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