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Metabolic Calculations - Purpose

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Estimate energy expenditure during steady state exercise

- 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

MEMORIZE

MEMORIZE

MEMORIZE

- 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

- VO2 = (0.2• F) + (1.33 • 1.8 • H • f) + 3.5

- 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.

- Estimates oxygen requirement (VO2) for various workloads
- Linear relationship
- Some variability (S.E.E. 7%)
assumptions

S.E.E. 7%

Anaerobic

Component

- “Steady State” or submax exercise:
O2 cost = O2 uptake

- “Maximal” Exercise
O2 cost > O2 uptake

=

Predicted

VO2max

VO2max

O2Requirement

Max Exer

Workload

you cannot predict maximal

Metabolic

Equivalent

Mechanical

Workload

- Meters.min-1
- kgm.min-1

- VO2
- METs
- kcals.min-1

We estimate one value based on

knowledge of the other

- 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)

- 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

- 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

- 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)

- Force = mass x acceleration
- “Weight” ~ mass undergoing gravitation acceleration
- examples: lbs. and kgs

- 1 kp 1 kg (cycle work - resistance)

- 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

- 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

- 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 = a + b x

a

Y

b

X

Y Unit = oxygen cost

X Unit = power output

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

- 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/minx 0.1
- VC(ml.kg-1.min-1) = % grade (decimal) x m/minx 1.8
- Resting (ml.kg-1.min-1) = 3.5

- 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

- 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

- 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/minx 0.2
- VC (ml.kg-1.min-1) = % grade (decimal) x m/minx 0.9
- Resting (ml.kg-1.min-1) = 3.5

- 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

- 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
- 7.2ml.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

- Loads 300-1200 kgm/min; 50-200 watts
- VO2 ml.kg-1.min-1= 1.8x 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

- Example: VO2 for an 80 kgperson cycling on a Monark™ cycle at 50 RPM, 2.0 kg load.
- Calculate kgm/min load
- kgm/min = 2 x 6 x50
- 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)

- 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 > METs for

lighter person

- 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

- 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 METs

Achieving the “minimal” kcal threshold

- Loads 150 to 750 kgm/min; 25-125 watts
- VO2 ml.kg-1.min-1= 3x 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

- 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/minx 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

- 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

- 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