Simulating heart rate kinetics during incremental and interval training

Abstract

SummaryStudy aim: To apply a recently proposed dynamical systems model to simulate, for the first time, the heart rate (HR) response to exercise of time-dependent intensity. Material and methods:The applied model is expressed in the form of two coupled ordinary differential equations, one giving the rate of change of HR and the other providing the time dependency of exercise intensity. According to the model, the HR is assumed to depend on time, velocity, lactate accumulation and the subject's overall cardiovascular condition. For the purposes of the present work, training sessions were simulated, consisting of exponentially and step-wise increasing intensities, as well as interval training. Results: Training sessions of exponentially and step-wise increasing velocity, as well as an interval training session, have been simulated. Successful simulations of the corresponding HR response were achieved. Conclusions: The present work successfully demonstrates the model's excellent performance in simulating the HR response to exercises of time-dependent intensity. The applied model has been shown to correctly simulate the heart rate response also during exercises of complicated intensity patterns, such as the interval training session. The study confirms the ability of the implemented mathematical model not only to simulate and predict heart rate kinetics for any given exercise intensities but also to provide important information regarding an individual's cardiovascular condition. This is of vast importance, not only in the area of fitness and sport, where it can serve as a fundamental tool for the design of efficient training sessions, but also in the areas of cardiovascular health, prediction and rehabilitation.

A Neural Network Model for Estimating the Heart Rate Response to Constant Intensity Exercises

“…The participant was a high-level professional runner, so he was able to keep the exercise intensity at constant levels and, thus, provide raw HR data of exceptional accuracy, as required by the study. He performed four running bouts of constant intensity exercise [9,10], ref. [18] followed by a passive recovery period, during which he laid horizontally and still on the floor.…”

“…Mathematical evaluations of this function have been proposed and extensively studied, as to their goodness of fit to raw HR data, as well as to their rigor and mathematical validity. In this sub-section, we will briefly reference the two main mathematical approaches, the exponential 3-phase model and the dynamical systems model (both discussed in more detail in [9,10]).…”

“…This study focuses on the estimation of the HR response to exercise of various constant exercise intensities. Mathematical models based on exponential fitting or, more recent dynamical systems models based on a system of coupled ordinary differential equations, have been proposed for the numerical simulation and prediction of the HR response to exercise [9,10]. Several methods may be found in the literature for the estimation of the parameters involved in the HR variability signals [11][12][13].…”

“…After describing the data collection process, as well as the basic steps of the NN modeling, we examine the performance of our proposed NN when compared to raw HR data of constant exercise intensity. We also provide a comparison between the estimated HR values provided by our NN model and the simulated values provided by a dynamical systems model [9,10].…”

Measurement, Prediction, and Control of Individual Heart Rate Responses to Exercise—Basics and Options for Wearable Devices

“…The published evaluation is performed visually without numeric values and based on a single protocol for two subjects. In Zakynthinaki ( 2016 ), the same model is used to predict different stress courses for synthetic data. Transferability to real training data seems to be not yet proved completely.…”