A novel mathematical method to detect stress

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Current mathematical models can analyse physiological signals in separate intervals. Oxford researchers have developed an algorithm which allows multiple signals to be analysed together over a defined time period. Analysing the signals in this way extracts more information regarding the individual’s state and reduces the risk of misdiagnoses. This technology can be implemented into a device to detect stress levels as well as other physical and emotional states that would add value to health and fitness systems.

Determining both physical and emotional states based on physiological signals is carried out in many fields including medicine, health, fitness and sport. The current approach typically extracts simple features such as heart rate and respiration rate over a fixed window and then trains a machine-learning classifier using these new static features.

The features extracted using this approach misses significant information about the fine-scale structure of the input paths, in particular the way in which a person breaths, how their breathing pattern changes over time, and the interactions between the changes in breathing and changes in heart rate. If improved methods were developed that utilise additional information contained in the high-frequency physiological signals, this would increase the number of cases correctly diagnosed.

Stress can have a significant impact on a person’s wellbeing by contributing to heart disease through to affecting mental health. Therefore, by having an accurate detection method it will allow appropriate management at an early stage.

A new mathematical approach

Mathematicians at the University of Oxford have been able to advance the processing of multiple high-frequency physiological signals to create a more accurate and reliable output regarding an individual’s state. For this technology, physiological signals are measured over a physiologically relevant time window, for example, one breath (inhale/exhale) or a heartbeat signal, rather than an arbitrary time limit.

This provides the physician with a natural window to extract meaningful features from through utilisation of some feature extraction technique such as the signature method. Using the breath as an example these features will not only contain the rate of breathing but also more fine-scale details about how that breath was breathed and how all these changes interact with other signals over the course of a breath.

These features can then be combined with feature over multiple breaths to train a machine-learning algorithm to come up with a more accurate state of an individual than the more traditional features alone.
This mathematical model can be incorporated into a device to, for example, determine stress levels, cardiac health or the presence of sleep apnoea.

Key advantages

With this technology, the accuracy in detecting physical and emotional states can potentially be improved compared to the current system as:

  • The relationship between multiple signals can now be analysed in an effective manner
  • The results from several time windows e.g. multiple breaths can effectively strengthen the signal
  • The use of a trained machine learning algorithm is fast, accurate and efficient


Oxford University Innovation filed patent applications directed to this technology and is looking for an industrial partner to develop this opportunity further.

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