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Cardio
The cardio module contains submodules of related equations for calculating cardiovascular measurements such as energy expenditure, heart rate, resting metabolic rate, and VO2Max. In the realm of cardiovascular sports (running, swimming, cycling), calculating cardiovascular metrics are useful for developing training plans, estimating required caloric intake, and evaluating fitness level.
The cardiac module is a collection of heart-related equations used in health assessments, and calculating heart rate training zones.
The energy module calculates the energy requirements of the human body to maintain stability. These values, such as Basal Metabolic Rate (BMR), Estimated Energy Requirement (EER) are used in estimating the required kilocalories (kcal) required by the human body based on activity level. This value is important in developing lifestyle-based nutrition plans.
The respiration module contains formulas for estimating the capacity of the lungs and for estimating the efficiency of the respiration system using VO2/VO2Max. These equations are used in general health assessments, aerobic performance assessments, and in developing training plans for endurance sports.
A module for calculating maximum heart rate and residual volume across fitness levels in children, adults, athletes, and older adults.
Estimator classes for predicting maximum heart rate (HRMax) based on age. All of these classes implement the Estimator interface. To change the equation for predicting HRMax, developers can swap out the estimator class rather than changing their application logic.
All classes do not have any required fields in the constructor, and use the predict(dob) method to predict the HRMax for an individual.
All classes also include an age(hr) method, which predicts the age of an individual (in years) based on maximum heart rate based on the HRMax equation.
The Astrand equation for estimating maximum heart rate (HRMax). For use on men and women ages 4 to 34 yr source
The Haskell & Fox equation for estimating maximum heart rate (HRMax). Recommended for use with older adults source
The Gellish equation for estimating maximum heart rate (HRMax). For use on men and women participants in an adult fitness program with broad range of age and fitness levels
Farazdaghi GR, Wohlfart B (November 2001). "Reference values for the physical work capacity on a bicycle ergometer for women between 20 and 80 years of age". site Clin Physiol. 21 (6): 682–7. doi:10.1046/j.1365-2281.2001.00373.x. PMID 11722475. Wohlfart B, Farazdaghi GR (May 2003). "Reference values for the physical work capacity on a bicycle ergometer for men -- a comparison with a previous study on women". site Clin Physiol Funct Imaging. 23 (3): 166–70. doi:10.1046/j.1475-097X.2003.00491.x. PMID 12752560.
The Gulati equation for estimating maximum heart rate (HRMax). For use on asymptomatic middle aged women referred for stress testing
Gulati M, Shaw LJ, Thisted RA, Black HR, Bairey Merz CN, Arnsdorf MF (2010). "Heart rate response to exercise stress testing in asymptomatic women: the st. James women take heart project". Circulation. 122 (2): 130–7. doi:10.1161/CIRCULATIONAHA.110.939249. PMID 20585008.
Nes, B. M., et al. "Age‐predicted maximal heart rate in healthy subjects: The HUNT Fitness Study." Scandinavian journal of medicine & science in sports 23.6 (2013): 697-704
Gellish RL, Goslin BR, Olson RE, McDonald A, Russi GD, Moudgil VK (2007). "Longitudinal modeling of the relationship between age and maximal heart rate". site Med Sci Sports Exerc. 39 (5): 822–9. doi:10.1097/mss.0b013e31803349c6. PMID 17468581.
Robergs R, Landwehr R (2002). "The Surprising History of the 'HRmax=220-age' Equation" (PDF). Journal of Exercise Physiology. 5 (2): 1–10.
The Tanaka equation for estimating maximum heart rate (HRMax). For use on healthy men and women
Tanaka H, Monahan KD, Seals DR (January 2001). "Age-predicted maximal heart rate revisited". site J. Am. Coll. Cardiol. 37 (1): 153–6. doi:10.1016/S0735-1097(00)01054-8. PMID 11153730. source
The Karvonen Method for target heart rate (THR) - using a range of 50% to 85% intensity. The formula is used to calculate heart rate for exercise at a percentage training intensity.
hrMax, and hrRest given in beats per minute (bpm).
intensity should be provided as a decimal value between 0 and 1.
Returned in beat per minute.
Zoladz Method for target heart rate (THR) - derives exercise zones by subtracting values from HRmax. Results are +/- 5 bpm
- Zone 1 Adjuster (easy exercise) = 50 bpm
- Zone 2 Adjuster = 40 bpm
- Zone 3 Adjuster = 30 bpm
- Zone 4 Adjuster = 20 bpm
- Zone 5 Adjuster (extremely tough exercise) = 10 bpm
A class for estimating the basal metabolic rate of children, adults, and older adults over a given time period.
gender is either Fit.Gender.Male or Fit.Gender.Female
dob is a Date instance
weight is a number measured in kilograms
height is a number measured in meters
The original Harris-Benedict Equation for basal metabolic rate.
Returns value in kcals/day.
Harris J, Benedict F (1918). "A Biometric Study of Human Basal Metabolism". PNAS. 4 (12): 370–3. Bibcode:1918PNAS....4..370H. doi:10.1073/pnas.4.12.370. PMC 1091498Freely accessible. PMID 16576330. Article PDF
The Revised Harris-Benedict Equation for basal metabolic rate (BMR). Accurately estimates the REE of normal-weight, overweight, and obese individuals but overestimate REE in underweight individuals.
Returns value in kcals/day.
Roza, Allan M; Shizgal, Harry M (1984). "The Harris Benedict equation reevaluated: resting energy requirements and the body cell mass". The American Journal of Clinical Nutrition. 40: 168–182.
The Mifflin St. Jeor Equation for basal metabolic rate (BMR). The American Dietetic Association (2003) recommends using this equation over Harris-Benedict to estimate RMR in healthy individuals. Returns value in kcals/day.
Mifflin, MD; St Jeor, ST; Hill, LA; Scott, BJ; Daugherty, SA; Koh, YO (1990). "A new predictive equation for resting energy expenditure in healthy individuals". The American Journal of Clinical Nutrition. 51 (2): 241–7. PMID 2305711.
A class for estimating resting metabilic rate (RMR)
gender is either Fit.Gender.Male or Fit.Gender.Female
dob is a Date
weight is a number measured in kilograms
height is a number measured in meters
A quick estimate of resting metabolic rate (RMR) based on body mass
Estimate resting metabolic rate based on body surface area (BSA)
Note: every decade after age 40, RMR decreases by 2-5% (Sharkey and Gaskill, 2007), which is not applied in the formula due to high variation.
The Katch-McArdle Formula for resting daily energy expenditure (RDEE). This formula takes lean body mass/fat-free mass (in kilograms) as the only argument.
McArdle, W (2006). Essentials of Exercise Physiology. Lippincott Williams & Wilkins. p. 266. ISBN 9780495014836.
The Cunningham equation for resting metabolic rate (RMR). This formula is similar to Katch-McArdle, but provides a slightly higher estimate.
lbm given as lean body mass/fat-free mass (in kilograms)
Returns RMR in kilocalories
A class for estimating the total energy expenditure (TEE) in children of varying levels of physical activity.
gender given as either Fit.Gender.Male or Fit.Gender.Female
pal given as a Fit.PAL
Returns TEE for children in kcal/day.
A class for estimating the total energy expenditure (TEE) in adults of varying levels of physical activity.
gender given as either Fit.Gender.Male or Fit.Gender.Female
pal given as a Fit.PAL
dob as a Date object
weight in kilograms
height in meters
Returns TEE for adults in kcal/day.
weight in kilograms
mets in kcal/kg/hour
Returns kcal/min based on the MET value of the activity performed.
Humphrey R, The Exercise Caloric Challenge, Clinical Applications, ACSM’s Health & Fitness Journal, March/April 2006, Vol. 10, No. 2 pp.40-41
The Pandolf, Givoni, and Goldman formula for calculating energy expenditure
weight of travelers (in kilograms)
load extra weight being carried (in kg)
speed of walking (meters/second)
Returns energy expenditure in kilocalories
The Pandolf, Givoni, and Goldman formula for calculating energy expenditure. Funded by the United States Army Research Institute of Environmental Medicine. Returns metabolic rate in watts.
terrain type in Terrain variables
slope of the terrain (in percent)
Pandolf K.B., Givoni B., Goldman R.F. Predicting energy expenditure with loads while standing or walking very slowly. J Appl Physiol 43: 577–581, 1977
The Santee formula for calculating energy expenditure. The formula is an updated version of the Pandolf formula that more accurately takes into account downhill travel. The formula is for use with negative (downhill) slopes.
terrain type in Terrain variables
slope of the terrain (in percent)
Returns metabolic rate in watts
Matthew W.T., Santee W.R., Berglund L.G. Solar Load Inputs for USARIEM Thermal Strain Models and the Solar Radiation-Sensitive Components of the WBGT Index (Technical Report T01/13– 01). Natick, MA: U.S. Army Research Institute of Environmental Medicine, 2001.
The respiration module provides methods for estimating residual volume, and VO2Max across genders, races, and age groups.
A class for calculating the residual volume of the lungs for men and women across the lifespan.
dob as a Date object
weight in kilograms
height in meters
Returns the residual volume in Liters
Berglund, E., Birath, G., Bjure, J., Grimby, G., Kjellmar, I., Sandvist, L., and Soderholm, B. 1963. Spirometric studies in normal subjects. I. Forced expirograms in subjects between 7 and 70 years of age. Acta Medica Scandinavica 173: 185-192.
Returns the residual volume in Liters Standard Error of the Estimate (SEE) = 0.46 Liters
Black, L.F., Offord, K., and Hyatt, R.E. 1974. Variability in the maximum expiratory flow volume curve in asymptomatic smokers and nonsmokers. American Review of Respiratory Diseases 110: 282-292.
Returns the residual volume in Liters Standard Error of the Estimate (SEE) = 0.53 Liters
Boren, H.G., Kory, R.C., and Syner, J.C. 1966. The Veteran's Administration-Army cooperative study of pulmonary functionsL II. The lung volume and its subdivisions in normal men. American Journal of Medicine 41: 96-114.
Returns the residual volume in Liters
Goldman, H.I., and Becklake, M.R. 1959. Respiratory function tests: Normal values at medium altitudes and the prediction of normal results. American Review of Tuberculosis and Respiratory Diseases 79: 457-467.
bsa is body surface area in meters^2
Returns the residual volume in Liters
Standard Error of the Estimate (SEE) = 0.49 Liters
O'Brien, R.J., and Drizd, T.A. 1983. Roentgenographic determination of total lung capacity: Normal values from a national population survey. American Review of Respiratory Diseases 128: 949-952.
A class for calculating VO2 and VO2Max in both male and female children, adults, and older adults.
dob as a Date object
weight in kilograms
height in meters
vo2Max in mL/kgmin
vo2Rest in mL/kgmin
Returns VO2 in mL/kg*min
VO2 Reserve (VO2R) is the difference between resting VO2 and VO2Max. Percent VO2 Reserve (%VO2R) is considered a more accurate metric for establishing relative exercise intensity than %VO2Max in both low-fit individuals and elite athletes.
Ehrman, Jonathan K. ACSM's Resource Manual for Guidelines for Exercise Testing and Prescription. 6th ed. Philadelphia: Wolters Kluwer Health/Lippincott Williams & Wilkins, 2010. Print.
distance in miles
Returns VO2max in mL/kg*min
The Cooper VO2Max test is a submaximal VO2Max test based on a population of healthy adults. Returns VO2Max in mL/kg*min.
COOPER, K.H. (1968) A means of assessing maximal oxygen intake. JAMA. 203, p. 135-138
For speeds between 50-100 minter/min (1.9-3.7mph).
speed in meters/minute
grade of treadmill in decimal form (10% = 0.10)
Returns Gross VO2max in mL/kg/min
Heyward, Vivian H. "Metabolic Equations for Estimating Gross VO2 (ACSM 2010)." 2010. Advanced Fitness Assessment and Exercise Prescription. 6th ed. Champaign, IL: Human Kinetics, 2010. N. pag. Print.
For speeds greater than 134 meters/min (5.0 mph). If truly jogging (not walking), this equation can be used for speed of 80-134 meters/min (3-5 mph)
speed in meters/minute
grade of treadmill in decimal form (10% = 0.10)
Returns Gross VO2max in mL/kg/min
Heyward, Vivian H. "Metabolic Equations for Estimating Gross VO2 (ACSM 2010)." 2010. Advanced Fitness Assessment and Exercise Prescription. 6th ed. Champaign, IL: Human Kinetics, 2010. N. pag. Print.
mass given in kilograms
work given in
Returns gross VO2max in mL/kg/min
Heyward, Vivian H. "Metabolic Equations for Estimating Gross VO2 (ACSM 2010)." 2010. Advanced Fitness Assessment and Exercise Prescription. 6th ed. Champaign, IL: Human Kinetics, 2010. N. pag. Print.
mass in kg
work in power output in Watts
Returns Gross VO2max in mL/kg/min
Heyward, Vivian H. "Metabolic Equations for Estimating Gross VO2 (ACSM 2010)." 2010. Advanced Fitness Assessment and Exercise Prescription. 6th ed. Champaign, IL: Human Kinetics, 2010. N. pag. Print.
Ehrman, Jonathan K. ACSM's Resource Manual for Guidelines for Exercise Testing and Prescription. 6th ed. Philadelphia: Wolters Kluwer Health/Lippincott Williams & Wilkins, 2010. Print.
height of bench in meters
frequency in steps/minute
Returns Gross VO2max in mL/kg/min
Heyward, Vivian H. "Metabolic Equations for Estimating Gross VO2 (ACSM 2010)." 2010. Advanced Fitness Assessment and Exercise Prescription. 6th ed. Champaign, IL: Human Kinetics, 2010. N. pag. Print.
The Uth–Sørensen–Overgaard–Pedersen estimation is a VO2Max estimate based on measurements of maximum heart rate and minimum heart rate in well-trained men aged 21 to 51. The formula is most reliable when based on actual measurement of maximum heart rate, rather than an age-related estimates.
The estimation uses the ratio of maximum heart rate (HrMax) to resting heart rate (restingHR) to predict VO2max, and returns VO2Max in mL/kg/minute.
hrMax given in beats/minute
restingHR given in beats/minute
Uth, Niels; Henrik Sørensen; Kristian Overgaard; Preben K. Pedersen (January 2004). "Estimation of VO2max from the ratio between HRmax and HRrest--the Heart Rate Ratio Method". Eur J Appl Physiol. 91 (1): 111–5. doi:10.1007/s00421-003-0988-y. PMID 14624296.
The equation for predicting VO2Max in a population of healthy adults using the sub-maximal Fox test.
hr5 given as the heart rate (in beats/minute) after 5 minutes of cycling
Return VO2Max in mL/kg/min
Fox, E. L. 1973. A simple, accurate technique for predicting maximal aerobic power. Journal of Applied Physiology, 35: 914 - 16
A single-stage treadmill walking test developed by Ebbeling and colleagues for estimating VO2max of low-risk, healthy adults 20-59 years.
speed in miles/hour
hr in beats/minute
Return VO2Max in mL/kg/min
Ebbeling, Cara B., Ann Ward, Elaine M. Puleo, Jeffrey Widrick, and James M. Rippe. "Development of a Single-stage Submaximal Treadmill Walking Test." Medicine & Science in Sports & Exercise 23.8 (1991): n. pag. NIH. Web. 5 Nov. 2016. https://www.ncbi.nlm.nih.gov/pubmed/1956273.
The Kline et al. (1987) formula for the 1-mile walk Rockport Test for VO2Max.
time in minutes
hrPeak in beats/minute
Returns VO2Max in mL/kg/min
Kline, Greg M., John P. Porcari, Robert Hintermeister, Patty S. Freedson, Ann Ward, Robert F. Mccarron, Jessica Ross, and James M. Rippe. "Estimation of &OV0312;O2max from a One-mile Track Walk, Gender, dob, and Body Weight." Medicine & Science in Sports & Exercise 19.3 (1987): n. pag. Web.
McSwegin P, Plowman S, Wolff G, Guttenberg G. The validity of a one-mile walk test for high school age individuals. Measurement in Physical Education and Exercise Science 1998;2:47-63.
George, J. D. et al. VO2max estimation from a submaximal 1-mile track jog for fit college-age individuals. Medicine and Science in Sports and Exercise, 25, 401-406, 1993.
The Larsen VO2Max formula for use in the 1.5 mile run/walk test. For use with young adults (18-29 years old).
time in minutes
hr in beats/minute
Returns VO2Max in mL/kg*min.
Standard Error of Estimation = 2.5 mL/kgmin TE = 2.68 mL/kgmin
LARSEN, G. et al. (2002) Prediction of maximum oxygen consumption from walking, jogging, or running. Research quarterly for exercise and sport, 73 (1), p. 66-72.
The Astrand Step Test formula for estimating a participant's VO2Max. hr given in beats/minute. Returns VO2Max in L/min.
Marley, W. P., and A. C. Linnerud. "Astrand-ryhming Step Test Norms for College Students." British Journal of Sports Medicine 10.2 (1976): 76-79. NIH. Web. 5 Nov. 2016. <http://bjsm.bmj.com/content/10/2/76.long>.
The Queen's College Step Test formula for estimating a participant's VO2Max.
hr given in beats/minute
Returns VO2Max in mL/kg/min
McArdle, W.D., Katch, F.I., Pechar, G.S., Jacobson, L., and Ruck, S. 1972. Reliability and interrelationships between maximal oxygen intake, physical working capacity and step-test scores in college women. Medicine and Science in Sports 4: 182-186.
The formula for the George single-stage jogging test formula. For use with the George 1 mile jog test.
time given in minutes
Returns VO2Max in mL/kg/min
George, J., Vehrs, P., Allsen, P., Fellingham, G., and Fisher, G. 1993. VO2max estimation from a sub-maximal 1-mile track jog for fit college-age individuals. Medicine & Science in Sports & Exercise 25: 401-406
The George formula for the 1 mile steady state jog test. Returns VO2Max in mL/kg/min.
speed in miles/hour
hr in beats/minute
George, J., Vehrs, P., Allsen, P., Fellingham, G., and Fisher, G. 1993. VO2max estimation from a sub-maximal 1-mile track jog for fit college-age individuals. Medicine & Science in Sports & Exercise 25: 401-406
speed in miles/hour
hr in beats/minute
Returns VO2Max in mL/kg/min.
George, J., Vehrs, P., Allsen, P., Fellingham, G., and Fisher, G. 1993. VO2max estimation from a sub-maximal 1-mile track jog for fit college-age individuals. Medicine & Science in Sports & Exercise 25: 401-406
sm1
hr1 in beats/minute
hrmax in beats/minute
Returns VO2Max in mL/kg/min.
Heyward, Vivian H. "Treadmill Submaximal Exercise Tests: single-stage Model." Advanced Fitness Assessment and Exercise Prescription. 6th ed. Champaign, IL: Human Kinetics, 2010. 85. Print.
sm1
hr1 in beats/minute
sm2
hr2 in beats/minute
hrmax in beats/minute
Returns VO2Max in mL/kg/min.
Heyward, Vivian H. "Treadmill Submaximal Exercise Tests: Multistage Model." Advanced Fitness Assessment and Exercise Prescription. 6th ed. Champaign, IL: Human Kinetics, 2010. 85. Print.
The Cureton formula for estimating VO2Peak in the 1.0 mile run/walk in children (8-17 years old).
time given in minutes
Returns VO2Max in mL/kg/min.
Cureton, K.J., Sloniger, M., O'Bannon, J., Black, D., and McCormack, W. 1995. A generalized equation for prediction of VO2peak from 1-mile run/walk performance. Medicine & Science in Sports & Exercise 27: 445-451.
Note: For evaluating the fitness of younger children (5-7 years old), the 0.5 mile run/walk test is recommended.
Rikli, Roberta E., Clayre Petray, and Ted A. Baumgartner. "The Reliability of Distance Run Tests for Children in Grades K-4." Research Quarterly for Exercise and Sport 63.3 (1992): 270-76. NCBI. Web. 10 Nov. 2016. <https://www.ncbi.nlm.nih.gov/pubmed/1513957>.
Balke and Ware (1959) exercise test protocols.
time given in minutes
Returns VO2Max in mL/kg/min.
Source (Men) Pollock, M.L., Bohannon, R.L., Cooper, K.H., Ayres, J.J., Ward, A., White, S.R., and Linnerud, A.C. 1976 A comparative analysis of four protocols for maximal treadmill strss testing. American Heart Journal 92: 39-46.
Source (Women) POLLOCK et al. (1982) Comparative analysis of physiologic responses to three different maximal graded exercise test protocols in healthy women. American Heart Journal, 103 (3), p. 363-373
The Balke formula for the 15 min run test for VO2Max.
distance in meters
Returns VO2Max in mL/kg/min.
The Bruce protocol equation for use with active and sedentary men. The Bruce protocol is used for estimating VO2Max based on treadmill exercise.
time, time2, and time3 given in minutes.
Returns VO2Max in mL/kg/min.
Standard Error of Estimate: 3.35 mL/kg/min
Note: For use with the standard Bruce protocol, not the Modified Bruce protocol
FOSTER et al. (1984) Generalized equations for predicting functional capacity from treadmill performance. American Heart Journal, 107 (6), p. 1229-1234
The Bruce protocol equation for use with active and sedentary women. The Bruce protocol is used for estimating VO2Max based on multi-stage treadmill exercise. The protocol increases the workload by changing both speed and grade of the treadmill.
Note: For use with the standard Bruce protocol, not the Modified Bruce protocol
time given in minutes
Returns VO2Max in mL/kg/min
Standard Error of Estimate: 2.7 mL/kg/min
POLLOCK et al. (1982) Comparative analysis of physiologic responses to three different maximal graded exercise test protocols in healthy women. American Heart Journal, 103 (3), p. 363-373
A VO2Max prediction equation for use with cardiac patients and elderly patients when using the Bruce Treadmill protocol.
time given in minutes
Returns VO2Max in mL/kg/min
Standard Error of Estimation: 4.9 mL/kg/min
Note: Used only for treadmill walking while holding the handrails
McConnell, Timothy R.;Clark, Bernard A., "Prediction of Maximal Oxygen Consumption During Handrail-Supported Treadmill Exercise". Journal Of Cardiopulmonary Rehabilitation And Prevention, 1987
A 20m Shuttle run test developed by Leger and colleagues (1988) to test the aerobic fitness of children, dobs 8-19 years. velocity given in km/hour. Returns VO2Max in mL/kg/min.
Leger, L. A., D. Mercier, C. Gadoury, and J. Lambert. "The Multistage 20 Metre Shuttle Run Test for Aerobic Fitness." Journal of Sports Sciences 6.2 (1988): 93-101. NCBI. Web. 10 Nov. 2016. <https://www.ncbi.nlm.nih.gov/pubmed/3184250>.
The Glibert-Daniels formula for VO2Max. This formula is used to calculate VO2Max from race results. velocity given in meters/minute. time given in minutes. Returns VO2Max in mL/kg/min.
DANIELS, J. (2005) Daniels Running Formula. 2nd Ed. Leeds, UK: Human Kinetics. p. 48