A survey of mathematical models of human performance using power and energy

The ability to predict the systematic decrease of power during physical exertion gives valuable insights into health, performance, and injury. This review surveys the research of power-based models of fatigue and recovery within the area of human performance. Upon a thorough review of available literature, it is observed that the two-parameter critical power model is most popular due to its simplicity. This two-parameter model is a hyperbolic relationship between power and time with critical power as the power-asymptote and the curvature constant denoted by W′. Critical power (CP) is a theoretical power output that can be sustained indefinitely by an individual, and the curvature constant (W′) represents the amount of work that can be done above CP. Different methods and models have been validated to determine CP and W′, most of which are algebraic manipulations of the two-parameter model. The models yield different CP and W′ estimates for the same data depending on the regression fit and rounding off approximations. These estimates, at the subject level, have an inherent day-to-day variability called intra-individual variability (IIV) associated with them, which is not captured by any of the existing methods. This calls for a need for new methods to arrive at the IIV associated with CP and W′. Furthermore, existing models focus on the expenditure of W′ for efforts above CP and do not model its recovery in the sub-CP domain. Thus, there is a need for methods and models that account for (i) the IIV to measure the effectiveness of individual training prescriptions and (ii) the recovery of W′ to aid human performance optimization

Cardiopulmonary responses to maximal aerobic exercise in patients with cystic fibrosis (article)

This is the final version. Available from Public Library of Science via the DOI in this record.The dataset associated with this article is located in ORE at: https://doi.org/10.24378/exe.1105Cystic fibrosis (CF) is a debilitating chronic condition, which requires complex and expensive disease management. Exercise has now been recognised as a critical factor in improving health and quality of life in patients with CF. Hence, cardiopulmonary exercise testing (CPET) is used to determine aerobic fitness of young patients as part of the clinical management of CF. However, at present there is a lack of conclusive evidence for one limiting system of aerobic fitness for CF patients at individual patient level. Here, we perform detailed data analysis that allows us to identify important systems-level factors that affect aerobic fitness. We use patients’ data and principal component analysis to confirm the dependence of CPET performance on variables associated with ventilation and metabolic rates of oxygen consumption. We find that the time at which participants cross the gas exchange threshold (GET) is well correlated with their overall performance. Furthermore, we propose a predictive modelling framework that captures the relationship between ventilatory dynamics, lung capacity and function and performance in CPET within a group of children and adolescents with CF. Specifically, we show that using Gaussian processes (GP) we can predict GET at the individual patient level with reasonable accuracy given the small sample size of the available group of patients. We conclude by presenting an example and future perspectives for improving and extending the proposed framework. The modelling and analysis have the potential to pave the way to designing personalised exercise programmes that are tailored to specific individual needs relative to patient’s treatment therapies.Wellcome TrustEngineering and Physical Sciences Research Counci

Redefining Exhaustion: Considerations for the Modeling of Critical Power

Background: The relationship between exercise intensity and the limit of tolerance is the focus of the Critical Power (CP) model. CP defines the upper limit for which exercise is steady state and is – in theory – indefinitely sustainable. However, this limit of tolerance at CP is often well below 30 min. Purpose: We want to test the hypothesis that 1) a clinically significant residual W’ capacity (W’res) does exist, 2) that the size of W’res is inversely related to tlim used in the testing protocols, and 3) that accounting for W’res will result in an improved calculation of the Critical Power (CP), as determined by an increased time to exhaustion at CP. Methods: Nine well-trained cyclists performed a ramp test and four high-intensity tests to exhaustion on a cycle ergometer to determine CP and the curvature constant (W’). Two tests to exhaustion were then performed at the traditional CP (CPtrad) and a novel, modified CP (CPmod) to test the practical significance of the residual capacity on the calculation of the CP. Results: All participants were able to perform work above CP even after reaching the limit of tolerance, despite no significant changes in physiological parameters. Including the W’res resulted in significantly lower estimations of CP (TRAD: 281W, MOD: 278 W; p = 0.015) and higher estimations of W’ (TRAD: 15.8 kJ, MOD: 17.8 kJ; p = 0.008). Significance: Athletes were able to continue generating power above CP, even after reaching the limit of tolerance. This residual capacity resulted in a significantly lower estimate of CP and significantly higher estimation of W’

Computational Modelling of Tissue-Engineered Cartilage Constructs

Cartilage is a fundamental tissue to ensure proper motion between bones and damping of mechanical loads. This tissue often suffers damage and has limited healing capacity due to its avascularity. In order to replace surgery and replacement of joints by metal implants, tissue engineered cartilage is seen as an attractive alternative. These tissues are obtained by seeding chondrocytes or mesenchymal stem cells in scaffolds and are given certain stimuli to improve establishment of mechanical properties similar to the native cartilage. However, tissues with ideal mechanical properties were not obtained yet. Computational models of tissue engineered cartilage growth and remodelling are invaluable to interpret and predict the effects of experimental designs. The current model contribution in the field will be presented in this chapter, with a focus on the response to mechanical stimulation, and the development of fully coupled modelling approaches incorporating simultaneously solute transport and uptake, cell growth, production of extracellular matrix and remodelling of mechanical properties.publishe

Determination of Critical Rest Interval using Repeated Sprint Ability Testing

The critical power (CP) concept has been used to determine the appropriate rest interval during intermittent exercise through the investigation of critical rest interval (CRI). Repeated sprint ability (RSA) testing has been developed to define the athlete’s ability to recover and maintain maximal effort during successive bouts. The CP model has been used to understand the physiological responses involved with intermittent exercise delineating between severe and heavy exercise intensity domains. The primary purpose of this study was to determine the CRI from the work-time relationship given by RSA testing using varying work to rest ratios. The secondary purpose was to determine the validity of CRI by evaluation of physiological responses above and below estimated rest interval values during intermittent cycling. Twelve recreationally trained males (mean ± SD; age 24.1 ± 3.6yr; height 175.8 ± 7.0cm; weight 77.6 ± 12.8kg; V̇ O2peak 43.3 ± 5.6ml/kg/min; Body Fat (%) 24.5 ± 4.4) were recruited for this study. Participants performed a graded exercise test to determine V̇ O2peak and peak heart rate. Eight participants completed the same three RSA protocols with 6s maximal sprints and varying rest intervals (12-24s) on a cycle ergometer. Intermittent critical power (ICP) was calculated through the linear total work (TW) and time-to-exhaustion (TTE) relationship, whereas CRI was estimated using the average work per sprint and ICP. Seven subjects completed trials above and below estimated CRI to evaluate the validity of this estimate through the examination of the physiological responses. Breath-by-breath oxygen consumption (V̇ O2) and heart rate (HR) values were recorded during the validation trials. One-way repeated measures analysis of variance (ANOVA) was used to analyze the variables from the RSA trials. Paired samples t-tests were performed to compare performance and physiological variables above or below CRI during the validation trials. Two-way repeated measures ANOVA was used to examined the changes in oxygen consumption (V̇ O2), HR, mean power (MP), and TW throughout the validation trials. Significant differences (p \u3c 0.1) were found for the number of intervals completed, TTE, average work per sprint, peak and mean V̇ O2 between RSA protocols. Linearity between TW and TTE was r2 = 0.952 ± 0.081. During the validation trials, TTE was significantly greater in the above versus the below CRI trial (2270.43 ± 941.15s vs. 1511.00 ± 811.0s). Furthermore, blood lactate concentration (8.94 ± 4.89mmol/L vs. 6.56 ± 3.45mmol/L), AveV̇ O2 (2.05 ± 0.36L/min vs. 1.78 ± 0.26L/min), V̇ O2peak (2.84 ± 0.48L/min vs. 2.61 ± 0.43L/min), and AveHR (151.14 ± 18.46bpm vs. 138.14 ± 17.51L/min) were significantly greater in the below CRI trial when compared to the above CRI trial. Significant interactions were found between above and below trials within minimal V̇ O2 response (F = 6.886, p = 0.024, η2 = 0.534) to the recovery intervals and maximal HR (F = 4.51, p = 0.016, η2 = 0.429) response to the work intervals. During the above CRI trial, minimal V̇ O2 response decreased over time (51-43%V̇ O2 peak) while maximal HR response achieved a steady state level (81-84%HRpeak). Conversely, minimal V̇ O2 response during the below CRI trial achieved a steady state level (54-58%V̇ O2 peak), whereas maximal HR response increased over time (84-90%HRpeak). The relationship between TW and TTE is appropriate for use with RSA testing with varying rest intervals. The differing physiological response during the validation trials may reflect changes in energy system contribution. In conclusion, CRI distinguished between physiological responses related to exercise intensity domains in a manner similar to CP estimates determined from other testing and exercise modalities

USSR Space Life Sciences Digest, Issue 18

This is the 18th issue of NASA's USSR Life Sciences Digest. It contains abstracts of 50 papers published in Russian language periodicals or presented at conferences and of 8 new Soviet monographs. Selected abstracts are illustrated with figures and tables from the original. A review of a recent Aviation Medicine Handbook is also included. The abstracts in this issue have been identified as relevant to 37 areas of space biology and medicine. These areas are: adaptation, aviation medicine, biological rhythms, biospherics, body fluids, cardiovascular and respiratory systems, cytology, developmental biology, endocrinology, enzymology, equipment and instrumentation, exobiology, gastrointestinal system, genetics, gravitational biology, group dynamics, habitability and environmental effects, hematology, human performance, immunology, life support systems, man-machine systems, mathematical modeling, metabolism, microbiology, musculoskeletal system, neurophysiology, nutrition, operational medicine, perception, personnel selection, psychology, radiobiology, reproductive biology, space biology and medicine, and space industrialization

A Minimal Power Model for Human Running Performance

Models for human running performances of various complexities and underlying principles have been proposed, often combining data from world record performances and bio-energetic facts of human physiology. Here we present a novel, minimal and universal model for human running performance that employs a relative metabolic power scale. The main component is a self-consistency relation for the time dependent maximal power output. The analytic approach presented here is the first to derive the observed logarithmic scaling between world (and other) record running speeds and times from basic principles of metabolic power supply. Various female and male record performances (world, national) and also personal best performances of individual runners for distances from 800m to the marathon are excellently described by this model, with mean errors of (often much) less than 1%. The model defines endurance in a way that demonstrates symmetry between long and short racing events that are separated by a characteristic time scale comparable to the time over which a runner can sustain maximal oxygen uptake. As an application of our model, we derive personalized characteristic race speeds for different durations and distances.Comment: 29 pages, 5 figure

Applications of the Critical Power Model to Dynamic Constant External Resistance Exercise: A Brief Review of the Critical Load Test

The study and application of the critical power (CP) concept has spanned many decades. The CP test provides estimates of two distinct parameters, CP and W0 , that describe aerobic and anaerobic metabolic capacities, respectively. Various mathematical models have been used to estimate the CP and W0 parameters across exercise modalities. Recently, the CP model has been applied to dynamic constant external resistance (DCER) exercises. The same hyperbolic relationship that has been established across various continuous, whole-body, dynamic movements has also been demonstrated for upper-, lower-, and whole-body DCER exercises. The asymptote of the load versus repetition relationship is defined as the critical load (CL) and the curvature constant is L0 . The CL and L0 can be estimated from the same linear and non-linear mathematical models used to derive the CP. The aims of this review are to (1) provide an overview of the CP concept across continuous, dynamic exercise modalities; (2) describe the recent applications of the model to DCER exercise; (3) demonstrate how the mathematical modeling of DCER exercise can be applied to further our understanding of fatigue and individual performance capabilities; and (4) make initial recommendations regarding the methodology for estimating the parameters of the CL test