Metabolic Calculations - Purpose
Estimate energy expenditure during steady Estimate energy expenditure during steady state exercisestate exercise
Importance of Metabolic Calculations
• It is imperative that the exercise physiologist is able to interpret test results and estimate energy expenditure.
• Optimizing exercise protocols.
• Exercise prescription.
• Weight loss.
• 1L= 1000 mL• 1kg= 2.2 lbs• 1mph= 26.8 mmin-1
• 1 lb of fat= 3500kcal• 1 MET = 3.5 mLkg-1min-1
• 1 W= 6 kgmmin-1
• 1L O2min-1 = 5 kcalmin-1
• 1 in = 0.0254m=2.54 cm• Pace: min/mile to mph = 60/time• 7.5 min/mile / 60 min/hr = 8mph
• Kcal/min =
METS * 3.5 * BW
200• 1L O2min-1
= 5 kcalmin-1
Metabolic Calculations (S=Speed; G=Grade)
• Walking (most accurate from 1.9-3.7 mph)– VO2 = (0.1• S) + (1.8 • S • G) + 3.5
• Treadmill and Outdoor Running (for speeds > 5 mph)– VO2 = (0.2• S) + (0.9 • S • G) + 3.5
• Leg Ergometry – VO2 = 1.8 (work rate)/(BM) + 3.5 + 3.5
• Arm Ergometry– VO2 = 3 (Work Rate)/(BM) + 3.5
• Stepping– VO2 = (0.2• F) + (1.33 • 1.8 • H • f) + 3.5
CARRY OUT EACH STEP TO 2 DECIMAL PLACES
Assumptions and Limitations• Measured VO2 is highly reproducible at a given
steady state workload. Failure to achieve steady state is an overestimation of VO2.
• Accuracy of equations is unaffected by most environmental conditions such as heat and cold.
• However, variables that change mechanical efficiency (gait abnormalities, wind, snow or sand) result in a loss of accuracy.
• Assumption that ergometers are calibrated and no holding on to hand rails occur during on tm.
Met Calc - Key Points
• Estimates oxygen requirement (VO2) for various workloads– Linear relationship– Some variability
(S.E.E. 7%)
assumptions
500
1000
1500
2000
2500
0 50 100 150 200
Watts
VO
2 (
ml/m
in)
S.E.E. 7%
Met Calc - Key Points (con’t)
• “Steady State” or submax exercise:O2 cost = O2
uptake
• “Maximal” ExerciseO2 cost > O2
uptake
O2 R
eq
uir
em
en
t
Workload
AnaerobicComponent
Max Exer
=
VO2max
Predicted
VO2max
you cannot predict maximal
Met Calc - General Principle
MechanicalWorkload
MetabolicEquivalent
• Meters.min-1
• kgm.min-1
• VOVO22
• METs• kcals.min-1
We estimate one value based onWe estimate one value based onknowledge of the otherknowledge of the other
Metabolic Units
• Absolute vs. Relative VO2 units
• Absolute
– independent of body weight
– non-weight bearing activities• leg and arm ‘cycling’
• liters of O2 per minute (l.min-1)
• milliliters of O2 per minute (ml.min-1)
Metabolic Units (cont.)
• Absolute vs. Relative VO2 units
• Relative
– dependent on body weight
– weight bearing activities• walking, jogging, stepping equations
– milliliters of O2 per kg per minute
• (ml.kg-1.min-1)
– METs: 1 MET = 3.5 ml.kg-1.min-1
Metabolic Units - Energy
• 1 calorie = the heat energy required to raise 1 gm H20, 1o C (@ 15o C)
• 1000 “small” calories = 1 “large” calorie or kilocalorie (kcal)
• Kilocalories per min (kcals . min-1)
• Application to Weight Control
Energy Conversions
• 1 liter O2 , VO2 ~ 5.0 kcals
• 1 lb of fat ~ 3500 kcals
• 1 MET 1.0 kcals . kg . hr-1
• Kcal.min-1 = METs x 3.5 x ( BW(kg) / 200)
– “caloric thresholds” for adaptation during training (200-300 kcals per session; 1000+ for week)
Mechanical Units - Force
• Force = mass x acceleration
• “Weight” ~ mass undergoing gravitation acceleration
• examples: lbs. and kgs
• Kilopond (kp) 1 kg mass under normal gravitational acceleration
• 1 kp 1 kg (cycle work - resistance)
Mechanical Units - Work
• Work = force x distance
• Units:
– kilogram meters (kg.m or kgm)
– kilopond meters (kp.m or kpm)
– foot pounds (ft.lbs)
• Walking/Running: we carry our mass (kg) a given distance (meters) and therefore we can estimate the “work” performed
Mechanical Units - Power
• Power = Work / Time• Units:
– kilogram meters per min (kg. m. min-1) – kilopond meters per min (kp. m.min-1)– watts (1 watt 6 kg. m. min-1)
• Cycle workloads or work rates• Metabolic (Aerobic) Power = Oxygen
Consumption; VO2
ACSM Metabolic Equations: Equation set-up
• Regression equations: estimate Y based upon X– Y = a + bx
• a = intercept
– “y” value when x = 0
• b = slope of line
– unit change in “y”, for every one unit change in “x”
Y
X
ba
Y Unit Y Unit = oxygen cost= oxygen costXX Unit Unit = power output= power output
YY = = aa + + b b xx
ACSM recommendations
Conversion to units: lb to kg, mph to m.min-1; etc. (metric)
Transform VO2 units to needed units: ml.min-
1 to l.min- 1 to ml.kg-1.min-
Write down the equation in appropriate form
ACSM Walking Equation
• Speeds 50-100 m/min; 1.9-3.7 mph
– (1 mph = 26.8 m/min)
• “Relative” VO2 unit (ml/kg/min; ml.kg-1.min -1)
• VO2 = Horizontal Walking (HW) + Vertical Climb (VC) + Resting
• HW (ml.kg-1.min-1) = m/min x 0.1
• VC (ml.kg-1.min-1) = % grade (decimal) x m/min x 1.8
• Resting (ml.kg-1.min-1) = 3.5
ACSM Walking Equation
• Example: VO2 for walking @ 3.0 mph
• Convert 3.0 mph to m/min– 3.0 x 26.8 = 80.4 m/min
• Calculate HW – 80.4 m/min x 0.1 – 8.04 ml.kg-1.min-1
• Total VO2 = 8.04 + 3.5 = 11.54 ml.kg-1.min-1
VO2 for walking 3.0 mph / 5% grade
• HW + Resting = 11.5 ml.kg-1.min-1 • Calculate VC
– 0.05 % grade x 80.4 m/min x 1.8– 0.05 x 80.4 x 1.8– 4.02 x 1.8
– 7.2 ml.kg-1.min-1
• Total VO2 = 8.04 + 7.2 + 3.5 = 18.7 ml.kg-1.min-1
• To convert to METs: 18.7 / 3.5 = 5.3 METs
ACSM Running Equation
• Speeds > 134 m/min; > 5.0 mph
– (1 mph = 26.8 m/min)
• “Relative” VO2 unit (ml.kg-1.min-1)
• VO2 = Horizontal Run + Vertical Climb+ Resting
• HR (ml.kg-1.min-1) = m/min x 0.2• VC (ml.kg-1.min-1) = % grade (decimal) x m/min x 0.9
• Resting (ml.kg-1.min-1) = 3.5
ACSM Running Equation
• Example: VO2 for running @ 6.0 mph• Convert 6.0 mph to m/min
– 6.0 x 26.8 = 160.8 m/min• Calculate HR
– 160.8 m/min x 0.2– 32.2 ml.kg-1.min-1
• Total VO2 = 32.2 + 3.5 = 35.7 ml.kg-1.min-1
VO2 for running 6.0 mph/5% grade
• HR + Resting = 35.7 ml.kg-1.min-1
• Calculate VC– 0.05 % grade x 160.8 m/min x 0.9– 0.05 x 160.8 x 0.9– 8.04 x 0.9– 7.2 ml.kg-1.min-1
• Total VO2 = 32.2 + 7.2 + 3.5 = 42.9 ml.kg-1.min-1
• To convert to METs: 42.9 / 3.5 = 12.3 METs
ACSM Leg Cycling Equation
• Loads 300-1200 kgm/min; 50-200 watts
• VO2 ml.kg-1.min-1 = 1.8 x kgm/min / BW + 3.5 ml.kg-1.min-1 + 3.5 ml.kg-1.min-1 – kgm/min = kg x meters/rev x RPM– Add resting twice : 1 for resting and 1 for
unloaded
• Monark™ bike: 6.0 meter/rev
ACSM Leg Cycling Equation
• Example: VO2 for an 80 kg person cycling on a Monark™ cycle at 50 RPM, 2.0 kg load.
• Calculate kgm/min load – kgm/min = 2 x 6 x 50– kgm/min = 600
• Calculate VO2
– ml.kg-1.min-1 = 1.8 x 600 / 80 + 3.5 + 3.5– ml.kg-1.min-1 = 1.8 x 7.5 + 3.5 + 3.5– ml.kg-1.min-1 = 20.5 (5.86 METS)
Different Body Weights?
• Compare “relative” VO2 during leg cycling at 600 kpm/min for 80 kg vs. 60 kg persons
• 80 kg ~ 5.86 METs• 60 kg:
– ml.kg-1.min-1 = 1.8 x 600 / 60 + 3.5 + 3.5– ml.kg-1.min-1 = 18 + 7– ml.kg-1.min-1 = 25– 25 / 3.5 = 7.14 METs
1.72 > 1.72 > METs forMETs forlighter lighter personperson
Kcal conversion example
• What is the kcal expenditure (kcal.min-1) for an 85 kg person exercising at an oxygen uptake of 5.86 METs?
• kcal.min-1 = METs x 3.5 x (BW (kg)/200)
• kcal.min-1 = 5.86 x 3.5 x (85/200)
• kcal.min-1 = 8.72
ACSM Weekly kcal threshold: Exercise Prescription
• Minimum caloric threshold 1000 kcals
• Minutes of exercise: 1000/8.72 = 114.7 min week
• 3 Workouts: 115/3 = 38.3 minutes
• 4 Workouts: 115/4 = 28.75 minutes
This is for an 85 kg individual @ 5.86 METsAchieving the “minimal” kcal threshold
ACSM Arm Cycling Equation
• Loads 150 to 750 kgm/min; 25-125 watts
• VO2 ml.kg-1.min-1 = 3 x kgm/min / BW + 3.5 ml.kg-1.min-1
– 3.0 = ml.min-1 per kpm/min ( from leg cycling)– Only 1 resting component (3.5)
• kgm/min = kg x meters/rev x RPM
• Monark™ Rehab Trainer: 2.4 meter/rev
ACSM Stepping Equation
• VO2 varies with Step height & rate• “Relative” VO2 unit (ml.kg-1.min-1)• VO2 (ml.kg-1.min- 1 ) = Horizontal + Vertical
+ Resting• Horizontal = steps/min x 0.2• Vertical = step ht x steps/min x 1.33 x 1.8
– Down cycle 0.33 VO2 of the up cycle (add this in by multiplying by “1.33”)
– 1.8 is the constant for vertical work• Step height is entered in meters
ACSM Stepping Equation
• Example: VO2 for stepping on a 12” bench at 30 steps per minute
• Calculate step height in meters– 12” x 2.54 = 30.5 cm / 100 = 0.305 meters
• Calculate Horiz VO2
– ml.kg-1.min-1= 30 steps/min x 0.2– ml.kg-1.min-1 = 6
ACSM Stepping Equation (cont.)
• Horiz VO2 ml.kg-1.min-1 = 6
• Calculate Vert VO2 ml.kg-1.min-1
– 0.305 meters x 30 steps/min x 1.33 x 1.8– 0.305 x 30 x 1.33 x 1.8– 21.9 ml.kg-1.min-1
• Total VO2 = 6 + 21.9 + 3.5
• Total VO2 = 31.4 ml.kg-1.min-1
• METs = 31.4/3.5 = 8.9