is 0.90.
This corresponds to an average data availability of 90\% per cycle, with an average loss of 10\%.
It should be noted, that both ovulation day and anovulation estimates are based on retrospective algorithmic inference, not human labels.
Further details are provided in section~\ref{sec:methodology}.
37934 cycles (94\%) were classified as biphasic and 2333 (6\%) as monophasic.
Users had a median age of 32 years (IQR: 29–36), median weight of 65 kg (IQR: 58–77), and median height of 168 cm (IQR: 163–172).
\subsubsection{Irregularities and Confounding Factors}
Core body temperature is influenced by various factors unrelated to the menstrual cycle.
Despite careful data collection, real-world measurements are subject to physiological and behavioral noise.
Especially core body temperature is influenced by various factors unrelated to the menstrual cycle.
Illnesses—especially those involving fever—can significantly affect temperature patterns.
This poses a challenge for any analysis relying on temperature data, as one of the key physiological indicators of ovulation is a post-ovulatory temperature rise (see Section~\ref{subsubsec:physiological_signs}).
Figure~\ref{fig:background_fever_cycle} shows an example of a cycle where an illness caused a marked increase in temperature.
This event is particularly problematic because the fever-induced rise occurs just before the expected ovulatory shift, potentially confounding ovulation detection.
This event is particularly problematic because the fever-induced rise occurs just before the expected ovulatory shift, potentially confounding fertility detection.
Distinguishing illness-related changes from cycle-related ones requires models that are sensitive to context and robust to outliers.
\begin{figure}[htbp]
@@ -254,39 +241,35 @@ Figure~\ref{fig:background_menstruation_data_gap} shows an example cycle with a
\label{fig:background_menstruation_data_gap}
\end{figure}
%TODO: more stats!
\subsubsection{Privacy}
The dataset used in this study contains sensitive personal health information and is handled with strict privacy safeguards.
All data is pseudonymized and processed exclusively on encrypted devices, ensuring that no identifiable information can be traced back to individual users.
VivoSensMedical does not share user data with third parties; the data is used solely for internal research and product improvement efforts that directly benefit users at no additional cost.
\subsection{Technical Background}\label{subsec:technological_background}
With a large, high-resolution dataset of longitudinal temperature measurements and associated metadata available,
the next challenge lies in how to model such sequential data effectively.
Accurate ovulation prediction requires algorithms that can handle temporal dependencies,
irregularities, and physiological variability across users.
To this end, we turn to machine learning techniques designed for time series analysis,
beginning with foundational concepts and progressing to modern neural architectures.
\subsubsection{Time Series Analysis}\label{subsubsec:time_series_analysis}
Time series analysis is a fundamental tool for studying sequential data that evolves over time.
Unlike other data types, time series data has an inherent temporal order, where each data point is associated
with a timestamp, capturing its dependence on past values.
Time series analysis typically serves two main goals:
Understanding the underlying mechanisms that lead to the observed data and predicting future data points based on the
historical information and potentially external factors~\cite{cryer_time_2008}
\\
Time series analysis encompasses various methods, ranging from simple statistical models to complex deep learning architectures.
Classical methods
In the following, we will introduce the two most common approaches used for machine learning on time series data,
LSTMs and transformers.
Temperature data recorded by the OvulaRing forms a high-resolution time series, where each measurement carries temporal context.
Time series analysis is essential to uncover meaningful patterns and predict future physiological states from such sequential data.
In machine learning, this often involves models that can learn temporal dependencies—most notably
Recurrent Neural Networks (RNNs) and the more recent Transformer architecture.
\subsubsection{RNN and LSTM Networks}\label{subsubsec:lstm_networks}
Recurrent Neural Networks (RNNs) are extensions of classical neural networks that incorporate cyclic connections between neurons.
These recurrent connections allow the network to retain information from previous inputs by feeding the hidden state
from a prior time step into the current one, enabling a form of temporal memory.
They process input \emph{sequentially}, maintaining this hidden state over time.
In practice, this means that input data is processed sequentially, one step at a time.
At each step \(t\), the input \(x_t\) is combined with the previous hidden state \(h_{t-1}\) to produce a new
hidden state \(h_t\), which contributes to the output \(o_t\).
This process allows the network to learn temporal dependencies and model sequential data effectively~\cite{medsker_recurrent_1999}.
This enables the network to learn temporal dependencies in sequential data~\cite{medsker_recurrent_1999}.
However, this approach has the downside that the model cannot explicitly control how it remembers or forgets information at each step,
limiting its ability to manage long-term dependencies.
@@ -366,7 +349,7 @@ as well as the biases for each gate in a cell, are learned through backpropagati
To build more expressive models, memory cells can be stacked in multiple layers, and their outputs concatenated or passed sequentially to higher layers.
LSTMs are widely used in biomedical applications due to their capacity to handle sequences of variable length and complexity.
In the context of ovulation prediction, where hormonal patterns exhibit periodicity but also irregularity,
In the context of fertility prediction, where hormonal patterns exhibit periodicity but also irregularity,
LSTMs are well-suited to learn relevant time-dependent signals from sequential physiological measurements.
While powerful, LSTMs can be computationally intensive and sensitive to hyperparameter tuning.
@@ -374,16 +357,19 @@ Therefore, they are often compared with alternative architectures,
including simpler feedforward networks and more recent attention-based models,
to evaluate trade-offs in performance, interpretability, and computational cost.
The next section introduce the \emph{Transformer} architecture, a more recent alternative that forgoes
Given their ability to learn from sequences with noisy periodic structure,
LSTMs offer a natural choice for modeling hormonal and temperature fluctuations across menstrual cycles.
The next section introduces the \emph{Transformer} architecture, a more recent alternative that forgoes
recurrence in favor of attention mechanisms.
\subsubsection{Transformer Models}\label{subsubsec:transformer_models}
Transformer models are a class of neural architectures that use \emph{self-attention}
to model dependencies in sequential data without relying on recurrence~\cite{vaswani_attention_2017}.
Unlike recurrent neural networks (RNNs), Transformers process input sequences in parallel,
Unlike recurrent neural networks (RNNs), Transformers process input sequences \emph{in parallel},
allowing them to model relationships between any pair of input tokens or timesteps directly.
This mitigates the limitations of recurrent models, such as long-term memory constraints
This design mitigates the limitations of recurrent models, such as long-term memory constraints
and vanishing gradients.
Originally introduced for machine translation, Transformers have proven broadly applicable to
@@ -423,13 +409,13 @@ to the model regardless of their location, even if they play different syntactic
Positional encodings, often based on sinusoidal functions, inject a unique position-dependent signal
into each token, enabling the model to distinguish between identical tokens in different positions.
In this work, we use since and cosine functions of different frequencies:
In this work, we use sine and cosine functions of different frequencies:
\begin{align}
PE_{\text{pos}, 2i} &= \sin\left(\frac{\text{pos}}{10000^{\frac{2i}{d_{\text{model}}}}}\right), \\
PE_{\text{pos}, 2i+1} &= \cos\left(\frac{\text{pos}}{10000^{\frac{2i}{d_{\text{model}}}}}\right)
\end{align}
where \(i\) is the dimension of the input and \(pos\) is the position in the sequence.
This was done according to the original paper~\cite{vaswani_attention_2017}.
where \(i\) is the dimension of the input and \(pos\) is the position in the sequence,
as in the original paper~\cite{vaswani_attention_2017}.
\begin{figure}[htbp]
\centering
@@ -553,6 +539,9 @@ including time-series forecasting and biomedical modeling~\cite{wu_deep_nodate,z
Its ability to model complex, long-range dependencies without recurrence makes it well-suited to domains like biomedical time-series,
where signals are often irregular and span diverse temporal resolutions.
This makes Transformers well-suited for learning long-range temporal dependencies in physiological data,
such as ovulatory trends spanning multiple days or cycles.
\subsubsection{Convolutional Layers as Temporal Feature Extractors}
For high-resolution time-series data, the input dimensionality can become large,
especially in models like Transformers that process the entire sequence in parallel.
@@ -578,3 +567,7 @@ The stride determines how far the filter moves at each step, affecting both the
\label{fig:background_convolution_example}
\end{figure}
In summary, time-series modeling offers a range of approaches, each with specific trade-offs.
RNNs and LSTMs provide explicit sequential modeling but suffer from training inefficiencies.
Transformers excel at long-range context capture but demand more memory and parallelization.
Convolutional layers offer efficient local feature extraction and often serve as useful pre-processing stages for both model families.