Task Energy Demands, Physical Work Capacity and Fatigue

• See Figure 1
• Metabolic substrates (glucose and oxygen) are combined to produce usable energy -- "Aerobic Metabolism"
• Metabolic substrates are delivered via arterial bloodflow
• Metabolites (CO₂ and H_{2O) are removed via venous blood bloodflow}
• O₂ and CO₂ are acquired and eliminated via respiration
• Energy expenditure can be estimated from O₂ and CO₂ differences in inspired and expired air and ventilation rates -- see below
• Glucose comes from ingested food. Small quantities may be stored in certain issues in the form of glycogen.
• Limited amounts energy are produced from glucose in the absence of oxygen -- "Anaerobic Metabolism"
• Latic acid is a metabolic byproduct of aerobic metabolism

  

  Figure 1: Cardiopulmonary system provides metabolic substrates and removes metabolites to and from working muscles

  Energy Expenditure and Oxygen Consumption

  • V_O2 = V_e (F_iO2 - F_eO2)
  • V_CO2 = Ve (F_eCO2 - F_iCO2)
  • RQ = V_O2 / V_CO2 ; Average RQ = 0.82 (40% carbohydrates; 60% fats)
  • E = 4.825 kcal/ l O₂ (RQ=0.82); note, 1 Kcal = 1 Cal
  • Metabolic equivalent or a unit of sitting, resting oxygen uptake; 1 MET = 3.5 ml/kg/min oxygen uptake.
  • note: 1 Kcal = 1,000 cal = 1 Cal= 4.19 joules = 3.96 Btu = 0.00116 kilowatt-hour = 3.086 ft-lb
• Energy is most often expressed as Cal/min or liters of O₂ per minute or ml O₂ per Kg body mass per minute

• Direct measurement (see in-class demonstration)
• Tabulated data in Tables 1 and 2)

Table 1: Average Energy Consumption (liters O₂/min)¹ for females by body weight².

		Females 18-24			Females 55-64
	ml/Kg	5%	Avg	95%	5%	Avg	95%
	/min	45Kg	58Kg	82Kg	47Kg	65Kg	92Kg
		45.4	58.2	82.3	47.3	65.4	92.3
Sleep	3.20	0.15	0.19	0.26	0.15	0.21	0.30
Sitting	4.00	0.18	0.23	0.33	0.19	0.26	0.37
Standing	4.80	0.22	0.28	0.39	0.23	0.31	0.44
Walk@2.0mph	9.00	0.41	0.52	0.74	0.43	0.59	0.83
Walk@3.0mph	12.50	0.57	0.73	1.03	0.59	0.82	1.15
Walk @4.0	16.00	0.73	0.93	1.32	0.76	1.05	1.48
Walk@4.5mph	20.00	0.91	1.16	1.65	0.95	1.31	1.85
Run@5.omph	24.00	1.09	1.40	1.97	1.13	1.57	2.21
Run@5.5mph	29.00	1.32	1.69	2.39	1.37	1.90	2.68
Bicyle@13.0	31.40	1.43	1.83	2.58	1.48	2.06	2.90
Run@7.0mph	38.00	1.73	2.21	3.13	1.80	2.49	3.51
Run@8.0mph	48.00	2.18	2.79	3.95	2.27	3.14	4.43
Run@10.0mph	57.00	2.59	3.32	4.69	2.69	3.73	5.26
Comp Swim	68.50	3.11	3.99	5.64	3.24	4.48	6.32

Table 2: Average Energy Consumption (liters O₂/min)¹ for males by body weight².

		Males 18-24			Males 55-64
		5%	Avg	95%	5%	Avg	95%
	ml/Kg /min	56Kg	73Kg	101 Kg	57 Kg	77 Kg	101 Kg
Sleep	3.20	0.18	0.23	0.32	0.18	0.25	0.32
Sitting	4.00	0.23	0.29	0.40	0.23	0.31	0.40
Standing	4.80	0.27	0.35	0.48	0.27	0.37	0.48
Walk@2.0mph	9.00	0.51	0.66	0.91	0.51	0.70	0.91
Walk@3.0mph	12.50	0.70	0.91	1.26	0.71	0.97	1.26
Walk @4.0	16.00	0.90	1.17	1.61	0.91	1.24	1.61
Walk@4.5mph	20.00	1.13	1.46	2.02	1.14	1.55	2.02
Run@5.omph	24.00	1.35	1.76	2.42	1.36	1.85	2.42
Run@5.5mph	29.00	1.63	2.12	2.93	1.65	2.24	2.93
Bicyle@13.0	31.40	1.77	2.30	3.17	1.78	2.43	3.17
Run@7.0mph	38.00	2.14	2.78	3.83	2.16	2.94	3.83
Run@8.0mph	48.00	2.71	3.51	4.84	2.73	3.71	4.84
Run@10.0mph	57.00	3.21	4.17	5.75	3.24	4.40	5.75
Comp Swim	68.50	3.86	5.01	6.91	3.89	5.29	6.91

¹Exercise Testing and Training of Apparently Healthy Individuals: A Hand Book for Physicians, The American Heart Association, 1972
² National Health Survey data

For a more detailed metabolic analysis see the UofM Energy Expenditure Prediction Program^TM (EEPP) software

Problem 1: Predict the energy demand for 21 and 57.5 year old males and females of average weight and condition walking at 3mph and 5mph?

• 21 Year old: E = VO₂ (ml/Kg/min) x Body mass (Kg) x 1.0 l/1,000mlx 4.825 Kcal/l O₂

• Physical Work Capacity, PWC is based on:
  • cardiovascular response to work (see Figure 2)
  • amount of O₂ consumed at maximum heart rate
  • maximum heart rate (beats/minute, bpm) = 220 - age
• Gender
• Weight
• Age
• Type of work
• Environmental influence
• Table 3

Figure 2: Heart rate versus energy expenditure rate.

Predicting Physical Work Capacity, PWC (Also Aerobic Capacity, Emax, VO2max, etc.)

• Direct measurment
• Prediction from standard data (Table 3)
  Army Data: Body Composition and Physical Capacity James A. Vogel and Karl E. Friedl

Table 3: Physical Work Capacities³ expressed as ml O₂ /kg body mass/min

Female	Maximal Oxygen Uptake (ml/kg/min)
Age	Low	Fair	Average	Good	High
20-29	<24	24-30	31-37	38-48	49+
30-39	<20	20-27	38-33	34-44	45+
40-49	<17	17-23	24-30	31-41	42+
50-59	<15	15-20	21-27	28-37	38+
60-69	<13	13-17	18-23	24-34	35+
Males
Age	Low	Fair	Average	Good	High
20-29	<25	25-33	34-42	43-52	53+
30-39	<23	23-30	31-38	39-48	49+
40-49	<20	20-26	27-35	36-44	45+
50-59	<18	18-24	25-33	34-42	43+
60-69	<16	16-22	23-30	31-40	41+

³ Exercise Testing and Training of Apparently Healthy Individuals: A Hand Book for Physicians, The American Heart Association, 1972

Problem 2: From Table 3, what would be the predicted physical work capacity for 25 and 50 year old males and females of average weight and condition? (use body weights from Tables 1 and 2)

• Label the vertical axis of Figure 2 with Borg ratings of perceived exertion.

Endurance

• Standard Time, ST = Normal Time (1 + Allowance/100) or ST = NT / (1 - All/100)

• Endurance, T_end, related to Energy Expenditure, E:

• log T_end = b_o + b₁ E

• T_end = 10^{(bo + b1E)}

• Assume 1/3 PWC can be maintained for 480 min

• Assume that PWC can be maintained for 4 min

• b₁ = (log 480 - log 4) / (1/3 PWC - PWC) = -3.119/PWC

• b_o = log 4 - b₁ PWC = 0.602 - b₁ PWC

Problem 3: Given a 35 year old female with PWC = 12 Kcal/min & a job that requires 6 Kcal/min, calculate T_end

• b₁ = = (log 480 - log 4) / (1/3 *12 - 12) = -3.119/PWC = -0.256

• b_o = log 4 - (-0.256 * 12) = 3.721

• T_end = 10^{(3.721-0.256E)}

• What would Tend be for E=8 Kcal/min? (44min) 6 Kcal/min? 4 Kcal min?

• What woud T_end be for a 55 year old male with average body weight and physical condition walking at 3mph? 5 mph?

Calculating Fatigue Allowance

• Average energy expenditure rate, E480, for 480 minutes of work and rest, T₄₈₀, < 1/3 PWC

• Determine the required rest time, Tr, for given energy expenditure rates during work and rest, Ew and Er, and a given work time, T_w

• T₄₈₀ E₄₈₀ = T_r E_r + T_w E_w

• T_w + T_r =T₄₈₀

• Fatigue Allowance: T_r / T₄₈₀% = (E₄₈₀ - E_w) / (E_r - E_w) (x100%)

Problem 4

• Is the afore mentioned Fatigue Allowance a percentage of standard time or normal time?

• Given a worker whose PWC = 12Kcal/min performs one task that requires 6Kcal/min and a second task that requires 2Kcal/min. How would you divide this worker's time between the two tasks.

Updated fatigue curves (Wu and Wang 2002)

Based on 6 healthy males and females between 25 & 30 years of age.

MAWT=95.33xe^{-7.28x%VO_2max}, r²=0.83; SEE=1.09 hour

MAWT=26.12xe^-4.81x%RHR, r²=0.87 See= 1.07 hour

MAWT=37.80xe^{-6.366x%RV_O2}, r²=0.83 SEE=1.12 hour

Where:

1. MAWT = Maximum Acceptable Work Time (hours)
2. VO_2max = Maximum oxygen uptate rate (aerobic capacity)
3. %VO_2max = Percent of maximum aerobic Capacity = (VO2_work ± VO2_rest)/(VO2_max ± VO2_rest) x 100%.
4. %RHR = Perent of Relative Heart Rate = (HR_work ± HR_rest)/(HR_max ± HR_rest) x 100%,