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      Modelling Heart Rate Kinetics

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      PLoS ONE
      Public Library of Science

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          Abstract

          The objective of the present study was to formulate a simple and at the same time effective mathematical model of heart rate kinetics in response to movement (exercise). Based on an existing model, a system of two coupled differential equations which give the rate of change of heart rate and the rate of change of exercise intensity is used. The modifications introduced to the existing model are justified and discussed in detail, while models of blood lactate accumulation in respect to time and exercise intensity are also presented. The main modification is that the proposed model has now only one parameter which reflects the overall cardiovascular condition of the individual. The time elapsed after the beginning of the exercise, the intensity of the exercise, as well as blood lactate are also taken into account. Application of the model provides information regarding the individual’s cardiovascular condition and is able to detect possible changes in it, across the data recording periods. To demonstrate examples of successful numerical fit of the model, constant intensity experimental heart rate data sets of two individuals have been selected and numerical optimization was implemented. In addition, numerical simulations provided predictions for various exercise intensities and various cardiovascular condition levels. The proposed model can serve as a powerful tool for a complete means of heart rate analysis, not only in exercise physiology (for efficiently designing training sessions for healthy subjects) but also in the areas of cardiovascular health and rehabilitation (including application in population groups for which direct heart rate recordings at intense exercises are not possible or not allowed, such as elderly or pregnant women).

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          Slow component of VO2 kinetics: mechanistic bases and practical applications.

          The V·O₂ slow component, a slowly developing increase in V·O₂ during constant-work-rate exercise performed above the lactate threshold, represents a progressive loss of skeletal muscle contractile efficiency and is associated with the fatigue process. This brief review outlines the current state of knowledge concerning the mechanistic bases of the V·O₂ slow component and describes practical interventions that can attenuate the slow component and thus enhance exercise tolerance. There is strong evidence that, during constant-work-rate exercise, the development of the V·O₂ slow component is associated with the progressive recruitment of additional (type II) muscle fibers that are presumed to have lower efficiency. Recent studies, however, indicate that muscle efficiency is also lowered (resulting in a "mirror-image" V·O₂ slow component) during fatiguing, high-intensity exercise in which additional fiber recruitment is unlikely or impossible. Therefore, it seems that muscle fatigue underpins the V·O₂ slow component, although the greater fatigue sensitivity of recruited type II fibers might still play a crucial role in the loss of muscle efficiency in both situations. Several interventions can reduce the magnitude of the V·O₂ slow component, and these are typically associated with an enhanced exercise tolerance. These include endurance training, inspiratory muscle training, priming exercise, dietary nitrate supplementation, and the inspiration of hyperoxic gas. All of these interventions reduce muscle fatigue development either by improving muscle oxidative capacity and thus metabolic stability or by enhancing bulk muscle O2 delivery or local Q·O₂-to-V·O₂ matching. Future honing of these interventions to maximize their impact on the V·O₂ slow component might improve sports performance in athletes and exercise tolerance in the elderly or in patient populations.
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            Oxygen uptake kinetics for various intensities of constant-load work.

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              The effect of endurance training on parameters of aerobic fitness.

              Endurance exercise training results in profound adaptations of the cardiorespiratory and neuromuscular systems that enhance the delivery of oxygen from the atmosphere to the mitochondria and enable a tighter regulation of muscle metabolism. These adaptations effect an improvement in endurance performance that is manifest as a rightward shift in the 'velocity-time curve'. This shift enables athletes to exercise for longer at a given absolute exercise intensity, or to exercise at a higher exercise intensity for a given duration. There are 4 key parameters of aerobic fitness that affect the nature of the velocity-time curve that can be measured in the human athlete. These are the maximal oxygen uptake (VO2max), exercise economy, the lactate/ventilatory threshold and oxygen uptake kinetics. Other parameters that may help determine endurance performance, and that are related to the other 4 parameters, are the velocity at VO2max (V-VO2max) and the maximal lactate steady state or critical power. This review considers the effect of endurance training on the key parameters of aerobic (endurance) fitness and attempts to relate these changes to the adaptations seen in the body's physiological systems with training. The importance of improvements in the aerobic fitness parameters to the enhancement of endurance performance is highlighted, as are the training methods that may be considered optimal for facilitating such improvements.
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                Author and article information

                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                2015
                13 April 2015
                : 10
                : 4
                : e0118263
                Affiliations
                [1 ]Department of Electronics, Technological Educational Institute of Crete, and Applied Mathematics and Computers Laboratory, Technical University of Crete, Chania, Greece
                Author notes

                Competing Interests: The author has declared that no competing interests exist.

                Conceived and designed the experiments: MSZ. Performed the experiments: MSZ. Analyzed the data: MSZ. Contributed reagents/materials/analysis tools: MSZ. Wrote the paper: MSZ. Designed the software used in analysis: MSZ.

                Article
                PONE-D-14-43444
                10.1371/journal.pone.0118263
                4395265
                25876164
                708cc5d8-0ee2-4480-bb9f-242045c24f8c
                Copyright @ 2015

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

                History
                : 26 September 2014
                : 16 December 2014
                Page count
                Figures: 16, Tables: 1, Pages: 26
                Funding
                The author received no specific funding for this work.
                Categories
                Research Article
                Custom metadata
                Study data are included as Supporting Information files.

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