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# ACSM Metabolic Equations

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ACSM Metabolic Equations
(HPRED 1410, Dr Bailey, Appendix D, Guidelines)

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### ACSM Metabolic Equations

1. 1. 1 ACSM Metabolic Equations (HPRED 1410, Dr Bailey, Appendix D, Guidelines) ACSM metabolic equations are typically used for two purposes: 1. To calculate oxygen consumption and from this, the energy expenditure of a given exercise. 2. To calculate the target workload for a client on the specific mode used. Note that each equation will have the following components: VO2 = horizontal component + vertical component + resting component Walking Walking: VO2 = H + V + R Walking: VO2 = 0.1(speed) + 1.8 (speed) (fractional grade) + 3.5 0.1 ml x kg-1 x min-1 = O2 cost of horizontal movement 1.8 ml x kg-1 x min-1 = O2 cost of vertical ascent Speed = speed in m x min-1 Running Running: VO2 = H + V + R Running: VO2 = 0.2 (speed) + 0.9 (speed)(fractional grade) + 3.5 0.2 ml x kg-1 x min-1 = O2 cost of horizontal motion 0.9 ml x kg-1 x min-1 = O2 cost of vertical ascent cost
2. 2. 2 Stepping Stepping: VO2 = H + V + R Stepping: VO2 = 0.2 (stepping rate) +1.33 x 1.8 (step height)(step freq) +3.5 = 0.2 (stepping rate) + 2.4 (step height)(step freq) +3.5 1.8 ml x kg-1 x min-1 = O2 cost of vertical ascent 1.33 = O2 cost of stepping down (vertical descent) (1.33 includes the positive component of stepping up (1.0), and the negative component of stepping down. (0.3) step height = step height in meters, step freq = stepping frequency in min-1 Leg and Arm Ergometry Note that there is no horizontal or vertical component here. All we see is the resistive component (V) from the ergometer. Leg Ergometry Leg Ergometry: VO2 = V (resistive) + R Note: 1. There is no horizontal component in leg ergometry 2. The vertical component is actually a resistive component. Leg Ergometry: VO2 = (10.8 x W x M-1 ) + 7 Use (mathematically equivalent); VO2 = 1.8 (work rate)/body mass + 7 1.8 ml x kg-1 x min-1 = cost of cycling against external load 3.5 ml x kg-1 x min-1 = cost of unloaded cycling above and beyond resting metabolism, so “7” is 3.5 + 3.5. W = watts, M = mass in Kgs
3. 3. 3 Arm Ergometry Arm Ergometry: VO2 = V (resistive) + R Arm Ergometry: VO2 = (18 x W x M-1 ) + 3.5 Use (mathematically equivalent); VO2 = 3 (work rate)/body mass + 3.5 Note: 1. There is no horizontal component in leg ergometry 2. The vertical component is actually a resistive component. 3. In arm ergometry, arm muscle mass is so small that there is no term for unloaded cyling. Hence, no “7” is seen. Also needed for arm and leg ergometry: Power (Kg x m x min-1 ) = (Kg setting)(D)(pedaling cadence in rpm) D = 6 meters for Monark = 3 meters for Tunturi = 2.4 for Monark arm ergometer Stepwise Approach to Metabolic Calculation 1. Conversion to appropriate units and knowledge of common equivalents. A. Convert all weights from pounds (lbs) to kilgrams. * Pounds/2.2 = kilograms B. Convert speed from miles per hour (m/hr) to meters per minute (m/min). * miles/hr x 26.8 = meters/minute * (also useful; 60/(min/mile) = miles per hour C. Common equivalents * (Caloric expenditure in kcals x min-1 )/5 = VO2 in L x min-1 * Liters O2 x 5 kcals/liter O2 = kcals * 1 pound of fat = 3,500 kcals * METs x 3.5 m x kg-1 x min-1 = VO2 in ml x kg-1 x min-1 * Gross VO2 in ml x kg-1 x min-1 / 3.5 = METs * Power in watts x 6 = workload in kg x m x min-1 * (kgm/min)/6 = watts
4. 4. 4 2. Transform VO2 into the most appropriate units. A. If weight bearing; walking, running, stepping, use ml x kg-1 x min-1 B. If cycling or arm, use ml/min C. If caloric expenditure needed, convert from ml x kg-1 x min-1 to liters/minute 3. Choose the proper equation for gross VO2: Walking: VO2 = 0.1(speed) + 1.8 (speed) (fractional grade) + 3.5 Running: VO2 = 0.2 (speed) + 0.9 (speed)(fractional grade) + 3.5 Stepping: VO2 = 0.2 (step rate) +1.33 x 1.8 (step height)(step rate) +3.5 (step height in meters, where 1 inch =.0254 m) Leg Ergometry: VO2 = 1.8 (work rate)/body mass + 7 Arm Ergometry VO2 = 3 (work rate)/body mass + 3.5 Power (Kg x m x min-1 ) = (Kg setting)(D)(pedaling cadence in rpm) Example from ACSM Guidelines 1. 30 year old man: He wants to walk at 3.5 mph * 180 lbs * RHR of 60 * MHR of 190 * VO2 max 48 ml/kg/min.. You want him at 70 % of his VO2 R A. What is his minimum training heart rate by the Karvonen method? THR = (.70)(190 - 60) + 60 THR = 91 + 60 = 151 beats/min B. What is his target VO2? VO2R = 48 ml/kg/min – 3.5 ml/kg/min = 44.5 = net VO2 = .70 x 44.5 = 31.2 ml/kg/min
5. 5. 5 C. How steep should the treadmill be if he is walking at his preferred 3.5 mph? VO2 = 0.1 (speed) + 1.8 (speed)(fractional grade) + 3.5 ml/kg/min 31.2 = 0.1 (93.8) + 1.8 (93.8) (frac grade) + 3.5 ml/kg/min 27.7 = 0.1 (93.8) + 1.8 (93.8)(frac grade) 27.7 = 9.38 + 168.8 (frac grade) 18.3 = 168.8 (frac grade) fractional grade = 10.8 % D. What is his target work rate on the Monark bike? His body mass = 180 lbs/2.2 = 81.8 kg VO2 = 7.0 +1.8 (work rate)/body mass VO2 = 7.0 +1.8 (work rate)/81.8 31.2 = 7.0 + 1.8 (work rate)/81.8 24.2 = 1.8 (work rate)/81.8 1980 = 1.8 (work rate) work rate = 1100 kg x m-1 x min-1 E. If he wants to pedal at 60 rpm on a Monark cycle, what resistance setting should be used. Power (Kg x m x min-1 ) = (Kg setting)(D)(pedaling cadence in rpm) Work rate = (resistance setting)(D)(pedal cadence) 1100 = (resistance setting)(6)(60) 1100 = (resistance setting)360 Resistance setting = 3.05 kg F. What is the caloric expenditure during 30 minutes of exercise? Net VO2 = 31.2 ml/kg/min (VO2 in ml/kg/min)(body mass)/1000 = VO2 L/min (31.2)(81.8)/1000 = 2.55 L/min 2.55 L/min x 5 = 12.8 kcal/min 12.8 kcal/min x 30 = 383 kcals
6. 6. 6 Text examples, page 311, Guidelines HPRED 1410, Feb 23, 2004 1. A man weighing 176 lbs runs a pace of 9 minutes per mile outdoors, on level ground. What is his estimated gross VO2 ? Conversion to appropriate units and knowledge of common equivalents. S = 9 minutes/mile, to convert to m x min-1 , 1. mph = 60  min/mile = mph = 60/9 = 6.66 2. m x min-1 = 6.66 x 26.8 = 178.5 Choose the proper equation for gross VO2: Running: VO2 = 0.2 (speed) + 0.9 (speed)(fractional grade) + 3.5 VO2 = (0.2 x 178.5 m x min-1 ) + 0 + 3.5 VO2 = 35.7 + 0 + 3.5 = 39.2 ml x kg-1 x min -1 2. To match this exercise intensity (from above) on a Tunturi cycle ergometer, what setting would you use at a pedal rate of 60 rpm? Conversion to appropriate units and knowledge of common equivalents. 176lbs/2.2 = 80 kgs Choose the proper equation for gross VO2: Leg Ergometry: VO2 = 1.8 (work rate)/mass + 7 39.2 ml x kg-1 x min -1 = (1.8 x W)/80 + 7 32.2 = 1.8W/80 1431 kg m min = work rate
7. 7. 7 Power (Kg x m x min-1 ) = (Kg setting)(D)(pedaling cadence in rpm) 1431 = Kg (3)(60) Kg = 7.95 3. If this same man exercised at this intensity 5 times a week for 30 minutes each session, how long would it take him to lose 12 pounds? (20) p. 311 top Net VO2 = 39.2 -3.5 = 35.7 Liter of oxygen used = 35.7 ml x kg-1 x min -1 x 80 kg/1000 = 2.856 L/min O2 Kcals used per minute = 2.856 L/min x 5 kcals/Liter O2 = 14.28 kcals Kcals per session = 14.28 kcals/min x 30 minutes = 428.4 kcals Kcals/week = 5 times/wk x 428.4 = 2142 kcals/wk Total Kcals to lose = 12 lbs x 3500 kcals/lb = 42000 kcals Weeks to lose it = 42000kcals/2142 kcals/week = 19.6 weeks 4. For a desired training intensity of 75 % of the VO2res, at what heart rate should a 45 year old woman exercise ? Her resting heart rate is 70 beats a minute. MHR = 220 - 45 = 175 HRR = 175- 70 = 105 .75 x 105 = 78.75 78.75 + 70 = 149 5. A 198 pound cardiac patient wishes to use an arm ergometer for part of his rehabilitation program. He works at a power output of 300 kgxmxmin for 15 minutes and then at 450 kgxmxmin for 15 minutes. What is his average net VO2 (in ml x kg-1 x min -1 ) over this session? 198/2.2 = 90 kgs
8. 8. 8 Arm Ergometry VO2 = 3 (work rate)/body mass + 3.5 First 15 minutes; VO2 = 3 (300)/90 + 3.5 Gross VO2 = 900/90 +3.5 = 13.5 ml x kg-1 x min -1 Net VO2 = 13.5 –3.5 = 10 ml x kg-1 x min -1 15 minutes x 10.0 = 150.0 ml x kg-1 x min -1 Second 15 minutes: VO2 = 3 (work rate)/body mass + 3.5 Gross VO2 = 3(450)/90 + 3.5 = 18.5 ml x kg-1 x min -1 Net VO2 = 18.5 – 3.5 = 15 ml x kg-1 x min -1 15 minutes x 15.0 = 225.0 ml x kg-1 x min -1 Average net= (150 + 225)/30 = 12.5 ml x kg-1 x min -1 6. If an individual reduces his or her dietary intake by 1750 kcal per week, how much weight (in lbs) would he or she lose in 6 months (26 weeks)? Weight lost per week = 1750/3500 = .5 pounds 26 x .5 = 13 pounds 7. If an 18 year old girl steps up and down on a 12 inch step at a rate of 20 steps (complete up and down cycles) per minute, what would her gross VO2 be (in ml x kg-1 x min -1 ) ? Stepping: Gross VO2 = 0.2 (step rate) +1.33 x 1.8 (step height)(step rate) +3.5 = 0.2(20) + 1.33 x 1.8 (12)(20) + 3.5 1 inch = 0.0254 meters step height in meters = 12 x .0254 = .3048
9. 9. 9 VO2 = 0.2(20) + 1.33 x 1.8 (.3048)(20) + 3.5 = 4 + 14.59 + 3.5 = 22.09 ml x kg-1 x min -1 8. A 71-year-old man weighing 180 pounds walks on a motor-driven treadmill at 3.5 mph and a 15 % grade. What is his gross MET level? Walking: VO2 = 0.1(speed) + 1.8 (speed) (fractional grade) + 3.5 3.5 mph x 26.8 = 93.8 m/min VO2 = 0.1(speed) + 1.8 (speed) (fractional grade) + 3.5 = 0.1(93.8) + 1.8(93.8)(.15) + 3.5 = 9.38 + 25.33 + 3.5 = 38.2 ml x kg-1 x min -1 Gross MET level = 38.2/3.5 = 10.9 METs
10. 10. 10 Case Studies for HPRED 1410 Case Study 1: 70 kg man uses 2 liters of oxygen in one minute. A. How many calories did he burn? B. What was his exercise in METs? Case Study 2: A man with the following information will burn how many kcals each exercise session while running? Treadmill at 1 % grade Speed = 6.5 mph Time = 30 minutes 5 times a week Body weight = 175 pounds = 79.5 kg Case Study 3: If the same man walks for 30 minutes per session, how many calories per session will he burn? Treadmill at 4 % grade Speed = 4.4 mph Time = 30 minutes 5 times a week Body weight = 175 pounds Case Study 4: 38 year old male, resting heart rate = 60, body weight of 170 pounds, percent body fat = 18% 1. Calculate his training heart rate range from 60 to 75 % of the heart rate reserve. 2. How many weeks would it take him to reduce his body weight to 12 % body fat if he adhered to a proper program?
11. 11. 11 Case Study 5: A 25 year old woman who weighs 130 pounds has a predicted VO2 max of 40 ml x kg-1 x min -1 . You decide that you want her to exercise (run) at 60 % of her VO2 R. 1. How fast should you set the treadmill speed in miles per hour assuming zero percent grade? 2. If she runs for 40 minutes, 4 days per week, how many calories wills she burn? 3. At this rate, many weeks would it take her to burn 10 pounds through this exercise? Case Study 6: A 24 year old male client tells you that during his last treadmill run, he measured his heart rate at 145 beats per minute. He tells you that his resting heart rate is 60. He wants to know “how intense” you, as an exercise physiologist, think this is. What percentage of the heart rate reserve (% VO2R ) was he running at? Case Study 7: You measure a 48 year old man’s VO2 max to be 30 ml x kg- 1 x min –1 . He tells you that he wants to begin shoveling snow from his driveway from now on for exercise, instead of hiring a local kid. According to the ACSM RM, heavy shoveling is about 9 MET exertion. What would you advise him? Your advice:
12. 12. 12 Case Study Solutions for ACSM Guidelines Problems Case Study 1: 70 kg man uses 2 liters of oxygen in one minute. A. How many calories did he burn? 2 liters x 5 kcals/liter = 10 kcals B. What was his exercise in METs? 1. 2 liters of oxygen = 2000 millilters of oxygen 2. 2000/70 kg = 28.6 ml/Kg oxygen in one minute 3. MET level = 28.6 ml x kg-1 x min-1 / 3.5 ml/kg/min= 8 METs 4. This is a light jog pace. Case Study 2: A man with the following information will burn how many kcals each exercise session while running? Treadmill at 1 % grade Speed = 6.5 mph Time = 30 minutes 5 times a week Body weight = 175 pounds = 79.5 kg Running: Gross VO2 = 0.2 (speed) + 0.9 (speed)(fractional grade) + 3.5 First you need speed in m/min: 6.5 mph x 26.8 = 174.2 m/min Gross VO2 = 0.2 (174.2) + 0.9 (174.2)(.01) + 3.5 = 34.84 + 1.57 + 3.5 = 39.9 ml x kg-1 x min -1 Net VO2 = 39.9 –3.5 = 36.4 ml x kg-1 x min -1 Liters/minute = (36.4 x 79.5)/1000 = 2.895 Liters/min 2.895 x 5 kcals/liter = 14.5 kcals/minute
13. 13. 13 30 x 14.5 = 434.3 kcals Case Study 3: If the same man walks for 30 minutes per session, how many calories per session will he burn? Treadmill at 4 % grade Speed = 4.4 mph Time = 30 minutes 5 times a week Body weight = 175 pounds Walking: Gross VO2 = 0.1(speed) + 1.8(speed)(fractional grade) + 3.5 4.4 mph x 26.8 = 117.92 m/min Gross VO2 = 0.1(117.92) + 1.8(117.92)(.04) + 3.5 11.79 + 8.49 + 3.5 = 23.7 ml x kg-1 x min –1 Net VO2 = 23.7 –3.5 = 20.2 ml x kg-1 x min -1 Liters/minute = (20.2 x 79.5)/1000 = 1.6 Liters/min 1.6 x 5 = 8 kcals/minute, 30 x 8 = 240 kcals Case Study 4: 38 year old male, resting heart rate = 60, body weight of 170 pounds, percent body fat = 18% 1. Calculate his training heart rate range from 60 to 75 % of the heart rate reserve. Minimum THR = (182 - 60) x .60 + 60 = 133.2 Maximum THR = (182 - 60) x .75 + 60 = 151.5 2. How many weeks would it take him to reduce his body weight to 12 % body fat if he adhered to a proper program?
14. 14. 14 Case Study 5: A 25 year old woman who weighs 130 pounds has a predicted VO2 max of 40 ml x kg-1 x min -1 . You decide that you want her to exercise (run) at 60 % of her VO2 R. 1. How fast should you set the treadmill speed in miles per hour assuming zero percent grade? VO2 R: 40 ml/kg/min – 3.5 ml/kg/min = 36.5 ml/kg/min Running: VO2 = 0.2 (speed) + 0.9 (speed)(fractional grade) + 3.5 Target VO2 = .60 x 36.5 ml x kg-1 x min –1 = 24 ml x kg-1 x min –1 . 21.9 = 0.2 (speed) + 0.9 (speed)(0) + 3.5 21.9 = 0.2 (speed) + 3.5 18.4 = 0.2 (speed) Speed = 92 meters/min miles/hr x 26.8 = meters/minute miles/hr x 26.8 = 92 meters/minute Speed in mph for the treadmill = 92/26.8 = 3.4 mph (Note: You might find that this client will prefer to walk and need to recalculate.) 2. If she runs for 40 minutes, 4 days per week, how many calories wills she burn? Weight in Kgs = 130/2.2 = 59.1 kgs Net VO2 = 24 -3.5 = 20.5 ml x kg-1 x min –1 (20.5 ml x kg-1 x min –1 x 59.1)/1000 = 1.211 Liters/O2 per minute Kcals burned per minute = 1.211 x 5 kcals/liter O2 = 6.06 kcals Kcals burned per session = 6.06 x 40 minutes = 242.31 kcals Kcals burned per wk = 242.31 kcals x 4 days/week = 969.2 kcals/week
15. 15. 15 3. At this rate, many weeks would it take her to burn 10 pounds through this exercise? 10 pounds x 3,500 kcals/pound = 35,000 kcals 35,000/969.2 = 36.1 weeks Case Study 6: A 24 year old male client tells you that during his last treadmill run, he measured his heart rate at 145 beats per minute. He tells you that his resting heart rate is 60. He wants to know “how intense” you, as an exercise physiologist, thinks this is. What percentage of the heart rate reserve (% VO2R ) was he running at? % VO2R = (Exercise HR - Resting HR)/(Max HR - Resting HR) % HRR = (145 – 60)/(196-60) = 85/136 = 62.5 % HRR Case Study 7: You measure a 48 year old man’s VO2 max to be 30 ml x kg- 1 x min –1 . He tells you that he wants to begin shoveling snow from his driveway from now on for exercise, instead of hiring a local kid. According to the ACSM RM, heavy shoveling is about 9 MET exertion. What would you advise him? Functional Capacity = 30/3.5 = 8.57 METs Your advice: This would often require supramaximal (above his VO2 max) exertion and he is 48 years old, at least “moderate risk”. Keep hiring the kid and begin a light supervised exercise program.