Why Does Metabolic Rate Increase Curvilinearly With Running Velocity?

Kipp, Shalaya (M.S., Integrative Physiology) Why Does Metabolic Rate Increase Curvilinearly With Running Velocity? Thesis directed by Associate Professor Emeritus, Rodger Kram The ‘cost of generating force’ model proposes that a major determinant of metabolic rate during running is the rate of muscular force production. However, the amount of muscle force needed during running is affected by the effective mechanical advantage (EMA), the ratio of the ground reaction force moment arm (R) to the muscle moment arm (r), R/r. The ‘cost of generating force’ model assumed that EMA and active muscle volume remain constant across velocity. With this assumption, the cost of generating force hypothesis explains 80% of the linear increase in metabolic rate in human runners across a moderate velocity range. Additionally, many studies have demonstrated a linear relationship between metabolic rate and running velocity for a diverse assortment of species. However, in humans there is less of a consensus of how to mathematically characterize the relationship. Using 7 sub-elite male runners, I performed a more systematic analysis of EMA over 6 different velocities (8, 10, 12, 14, 16 and 18km/hr) to explain both the remaining 20% and the curvilinear increase in metabolic rate. I hypothesized that the curvilinear metabolic rate pattern observed in elite runners at fast sub-maximal velocities can be explained by a decrease in EMA at the hip, knee and ankle joints, which necessitates a greater volume of active muscle recruitment. Over the velocity range, all subjects demonstrated a curvilinear increase in metabolic rate. Ankle EMA decreased by 14.5 ± 4.1%, while hip EMA showed the largest magnitude decrease of 51.2 ± 30.2%. Accordingly, the active volume of hip extensor muscles increased 50.1% from 448 ± 245 cm3 to 898 ± 250cm3 across the velocity range. The ankle extensor active muscle volume increased by 32.8% from 713 ±145cm3 to 1061 ± 159cm3. I extended the cost of generating force model and found that in human runners, metabolic rate is proportional to the rate of force generation multiplied by the volume of muscle activated. !

velocity range. The ankle extensor active muscle volume increased by 32.8% from 713 ±145cm3 to 1061 ± 159cm3. I extended the cost of generating force model and found that in human runners, metabolic rate is proportional to the rate of force generation multiplied by the volume of muscle activated. !

iv Table of Contents Chapter I. Literature Review……….…………………………………………………………….....1 II. Why Does Metabolic Rate Increase Curvilinearly With Running Velocity?…....………..…15 Introduction…………………………………………………………………...........15 Methods………………………………………………………………………..........20 Results……..……………………………………………………………………..….25 Discussion……………………………………………………………………...........34 References….………………………………………………………………….........37

v List of Tables Why Does Metabolic Rate Increase Curvilinearly With Running Velocity? Tables 1. Muscle data from 4 male cadavers ……………………………………………………..24 2. Metabolic variables for 7 subjects across velocity …………………………………..33 3. Biomechanical variables or 7 subjects across velocity ……………………………..33 4. Net joint moments for the Ankle, Knee and Hip……………………………………...34

vi List of Figures Literature Review Figures 1. Metabolic rate plotted vs. velocity with linear and curvilinear line fits. …………………3 2. vs. velocity for Average and Sub-elite populations ………...………...………...……4 3. Metabolic rate vs. velocity for Average and Sub-elite populations………..……………...5 4. Oxygen consumption ratio for loaded and unloaded weights……………………………..8 5. Example of effective mechanical advantage (EMA) of the ankle. ………………..…….11 6. Changes in muscle EMA at the hip, knee, and ankle across velocity……………….…..12 7. Estimated active volume of muscles at the hip, knee, and ankle joints ………….....…..13 Why Does Metabolic Rate Increase Curvilinearly With Running Velocity? Figures 1. Metabolic rate () vs. velocity (v) ……………………………………………….25 2. Ground contact time (tc) and rate of force production (1/tc) across velocity.…...…...….26 3. Example vertical GRF trace over the velocity range ………………………………...….27 4. Net joint moments over the velocity range at the hip, knee and ankle.………...……..…28 5. EMA across velocity for ankle, knee, hip joints. ………………………………...……...29 6. Mean estimated active muscle volume across velocity……………………………..…...30 7. The cost coefficient (c’) vs. the new cost coefficient (c’*)………………….…………..32

1 Chapter I: Literature Review The rate at which a runner consumes metabolic energy when they run at a submaximal velocity is most commonly approximated through the rate of oxygen uptake (). This rate in mlO2/kg/min is often referred to as an individual's running economy (RE) and is a key determinant of running performance (Daniels, 1985; Conley & Krahenbuhl, 1980). The intensity of exercise influences the relative rate of carbohydrate (CHO) and fat metabolism, and therefore the amount of energy made available per liter of oxygen uptake varies with intensity or running velocity (Blaxter, 1989). The respiratory exchange ratio (RER) is defined as the ratio of the rate of carbon dioxide production () produced to the rate of O2 consumed. From stoichiometry, a RER of 0.7 indicates 100% fat metabolism and 1.0 indicates 100% CHO metabolism. Thus, RER indicates the relative amount of CHO and fats utilized. It is well established that RER increases as submaximal running velocity increases (Saunders et al., 2004; Fletcher et al., 2009). Measuring only does not take into account the changes in substrate utilization that take place with changes in intensity. Thus, to quantify the rate of energy consumed in running, it is more accurate to use both and to calculate how much of the energy is being metabolized from fats and CHOs. Fletcher et al. (2009) found that expressing RE in units of energy cost (W/kg) was more sensitive to changes in intensity than expressing RE in terms of just because it takes into account the different substrates used at different submaximal velocities. This conclusion was corroborated several years later by Shaw et al. (2014) who found oxygen cost per distance to be insensitive to changes in running velocity and therefore not a valid index for the actual energetic cost of running.

2 Traditionally, researchers have found that the rate of energy expenditure increases linearly at faster running velocities when using both (ml/kg/min) and the rate of energy expenditure (W/kg). Numerous studies have supported this over a submaximal range of velocities from ~2-4 m⋅s-1 in average to good runners (Margaria et al., 1963, Helgerud, 1994; Helgerud, et al., 2010; Menier & Pugh, 1968). However, there is disagreement about the nature of the relationship between metabolic cost and velocity in high-caliber runners who can sustain a wider range of submaximal velocities. Steudel-Numbers and Wall-Scheffler (2009) reported that metabolic rate increases curvilinearly with running velocity in well-trained distance runners during treadmill running over a velocity range of ~2.01-4.9 m⋅s-1 (Figure 1). Similarly, Tam et al. (2012) reported significant increases in oxygen cost per distance at 5.0 m⋅s-1 compared to 3.33 m⋅s-1 in elite distance runners. Tam suggested that the finding could be explained by the increasing contribution of aerodynamic resistance to the metabolic rate during their over-ground running protocol. However, this does not explain the previous findings collected on treadmills, which involve negligible aerodynamic resistance. Most recently, Batliner et al. (2017) compared average and sub-elite runners over a wide range of submaximal velocities. Average runners completed trials spanning a velocity range of 1.78-4.08 m⋅s-1 submaximally, while the sub-elite runners were capable of a wider velocity range of 1.78-5.14 m⋅s-1 submaximally. Over the wider range of velocities sustained by the sub- elite runners, both the oxygen uptake rate and metabolic rate vs. velocity relationships were best described by curvilinear fits (Figure 2 and 3). Even though Batliner et al. (2017) studied both average and sub-elite runners across their full range of submaximal velocities, the curvilinear increase in energetic cost was only observed in the sub-elite group of runners, who were able to

3 complete a wider range of velocities. This suggests that the sub-elite curvilinear increase in metabolic rate was not caused by a physiological parameter, but a biomechanical factor. Figure 1. Each individual participant’s metabolic rate (Cal/min) plotted vs. running speed with both linear and curvilinear line fits. Open diamonds are males; closed diamonds are females. The R2 values on the bottom left are for the linear fit; the values on the top right are for the curvilinear fit. Data from Steudel-Numbers and Wall-Scheffler, 2009.

4 Figure 2. vs. running speed for Average and Sub-elite subjects calculated from mean slopes, intercepts, quadratic coefficients, linear coefficients, and R2 values for linear and curvilinear (2nd order polynomial) fits. Data from Batliner et al., 2017.

5 Figure 3. Metabolic rate vs. running speed for Average and Sub-elite groups calculated from mean slopes, intercepts, quadratic coefficients, linear coefficients, and R2 values for linear and curvilinear (2nd order polynomial) fits. Data from Batliner et al., 2017.

Analysis of how metabolic rate changes with running velocity in human runners.