Mathematical modeling of exercise fatigability in the severe domain: A unifying integrative framework in isokinetic condition

Muscle fatigue is the decay in the ability of muscles to generate force, and results from neural and metabolic perturbations. This article presents an integrative mathematical model that describes the decrease in maximal force capacity (i.e. fatigue) over exercises performed at intensities above the critical force Fc (i.e. severe domain). The model unifies the previous Critical Power Model and All-Out Model and can be applied to any exercise described by a changing force F over time. The assumptions of the model are (i) isokinetic conditions, an intensity domain of Fc Collapse

Key Words

• All-out
• Anaerobic capacities
• Critical power
• Endurance
• Exercise fatigability
• Fatigue
• Maximal force capacity
• Muscular capacities
• Power-time relationship
• Time to exhaustion

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MESH Headings

• Exercise/physiology
• Muscle Fatigue
• Muscles/physiology
• Models, Theoretical
• Muscle, Skeletal/physiology

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Grants Collapse

Affiliation(s)

M Bowen Laboratoire Interuniversitaire de Biologie de la Motricité LIBM, EA 7424, Savoie Mont Blanc University, F-7300, Chambéry, France.
P Samozino Laboratoire Interuniversitaire de Biologie de la Motricité LIBM, EA 7424, Savoie Mont Blanc University, F-7300, Chambéry, France
M Vonderscher Laboratoire Interuniversitaire de Biologie de la Motricité LIBM, EA 7424, Savoie Mont Blanc University, F-7300, Chambéry, France
D Dutykh Mathematics Department, Khalifa University of Science and Technology, PO Box 127788, Abu Dhabi, United Arab Emirates; Causal Dynamics Pty Ltd, WA 6009, Perth, Australia
B Morel Laboratoire Interuniversitaire de Biologie de la Motricité LIBM, EA 7424, Savoie Mont Blanc University, F-7300, Chambéry, France

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An innovative cardiac rehabilitation based on the power-force-velocity profile to further improve cardiorespiratory capacities in coronary artery disease patients

Funding Acknowledgements

Type of funding sources: Other. Main funding source(s): Doctoral contract 2018-2022

Background

Several studies have shown the importance of the relationship between the power-force-velocity profile (PFVP) and sport performance in elite athletes through optimised exercise training.[1] Optimising the training programme is constantly sought in rehabilitation among patients always younger with coronary artery disease. Nowadays, it is well established that intermittent training should be offered to coronary patients during the rehabilitation cycle.[2] In this continuity, the assessment of the PFVP at the beginning of the cardiac rehabilitation (CR) would allow to better adapt the CR training programme for each patient.

Purpose

The aim of this study was to compare the effects of two exercise training programmes: a traditional CR versus a new CR relied on patient’s PFVP on cardiorespiratory, functional and autonomic systems in coronary patients.

Methods

This prospective randomized controlled trial was conducted from May 2020 to July 2021 in an university hospital. A total of 89 patients were randomly assigned (1:1) to test or control group. Before starting CR, participants performed two sprints of 8 s on a cycle ergometer to define the PFVP. The PFVP was analysed to determine whether the participant had a force or velocity deficit. Patients included in test group followed a specific cycling training programme based on their weak point (i.e., specific force training with high resistance and low pedalling frequency on the cycle if the PFVP was oriented in velocity and reversely). While control patients attended a conventional CR programme.

The 3-week training intervention consisted of 40 min of cycling, 30 min of walking on treadmill and 20 min of strength training (4/week).

Cardiopulmonary exercise test (VO2 at the first ventilatory threshold, SV1 and VO2 peak in ml/min/kg), functional assessments (distance of 6-min walk test, handgrip strength, 10 sit-to-stand repetitions, cholesterol levels, LDL-C and quality of life) and autonomic nervous system (heart rate variability and sensitivity baroreflex) were performed at the baseline and after CR.

A two-way ANOVA with one repeated measure (pre vs. post) and one independent factor (test vs. control) was realized.

Results

The mean age was 61.0 ± 9.6 years, 18% were women. A significant difference was observed in VO2 peak (test: +22.0 ± 19.1% vs. control: +10.2 ± 15.8%, p=0.003) and VO2 SV1 (test: +35.9 ± 33.9% vs. control: +11.9 ± 34.4%, p<0.001), LDL-C (p=0.016) and quality of life (p<0.001). No significant change between groups in other functional tests and autonomic activity occurred after CR programme.

Conclusion

Cardiopulmonary activity, cholesterol and quality of life were improved after 3-week exercise programme. The novel CR depending on initial PFVP showed greater cardiorespiratory benefits than a conventional CR. Therefore, the PFVP can be used in CR to adapt specifically the content of training sessions.

Neuromuscular fatigability during repeated sprints assessed with an innovative cycle ergometer

PURPOSE

Repeated sprint ability is an integral component of team sports. This study aimed to evaluate fatigability development and its aetiology during and immediately after a cycle repeated sprint exercise performed until a given fatigability threshold.

METHODS

On an innovative cycle ergometer, 16 healthy males completed an RSE (10-s sprint/28-s recovery) until task failure (TF): a 30% decrease in sprint mean power (Pmean). Isometric maximum voluntary contraction of the quadriceps (IMVC), central alterations [voluntary activation (VA)], and peripheral alterations [twitch (Pt)] were evaluated before (pre), immediately after each sprint (post), at TF and 3 min after. Sprints were expressed as a percentage of the total number of sprints to TF (TS_TF). Individual data were extrapolated at 20, 40, 60, and 80% TS_TF.

RESULTS

Participants completed 9.7 ± 4.2 sprints before reaching a 30% decrease in Pmean. Post-sprint IMVCs were decreased from pre to 60% TS_TF and then plateaued (pre: 345 ± 56 N, 60% 247 ± 55 N, TF: 233 ± 57 N, p < 0.001). Pt decreased from 20% and plateaued after 40% TS_TF (p < 0.001, pre-TF = - 45 ± 13%). VA was not significantly affected by repeated sprints until 60% TS_TF (pre-TF = - 6.5 ± 8.2%, p = 0.036). Unlike peripheral parameters, VA recovered within 3 min (p = 0.042).

CONCLUSION

During an RSE, Pmean and IMVC decreases were first concomitant to peripheral alterations up to 40% TS_TF and central alterations was only observed in the second part of the test, while peripheral alterations plateaued. The distinct recovery kinetics in central versus peripheral components of fatigability further confirm the necessity to reduce traditional delays in neuromuscular fatigue assessment post-exercise.

Effects of the foot strike pattern on muscle activity and neuromuscular fatigue in downhill trail running

Minimizing musculo-skeletal damage and fatigue is considered paramount for performance in trail running. Our purposes were to investigate the effects of the foot strike pattern and its variability on (a) muscle activity during a downhill trail run and (b) immediate and delayed neuromuscular fatigue. Twenty-three runners performed a 6.5-km run (1264 m of negative elevation change). Electromyographic activity of lower-limb muscles was recorded continuously. Heel and metatarsal accelerations were recorded to identify the running technique. Peripheral and central fatigue was assessed in knee extensors (KE) and plantar flexors (PF) at Pre-, Post-, and 2 days post downhill run (Post2d). Anterior patterns were associated with (a) higher gastrocnemius lateralis activity and lower tibialis anterior and vastus lateralis activity during the run and (b) larger decreases in KE high-frequency stimulus-evoked torque Post and larger decrements in KE MVC Post2d. High patterns variability during the run was associated with (a) smaller decreases in KE Db100 Post and MVC Post2d and (b) smaller decreases in PF MVC Post and Post2d. Anterior patterns increase the severity of KE peripheral fatigue. However, high foot strike pattern variability during the run reduced acute and delayed neuromuscular fatigue in KE and PF.

How 100-m event analyses improve our understanding of world-class men's and women's sprint performance

This study aimed to compare the force (F)-velocity (v)-power (P)-time (t) relationships of female and male world-class sprinters. A total of 100 distance-time curves (50 women and 50 men) were computed from international 100-m finals, to determine the acceleration and deceleration phases of each race: (a) mechanical variables describing the velocity, force, and power output; and (b) F-P-v relationships and associated maximal power output, theoretical force and velocity produced by each athlete (P_max , F₀ , and V₀ ). The results showed that the maximal sprint velocity (V_max ) and mean power output (W/kg) developed over the entire 100 m strongly influenced 100-m performance (r > -0.80; P ≤ 0.001). With the exception of mean force (N/kg) developed during the acceleration phase or during the entire 100 m, all of the mechanicals variables observed over the race were greater in men. Shorter acceleration and longer deceleration in women may explain both their lower V_max and their greater decrease in velocity, and in turn their lower performance level, which can be explained by their higher V₀ and its correlation with performance. This highlights the importance of the capability to keep applying horizontal force to the ground at high velocities.

Acute and delayed peripheral and central neuromuscular alterations induced by a short and intense downhill trail run

Downhill sections are highly strenuous likely contributing to the development of neuromuscular fatigue in trail running. Our purpose was to investigate the consequences of an intense downhill trail run (DTR) on peripheral and central neuromuscular fatigue at knee extensors (KE) and plantar flexors (PF). Twenty-three runners performed a 6.5-km DTR (1264-m altitude drop) as fast as possible. The electromyographic activity of vastus lateralis (VL) and gastrocnemius lateralis (GL) was continuously recorded. Neuromuscular functions were assessed Pre-, Post-, and 2-day Post-DTR (Post2d). Maximal voluntary torques decreased Post (∼ -19% for KE, ∼ -25% for PF) and Post2d (∼ -9% for KE, ∼ -10% for PF). Both central and peripheral dysfunctions were observed. Decreased KE and PF voluntary activation (VA), evoked forces, VL M-wave amplitude, and KE low-frequency fatigue were observed at Post. Changes in VL M-wave amplitude were negatively correlated to VL activity during DTR. Changes in PF twitch force and VA were negatively correlated to GL activity during DTR. The acute KE VA deficit was about a third of that reported after ultramarathons, although peripheral alterations were similar. The prolonged force loss seems to be mainly associated to VA deficit likely induced by the delayed inflammatory response to DTR-induced ultrastructural muscle damage.

Influence of Ergometer Design on Physiological Responses during Rowing

The aim of this study was to compare the physiological responses and rowing efficiency on 2 different rowing ergometers: stationary vs. dynamic ergometers manufactured by Concept2. 11 oarswomen and oarsmen rowed 4 min at 60% and 70% of peak power output on both ergometers (randomized order). Power output, stroke rate, heart rate, oxygen uptake, carbon dioxide production, lactate accumulation and rating of perceived exertion were recorded at each stage on the 2 ergometers. Gross and net efficiencies were computed. Exercise intensity was associated with increases in all parameters. Rowing on dynamic ergometer was associated with higher heart rate, oxygen uptake, carbon dioxide production and stroke rate, concomitantly to lower blood lactate accumulation but also to lower gross and net efficiencies. The present study showed that rowing efficiency and blood lactate accumulation were lower on the Concept2 dynamic ergometer than on its stationary counterpart. If the use of the Concept2 dynamic ergometer may provide some advantages (reduced risk of injuries), its utilization requires a specific evaluation of physiological responses during an incremental exercise for an adapted management of training.

Sprint mechanics in world-class athletes: a new insight into the limits of human locomotion

The objective of this study was to characterize the mechanics of maximal running sprint acceleration in high-level athletes. Four elite (100-m best time 9.95-10.29 s) and five sub-elite (10.40-10.60 s) sprinters performed seven sprints in overground conditions. A single virtual 40-m sprint was reconstructed and kinetics parameters were calculated for each step using a force platform system and video analyses. Anteroposterior force (FY), power (PY), and the ratio of the horizontal force component to the resultant (total) force (RF, which reflects the orientation of the resultant ground reaction force for each support phase) were computed as a function of velocity (V). FY-V, RF-V, and PY-V relationships were well described by significant linear (mean R(2) of 0.892 ± 0.049 and 0.950 ± 0.023) and quadratic (mean R(2) = 0.732 ± 0.114) models, respectively. The current study allows a better understanding of the mechanics of the sprint acceleration notably by modeling the relationships between the forward velocity and the main mechanical key variables of the sprint. As these findings partly concern world-class sprinters tested in overground conditions, they give new insights into some aspects of the biomechanical limits of human locomotion.

Effects of hamstring-emphasized neuromuscular training on strength and sprinting mechanics in football players

The objective of this study was to examine the effects of a neuromuscular training program combining eccentric hamstring muscle strength, plyometrics, and free/resisted sprinting exercises on knee extensor/flexor muscle strength, sprinting performance, and horizontal mechanical properties of sprint running in football (soccer) players. Sixty footballers were randomly assigned to an experimental group (EG) or a control group (CG). Twenty-seven players completed the EG and 24 players the CG. Both groups performed regular football training while the EG performed also a neuromuscular training during a 7-week period. The EG showed a small increases in concentric quadriceps strength (ES = 0.38/0.58), a moderate to large increase in concentric (ES = 0.70/0.74) and eccentric (ES = 0.66/0.87) hamstring strength, and a small improvement in 5-m sprint performance (ES = 0.32). By contrast, the CG presented lower magnitude changes in quadriceps (ES = 0.04/0.29) and hamstring (ES = 0.27/0.34) concentric muscle strength and no changes in hamstring eccentric muscle strength (ES = -0.02/0.11). Thus, in contrast to the CG (ES = -0.27/0.14), the EG showed an almost certain increase in the hamstring/quadriceps strength functional ratio (ES = 0.32/0.75). Moreover, the CG showed small magnitude impairments in sprinting performance (ES = -0.35/-0.11). Horizontal mechanical properties of sprint running remained typically unchanged in both groups. These results indicate that a neuromuscular training program can induce positive hamstring strength and maintain sprinting performance, which might help in preventing hamstring strains in football players.

Force-velocity profile: imbalance determination and effect on lower limb ballistic performance

This study sought to lend experimental support to the theoretical influence of force-velocity (F-v) mechanical profile on jumping performance independently from the effect of maximal power output (P max ). 48 high-level athletes (soccer players, sprinters, rugby players) performed maximal squat jumps with additional loads from 0 to 100% of body mass. During each jump, mean force, velocity and power output were obtained using a simple computation method based on flight time, and then used to determine individual linear F-v relationships and P max values. Actual and optimal F-v profiles were computed for each subject to quantify mechanical F-v imbalance. A multiple regression analysis showed, with a high-adjustment quality (r²=0.931, P<0.001, SEE=0.015 m), significant contributions of P max , F-v imbalance and lower limb extension range (h PO ) to explain interindividual differences in jumping performance (P<0.001) with positive regression coefficients for P max and h PO and a negative one for F-v imbalance. This experimentally supports that ballistic performance depends, in addition to P max , on the F-v profile of lower limbs. This adds support to the actual existence of an individual optimal F-v profile that maximizes jumping performance, a F-v imbalance being associated to a lower performance. These results have potential strong applications in the field of strength and conditioning.

Injuries in Youth and National Combined Events Championships

In major track and field competitions, the most risky discipline is the combined event. Therefore, we aimed to record and analyze the incidence and characteristics of sports injuries incurred during the Youth and National Combined Events Championships. During the French Athletics Combined Events Championships in 2010, all newly occurred injuries were prospectively recorded by the local organising committee of physicians and physiotherapists working in the medical centres at the stadium, in order to determine incidence and characteristics of newly occurred injuries. In total, 51 injuries and 9 time-loss injuries were reported among 107 registered athletes, resulting in an incidence of 477 injuries and 84 time-loss injuries per 1,000 registered athletes. Approximately 72% of injuries affected lower limbs and 60% were caused by overuse. Thigh strain (17.6%) was the most common diagnosis. 14 dropouts were recorded, 8 were caused by an injury (57.1%). During the National and Youth Combined Events Championships, over one third of the registered athletes incurred an injury, with an injury incidence higher than in international elite track and field competitions. Interestingly, this higher injury risk concerned the younger population affecting immature musculoskeletal structures. In combined events, preventive interventions should mainly focus on overuse and thigh injuries.

Effects of altered stride frequency and contact time on leg-spring behavior in human running

Many studies have demonstrated that contact time is a key factor affecting both the energetics and mechanics of running. The purpose of the present study was to further explore the relationships between contact time (t(c)), step frequency (f) and leg stiffness (k(leg)) in human running. Since f is a compound parameter, depending on both contact and aerial time, the specific goal of this study was to independently vary f and t(c) and to investigate their respective effects on spring-mass characteristics during running, seeking to determine if the changes in k(leg) observed when running at different f are mainly due to inherent changes in t(c). We compared three types of constant 3.33 m s(-1) running conditions in 10 male subjects: normal running at the subject's freely chosen f, running with decreased and increased f, and decreased and increased t(c) at the imposed freely chosen f. The data from the varied f trials showed that the variation of t(c) was strongly correlated to that of k(leg) (r(2)=0.90), and the variation of f was also significantly correlated to that of k(leg) (r(2)=0.47). Further, changes in t(c) obtained in various t(c) conditions were significantly correlated to changes in k(leg) (r(2)=0.96). These results confirm that leg stiffness was significantly influenced by step frequency variations during constant speed running, as earlier demonstrated, but our more novel finding is that compared to step frequency, the effect of contact time variations appears to be a stronger and more direct determinant of k(leg). Indeed, 90-96% of the variance in k(leg) can be explained by contact time, whether this latter parameter is directly controlled, or indirectly controlled through its close relationship with step frequency. In conclusion, from the comparison of two experimental procedures, i.e. imposing various step frequency conditions vs. asking subjects to intentionally vary contact time at their freely chosen step frequency, it appears that changes in leg stiffness are mainly related to changes in contact time, rather than to those in step frequency. Step frequency appears to be an indirect factor influencing leg stiffness, through its effect on contact time, which could be considered a major determinant of this spring-mass characteristic of human running.