Optimal Pacing Strategy Research Articles

Pacing strategies in marathons: A systematic review

BackgroundThe pacing strategy embodies the tactical behavior of athletes in distributing their energy across different segments of a race; therefore, a quantitative analysis of pacing strategies in marathon races could deepen the understanding of both pacing behavior and physical capacity in marathon athletics. ObjectiveThe objective of this systematic review was to synthesize and characterize pacing strategies in marathon road races by exploring the categories of pacing strategies and the factors that influence these strategies during marathon events. MethodsPreferred Reporting Items for Systematic Reviews guidelines were followed for systematic searches, appraisals, and syntheses of literature on this topic. Electronic databases such as Science Direct, SPORTDiscuss, PubMed, and Web of Science were searched up to July 2024. Records were eligible if they included pace performance measurements during competition, without experimental intervention that may influence their pace, in healthy, adult athletes at any level. ResultsA total of 39 studies were included in the review. Twenty-nine were observational studies, and 10 were experimental (randomized controlled trials). The assessment of article quality revealed an overall median NOS score of 8 (range 5–9). The included studies examined the pacing profiles of master athletes and finishers in half-marathon (n = 7, plus numbers compared to full marathon), full-marathon (n = 21), and ultramarathon (n = 11) road races. Considering that some studies refer to multiple pacing strategies, in general, 5 studies (∼13 %) reported even pacing, 3 (∼8 %) reported parabolic pacing, 7 (∼18 %) reported negative pacing, and 30 (∼77 %) reported positive pacing during marathon competitions. Gender, age, performance, pack, and physiological and psychological factors influence pacing strategies. ConclusionThis study synthesized pacing performance in marathons and highlighted the significance of examining pacing strategies in these events, offering valuable insights for coaches and athletes. Several key findings were highlighted: (1) pacing profiles and pacing ranges were identified as the primary indicators of pacing strategies; (2) the pacing strategy was found to be dynamic, with the most substantial effects attributed to gender and distance; and (3) three distinct types of pacing strategies for marathons were classified: positive, negative, and even pacing. These findings advance the understanding of marathon pacing strategies by shedding light on the factors that influence athletes’ pacing decisions and behaviors. Additionally, these findings offer practical benefits, aiding athletes in making well-informed tactical choices and developing effective pace plans to enhance marathon performance. However, due to the complex nature of marathon racing, further research is required to explore additional factors that might impact pacing strategies. A better grasp of optimal pacing strategies will foster progress in this area and serve as a basis for future research and advancements.

The CHOIR study: acute hemodynamic effects of different pacing strategies in hypertrophic obstructive cardiomyopathy

Abstract Background The majority of patients with hypertrophic cardiomyopathy present with dynamic left ventricular (LV) outflow tract obstruction (LVOTO), referred to as hypertrophic obstructive cardiomyopathy (HOCM). Symptomatic treatment aims at reducing LVOTO with either medical therapy, invasive septal reducing therapies, or pacemaker therapy. There is conflicting evidence regarding the efficacy of pacemaker therapy. The effect of pacing strategies at physical exertion has not been investigated in HOCM. Purpose To identify the optimal pacing strategy for reducing LVOTO without compromising cardiac output at rest and exercise in HOCM. Methods In this ongoing project, we have so far included eight patients with symptomatic HOCM referred to our hospital for alcohol septal ablation (ASA). The day before ASA, we placed temporary pacing leads in the right atrium, the right ventricular (RV) apex and on the LV lateral wall. We also inserted a pulmonary artery catheter and performed per operative echocardiography. All patients had sinus rhythm. Intrinsic rhythm served as baseline and was followed by atrial sensed RV pacing, LV pacing and biventricular (BiV) pacing at rest and during supine cycling. We assessed LVOTO by echocardiography, and cardiac output by the thermodilution method under intrinsic rhythm and all pacing modalities. Results The mean age was 52±15 years, and two of eight patients were female. The mean maximal LV wall thickness was 16±1 mm. The resting LVOTO was 50±23 mmHg. Due to difficulties in placing the LV lead within a reasonable time frame, complete study protocol was not performed in all patients. All eight patients performed RV pace at rest, but only five patients (63 %) were LV and BiV paced at rest. Five patients performed supine cycling but only four patients completed with RV and BiV pacing. The graphs display LVOTO and CO in sinus rhythm and the different pacing maneuvers at rest and during supine cycling. At rest, 6 out of 8 patients (75%) had LVOTO reduction during RV pace, and CO was unchanged. Four of five patients (80%) had LVOTO reduction during BiV and LV pace compared to sinus rhythm, also with unchanged CO. During supine cycling four of five patients (80%) had a reduction of the LVOTO gradient during RV and BiV pacing, without significant CO change. No complications occurred during the interventions. Conclusion In this ongoing study on cardiac pacing in HOCM, RV, LV, and BiV pacing reduced LVOTO while CO remained unchanged at rest and during exercise.

CORE™ wearable sensor: Comparison against gastrointestinal temperature during cold water ingestion and a 5 km running time-trial

Five km running time-trials (TT) are associated with rapid and significant increases in core body temperature (TC). For such races, real-time feedback from pre-exercise and exercise TC may be helpful in the design of an optimal pacing strategy aimed at limiting the possibility of developing heat-related illnesses. This study compared measurements of TC obtained with a wearable device, the CORE™, to those of a gastrointestinal pill (GI pill), during cold water ingestion and a 5 km running TT. Twelve participants (25 ± 4 yrs) ingested 7.5 mL/kg fat-free mass of 4 °C water over the first 5 min of a 120 min sitting period, after which they completed a 5 km running TT at 30 °C, 50% relative humidity. A TC difference > ± 0.25 °C between sensors was deemed clinically unacceptable. Prior to water ingestion, the CORE-derived TC was 0.49 ± 0.25 °C lower than the GI pill. The CORE was irresponsive to the 0.26 ± 0.22 °C peak decline in TC captured with the GI pill 40 min following water ingestion. Prior to the TT, TC was 0.30 ± 0.25 °C lower with the CORE than the GI pill. During the TT, the CORE underestimated the rate of increase in TC by 0.0125 ± 0.019 °C/min compared with the GI pill, and mean absolute difference in TC between sensors was of 0.47 ± 0.34 °C. In conclusion, the CORE does not capture the cooling effect of cold water ingestion and provides a clinically relevant underestimation of TC during a 5 km running TT in the heat.

Time Trial Pacing Optimization Strategy Based on Muscle Fatigue and Aerobic and Anaerobic Respiration

In the time trial, the rider should organize his/her power wisely so that he/she can minimize the time for the entire contest. In order to design the optimal power output strategy for different riders in different road situations , we build a model to describe the rider based on the aerobic and anaerobic respiration and muscle fatigue and recovery process . Then we use the greedy algorithm to obtain the optimal pacing strategy for the rider on the plane road. Then we use the image processing to get the road data in UCI and Tokyo Olympics and use modify the model so that it can give the optimal pacing strategy on the roads with turns and slope.

Optimal pacing strategy modeling of cycling individual time trials

Improving the performance of professional cyclists during individual time trials has been a challenge for several decades. In this study, the fatigue power profiles of male and female professional cyclists were characterized and a novel optimal pacing strategy model was established to determine the output power distribution based on the simulated annealing algorithm. Moreover, the model was implemented on the male 2021 UCI ITT course and the female 2021 Olympic ITT course. Compared with the actual performance of the professional cyclists, the race scores predicted by this model are among the best, which indicates that the model is highly practical and instructive. Considering riders are unlikely to follow the detailed plan exactly and their output power can deviate from the optimal power, a sensitivity analysis was conducted and the results demonstrated the high stability and reliability of the model.

The Relationship between Stroke Metrics, Work Rate and Performance in Slalom Kayakers

The purpose of this study was to assess the relationship between work rate, stroke metrics, and performance in whitewater slalom. Twelve Spanish, nationally competitive whitewater slalom kayakers took part in a simulated competition while using an instrumented kayak paddle to record stroke metrics over a simulated race, total duration and sectional splits. Performance time was highly correlated to overall power output (r2 = 0.511, p < 0.001), where kayakers demonstrated a positive pacing strategy with power output significantly decreasing over successive sectional splits (158 ± 40, 112 ± 32 and 65 ± 33 W, p < 0.001). This resulted in an increased stroke duration (p < 0.001), time to peak force (p < 0.001), a decrease in stroke peak force (p < 0.001), and rate of peak force development (p < 0.001) over elapsed time. As such, work rate is deemed an objective metric to monitor performance, prescribe training, and ascertain optimal pacing strategies in canoe slalom.

Cardiac Magnetic Resonance Assessment of Response to Cardiac Resynchronization Therapy and Programming Strategies

ObjectivesThe objective was to determine the feasibility and effectiveness of cardiac magnetic resonance (CMR) cine and strain imaging before and after cardiac resynchronization therapy (CRT) for assessment of response and the optimal resynchronization pacing strategy. BackgroundCMR with cardiac implantable electronic devices can safely provide high-quality right ventricular/left ventricular (LV) ejection fraction (RVEF/LVEF) assessments and strain. MethodsCMR with cine imaging, displacement encoding with stimulated echoes for the circumferential uniformity ratio estimate with singular value decomposition (CURE-SVD) dyssynchrony parameter, and scar assessment was performed before and after CRT. Whereas the pre-CRT scan constituted a single “imaging set” with complete volumetric, strain, and scar imaging, multiple imaging sets with complete strain and volumetric data were obtained during the post-CRT scan for biventricular pacing (BIVP), LV pacing (LVP), and asynchronous atrial pacing modes by reprogramming the device outside the scanner between imaging sets. Results100 CMRs with a total of 162 imaging sets were performed in 50 patients (median age 70 years [IQR: 50-86 years]; 48% female). Reduction in LV end-diastolic volumes (P = 0.002) independent of CRT pacing were more prominent than corresponding reductions in right ventricular end-diastolic volumes (P = 0.16). A clear dependence of the optimal CRT pacing mode (BIVP vs LVP) on the PR interval (P = 0.0006) was demonstrated. The LVEF and RVEF improved more with BIVP than LVP with PR intervals ≥240 milliseconds (P = 0.025 and P = 0.002, respectively); the optimal mode (BIVP vs LVP) was variable with PR intervals <240 milliseconds. A lower pre-CRT displacement encoding with stimulated echoes (DENSE) CURE-SVD was associated with greater improvements in the post-CRT CURE-SVD (r = −0.69; P < 0.001), LV end-systolic volume (r = −0.58; P < 0.001), and LVEF (r = −0.52; P < 0.001). ConclusionsCMR evaluation with assessment of multiple pacing modes during a single scan after CRT is feasible and provides useful information for patient care with respect to response and the optimal pacing strategy.

Women Pace Better Than Men In A 100-mile Distance Running Race

PURPOSE: Even or negative split pacing strategies in long-distance running have been well-established to yield the best performances up to the marathon distance. In addition, women have been found to pace better than men in the marathon. Optimal pacing strategy and sex differences in ultramarathon running are not well-known. The purpose of this study was to determine pacing strategies employed by the fastest finishers in a 100-mile distance run and determine if any sex differences exist. METHODS: Ten years (2010-2019) of finish times from 991 men and 462 women in the Umstead 100-mile endurance run were obtained from publicly available data. The course is a 12.5-mile loop repeated 8 times over relatively flat terrain with 16 splits recorded for each runner at checkpoints (CP) located at miles 5.65 and 12.5. Pace was normalized by expressing the data as %mean running speed (%MRS) and compared by sex and quartile finish. Data were statistically analyzed by one- and two-way ANOVA for repeated measures. RESULTS: Women had a significantly lower %MRS at CPs 2, 3, 4 and 5 as compared to men and had a significantly higher %MRS at the 16th and final CP. Quartile analysis revealed that the fastest runners in the 1st quartile adopted a significantly more even pacing strategy than 2nd, 3rd or 4th quartile finishers and 2nd quartile finishers adopted a significantly more even pacing strategy than 3rd or 4th quartile finishers. Differences in pacing were greatest early in the race with the best performers beginning at 125 + 1.2 %MRS, while the poorest performers began the race at 140 + 1.2 %MRS. While there were few sex differences in 1st, 2nd or 3rd quartile finishers across CPs, in the 4th quartile women adopted a significantly more conservative pace in CPs 1-8, 10 and had a significantly higher %MRS at CPs 14, 15 and 16. CONCLUSIONS: In the 100-mile distance, overall women adopted a more conservative pacing strategy at earlier CPs and finished with a faster %MRS as compared to men. Runners who performed better (finished in higher quartiles) adopted a more even pacing strategy as compared to performers who finished in lower quartiles. The sex difference in pacing was most striking in the 4th quartile with women adopting a more even pacing strategy than men through the first half of the race and finishing at a faster %MRS in the final 3 CPs of the 100-mile distance.

Temporal Incidence and Predictors of High‐Grade Atrioventricular Block After Transcatheter Aortic Valve Replacement

BackgroundThe temporal incidence of high‐grade atrioventricular block (HAVB) after transcatheter aortic valve replacement (TAVR) is uncertain. As a result, periprocedural monitoring and pacing strategies remain controversial. This study aimed to describe the temporal incidence of initial episode of HAVB stratified by pre‐ and post‐TAVR conduction and identify predictors of delayed events.Methods and ResultsConsecutive patients undergoing TAVR at a single center between February 2012 and June 2019 were retrospectively assessed for HAVB within 30 days. Patients with prior aortic valve replacement, permanent pacemaker (PPM), or conversion to surgical replacement were excluded. Multivariable logistic regression was performed to assess predictors of delayed HAVB (initial event >24 hours post‐TAVR). A total of 953 patients were included in this study. HAVB occurred in 153 (16.1%). After exclusion of those with prophylactic PPM placed post‐TAVR, the incidence of delayed HAVB was 33/882 (3.7%). Variables independently associated with delayed HAVB included baseline first‐degree atrioventricular block or right bundle‐branch block, self‐expanding valve, and new left bundle‐branch block. Forty patients had intraprocedural transient HAVB, including 16 who developed HAVB recurrence and 6 who had PPM implantation without recurrence. PPM was placed for HAVB in 130 (13.6%) (self‐expanding valve, 23.7% versus balloon‐expandable valve, 11.9%; P<0.001). Eight (0.8%) patients died by 30 days, including 1 unexplained without PPM present.ConclusionsDelayed HAVB occurs with higher frequency in patients with baseline first‐degree atrioventricular block or right bundle‐branch block, new left bundle‐branch block, and self‐expanding valve. These findings provide insight into optimal monitoring and pacing strategies based on periprocedural ECG findings.

Adaptive feedback system for optimal pacing strategies in road cycling

In road cycling, the pacing strategy plays an important role, especially in solo events like individual time trials. Nevertheless, not much is known about pacing under varying conditions. Based on mathematical models, optimal pacing strategies were derived for courses with varying slope or wind, but rarely tested for their practical validity. In this paper, we present a framework for feedback during rides in the field based on optimal pacing strategies and methods to update the strategy if conditions are different than expected in the optimal pacing strategy. To update the strategy, two solutions based on model predictive control and proportional–integral–derivative control, respectively, are presented. Real rides are simulated inducing perturbations like unexpected wind or errors in the model parameter estimates, e.g., rolling resistance. It is shown that the performance drops below the best achievable one taking into account the perturbations when the strategy is not updated. This is mainly due to premature exhaustion or unused energy resources at the end of the ride. Both the proposed strategy updates handle those problems and ensure that a performance close to the best under the given conditions is delivered.

Modeling in Road Cycling for Optimal Pacing Strategies : Theory vs. Practice

Introduction: The right choice of a pacing strategy for a time trial race is important and often difficult to establish. With the increasing popularity of online sports data platforms like Strava (www.strava.com), pacing strategies may become interesting even for recreational cyclists since they can compete against each other virtually on selected segments. Methods are now available to generate pacing strategies that are optimal, however, only in a mathematical sense. Until now, they were tested in practice only under laboratory conditions [1]. Pacing strategies are generally based on two mathematical models: (1) to describe the relation between power output and speed [2], and (2) to describe the fatigue of the rider related to the power output [3]. The quality and validity of these pacing strategies relies on the accuracy of the predictions made by those models.In this paper, we describe our findings on a pilot study during a two week period of cycling with regard to the prediction quality of the two models while following precalculated optimal pacing strategies in the field rides. This is not meant to be a fully-fledged study applying, e.g., a statistical analysis for a sufficiently large number of participants. This pilot study rather intended to demonstrate that, in principle, the theoretically optimal pacing strategies can in fact be implemented for field rides in practice. Moreover, it was the purpose of the study to identify the problems of the approach occurring in practice, and to outline solutions for these.Methods: The physiological model is similar to the one used in [1]: an extension of the critical power (CP) concept with reduced recovery. The physical model to predict speed from the rider’s power output is taken from [4]. The optimization of the pacing strategy for an uphill time trial proceeded as in [1]. To calibrate the CP model, four tests were performed in the laboratory for a single hobbyist rider, followed by a number of rides on Strava segments with the goal to achieve personal bests by pursuing the given optimal pacing strategies.The precalculated pacing strategies were communicated during the field rides by means of a custom developed App on a smartphone mounted on the handle bar. Feedback was given numerically, e.g., the current deviation from the optimal speed, and visually by a dash board type gauge. Accumulated deviations from the optimal pacing were attempted to be corrected using a PID control mechanism. These rides were taken to update the parameters of the CP model continually.Results and Discussion: Four rides with optimal feedback were performed on three different Strava Segments. These segments were mainly climbs with a length of 3.5 to 5 km and an average grade from 5.6 to 7 %. The rider’s critical power ranged from 230 to 257 W depending on which tests were used for calibration. The feedback was followed with a root-mean-square error of 0.77 m/s in speed and 48 W in power. Modelling errors and deviations from theoptimal strategy lead to time differences at the end of the segment ranging from 15 s quicker to 100 s slower than the optimal strategy predicted.This discrepancy in time is partly explained by having short downhill parts within the segments and errors in the estimation of the slope profile, which is shown in Figure 1. In the downhill parts, the optimal strategy suggested speeds higher than those during the field ride in which additionally braking was necessary. This error could be reduced by adding a more realistic speed constraint to the optimization and consider braking in the pacing strategy.While the physiological model first was calibrated using tests with a length of about 30 min, the model prediction for the first ride on a shorter segment showed quite poor performance. Adding this segment to the parameter estimation changed the parameters in a way that critical power was reduced and anaerobic capacity increased. With this new parameter set, short as well as mid-range segments were predicted quite well. This shows how important it is to use a range of test durations that covers the future applications.Conclusions: The results showed, that the models work quite well in general and they can be applied to uncontrolled conditions when considering some limitations. Downhill parts are difficult to model and time differences between prediction and ride must be expected in these scenarios. The physiological model needs to be calibrated using segments similar in length and load to the ones that are predicted. With proper model parameter selection and visual feedback with respect to an optimal pacing strategy, significant performance gains for uphill time-trials of hobbyist, amateur, and perhaps also professional athletes can be expected.

The new Exposure Variation Analysis (EVA) method to compare pacing strategy and performance during professional time-trial competitions

Abstract: Several studies underlined the impact of pacing strategy on cycling time-trial performance. It has been reported that under steady environmental conditions, maintaining a constant power output (PO) is the most efficient strategy to improve performance (Wells et al. 2013). The Exposure Variation Analysis (EVA) method has recently been proposed to evaluate these pacing strategies, quantifying for an optimal constant pacing strategy the times spent at an accurate PO (APO), at an inappropriate PO (IPO), and the short-time regulations of inappropriate PO (REG) (Ouvrard et al. 2017). It has been demonstrated that increasing time spent at APO and decreasing time spent at IPO allows cyclists to develop higher mean PO and improve performance (Ouvrard et al. 2018. Under review). However, as these indexes are influenced by time-trials course, they were never used to monitor pacing strategies and performance for several time-trials performed by the same cyclists yet. The aim of this study was to analyse the relationships between changes of performance, mean PO and EVA pacing parameters in two professional cyclists during seven official competitive time-trials.  Methods: PO were collected for two professional cyclists (mean VO 2 max 79.0 ± 8.5 mL.min -1 .kg -1 ) during the seven-same time-trials (performed between April 2013 and June 2017 and ranged from 18.7 to 51.6 km). PO fluctuations were analysed from EVA to quantify times spent at APO (PO between 90 and 110 % of mean time-trial PO), IPO (PO lower than 90 % or higher than 110 % of mean PO for more than 10 s) and REG (PO lower than 90 % or higher than 110 % of mean PO for less than 10 s). Relationships between I” meanPO (differences between subject 1 and subject 2 mean PO for each time-trial) and I” meanPO% (differences between subject 1 and subject 2 mean PO, each expressed as a percentage of the subject’s record PO on the time trial duration) and I” APO (differences between subject 1 and subject 2 times spent at APO), I” IPO (differences between subject 1 and subject 2 times spent at IPO), and I” REG (differences between subject 1 and subject 2 REG) were assessed thanks to Pearson correlation coefficients.  Results: I” meanPO ranged from -24 to +39 W for similar physical potentials (20-min record PO 432 vs 428 W). A trend to a negative relationship was identified between I” meanPO and I” IPO (r = -0.70, p = 0.08). Stronger and significant relationships were identified between I” meanPO% and I” IPO (r = -0.94, p = 0.002) and I” APO (r = 0.86, p = 0.01, Figure 1).  Discussion: The main finding of this study is that, when comparing two cyclists during several time-trials, changes of EVA pacing parameters were related to changes of cyclists’ ability to develop high mean PO. The more the cyclists were able to decrease their time spent at IPO and increase their time spent at APO, the more they had a maximal use of their physical capacity during the time-trial, allowing them to develop higher mean PO expressed as a percentage of their record PO. These results are in accordance with Wells et al. (2013), who demonstrated that maintaining a constant PO, and thus increasing time spent at APO, is optimal for time-trial performance under steady environmental conditions. Conversely, increasing PO variations, and consequently time spent at IPO or REG, reflect poor adherence to constant speed, increasing biomechanical losses or fatigue.  Conclusion: EVA seems to be a valuable method to monitor pacing and performance changes for two cyclists during several time-trials.  Values of times spent at IPO and APO can be compared between cyclists to determine if their pacing strategy were optimal to achieve the best performance possible.

Ventricular force-frequency relationships during biventricular or multisite pacing in congenital heart disease.

Traditional indices to evaluate biventricular (BiV) pacing are load dependent, fail to assess dynamic changes, and may not be appropriate in patients with congenital heart disease (CHD). We therefore measured the force-frequency relationship (FFR) using tissue Doppler-derived isovolumic acceleration (IVA) to assess the dynamic adaption of the myocardium and its variability with different ventricular pacing strategies. This was a prospective pilot study of pediatric and young adult CHD patients with biventricular or multisite pacing systems. Color-coded myocardial velocities were recorded at the base of the systemic ventricular free wall. IVA was calculated at resting heart rate and with incremental pacing. FFR curves were obtained by plotting IVA against heart rate for different ventricular pacing strategies. Ten patients were included (mean: 22±7years). The FFR identified a best and worst ventricular pacing strategy for each patient, based on the AUC at baseline, submaximal, and peak heart rates (P<.001). However, there was no single best ventricular pacing strategy that was optimal for all patients. Additionally, the best ventricular pacing strategy often differed within the same patient at different heart rates. This novel assessment demonstrates a wide variability in optimal ventricular pacing strategy. These inherent differences may play a role in the unpredictable clinical response to BiV pacing in CHD, and emphasizes an individualized approach. Furthermore, the optimal ventricular pacing varies with heart rate within individuals, suggesting that rate-responsive ventricular pacing modulation may be required to optimize ventricular performance.

Pacing Decision Making in Sport and the Effects of Interpersonal Competition: A Critical Review.

An athlete's pacing strategy is widely recognised as an essential determinant for performance during individual events. Previous research focussed on the importance of internal bodily state feedback, revealed optimal pacing strategies in time-trial exercise, and explored concepts such as teleoanticipation and template formation. Recently, human-environment interactions have additionally been emphasized as a crucial determinant for pacing, yet how they affect pacing is not well understood. Therefore, this literature review focussed on exploring one of the most important human-environment interactions in sport competitions: the interaction among competitors. The existing literature regarding the regulation of exercise intensity and the effect of competition on pacing and performance is critically reviewed in this paper. The PubMed, CINAHL and Web of Science electronic databases were searched for studies about pacing in sports and (interpersonal) competition between January 2000 to October 2017, using the following combination of terms: (1) Sports AND (2) Pacing, resulting in 75 included papers. The behaviour of opponents was shown to be an essential determinant in the regulation of exercise intensity, based on both observational (N = 59) and experimental (N = 16) studies. However, adjustment in the pacing response related to other competitors appears to depend on the competitive situation and the current internal state of the athlete. The findings of this review emphasize the importance of what is happening around the athlete for the outcome of the decision-making process involved in pacing, and highlight the necessity to incorporate human-environment interactions into models that attempt to explain the regulation of exercise intensity in sports and exercise.

Optimal pacing in road cycling using a nonlinear power constraint

In the individual road cycling discipline known as a time-trial, variable power pacing under variable grade conditions leads to improved performance. However, it is unclear whether these power variations result in an optimal finishing time. Typical pacing strategies use an average power constraint, which requires maintaining a constant speed regardless of grade fluctuations; however, this is physiologically infeasible for cyclists. We used an exponentially weighted average (EWA) power constraint in which a nonlinear relationship between the power output and physiological cost was assumed. We defined the optimal pacing (OP) strategy by minimizing the total cycling time subject to the EWA power constraint, and set the EWA of the power output of both the OP and constant power (CP) strategies to the same baseline value. The model showed that the OP strategy outperformed the CP strategy in terms of minimizing the finishing time under variable grade conditions, the power distribution of the OP strategy was identical to that of the CP strategy under constant grade conditions, and the average power output of the OP strategy was always lower than that of the CP strategy under variable grade conditions. Numerical simulations were performed on two hypothetical 40-km courses using both the CP and OP strategies. We found that under variable grade conditions, the time-saving rates of the OP strategy relative to the CP strategy were 2.7 and 2.8% for the two simulated courses.

Optimal pacing and carbohydrate intake strategies for ultramarathons.

The purpose of this research is to determine the pacing and nutrition strategies which minimize completion time and carbohydrate intake for athletes competing in ultramarathon races. We present the formulation of a two-phase optimization model. The first-phase mixed-integer nonlinear program (MINLP) determines the minimum completion time subject to the altitude, terrain, and distance of the race, as well as the mass and cardiovascular fitness of the athlete. The second-phase MINLP determines the minimum carbohydrate intake required for the athlete to achieve the completion time prescribed by the first-phase subject to the flow of carbohydrates through the stomach, liver, and muscles. Consequently, the second-phase model provides the optimal pacing and nutrition strategies for a particular athlete for each kilometer of a particular race. We validate model results for a wide range of athlete parameters by comparing completion times to those reported for two case-study events. We also compare the kilometer-by-kilometer pacing and nutrition strategies prescribed by the model to those of a particular athlete. In all cases, the model results closely match those witnessed in the actual events. We have developed a baseline metabolic model that provides athletes prescriptive guidance regarding optimal pacing and carbohydrate intake strategies prior to competing in ultramarathon races. Given the highly variable topographical characteristics common to many ultramarathon courses and the potential inexperience of many athletes with such courses, our model provides valuable insight to competitors who might otherwise fail to complete the event due to exhaustion or carbohydrate depletion.

Physiological intensity profile, exercise load and performance predictors of a 65-km mountain ultra-marathon

ABSTRACTThe aims of the study were to describe the physiological profile of a 65-km (4000-m cumulative elevation gain) running mountain ultra-marathon (MUM) and to identify predictors of MUM performance. Twenty-three amateur trail-runners performed anthropometric evaluations and an uphill graded exercise test (GXT) for VO2max, ventilatory thresholds (VTs), power outputs (PMax, PVTs) and heart rate response (HRmax, HR@VTs). Heart rate (HR) was monitored during the race and intensity was expressed as: Zone I (<VT1), Zone II (VT1-VT2), Zone III (>VT2) for exercise load calculation (training impulse, TRIMP). Mean race intensity was 77.1%±4.4% of HRmax distributed as: 85.7%±19.4% Zone I, 13.9%±18.6% Zone II, 0.4%±0.9% Zone III. Exercise load was 766±110 TRIMP units. Race time (11.8±1.6h) was negatively correlated with VO2max (r = −0.66, P <0.001) and PMax (r = −0.73, P <0.001), resulting these variables determinant in predicting MUM performance, whereas exercise thresholds did not improve performance prediction. Laboratory variables explained only 59% of race time variance, underlining the multi-factorial character of MUM performance. Our results support the idea that VT1 represents a boundary of tolerable intensity in this kind of events, where exercise load is extremely high. This information can be helpful in identifying optimal pacing strategies to complete such extremely demanding MUMs.

Bicycle change strategy for uphill time-trial races

In uphill time-trial cycling races, riders have to travel along routes characterized by high-gradient variations in the shortest time possible. Due to this gradient variation, the appropriate selection among time-trial bicycles and traditional road bicycles is essential to reduce the power demand. For some uphill courses, the bicycle selection is not necessarily unique, with the possibility of a bicycle change during the race to take advantage of the performance of each type of bicycle for specific sections of the route. In this study, a method for planning the bicycle-changing strategy is proposed. A dynamic model to predict the race time for two types of bicycles is implemented, and an optimization problem for minimizing the race time is presented. A case study is analyzed in which the uphill time-trial route of the Giro d’Italia 2014 is studied in the context of professional cyclists’ performance. It was found that the use of the bicycle change strategy led to a time saving of about 43 s with respect to the time obtained when using only a road bicycle. It was also found that a combination of the bicycle change strategy with an optimal pacing strategy led to a time saving of about 92 s.

Exposure Variation Analysis (EVA) method to monitor ability to optimally regulate exercise intensity of professional cyclists during time-trial competitions

Introduction Pacing strategies during endurance performance is becoming one of the main topics in sport sciences. Several studies proved that a constant pacing strategy, adjusted from course main difficulties, is optimal for individual time-trial (ITT) performance. However, the regulation mechanisms that allow athletes to maintain a constant power output (PO) remain poorly studied (Abbiss and Laursen 2008). The “Exposure Variation Analysis” (EVA) was recently proposed as a new innovative method to quantify short-time PO fluctuations during ITT (Abbiss et al. 2010; Peiffer and Abbiss 2011). This method appears to offer an interesting way to investigate the athlete ability to optimally regulate exercise intensity during ITT in order to maintain a constant optimal pacing strategy. The aim of this study was to assess the relationship between the exercise intensity regulation mechanisms quantified thanks to the EVA method and the evolutions of performance of Word-Tour cyclists during an official competitive ITT performed on the same course during two consecutive years.  Methods After a maximal exhaustive aerobic test, a group of physically active individuals and trained cyclists (N= 12; MAP 352 ± 49 W) in randomized order performed one FTP test over 20 minutes (FTP20) and one CP test, comprising of maximal time trial efforts (TT) of 12 min, 7 min and 3 min, interspersed by 30 min rest (9). Tests were performed on a Cyclus2 ergometer (RBM Elektronik GmbH, Leipzig, Germany). During TTs and FTP test, participants utilised a self-pacing strategy were gearing was adjusted throughout efforts using the virtual gear changer mounted to the handlebars. CP was determined using the power-inverse time model (P = Wi‚¢(1/t) + CP) and FTP60 was calculated as 95% of the FTP20 mean PO. Differences of statistical significance between CP and FTP values were tested using a paired samples t-tests. Relationships were assessed using Pearson product moment correlation coefficients. The agreement between CP and FTP60 values was assessed using Limits of Agreement (LoA). Linear regression was used to calculate the standard error of estimate (SEE) associated with predicting FTP60 values as well as for individual CP values.  Results The mean difference between CP and FTP60 values was 5 ± 11 W, which was non-significant (t(11) = 1.7, p = .108). LoA between values were -38 – 29 W (Fig 1A). The standard error associated with the prediction of FTP60 was 18 W (Cl, 13 - 28W), when expressed as percentage error resulted in 7.9% (Cl, 5.8 – 12.9%). The correlation between CP and FTP60 values was r = 0.93, P ≤ 0.001 (Fig 1B). The mean SEE for CP values was 4 ± 2 W.  Discussion Results demonstrate low LoA between CP and FTP60 values and a high prediction error when using a group of mixed trained athletes. This suggests that CP and FTP60 results cannot be used interchangeably. By using more than one data point, an advantage of CP over FTP60 is a reduction in random error (expressed as SEE). This can be useful for coaches as it minimizes the biological re-test variability caused by the athlete. CP testing also allows the determination of W', i.e. the maximum amount of work that can be expended above the intensity of CP. It therefore offers more information about the performance capabilities of an athlete. With some agreement present for the trained cyclists, future studies should focus on this population.  Conclusion For a same ITT, mean PO of a professional cyclist remain extremely stable over years. Accordingly, he will be more able to improve his performance thanks to a better effort regulation than by increasing his mean PO. EVA method appears to be an innovative tool to evaluate cyclists’ ability to optimally regulate exercise intensity during ITT.

A Variational Approach to Determine the Optimal Power Distribution for Cycling in a Time Trial

The optimal pacing strategy of a cyclist in an individual time-trial depends on terrain, weather conditions and the cyclists endurance capacity. Previous experimental and theoretical studies have shown that a suboptimal pacing strategy may have a substantial negative effect. In this paper we express the optimal pacing problem as a mathematical optimal control problem which we solve using Pontryagin's maximum principle. Our solution of the pacing problem is partly numerical and partly analytical. It applies to a straight course without bends. It turns out that the optimal pacing problem is a singular control problem. Intricate mathematical arguments are required to prove that the singular control times form a single interval: optimal pacing starts with maximum power and decays through a singular control, which may be degenerate, to minimum power.