Estimation of respiratory frequency from Heart Rate Variability

Abstract

In this master's thesis the ability to estimate the respiratory frequency from heart rate variability measurement is analyzed. The goal was to implement a solution that is easily transferable to real time. Starting from the initial processing of data, continuing with two different spectrogram implementations, a single spectrogram and a multitaper spectrogram, combined with three different methods of spectral estimates for each time step in the two spectrograms, the respiratory frequency is estimated. A relatively limited real data set, in combination with the necessity to evaluate the different permutations of methods in a controlled environment, created the need to start on simulated data. The different permutations of methods were evaluated on the simulated data with sane defaults in order to find the best performing methods. The chosen methods were then applied to real data containing 97 different individuals. In order to maximize the different methods' capabilities the real data was divided into two data sets, one for training, and one for validation, containing 31 and 66 individuals each. The best performing methods found in the simulations were then evaluated with different parameter choices, and the weights for a multitaper spectrogram method were optimized.

The conclusion is that the respiratory frequency is possible to estimate with a low margin of error from the traditional high frequency band, $0.12-0.4$Hz, of the heart rate variability. The ever present time-delay of time-frequency estimates when using a spectrogram is the main contributor to the errors when estimating the actual frequency of a signal, when no noise is present. This is also the case when estimating the true respiratory frequency from the heart rate variability. If the minimization of time-delay in the frequency estimate is needed, a standard spectrogram, combined with a high heart rate will maximize the possibility of accurately estimating the respiratory frequency from the heart rate variability. For most applications outside a controlled environment however, the signal-to-noise ratio is a problem. With the small drawback of a few seconds more of extra time-delay, any multitaper spectrogram solution will perform equal or better than a single spectrogram method for time-frequency estimation. If a ''real time'' estimation is of no concern, a simple offset in time in post-processing of the estimated respiratory frequency will yield a result with the best of two worlds.

Popular Abstract

More and more devices are today collecting data about individuals' heart rate. Smartphone applications are today using data collected from different heart rate monitoring devices, e.g. smart-watches and chest straps, and using a combination of resting heart rate and the heart rate variability in order to help people make smarter training and lifestyle choices. In this study the exploration of heart rate continues, namely what more is possible to determine with the use of only heart beats. The breathing speed of an individual is closely connected to the speed in which the heart beats. The goal was to explore the implications of this connection, and evaluate under which assumptions this connection can be used in order to predict the breathing speed of an individual.

The correlation between the heart rate variability (HRV) and the respiratory frequency (RF) is established, and the HRV is possible to estimate with good precision from the RF of an individual. The opposite is not yet fully explored, the problem with the HRV as a predictor for the RF is that the nervous system of an individual regulates a plethora of different body functions. The high frequency HRV band (HF-HRV) is the main component related to the connection between the RF and the HRV. Using this connection the precision of the estimated RF from HRV was mainly determined by time-delay, the disturbance present, and the speed of which the heart rate and the RF was changing.

With the goal of a low-latency solution on data from a controlled environment, and sufficiently close estimation, different methods of RF estimation were explored. The time-delay needed in order to estimate the RF ''properly'' was determined to be about $15-25$ seconds on data collected with the usage of an ECG. In order to make the solution more robust to disturbances, a couple more methods were evaluated, with mixed performance, and a robust solution against disturbances was found with equal or even lower time delay needed. When a chest strap was used instead of an ECG signal in order to estimate the RF, the time-delay needed exceeded $45$ seconds.

Further development of the precise tracking of RF from HRV in combination with the increased precision of measuring heart rate related metrics in consumer devices, will in the future enable individuals to generate more relevant metrics about their health with less apparatus needed. A low time delay between RF and HRV will enable individuals during a data-driven workout to not only keep track of the heart rate, but also how much they are breathing.

The goal of a low-latency solution for frequency estimation once again brought to light the problems associated with knowing both time and frequency at the same time.

• author: Ågärd, Daniel
• supervisor: Maria Sandsten
• organization: Mathematical Statistics
• alternative title: Estimation of RF from HRV
• course: FMSM01 20231
• year: 2023
• type: H2 - Master's Degree (Two Years)
• subject: Mathematics and Statistics
• keywords: time-frequency analysis, multitaper spectrogram, Optimization, signal processing, heart rate variability
• publication/series: Master's Theses in Mathematical Sciences
• report number: LUTFMS-3473-2023
• ISSN: 1404-6342
• other publication id: 2023:E22
• language: English
• id: 9117417
• date added to LUP: 2023-05-29 12:50:20
• date last changed: 2023-05-29 12:50:20