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Matematiksel Kritik Eşik Kavramı

Yıl 2017, Cilt: 28 Sayı: 4, 220 - 236, 08.06.2018
https://doi.org/10.17644/sbd.342822

Öz

Direnç
egzersizlerinde kritik tork (KT) ve bu değerin zaman-tork hiperbolik
modelindeki eğim sabitini veren anaerobik iş kapasitesi (
T’), egzersiz şiddeti ve bitkinlik süresi arasındaki ters ilişkiyi
ortaya koymuştur. Sonraki yıllarda, bu parametrelerin büyük kas gruplarının katılımıyla
gerçekleştirilen egzersizlere uyarlanmasıyla kritik güç (KG) ve kritik hız (KH)
ile bu kriterlere ait fonksiyonlar (sırasıyla
W’ ve D’) tanımlanmıştır.
Bu kavramlar “kritik bir metabolik oran” olarak bilinen kritik eşik (KE)
değerini verir. Matematiksel temelli bu KE, “yorgunluk oluşmadan uzun süreler devam
ettirilebilen en yüksek oran” olarak değeridir. Bu değer “VO
2’de
halen denge görülen (≤2,1 ml O
2 dk-1·kg-1
değişim) en yüksek egzersiz şiddeti” olarak fizyolojik bir temele
oturtulmuştur. Dolayısıyla KE, çok ağırdan (-very heavy) şiddetli (-severe)
egzersiz alanına geçişin sınırı olarak kabul edilir. KE belirlemede kullanılan
sabit şiddetli egzersiz sayıları genellikle üç ile yedi arasında değişir. Güvenilir
ve geçerli bir KE tahmin etmede seçilecek egzersiz şiddetlerinin, 1-2 dakikadan
10-12 dakikaya değişen sürelerde bitkinlik yaratacak düzeylerde olması gerekir.
Ancak matematiksel teorilerle açıklanan KE bir miktar düşük geçerliliğe sahip
bir performans bileşenidir. KE üzeri egzersiz şiddetlerinde bitkinliğe kadar VO
2’de
izlenen yavaş komponentin her durumda VO
2maks ile sonlanmayabileceği
gösterilmiştir. Bu derleme, ilgili kavramların teorik ve pratik temellerini
açıkladıktan sonra, gerçek bir kritik eşik belirlemenin inceliklerini aktarmak amacıyla
hazırlanmıştır.

Kaynakça

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  • Barstow, T. J., Jones, A. M., Nguyen, P. H., & Casaburi, R. (1996). Influence of muscle fiber type and pedal frequency on oxygen uptake kinetics of heavy exercise. Journal of Applied Physiology, 81(4), 1642-1650.
  • Bearden, S. E., & Moffatt, R. J. (2000). VO2 kinetics and the O2 deficit in heavy exercise. Journal of Applied Physiology, 88(4), 1407-1412.
  • Beaver, W. L., Wasserman, K., & Whipp, B. J. (1986). A new method for detecting anaerobic threshold by gas exchange. Journal of Applied Physiology, 60(6), 2020-2027.
  • Belardinelli, R., Barstow, T. J., Porszasz, J., & Wasserman, K. (1995). Skeletal muscle oxygenation during constant work rate exercise. Medicine and Science in Sports and Exercise, 27(4), 512-519.
  • Bergstrom, H. C., Housh, T. J., Zuniga, J. M., Camic, C. L., Traylor, D. A., Schmidt, R. J., & Johnson, G. O. (2012). A new single work bout test to estimate critical power and anaerobic work capacity. The Journal of Strength and Conditioning Research, 26(3), 656-663.
  • Bergstrom, H. C., Housh, T. J., Zuniga, J. M., Traylor, D. A., Camic, C. L., Lewis J, R. W., Schmidt, R. J., & Johnson, G. O. (2013a). The relationships among critical power determined from a 3-min all-out test, respiratory compensation point, gas exchange threshold, and ventilatory threshold. Research Quarterly for Exercise and Sport, 84(2), 232-238.
  • Bergstrom, H. C., Housh, T. J., Cochrane, K. C., Jenkins, N. D., Lewis Jr, R. W., Traylor, D. A., Zuniga, J. M., Schmidt, R. J., Johnson, G. O., & Cramer, J. T. (2013b). An examination of neuromuscular and metabolic fatigue thresholds. Physiological measurement, 34(10), 1253.
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  • Billat, V., Binsse, V., Petit, B., & Koralsztein, J. J. (1998a). High level runners are able to maintain a VO2 steady-state below VO2max in an all-out run over their critical velocity. Archives of Physiology and Biochemistry, 106(1), 38-45.
  • Billat, V. L., Richard, R., Binsse, V. M., Koralsztein, J. P., & Haouzi, P. (1998b). The VO2 slow component for severe exercise depends on type of exercise and is not correlated with time to fatigue. Journal of Applied Physiology, 85(6), 2118-2124.
  • Billat, V. L., Blondel, N., & Berthoin, S. (1999). Determination of the velocity associated with the longest time to exhaustion at maximal oxygen uptake. European Journal of Applied Physiology and Occupational Physiology, 80(2), 159-161.
  • Binder, R. K., Wonisch, M., Corra, U., Cohen-Solal, A., Vanhees, L., Saner, H., & Schmid, J. P. (2008). Methodological approach to the first and second lactate threshold in incremental cardiopulmonary exercise testing. European Journal of Cardiovascular Prevention and Rehabilitation, 15(6), 726-734.
  • Black, M. I., Durant, J., Jones, A. M., & Vanhatalo, A. (2014). Critical power derived from a 3-min all-out test predicts 16.1-km road time-trial performance. European Journal of Sport Science, 14(3), 217-223.
  • Black, M. I., Jones, A. M., Kelly, J. A., Bailey, S. J., & Vanhatalo, A. (2016). The constant work rate critical power protocol overestimates ramp incremental exercise performance. European journal of applied physiology, 116(11-12), 2415-2422.
  • Broxterman, R. M., Ade, C. J., Barker, T., & Barstow, T. J. (2015a). Influence of pedal cadence on the respiratory compensation point and its relation to critical power. Respiratory Physiology & Neurobiology, 208, 1-7.
  • Broxterman, R. M., Ade, C. J., Craig, J. C., Wilcox, S. L., Schlup, S. J., & Barstow, T. J. (2015 b). The relationship between critical speed and the respiratory compensation point: coincidence or equivalence. European Journal of Sport Science, 15(7), 631-639.
  • Clark, I. E., Murray, S. R., Pettitt, C. D., Kernozek, T. W., & Pettitt, R. W. (2012). Alternative procedures for the 3-min all-out exercise test. Journal of Strength and Conditioning Research, 27(8), 2014-2112.
  • Constantini, K., Sabapathy, S., & Cross, T. J. (2014). A single-session testing protocol to determine critical power and W′. European Journal of Applied Physiology, 114(6), 1153-1161.
  • Dekerle, J., Sidney, M., Hespel, J. M., & Pelayo, P. (2002). Validity and reliability of critical speed, critical stroke rate, and anaerobic capacity in relation to front crawl swimming performances. International Journal of Sports Medicine, 23(02), 93-98.
  • Dekerle, J., Baron, B., Dupont, L., Vanvelcenaher, J., & Pelayo, P. (2003). Maximal lactate steady state, respiratory compensation threshold and critical power. European Journal of Applied Physiology, 89(3-4), 281-288.
  • Dickstein, K., Barvik, S., Aarsland, T., Snapinn, S., & Karlsson, J. (1990). A comparison of methodologies in detection of the anaerobic threshold. Circulation, 81(1 Suppl), II38-46.
  • Endo, M. Y., Kobayakawa, M., Kinugasa, R., Kuno, S., Akima, H., Rossiter, H. B., Miura, A., & Fukuba, Y. (2007). Thigh muscle activation distribution and pulmonary VO 2 kinetics during moderate, heavy, and very heavy intensity cycling exercise in humans. American Journal of Physiology-Regulatory, Integrative and Comparative Physiology, 293(2), 812-820.
  • Gaesser, G. A., & Wilson, L. A. (1988). Effects of continuous and interval training on the parameters of the power-endurance time relationship for high-intensity exercise. International Journal of Sports Medicine, 9(06), 417-421.
  • Gaesser, G. A., Carnevale, T. J., Garfinkel, A., Walter, D. O., & Womack, C. J. (1995). Estimation of critical power with nonlinear and linear models. Medicine and Science in Sports and Exercise, 27(10), 1430-1438.
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Mathematical Critical Threshold Concepts

Yıl 2017, Cilt: 28 Sayı: 4, 220 - 236, 08.06.2018
https://doi.org/10.17644/sbd.342822

Öz

Critical torque during resistance trainings and its

asymptotic slope constant of time-torque hyperbolic

equation as anaerobic work capacity (T’), manifested

an inverse relationship between exercise intensity

and time limit. In the following years, by means

of the adaptations of these parameters to exercises

performed with large muscle involvements, critical

power, critical velocity, and their mathematical functions

were identified as W’ and D’. Those concepts

have given critical threshold (CT) known as a “critical

metabolic rate”. Mathematically based CT is identified

as “the highest rate that can be sustained for a very

long time without fatigue”. CT has been based upon a

physiological basis by “the highest exercise intensity

that can be remained a stable O2”. Thereby, CT represents

a boundary that separates exercise intensity domains

between very heavy and severe. The number of

constant-intensity exhausted exercises to define the

CT mostly vary between three and seven. A number

of exercises within the severe zone that can be caused

exhaustion within 1-2 to 10-12 minutes, should be adjusted

in order to evaluate a reliable and valid CT. On the

other hand, mathematically based CT as a performance

criterion has a lack of accuracy. It was shown that

slow component of O2 may not always reach to O2max

via exercises to volitional exhaustion performed with

supra-critical threshold. This review was prepared to 

explain theoretical and practical bases of the critical

threshold and then, to clarify key points to detect a real

critical threshold.

Kaynakça

  • Barstow, T. J., & Molé, P. A. (1991). Linear and nonlinear characteristics of oxygen uptake kinetics during heavy exercise. Journal of Applied Physiology, 71(6), 2099-2106.
  • Barstow, T. J., Jones, A. M., Nguyen, P. H., & Casaburi, R. (1996). Influence of muscle fiber type and pedal frequency on oxygen uptake kinetics of heavy exercise. Journal of Applied Physiology, 81(4), 1642-1650.
  • Bearden, S. E., & Moffatt, R. J. (2000). VO2 kinetics and the O2 deficit in heavy exercise. Journal of Applied Physiology, 88(4), 1407-1412.
  • Beaver, W. L., Wasserman, K., & Whipp, B. J. (1986). A new method for detecting anaerobic threshold by gas exchange. Journal of Applied Physiology, 60(6), 2020-2027.
  • Belardinelli, R., Barstow, T. J., Porszasz, J., & Wasserman, K. (1995). Skeletal muscle oxygenation during constant work rate exercise. Medicine and Science in Sports and Exercise, 27(4), 512-519.
  • Bergstrom, H. C., Housh, T. J., Zuniga, J. M., Camic, C. L., Traylor, D. A., Schmidt, R. J., & Johnson, G. O. (2012). A new single work bout test to estimate critical power and anaerobic work capacity. The Journal of Strength and Conditioning Research, 26(3), 656-663.
  • Bergstrom, H. C., Housh, T. J., Zuniga, J. M., Traylor, D. A., Camic, C. L., Lewis J, R. W., Schmidt, R. J., & Johnson, G. O. (2013a). The relationships among critical power determined from a 3-min all-out test, respiratory compensation point, gas exchange threshold, and ventilatory threshold. Research Quarterly for Exercise and Sport, 84(2), 232-238.
  • Bergstrom, H. C., Housh, T. J., Cochrane, K. C., Jenkins, N. D., Lewis Jr, R. W., Traylor, D. A., Zuniga, J. M., Schmidt, R. J., Johnson, G. O., & Cramer, J. T. (2013b). An examination of neuromuscular and metabolic fatigue thresholds. Physiological measurement, 34(10), 1253.
  • Billat, L. V., & Koralsztein, J. P. (1996). Significance of the velocity at VO2max and time to exhaustion at this velocity. Sports Medicine, 22(2), 90-108.
  • Billat, V., Binsse, V., Petit, B., & Koralsztein, J. J. (1998a). High level runners are able to maintain a VO2 steady-state below VO2max in an all-out run over their critical velocity. Archives of Physiology and Biochemistry, 106(1), 38-45.
  • Billat, V. L., Richard, R., Binsse, V. M., Koralsztein, J. P., & Haouzi, P. (1998b). The VO2 slow component for severe exercise depends on type of exercise and is not correlated with time to fatigue. Journal of Applied Physiology, 85(6), 2118-2124.
  • Billat, V. L., Blondel, N., & Berthoin, S. (1999). Determination of the velocity associated with the longest time to exhaustion at maximal oxygen uptake. European Journal of Applied Physiology and Occupational Physiology, 80(2), 159-161.
  • Binder, R. K., Wonisch, M., Corra, U., Cohen-Solal, A., Vanhees, L., Saner, H., & Schmid, J. P. (2008). Methodological approach to the first and second lactate threshold in incremental cardiopulmonary exercise testing. European Journal of Cardiovascular Prevention and Rehabilitation, 15(6), 726-734.
  • Black, M. I., Durant, J., Jones, A. M., & Vanhatalo, A. (2014). Critical power derived from a 3-min all-out test predicts 16.1-km road time-trial performance. European Journal of Sport Science, 14(3), 217-223.
  • Black, M. I., Jones, A. M., Kelly, J. A., Bailey, S. J., & Vanhatalo, A. (2016). The constant work rate critical power protocol overestimates ramp incremental exercise performance. European journal of applied physiology, 116(11-12), 2415-2422.
  • Broxterman, R. M., Ade, C. J., Barker, T., & Barstow, T. J. (2015a). Influence of pedal cadence on the respiratory compensation point and its relation to critical power. Respiratory Physiology & Neurobiology, 208, 1-7.
  • Broxterman, R. M., Ade, C. J., Craig, J. C., Wilcox, S. L., Schlup, S. J., & Barstow, T. J. (2015 b). The relationship between critical speed and the respiratory compensation point: coincidence or equivalence. European Journal of Sport Science, 15(7), 631-639.
  • Clark, I. E., Murray, S. R., Pettitt, C. D., Kernozek, T. W., & Pettitt, R. W. (2012). Alternative procedures for the 3-min all-out exercise test. Journal of Strength and Conditioning Research, 27(8), 2014-2112.
  • Constantini, K., Sabapathy, S., & Cross, T. J. (2014). A single-session testing protocol to determine critical power and W′. European Journal of Applied Physiology, 114(6), 1153-1161.
  • Dekerle, J., Sidney, M., Hespel, J. M., & Pelayo, P. (2002). Validity and reliability of critical speed, critical stroke rate, and anaerobic capacity in relation to front crawl swimming performances. International Journal of Sports Medicine, 23(02), 93-98.
  • Dekerle, J., Baron, B., Dupont, L., Vanvelcenaher, J., & Pelayo, P. (2003). Maximal lactate steady state, respiratory compensation threshold and critical power. European Journal of Applied Physiology, 89(3-4), 281-288.
  • Dickstein, K., Barvik, S., Aarsland, T., Snapinn, S., & Karlsson, J. (1990). A comparison of methodologies in detection of the anaerobic threshold. Circulation, 81(1 Suppl), II38-46.
  • Endo, M. Y., Kobayakawa, M., Kinugasa, R., Kuno, S., Akima, H., Rossiter, H. B., Miura, A., & Fukuba, Y. (2007). Thigh muscle activation distribution and pulmonary VO 2 kinetics during moderate, heavy, and very heavy intensity cycling exercise in humans. American Journal of Physiology-Regulatory, Integrative and Comparative Physiology, 293(2), 812-820.
  • Gaesser, G. A., & Wilson, L. A. (1988). Effects of continuous and interval training on the parameters of the power-endurance time relationship for high-intensity exercise. International Journal of Sports Medicine, 9(06), 417-421.
  • Gaesser, G. A., Carnevale, T. J., Garfinkel, A., Walter, D. O., & Womack, C. J. (1995). Estimation of critical power with nonlinear and linear models. Medicine and Science in Sports and Exercise, 27(10), 1430-1438.
  • Galbraith, A., Hopker, J. G., Jobson, S. A., & Passfield, L. (2011). A novel field test to determine critical speed. Journal of Sports Medicine and Doping Studies, 1(1), 1-4.
  • Galbraith, A., Hopker, J., Lelliott, S., Diddams, L., & Passfield, L. (2014). A single-visit field test of critical speed. International Journal of Sports Physiology and Performance, 9(6), 931-935.
  • Grassi, B., Poole, D. C., Richardson, R. S., Knight, D. R., Erickson, B. K., & Wagner, P. D. (1996). Muscle O2 uptake kinetics in humans: implications for metabolic control. Journal of Applied Physiology, 80(3), 988-998.
  • Hendrix, C. R., Housh, T. J., Mielke, M., Zuniga, J. M., Camic, C. L., Johnson, G. O., & Schmidt, R. J. (2009). Critical torque, estimated time to exhaustion, and anaerobic work capacity from linear and nonlinear mathematical models. Medicine & Science in Sports & Exercise, 41(12), 2185-2190.
  • Henry, F. M. (1955). Prediction of world records in running sixty yards to twenty-six miles. Research Quarterly. American Association for Health, Physical Education and Recreation, 26(2), 147-158.
  • Hill, A. V. (1925). The physiological basis of athletic records. The Lancet, 206(5323), 481-486.
  • Hill, A. V. (1927). Muscular Movement in Man: The Factors Governing Speed and Recovery from Fatigue. Muscular Movement in Man: The Factors governing Speed and Recovery from Fatigue.
  • Hill, D. W. (1993). The critical power concept. Sports medicine, 16(4), 237-254.
  • Hill, D. W., & Smith, J. C. (1993). A comparison of methods of estimating anaerobic work capacity. Ergonomics, 36(12), 1495-1500.
  • Hill, D. W., Alain, C., & Kennedy, M. D. (2003). Modeling the relationship between velocity and time to fatigue in rowing. Medicine and Science in Sports and Exercise, 35(12), 2098-2105.
  • Housh, D. J., House, T. J., & Bauge, S. M. (1989). The accuracy of the critical power test for predicting time to exhaustion during cycle ergometry. Ergonomics, 32(8), 997-1004.
  • Housh, D. J., Housh, T. J., & Bauge, S. M. (1990). A methodological consideration for the determination of critical power and anaerobic work capacity. Research Quarterly for Exercise and Sport, 61(4), 406-409.
  • Housh, T. J., Cramer, J. T., Bull, A. J., Johnson, G. O., & Housh, D. J. (2001). The effect of mathematical modeling on critical velocity. European Journal of Applied Physiology, 84(5), 469-475.
  • Hughson, R. L., Orok, C. J., & Staudt, L. E. (1984). A high velocity treadmill running test to assess endurance running potential. International Journal of Sports Medicine, 5(01), 23-25.
  • Jenkins, D. G., & Quigley, B. M. (1990). Blood lactate in trained cyclists during cycle ergometry at critical power. European Journal of Applied Physiology and Occupational Physiology, 61(3), 278-283. Jenkins, D. G., & Quigley, B. M. (1991). The y-intercept of the critical power function as a measure of anaerobic work capacity. Ergonomics, 34(1), 13-22.
  • Johnson, T. M., Sexton, P. J., Placek, A. M., Murray, S. R., & Pettitt, R. W. (2011). Reliability analysis of the 3-min all-out exercise test for cycle ergometry. Medicine and Science in Sports and Exercise, 43(12), 2375-2380.
  • Jones, A. M., Vanhatalo, A., Burnley, M., Morton, R. H., & Poole, D. C. (2010). Critical power: implications for determination of VO2max and exercise tolerance. Medicine and Science in Sports and Exercise, 42(10), 1876-90.
  • Keir, D. A., Fontana, F. Y., Robertson, T. C., Murias, J. M., Paterson, D. H., Kowalchuk, J. M., & Pogliaghi, S. (2015). Exercise intensity thresholds: identifying the boundaries of sustainable performance. Medicine and Science in Sports and Exercise, 47(9), 1932-40.
  • Kennelly, A. E. (1906). An approximate law of fatigue in the speeds of racing animals. In Proceedings of the American Academy of Arts and Sciences (Vol. 42, No. 15, pp. 275-331). American Academy of Arts & Sciences.
  • Laursen, P. B., Francis, G. T., Abbiss, C. R., Newton, M. J., & Nosaka, K. (2007). Reliability of time-to-exhaustion versus time-trial running tests in runners. Medicine and Science in Sports and Exercise, 39(8), 1374-1379.
  • Leo, J. A., Sabapathy, S., Simmonds, M. J., & Cross, T. J. (2017). The Respiratory Compensation Point is Not a Valid Surrogate for Critical Power. Medicine and Science in Sports and Exercise.
  • Manns, P. J., Tomczak, C. R., Jelani, A., & Haennel, R. G. (2010). Oxygen uptake kinetics: associations with ambulatory activity and physical functional performance in stroke survivors. Journal of Rehabilitation Medicine, 42(3), 259-264.
  • McGawley, K. (2010). The application of the critical power construct to endurance exercise (Doctoral dissertation, University of Brighton, Faculty of Education and Sport).
  • McLellan, T. M., & Cheung, K. S. (1992). A comparative evaluation of the individual anaerobic threshold and the critical power. Medicine and Science in Sports and Exercise, 24(5), 543-550.
  • Meade, G. P. (1916). An analytical study of athletic records. The Scientific Monthly, 2(6), 596-600.
  • Monod, H., & Scherrer, J. (1965). The work capacity of a synergic muscular group. Ergonomics, 8(3), 329-338.
  • Moritani, T., Nagata, A., Devries, H. A., & Muro, M. (1981). Critical power as a measure of physical work capacity and anaerobic threshold. Ergonomics, 24(5), 339-350.
  • Morton, R. H. (1994). Critical power test for ramp exercise. European Journal of Applied Physiology and Occupational Physiology, 69(5), 435-438.
  • Overend, T. J., Cunningham, D. A., Paterson, D. H., & Smith, W. D. F. (1992). Physiological responses of young and elderly men to prolonged exercise at critical power. European Journal of Applied Physiology and Occupational Physiology, 64(2), 187-193.
  • Ozyener, F., Rossiter, H. B., Ward, S. A., & Whipp, B. J. (2001). Influence of exercise intensity on the on‐and off‐transient kinetics of pulmonary oxygen uptake in humans. The Journal of Physiology, 533(3), 891-902.
  • Ozyener, F., Rossiter, H. B., Ward, S. A., & Whipp, B. J. (2003). Negative accumulated oxygen deficit during heavy and very heavy intensity cycle ergometry in humans. European Journal of Applied Physiology, 90(1-2), 185-190.
  • Parker Simpson, L., & Kordi, M. (2016). Comparison of Critical Power and W′ Derived from Two or Three Maximal Tests. International Journal of Sports Physiology and Performance, 1-24.
  • Poole, D. C., Ward, S. A., Gardner, G. W., & Whipp, B. J. (1988). Metabolic and respiratory profile of the upper limit for prolonged exercise in man. Ergonomics, 31(9), 1265-1279.
  • Poole, D. C., Burnley, M., Vanhatalo, A., Rossiter, H. B., & Jones, A. M. (2016). Critical power: an important fatigue threshold in exercise physiology. Medicine and Science in Sports and Exercise, 48(11), 2320-34.
  • Poole, D. C., & Jones, A. M. (2017). Measurement of the maximum oxygen uptake V̇o 2max: V̇O2peak is no longer acceptable. Journal of Applied Physiology, 122(4), 997-1002.
  • Reinhard, U., Müller, P. H., & Schmülling, R. M. (1979). Determination of anaerobic threshold by the ventilation equivalent in normal individuals. Respiration, 38(1), 36-42.
  • Robergs, R. A. (2014). A critical review of the history of low-to moderate-intensity steady-state VO2 kinetics. Sports Medicine, 44(5), 641-653.
  • Roston, W. L., Whipp, B. J., Davis, J. A., Cunningham, D. A., Effros, R. M., & Wasserman, K. (1987). Oxygen Uptake Kinetics and Lactate Concentration During Exercise in Humans 1–3. American Review of Respiratory Disease, 135(5), 1080-1084.
  • Sawyer, B. J., Morton, R. H., Womack, C. J., & Gaesser, G. A. (2012). V O2max may not be reached during exercise to exhaustion above critical power. Medicine and Science in Sports and Exercise, 44(8), 1533-1538.
  • Smith, C. G., & Jones, A. M. (2001). The relationship between critical velocity, maximal lactate steady-state velocity and lactate turn-point velocity in runners. European Journal of Applied Physiology, 85(1), 19-26.
  • Stringer, W., Wasserman, K., Casaburi, R., Porszasz, J., Maehara, K., & French, W. (1994). Lactic acidosis as a facilitator of oxyhemoglobin dissociation during exercise. Journal of Applied Physiology, 76(4), 1462-1467.
  • Vandewalle, H., Kapitaniak, B., Grün, S., Raveneau, S., & Monod, H. (1989). Comparison between a 30-s all-out test and a time-work test on a cycle ergometer. European Journal of Applied Physiology and Occupational Physiology, 58(4), 375-381.
  • Vandewalle, H. (1995). Critical power test for ramp exercise. European journal of applied physiology and occupational physiology, 71(2), 285-286.
  • Vandewalle, H., Vautier, J. F., Kachouri, M., Lechevalier, J. M., & Monod, H. (1997). Work-exhaustion time relationships and the critical power concept. A critical review. Journal of Sports Medicine and Physical Fitness, 37(2), 89-102.
  • Vanhatalo, A., Doust, J. H., & Burnley, M. (2007). Determination of critical power using a 3-min all-out cycling test. Medicine and Science in Sports and Exercise, 39(3), 548-555.
  • Wakayoshi, K., Yoshida, T., Udo, M., Kasai, T., Moritani, T., Mutoh, Y., & Miyashita, M. (1992a). A simple method for determining critical speed as swimming fatigue threshold in competitive swimming. International journal of sports medicine, 13(05), 367-371.
  • Wakayoshi, K., Ikuta, K., Yoshida, T., Udo, M., Moritani, T., Mutoh, Y., & Miyashita, M. (1992b). Determination and validity of critical velocity as an index of swimming performance in the competitive swimmer. European Journal of Applied Physiology and Occupational Physiology, 64(2), 153-157.
  • Wasserman K., Whipp BJ., Koyl, S. N., & Beaver, W. L. (1973). Anaerobic threshold and respiratory gas exchange during exercise. Journal of Applied Physiology, 35(82), 236.
  • Whipp, B. J., Ward, S. A., Lamarra, N., Davis, J. A., & Wasserman, K. (1982). Parameters of ventilatory and gas exchange dynamics during exercise. Journal of Applied Physiology, 52(6), 1506-1513.
  • Whipp, B. J., Davis, J. A., & Wasserman, K. (1989). Ventilatory control of the ‘isocapnic buffering region in rapidly-incremental exercise. Respiration physiology, 76(3), 357-367.
  • Whipp, B. J. (1994). The slow component of O2 uptake kinetics during heavy exercise. Medicine and science in sports and exercise, 26(11), 1319-1326.
  • Whipp, B. J., Ward, S. A. & Rossiter, H. B. (2005). Pulmonary O2 uptake during exercise: Conflating muscular and cardiovascular responses. Medicine and Science in Sports and Exercise, 37(9): 1574-1585.
  • Yeh, M. P., Gardner, R. M., Adams, T. D., Yanowitz, F. G., & Crapo, R. O. (1983). "Anaerobic threshold": problems of determination and validation. Journal of Applied Physiology, 55(4), 1178-1186.
Toplam 78 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Spor Hekimliği
Bölüm Makaleler
Yazarlar

Özgür Özkaya

Görkem Aybars Balcı Bu kişi benim

Muzaffer Çolakoğlu

Yayımlanma Tarihi 8 Haziran 2018
Gönderilme Tarihi 11 Ekim 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 28 Sayı: 4

Kaynak Göster

APA Özkaya, Ö., Balcı, G. A., & Çolakoğlu, M. (2018). Matematiksel Kritik Eşik Kavramı. Spor Bilimleri Dergisi, 28(4), 220-236. https://doi.org/10.17644/sbd.342822

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