Measured and predicted mechanical internal work in human locomotion

Human Movement Science 30 (2011) 90–104

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Human Movement Science journal homepage: www.elsevier.com/locate/humov

Measured and predicted mechanical internal work in human locomotion Francesca Nardello a,⇑, Luca P. Ardigò a, Alberto E. Minetti b a

Faculty of Exercise and Sport Science, Department of Neurological, Neuropsychological, Morphological and Movement Sciences, University of Verona, Italy Faculty of Medicine, Department of Human Physiology, University of Milano, Italy

b

a r t i c l e

i n f o

Article history: Available online 5 November 2010 PsycINFO classification: 2220 2260 Keywords: Human locomotion Mechanical internal work Model equation Velocity Gradient

a b s t r a c t Predictive methods estimating mechanical internal work (Wint, i.e., work to accelerate limbs with respect to BCOM during locomotion) are needed in absence of experimental measurements. A previously proposed model equation predicts such a parameter based upon velocity, stride frequency, duty factor, and a compound critical term (q) accounting for limb geometry and inertial properties. That first predicted Wint estimate (PWint) has been validated only for young males and for a limited number of horses. The present study aimed to extend the comparison between model predictions and experimentally measured Wint (MWint) data on humans with varying gender, age, gait, velocity, and gradient. Seventy healthy subjects (males and females; 7 age groups: 6–65 years) carried out level walking and running on treadmill, at different velocities. Moreover, one of the subject groups (25–35 years) walked and ran also at several uphill/downhill gradients. Reference values of q represent the main important results: (a) males and females have similar q values; (b) q is independent on velocity and gradient. Also, different data filtering depth was found to affect MWint and, indirectly, PWint, thus also the reference q values here obtained (0.08 in level, 0.10 in gradient) suffer a – 20% underestimation with respect to the previous predicting model. Despite of this effect, the close match between MWint and PWint trends indicates that the model equation could be satisfactorily applied, in various locomotion conditions. Ó 2010 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Address: Faculty of Exercise and Sport Science, University of Verona, Via Felice Casorati, 43, 37131 Verona, Italy. Tel.: +39 045 8425139; fax: +39 045 8425131. E-mail address: [email protected] (F. Nardello). 0167-9457/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.humov.2010.05.012

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Nomenclature Wtot Wext Wint BCOM PE KE TE MWint PWint s SF DF a b g m mL, mU mL ; mU q sST sSW

mechanical total work per unit mass and distance [J/(kg m)] mechanical external work per unit mass and distance [J/(kg m)] mechanical internal work per unit mass and distance [J/(kg m)] body center of mass gravitational potential energy of the body center of mass [J] kinetic energy of the body center of mass [J] total energy of the body center of mass, expressed as the sum of PE and KE [J] measured mechanical internal work per unit mass and distance [J/(kg m)] predicted mechanical internal work per unit mass and distance [J/(kg m)] speed of progression [m/s] stride frequency, i.e., the number of strides performed within one second [Hz] duty factor, i.e., the fraction of the duration of the stride period when each foot is on the ground [%] fractional distance of the lower limb center of mass to the proximal joint length of the upper limb, as a fraction of the lower limb one average radius of gyration of limbs, as a fraction of the limb length body mass [kg] lower and upper limb mass [kg] lower and upper limb mass, as a fraction of m compound dimensionless term accounting for limb geometry and fractional mass the average speed, relative to the BCOM, of the foot when in contact with the ground (stance) [m/s] the average speed, relative to the BCOM, of the foot during the swing [m/s]

1. Introduction Analysis of the motion of the body during locomotion is of great interest to many biological disciplines (e.g., physiology, physics, biomechanics and so on). A common aim within the study of the mechanics of human locomotion is the calculation of the mechanical work performed (Williams & Cavanagh, 1983). Particularly, the total work of locomotion (Wtot) has been traditionally regarded as the sum of mechanical external work (Wext) and mechanical internal work (Wint), which are considered two separate entities (Cavagna & Kaneko, 1977; Saibene & Minetti, 2003). The mechanical external work (Wext) represents the work necessary to lift and accelerate the body center of mass (BCOM) within the environment (Saibene & Minetti, 2003). It has been investigated in many different conditions and populations (Cavagna, Franzetti, & Fuchimoto, 1983; Minetti, Ardigò, & Saibene, 1993; Minetti, Ardigò, & Saibene, 1994; Saibene & Minetti, 2003; Schepens, Willems, & Cavagna, 1998; Schepens, Willems, & Cavagna, 2001). From the above definition, Wext requires the gravitational potential energy (PE) and the kinetic energy (KE) of the BCOM to be measured; then, it needs to be calculated the total energy (TE = PE + KE) over time (Cavagna, Thys, & Zamboni, 1976; Saibene & Minetti, 2003; Willems, Cavagna, & Heglund, 1995). This goal can be achieved both by using dynamometric (direct dynamics) and motion analysis (inverse dynamics) technique (Purkiss, Gordon, & Robertson, 2003; Winter, 2005). The reciprocal movements of the body segments, that do not affect the trajectory of the BCOM (Cavagna, Saibene, & Margaria, 1964; Minetti, 1998; Winter, 1978), are to a large extent brought about by forces internal to the body and, consequently, the work associated with the energy changes relative to the BCOM is called the mechanical internal work (Wint) (Willems et al., 1995). Therefore, the mechanical internal work (Wint) represents the work necessary to accelerate the limbs reciprocally with respect to the BCOM also during human locomotion (Cavagna & Kaneko, 1977; Cavagna, Legramandi, & Peyre-Tartaruga, 2008; Cavagna et al., 1964; Minetti, 1998; Minetti, Ardigò, Renaich,

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& Saibene, 1999; Minetti & Saibene, 1992; Minetti et al., 1993; Minetti et al., 1994; Saibene & Minetti, 2003; Schepens et al., 1998, 2001; Winter, 1979). It is computed from both segment movements and anthropometric parameters (Schepens et al., 2001). Historically, the concept of Wint was introduced by Fenn (for running at top velocities, 1930) (Cavagna et al., 1964); it was then formalized by Cavagna and Kaneko (1977). Wint derives from the König theorem of total kinetic energy in a system. This theorem stated that ‘the kinetic energy of a system of particles is the kinetic energy associated to the movement of the center of mass and the kinetic energy associated to the movement of the particles relative to the center of mass’ (Cavagna & Franzetti, 1986). Therefore, in a linked multi-segment system, ‘the total kinetic energy can be partitioned in two different components: first of all, that of the BCOM with respect to the environment’ (the so-called Wext); ‘and, secondly, that of single segments with respect to the BCOM’ (the so-called Wint). Consequently, the biomechanical interest in Wint resides in the capability to consider the acceleration of body segments which is the case of human locomotion (walking and running, in particular), where limbs are moved quasisymmetrically with respect to the BCOM (Minetti, 1998; Minetti et al., 1993). Unfortunately, calculation of Wint is more complicated than of Wext. The recordings of the mechanical energy level of the individual body segments, obtained by cinematography, are far more complex and difficult to interpret (Zatsiorsky, 2002). Furthermore, calculation of Wint requires assumptions about the physical properties of the body segments, as well as regarding the transfer of energy to and from different body segments. In fact, Wint can be calculated by summing the kinetic energy curves of single segments (in a way which allows energy transfer only among within-limb segments), and by summing up all the energy increases of the resulting curves (Willems et al., 1995). Different computational models have been proposed to calculate mechanical internal work. Most of these models use the traditional approach of examining changes in segmental energies (Purkiss et al., 2003; Winter, 1978); otherwise, most of these models use inverse dynamics and joint power analysis (Formenti, Ardigò, & Minetti, 2005; Purkiss et al., 2003). The various models/techniques for calculating the mechanical internal work (in the field of human gait) have undergone a general improvement over the years. Fenn (1930) summed the increases of each of the major segments energies, over the stride period, to yield the mechanical work. His hypothesis was that ‘the kinetic energy turns out to be high in that limb where the work is being done. If the kinetic energy is calculated in relation to the ground, then the limb going backwards has very small kinetic energy although the actual effort on the part of the runner is as great in pushing it backwards as in pushing it forwards’. Indeed, he did consider the possibility of both energy exchanges within segments and passive transfers between segments (Cavagna & Kaneko, 1977). Ralston and Lukin (1969) and Winter (1979) calculated the kinetic and potential energies of the major segments by means of displacement transducers and TV imaging techniques. Unfortunately, their calculation underestimated the simultaneous energy generation and absorption at different joints. Cavagna and Kaneko (1977) determined Wint in relation to the velocity of the shoulder joint for both the arm and the hip joint for the leg, with the assumption that these joints do not move relatively to the BCOM during locomotion. However, BCOM is expected to move more ‘smoothly’ than those joints and their kinetic energy might change less than the amount obtained with that methodology. Finally, Winter (1979) calculated the internal work from the sum of segment energies which he then compared to the same calculation on the BCOM energy (Winter, 2005). Since its biomechanical definition, Wint has been widely investigated in the literature (Cavagna & Franzetti, 1981; Cavagna & Kaneko, 1977; Cavagna et al., 1964; Cavagna et al., 1983; Cavagna et al., 2008; Minetti, 1998; Minetti & Saibene, 1992; Minetti et al., 1993; Minetti et al., 1994; Minetti et al., 1999; Purkiss et al., 2003; Schepens et al., 1998; Schepens et al., 2001; Willems et al., 1995; Williams & Cavanagh, 1983; Winter, 1978;). As a result, it is proved to be useful in comparative and intra-species analysis of mechanical relationships during human locomotion in different conditions (Cavagna, Mantovani, Willems, & Musch, 1997), gaits (Minetti et al., 1993), gradients (Minetti et al., 1993) and stride frequencies (Cavagna & Franzetti, 1986; Cavagna, Willems, Franzetti, & Detrembleur, 1991; Cavagna et al., 1983; Minetti & Saibene, 1992). Despite its scientific relevance (Cavagna & Franzetti, 1981; Cavagna & Kaneko, 1977; Cavagna et al., 1964; Cavagna et al., 1983; Schepens et al., 1998; Schepens et al., 2001; Winter, 1978), only few laboratories measure this variable, because of equipment availability. Diversely from Wext, Wint preferentially requires the expensive cinematographic method with a complex ad hoc computer program (Minetti, 1998). As a consequence,

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nowadays very little data from direct measurements (inverse dynamics) exists of the mechanical internal work actually done by the muscles in human exercises such as walking and running. Such a state of the art stimulated the design of a mathematical standard model to evaluate this biomechanical variable when the direct measurement is not available. Therefore, Minetti (1998) has provided a general mathematical equation to estimate the mechanical internal work (Wint) in human locomotion at different gaits, velocities, frequencies and gradients. In this study, according to the previous literature, we have therefore used two different methods to compute the mechanical internal work (Wint): (1) kinematic data (direct measurement) in order to calculate the measured internal work (MWint), and (2) the model equation proposed by Minetti (indirect measurement) in order to calculate the predicted internal work (PWint) (Formenti et al., 2005). The statement of a critical q value allows us to highlight its importance as testing conditions vary. Finally, results obtained in the study of 1998 have been indeed verified in a large population: males and females of different age groups moving (walking and running) at different velocities, both at the level gradient and at different (uphill and downhill) gradients. 2. The prediction of mechanical internal work By refining a previously published model, Minetti (1998) proposed a simple equation for the estimation of the mechanical internal work during human locomotion (see ‘‘Appendix’’). The predicted mechanical internal work (PWint) expressed as J/kg of body mass per unit distance travelled (m), the customary unit for the specific cost of transport, can be expressed as:

PW int ¼ SF  s  1 þ



DF 1  DF

2 !

q

ð1Þ

where SF is the stride frequency (Hz), s is the average progression velocity (m/s), DF is the duty factor, and q is a compound dimensionless term accounting for the inertial properties of the limbs and the mass partitioned between the limbs and the rest of the body. The practical meaning of the standard Eq. (1) is that PWint can be predicted by knowing a few parameters, regardless of the gait type. The main approximation in this model is the definition of the term q which is expressed as:

q¼

p2 4

2

 ½ða2 þ g 2 Þ  ðmL þ b  mU Þ

ð2aÞ

where a is the fractional distance of the lower limb center of mass to the proximal joint, g is the average radius of gyration of limbs, as a fraction of the limb length, b is the length of the upper limb, as a fraction of the lower limb one, with mu* and ml* being the fractional mass of the upper and lower limb with the respect to the body mass, respectively. The required anthropometric parameters can be obtained from Winter (2005) for males, and from both Winter and de Leva (1996) for females, and from many others (Dempster, Gabel, & Felts, 1959; Zatsiorsky, Seluyanov, & Chugunova, 1990). Moreover, as stated in the PWint equation, q values reflect the inertial properties of the limbs. But, a and g vary according to the degree of flexion of the different limb segments during the swing phase (Minetti et al., 1994); thus q values need to be estimated in dynamical conditions. Eq. (2b) shows that, according to Minetti (1998) and by using Eq. (1), the term q could also be calculated as:

q¼

MW int   DF 2  SF  s  1 þ 1DF

ð2bÞ

where MWint is the experimental average internal work (J/(kg m)), derived from kinematic data (see par. 3.3 ‘Data acquisition and analysis’). In the present study, the term q was calculated according to Eq. (2b), to verify its robustness to gender, age, type of locomotion, velocity and gradient.

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3. Materials and methods 3.1. Study population Seventy healthy subjects (35 males and 35 females), recruited within the faculty of Exercise and Sport Science, volunteered to participate in this study. They were presented with a simple description of the experimental protocol and were asked to sign consent forms approved by the Institution’s Ethics Committee of Verona University. Subjects came from a heterogeneous population of sedentary, normal or moderately active people, with no neurological or musculoskeletal impediments affecting gait. The seventy subjects were sorted out into 7 age groups, ranging from 6 to 65 (6  13, 14  17, 18  24, 25  35, 36  45, 46  55 and 56  65 years). Thus, there were 5 males and 5 females per group. Table 1 shows the average subject anthropometric characteristics. 3.2. Experimental protocol Each subject was instructed to walk and run naturally and looking straight ahead on a treadmill (H/ P/Cosmos, Saturn 300/100r, Germany). An adequate period of familiarization (at least 20 min, according to the literature) was proposed before starting the recordings. Locomotion occurred at the level gradient, at 10 different velocities (from 0.83 to 1.94 m/s for walking, step 0.28 m/s; and from 1.94 to 3.06 m/s for running, step 0.28 m/s). Each testing condition was proposed in a random order and maintained for at least 60 s (Minetti & Saibene, 1992). Subjects aged 25–35 (5 males and 5 females) had to walk and run also at several different gradients (downhill: from  5% to  25%; uphill: from 5% to 25%, step 5%), at the same walking and running velocities. Each testing condition was maintained for at least 30 s (Minetti & Saibene, 1992). 3.3. Data acquisition and analysis Kinematics data was obtained by recording human movements with the motion capture technique, at a sampling rate of 100 Hz (Chou, Kaufman, Hahn, Brey, & Draganich, 2001). Eight infrared MX13 cameras (ViconÒ MX System, USA) recorded the 3D positions of 18 markers (Minetti & Saibene, 1992; Minetti et al., 1993; Minetti et al., 1994;) positioned on both body sides during treadmill locomotion (Minetti et al., 1993; Minetti et al., 1994). The body was then considered divided into 12 rigid segments (Table 2) (Minetti & Saibene, 1992; Minetti et al., 1993; Minetti et al., 1994). Each segment’s mass, center of mass position and gyration radius were taken from Winter’s anthropometric tables

Table 1 Average anthropometric characteristics of the investigated groups (mean ± SD). Age groups (y)

Body mass (kg) ± SD

Height (cm) ± SD

6–13

(Males) M = 37.4 ± 4.8 (Females) F = 35.6 ± 8.7 M = 61.6 ± 12.6 F = 58.0 ± 5.8 M = 69.7 ± 13.7 F = 54.6 ± 3.8 M = 82.2 ± 9.4 F = 54.6 ± 6.1 M = 84.6 ± 3.6 F = 63.4 ± 15.9 M = 92.6 ± 22.6 F = 64.0 ± 10.2 M = 88.6 ± 11.3 F = 58.8 ± 6.9

M = 145.2 ± 6.0 F = 140.2 ± 9.5 M = 174.2 ± 10.9 F = 165.6 ± 5.2 M = 178.7 ± 6.6 F = 165.0 ± 3.7 M = 182.0 ± 4.6 F = 169.6 ± 6.3 M = 182.8 ± 3.4 F = 169.6 ± 6.4 M = 180.4 ± 8.1 F = 163.6 ± 10.3 M = 180.2 ± 1.8 F = 161.0 ± 4.2

14–17 18–24 25–35 36–45 46–55 56–65

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F. Nardello et al. / Human Movement Science 30 (2011) 90–104 Table 2 Males (M) and females (F) segment definitions. Segments (males and females)

Segment definition

Mass (%) body mass

Proximal BCOM segment length

Radius gyration/ segment length

(Trunk and head)/2

Trunk = greater trochanter/ear canal

Thigh

Greater trochantry/femoral condyle

Shank

Femoral condyle/lateral malleolus

Foot

Lateral malleolus/head metatarsal II

Upper arm

Glenohumeral axis/elbow axis

Forearm

Elbow axis/ulnar styloid

M = 0.2890 F = 0.2824 M = 0.1000 F = 0.1044 M = 0.0465 F = 0.0517 M = 0.0145 F = 0.0137 M = 0.0280 F = 0.0263 M = 0.0220 F = 0.0191

M = 0.6600 F = 0.6107 M = 0.4330 F = 0.3819 M = 0.4330 F = 0.4288 M = 0.5000 F = 0.4546 M = 0.4360 F = 0.4346 M = 0.6820 F = 0.6798

M = 0.5030 F = 0.4827 M = 0.3230 F = 0.3623 M = 0.3020 F = 0.3209 M = 0.4750 F = 0.5526 M = 0.3220 F = 0.3141 M = 0.4680 F = 0.4426

(2005) for males, and estimated from Winter (2005) and de Leva (1996), Zatsiorsky et al. (1990) for females. Other detailed information about the methods can be found in previous papers (Minetti et al., 1993; Minetti et al., 1994). All cinematographic data was elaborated by means of a custom-written software, in LabVIEW (National Instrument, USA) (Minetti et al., 1993), to evaluate some simple (stride frequency, SF; and duty factor, DF) and complex (measured mechanical internal work, MWint) variables, in each testing condition. The software calculates, for each body segment, the absolute angular speed and the relative speed of its center of mass with respect to the BCOM. Then the rotational and linear kinetic energies are obtained and summed. The time course of the overall kinetic energy of each limb is the sum of the previous energies for all the segments within the limb (this corresponds to allowing intra-limb energy transfer). The internal work of each limb is then computed as the sum of positive increments in that time course. The total MWint results from the sum of the internal work of the 4 limbs and the one of the trunk-head segment (this procedure corresponds to assuming no energy transfer among limbs). Differently to previous work (Minetti, 1998, who used the ‘adaptive filtering’ procedure; Ferrigno, Borghese, & Pedotti, 1990), in this ad hoc software a ‘non adaptive filtering’ has been used (5th order Butterworth filter with a 8.5 Hz cut off frequency). This filter has been used because of previous experiences with unfiltered spatial data manually digitized on analogue movie-frames. In that case the scatter was so high that a high order filter was needed to smooth the data. Since our data have been captured from a Vicon MX System with no filtering, the same filter settings (5th order Butterworth filter) were implemented in the post-processing program in the first instance. Consequently, those biomechanical values have been included into Eq. (2b) in order to obtain the term q. To predict the mechanical internal work (PWint), the average q (=0.08 at level gaits; and =0.10 at gradients gaits) has been used in the Eq. (1). A total of about 32750 level strides and about 45300 gradient strides have been analyzed. 3.4. Statistical analysis Results will be presented as mean ± standard deviation (SD). The alpha test level set for statistical significance was .05. Effect of velocity (or Froude number) on the dependent variables DF and q was assessed by using a one-way ANOVA for repeated measures. Additionally, a post hoc Tukey test (with Bonferroni correction) was used to detect differences. For this statistical analysis, only the velocities from 0.83 to 2.50 m/s were considered due to discarding of tests at higher values. Indeed, velocities above 2.50 m/s were rejected because of the small number of subjects capable to carry out the whole protocol and, in fewer cases, when the kinematic data stream was incomplete. Moreover, effect of velocity on the dependent variables MWint and PWint was assessed separately by using a one-way ANOVA for repeated measures. Additionally, a post hoc Tukey test (with Bonferroni correction) was used to detect

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differences. For this statistical analysis, however, only the velocities from 0.83 to 2.22 m/s were considered due to discarding of tests at higher values. Velocities above 2.22 m/s were rejected according to the same reasons already described and discussed. Effect of gradient on each dependent variable was assessed by using a one-way ANOVA for repeated measures. In addition, a post hoc paired t-test (with Bonferroni correction) was used to detect differences between each dependent variable and gradient. Effect of MWint on the dependent variable PWint was assessed by using a one-way ANOVA for repeated measures with an additional post hoc Tukey test (with Bonferroni correction). In this last case, the statistical analysis was not applied to female data, because of some discarded tests. All statistical analysis was made using SPSS program (version 12.0 for Windows). 4. Results As far as stride frequency is concerned, our results wholly concur with the documented data (Cavagna, Franzetti, Heglund, & Willems, 1988; Minetti, 1998). In fact, SF (a) is similar in males and females, independently of age; (b) is greater in running than in walking, increasing linearly with velocity (p < .001 in walking and p < .05 in running); and (c) is independent of gradient. Experimental average values of each dependent variable (DF, MWint, term q and PWint) are plotted in two-dimensional graphs as a function of both average progression velocity (or Froude Number) and gradient. Males and females were found not to differ in both duty factor and, measured internal work; thus, only male average values are plotted in these graphs. Fig. 1a shows DF as a function of Froude Number at the level gradient. As expected, DF (a) is only little related to age (p < .05); and (b) as expected, it is always greater in walking than in running, decreasing linearly with increasing velocity, together with the stance time decrease (p < .05). Fig. 1b shows the independent relationship between DF and gradient, in walking and running. Fig. 2a shows MWint as a function of velocity at the level gradient. MWint increases with velocity (p < .001 in walking, and p < .01 in running), regardless of age group. Fig. 2b shows MWint as a function of gradient, in walking and running. In each testing condition, there is no significance in MWint as a function of gradient. However, only in some isolated cases (running at 2.78 and 3.06 m/s), MWint slightly increases with gradient from 10% to 25% (p < .05).

a

b

70

70

33

50

34 34 35

60

WALK

40 34

30

34

34 34

33

25

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WALK

40 30 24 25

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0 -30 -25 -20 -15 -10 -5

0

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10 0 0.0

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Duty Factor (%)

Duty Factor (%)

60

0.2

0.4

0.6

0.8

1.0

Froude Number

1.2

1.4

5

10 15 20 25 30

Gradient (%)

Fig. 1. Duty factor (DF) is plotted as a function of Froude Number at the level gradient, in males. The symbols refer to different age groups as follows: subjects aged 6–13 h; subjects aged 14–17 D; subjects aged 18–24 *; subjects aged 25–35 s; subjects aged 36–45 x; subjects aged 46–55 +; and subjects aged 56–65 e (same in Figs. 2a, 3, 5 and 8). The vertical bars represent positive and negative standard deviations of the higher and lower Froude Number curves, respectively. Numbers in proximity refer to the sample size of the relevant condition (number of kinematic analysis made); walk and run gaits have been specified, as well (same in Fig. 1b). (b) DF is plotted as a function of gradient in walking and running, in males. The symbols refer to different velocities as follows: walking at 0.83 m/s h; walking at 1.11 m/s s; walking at 1.39 m/s D; walking at 1.67 m/s *; walking at 1.94 m/s e; running at 1.94 m/s j; running at 2.22 m/s d; running at 2.50 m/s N; running at 2.78 m/s x; and running at 3.06 m/s  (same in Figs. 2b, 4, 6, and 7).

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b

0.8

0.6 RUN

0.4 WALK

0.2

0.0 0.0

0.5

1.0

1.5

2.0

2.5

0.8

Measured mechanical internal work (J/(kg•m))

Measured mechanical internal work (J/(kg•m))

a

3.0

0.6 RUN

0.4

0.2 WALK

0.0 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 Gradient (%)

3.5

Speed (m/s)

Fig. 2. Measured mechanical internal work (MWint) is plotted as a function of velocity at the level gradient, in males. Walk and run gaits have been specified (same in Fig. 2b). Symbols as in Fig. 1a. (b) MWint is plotted as a function of gradient in walking and running, in males. Symbols as in Fig. 1b.

0.25

b 0.25

0.20

0.20

0.15 WALK

Term q

Term q

a

RUN

0.10

0.15

RUN 33

34

0.10

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35

0.05

0.05

24 32

WALK

31 32

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29

3.0

3.5

Speed (m/s)

Fig. 3. Symbols as in Fig. 1a. (a). The term q is plotted as a function of velocity at the level gradient, in males. Walk and run gaits have been specified (same in Fig. 3b). (b) q is plotted as a function of velocity at the level gradient, in females. Numbers in proximity refer to the sample size of the relevant condition (number of kinematic analysis made).

Experimental average MWint, SF and DF at each velocity have been processed to obtain average (±SD) q values, which are similarly plotted as a function of both average progression velocity and gradient. Fig. 3 shows the term q as a function of velocity at the level gradient, in males (a) and females (b). In detail, the constancy of the term q suggested by Minetti (1998) has been only partially confirmed by our data: (a) in males, the average q value at the level gradient is 0.070 (±0.007 SD) in walking (n = 172); and 0.080 (±0.003 SD) in running (n = 169), regardless of age and velocity; (b) similarly, in females, the average q value is 0.074 (±0.025 SD) in walking (n = 168); and 0.084 (±0.013 SD) in running (n = 148); therefore (c), independently of gaits, the final average value of q is 0.075 (±0.005 SD) in males; and 0.079 (±0.019 SD) in females. In detail, both in walking and running, the term q: (a) does not significantly change with velocity, regardless of gender and age group; (b) young females (aged 6–13) seem to have the highest values of q; furthermore, (c) in running, q reaches its lowest value in males aged 56 to 65 and in females both aged 25 to 35 and 56 to 65.

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Consequently, in level gaits, the average value of q seems to come near 0.08, and the reference equation to estimate internal work (PWint) of level human locomotion can be written as:



PW int

DF ¼ SF  s  1 þ 1  DF

2 !  0:08

ð3aÞ

Fig. 4 shows q as a function of gradient, in males (a) and females (b). Minetti (1998) stated that a similar value of q was found if the same analysis was extended to gradients ± 15% (step 5%). The test protocol we adopted extended and completed the range of gradients investigated (±25%, step 5%). Our results do not wholly confirm this statement. In fact: (a) in males, the average q value is 0.091 (±0.025 SD) in gradient walking (n = 257); and 0.095 (± 0.018 SD) in gradient running (n = 266), regardless of gradient and velocity; (b) in females, the average q value is 0.096 (±0.027 SD) in gradient walking (n = 249); and 0.111 (±0.033 SD) in gradient running (n = 238); therefore c), independently of gaits, the final average value of q is 0.093 (±0.022 SD) in males; and 0.103 (±0.030 SD) in females.

a

b

0.25

0.25 WALK

0.20

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RUN

24 25

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Term q

Term q

17

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5

0.00 -30 -25 -20 -15 -10 -5

10 15 20 25 30

25 24

RUN

0

21

5

WALK

10 15 20 25

Gradient (%)

Gradient (%)

Fig. 4. Symbols as in Fig. 1b. (a) q is plotted as a function of gradient in walking and running, in males. Walk and run gaits have been specified (same in Fig. 4b) (b) q is plotted as a function of gradient in walking and running, in females. Numbers in proximity refer to the sample size of the relevant condition (number of kinematic analysis made).

b

0.8

Predicted mechanical internal work (J/(kg•m))

Predicted mechanical internal work (J/(kg•m))

a

0.6 RUN

0.4

WALK

0.2

0.0 0.0

0.5

1.0

1.5

2.0

Speed (m/s)

2.5

3.0

3.5

0.8

0.6 RUN WALK

0.4

0.2

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Speed (m/s)

Fig. 5. Symbols as in Fig. 1a. (a) Predicted mechanical internal work (PWint) is plotted as a function of velocity at the level gradient, in males. Walk and run gaits have been specified (same in Fig. 5b). (b) PWint is plotted as a function of velocity at the level gradient, in females.

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In detail, both in walking and running, the term q: (a) shows similar trends in men and women with speed and gradient, and (b) in females, q seems to more rapidly increase at the highest investigated uphill gradients. As a result, the reference equation to estimate internal work (PWint) of gradient human locomotion can be written as:



PW int

DF ¼ SF  s  1 þ 1  DF

2 !  0:10

ð3bÞ

In level gaits, the reference average value q (= 0.08) has been computed and fed back into Eq. (1) to predict internal work (PWint) from individual data on stride frequency, velocity and duty factor. Fig. 5 shows PWint as a function of velocity at the level gradient, in males (a) and females (b). PWint is highly dependent on velocity (p < .001), independently of gender, age or type of locomotion. Subjects (males and females) aged 56–65 have the highest values of PWint. Despite of their lowest value of the term q, a higher stride frequency of running with respect to the 25  35 yrs group (+14.0% and +8.3% for males and females, respectively) and an eventually different limb kinematics may generate the observed PWint overestimation.

b

0.8

0.8

Predicted mechanical internal work (J/(kg•m))

Predicted mechanical internal work (J/(kg•m))

a

0.6

0.4

0.2

0.0 -30 -25 -20 -15 -10 -5

0

5

0.6

0.4

0.2

0.0 -30 -25 -20 -15 -10 -5

10 15 20 25 30

Gradient (%)

0

5

10 15 20 25 30

Gradient (%)

Fig. 6. Symbols as in Fig. 1b. (a) PWint is plotted as a function of gradient in walking, in males. (b) PWint is plotted as a function of gradient in walking, in females.

b

0.8

Predicted mechanical internal work (J/(kg•m))

Predicted mechanical internal work (J/(kg•m))

a

0.6

0.4

0.2

0.0 -30 -25 -20 -15 -10 -5

0

5

10 15 20 25 30

Gradient (%)

0.8

0.6

0.4

0.2

0.0 -30 -25 -20 -15 -10 -5

0

5

10 15 20 25 30

Gradient (%)

Fig. 7. Symbols as in Fig. 1b. (a) PWint is plotted as a function of gradient in running, in males. (b) PWint is plotted as a function of gradient in running, in females.

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In gradient gaits, the reference average value q (= 0.10) has been computed and fed back into Eq. (1) to predict internal work (PWint). Fig. 6 shows PWint as a function of gradient walking, in males (a) and females (b). In each testing condition, PWint is only slightly dependent on gradient (p < .05). Fig. 7 shows PWint as a function of gradient running, in males (a) and females (b). In each testing condition, PWint is not dependent on gradient. Finally, PWint values are plotted versus MWint for both level (Fig. 8) and gradient (Fig. 9) gaits, in males (a) and females (b). Despite of some variability in those relationships, points tend to distribute along the identity line in both figures. The hypothesis that the regression slopes are different from 1

b

1.0

Predicted mechanical internal work (J/(kg•m))

Predicted mechanical internal work (J/(kg•m))

a

0.8

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

0.8

0.6

0.4

0.2

0.0 0.0

1.0

Measured mechanical internal work (J/(kg•m))

0.2

0.4

0.6

0.8

1.0

Measured mechanical internal work (J/(kg•m))

Fig. 8. Symbols as in Fig. 1a. (a) PWint versus MWint at the level gradient, in males. The points represent mean values of both PWint and MWint obtained by grouping subjects in the forward velocities (from 0.83 to 1.94 m/s for walking, step 0.28 m/s; and from 1.94 to 3.06 m/s for running, step 0.28 m/s). The dotted lines are the lines of identity (same in Fig. 9). (b) PWint versus MWint at the level gradient, in females.

b

1.0

Predicted mechanical internal work (J/(kg•m))

Predicted mechanical internal work (J/(kg•m))

a

0.8

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Measured mechanical internal work (J/(kg•m))

1.0

0.8

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Measured mechanical internal work (J/(kg•m))

Fig. 9. The symbols refer to different gradients as follows: walking and running at – 25% j; walking and running at – 20% N; walking and running at – 15% *; walking and running at – 10% d; walking and running at – 5% ; walking and running at 0% –; walking and running at 5% e; walking and running at 10% s; walking and running at 15% x; walking and running at 20% 4; and walking and running at 25% h. The points represent mean values of both PWint and MWint obtained by grouping subjects at all velocities (from 0.83 to 3.06 m/s). (a) PWint versus MWint in gradient walking and running, in males. (b) PWint versus MWint in gradient walking and running, in females.

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has been statistically tested and rejected (p = .265, .444, .066 and .420, in Figs. 8(a-b), 9a and 9b, respectively).

5. Discussion In all the investigated experimental conditions, the stride frequency and the duty factor, which are used in the equations to predict the mechanical internal work, are found to be similar to previous documented data (Cavagna & Franzetti, 1986; Cavagna et al., 1988; Cavagna et al., 1991; Cavagna et al., 1997; Cavagna et al., 2008; Minetti, 1998; Minetti & Saibene, 1992; Schepens et al., 1998). As expected and widely demonstrated in literature, both stride frequency and duty factor are more dependent on velocity than on gradient. In humans (bipeds), fore and hind limbs are alternatively in contact with the ground, while the upper limbs oscillate freely both during the stance and the swing phase. For the mathematical model to work properly, it has been assumed that the duty factor to put in the equation will be the same both in upper and lower limbs (see ‘Appendix’). This approximation is mitigated by the lower mass and the inertial moment of upper limbs with respect to lower limbs (Dempster et al., 1959). The lowest walking and running values of duty factor in young children (aged 6–13) are probably due to their small body size effect. Indeed, in walking gait, the limb speed, with respect to the center of mass, during the swing phase is slightly higher than the one during the stance; however, in running gait, it is slightly lower (Minetti & Saibene, 1992). Moreover, the highest running values of DF in elderly adults (aged 56–65) are probably due to a reduced stiffness in tendons as demonstrated in Magnusson, Narici, Maganaris, and Kjaer (2008). In fact, we can expect a higher length change in a lower stiffness spring, so that the same energy storing during stance could take a longer time. In addition, this decrease in tendon stiffness is at least partly due to tendon material deterioration (Narici, 2005). Because of the close relationship between length changes of tendon properties and reflex responses, it is also possible that the adaptation to changing velocities could be reduced in elderly persons. Clearly, this implies a relatively smaller amount of elastic energy stored during the deceleration phase of the center of mass coupled with greater metabolic energy expenditure (Cavagna et al., 2008). Measured mechanical internal works herein obtained are smaller than those reported by Cavagna and Kaneko (1977), Cavagna et al. (1991), Willems et al. (1995), and Schepens et al. (2001). In detail, our male and female children (aged 6–13) present the greatest values at the level gradient (walking and running). This is probably due to the effect of leg length on the effective step frequency (Schepens et al., 2001). Moreover, differently from what was illustrated in Cavagna et al. (2008), our male elderly adults (aged 56–65) present the lowest measured internal work at level running. This finding seems a bit odd because the stride frequency and the duty factor of these subjects are greater with respect to other age groups. However, this result could be ascribed both to a more stabilized movement of the upper limbs and a different motion pattern in general. Importantly, our results suggest that the procedure used in this study generates measured Wint values lower than in Cavagna et al. (1991), and even 20% lower with respect to the previous predicting model (Minetti, 1998). We hypothesized that the data filtering techniques could have had a role in this, thus a test was issued. The same kinematic data series (3 subjects walking at 5 speeds at the level gradient) underwent Wint measurements according to no-filtering and to the 1st, 3rd and 5th orders of the Butterworth filter. Also, data of one subject walking at 1.94 m/s were processed also including intermediate orders (2nd and 4th). Results from the test pointed out that 1st order filtering produces Wint values very similar to the Ferrigno’s adaptive procedure (Ferrigno et al., 1990) adopted in many papers in the literature (since it is included in the BTS motion analysis software, e.g., Minetti et al., 1993; Minetti et al., 1994) and close to what was expected from the previous Wint model (Minetti, 1998). Those values are about 40% lower than in Cavagna et al. (1991) and in Willems et al. (1995), whose results, obtained through a different smoothing technique (Savitzky & Golay, 1964), correspond to a no-filtering procedure. By increasing the filtering order, Wint values become even smaller, up to a – 20% with respect to 1st order Butterworth. Thus, it is important to realize that the adopted filtering protocol (see par. 3.3 ‘Data acquisition and analysis’), among all the other methodological differences, can be responsible of the Wint discrepancies found in the literature. Despite of the different Wint values depending on the different filtering

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techniques, the relationships among the values of all the conditions studied in the present investigation is supposed to be preserved. It is sufficient to remember that both Wint measurements and prediction, together with the estimated q values, could be 20% higher in case of a more customary filtering procedure (1st order Butterworth filter). The term q was estimated by Minetti (1998) both for humans and animals based on the inertial properties of limbs. With straight limbs, q reflects the mass distribution along the segments, while during locomotion the folding of limbs certainly implies some reduction in q values. Thus, a consistent decrease of q at high velocities could be interpreted as an energy minimization strategy. This capacity in reducing the term q has been demonstrated only in horse locomotion. In fact, horses display ‘a much greater decrease when passing from walk to trot and then to gallop’ (Minetti, 1998, p. 467). In humans, q values resulted to be almost constant (=0.100 ± 0.013 SD) throughout all the gaits, velocities and gradients, as expected. In fact, the geometry in the middle of the stance and swing phases is similar as gaits, velocities and gradients change. In our study, we have tried to verify and demonstrate validity and applicability of the constancy of q in different age groups, in subjects of different genders who walked/ran at different velocities, both at the level gradient and/or at extreme slopes (downhill and uphill). The constancy of the term q suggested by Minetti (1998) has been only partially confirmed over our data. Also, our results make clear that the difference between males and females is not statistically significant. Moreover, despite the consistently negative trend of stride frequency and the positive trend of duty factor with respect of velocity, in young children (aged 6–13) and in elderly adults (aged 56–65) q values result to be constant regardless of age and gait, according to Minetti (1998). Our smaller term q could be probably due to our lower values in measured mechanical internal work. Furthermore, especially in females, our results strongly confirm the statement that ‘the slightly decrease in q during running could reflect a greater knee flexion at high velocities, thus a reduced angular moment during the swing phase’ (Minetti, 1998, p. 466). Due to a lower MWint values with respect to those measured by Cavagna et al. (1976, 1995), Willems et al. (1995) and Minetti (1998), as already mentioned, also our PWint values are smaller than those predicted by Cavagna et al. (1991), and Minetti (1998). Such an underestimation was mainly caused by a different filtering methodology (see above). However, when comparing the present PWint and MWint, that bias should be minimum, and the potential discrepancy/variability between the two could be the effect of having assumed for PWint (1) a constant q value, independently of speed and gradient, and (2) a sinusoidal oscillation pattern for all limbs. As expected, in level gaits, q values are quite constant at different velocities (for both genders). Among the others, this implies that the predicted internal work calculated by assuming a constant q (= 0.08) well concurs with the experimentally measured work. The match between the two methods is very close (in males: n = 70, R2 = .617; in females: n = 70, R2 = .620). In gradient gaits, the q values are quite constant at the different velocities. Accordingly, we adopted a q = 0.10 as a reasonable working reference constant both for males and females, and the predicted internal work well concurs with the experimentally measured work. The match between the two methods is close (excepted for a few points), too (in males: n = 110, R2 = .525; in females: n = 110, R2 = .295).

6. Conclusion The results of this study showed that the direct measurements of mechanical internal work can be compared to the indirect, model-based predictions, in human locomotion when different gender, age, gait, velocity and gradient are taken into account. Different values of the term q in the model equation, referring to the inertial properties of the oscillating limbs, have been found at level (0.08) and at gradient (0.10) gaits. By having been applied for a wide number of conditions, the model equation (together with the corresponding q values) seems robust enough to be appropriately used whenever the direct experimental measurement is unavailable. Another outcome from the present investigation is that the internal mechanical work is quite affected, in absolute value but not in its trends, by the filtering technique of the kinematic data.

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Areas for further research may include a similar analysis for other age groups, like younger subjects (< 6 years) for their different locomotion techniques and lower limb lengths, and older ones (> 65 years) for their physiological constraints due to the increased age. Appendix This Appendix briefly summarizes two papers (Minetti, 1998; Minetti & Saibene, 1992), which originated both Eq. (1) and Eq. (2) of the model. Minetti and Saibene (1992) schematized a stiff limb diagram adopted to formalize the mechanical internal work model. The main assumptions within this model are: 4 stiff limbs, no double support, the center of mass of the rest of the body located in the hip joint. Precisely, four stiff segments (two lower and two upper limbs) are involved in the computation. The lower limb length, the proximal distance of the lower limb center of mass, the upper limb length (as a fraction of the lower limb length), the radii of gyration of lower and upper limbs have been taken from the literature. Assuming that the limb extremities follow a sinusoidal displacement with respect to the body center of mass, which is placed in the head-trunk segment and does not move horizontally because of the symmetrical positions of the limbs, the mechanical internal work (Wint) has been evaluated from the oscillations in kinetic energy (both translational and rotational) according to the König theorem, as suggested in Cavagna and Kaneko (1977). Indeed, the energy transfer among segments is not relevant because of the in-phase shapes of the kinetic energy curves. Minetti and Saibene (1992) have modeled a mathematical equation to calculate the work needed to accelerate the body limbs with respect to the body center of mass during walking as

W int ¼ SF  s2 

p2 2

2

 ½ða2 þ g 2 ÞðmL þ b mU Þ

ðA1Þ

where SF is the stride frequency (Hz), s is the average progression velocity (m/s), a represents the average proximal distance, and g the mean radius of gyration of the upper and lower limbs (as a fraction of limb length), mL and mU refer to the lower and upper limb mass with respect to the body mass (kg), and b is the upper limb length (as a fraction of the lower one). In the Eq. (A1) equal amounts of time spent by the limbs in the stance and the swing phase have been assumed. Clearly, such approximation is not available when different gaits have to be simultaneously taken into account. In Wint measurements, the time course of the limb kinetic energy shows two different peaks, one related to the progression speed (sST, the top speed during the stance time), and the other reflecting the limb speed relative to the overall center of mass, during the swing phase (sSW). Therefore, the reference to speed in the Equation above can be modified to accommodate this rationale by replacing.

s2 ¼

1 2 1  s þ  s2 2 ST 2 SW

ðA2Þ

and by considering that sST is equal to s, and sSW can be calculated by introducing the ‘‘duty factor’’ as

sSW ¼ sST 



DF 1  DF

 ðA3Þ

This means that the limb speed, with respect to the center of mass, during the swing phase is higher than the one during the stance when DF is greater than 0.5, as in walking, but it is expected to be lower in running. By including Eqs. (A2) and (A3) into Eq. (A1), we obtain the initial Eq. (1). References Cavagna, G. A., & Franzetti, P. (1981). Mechanics of competition walking. Journal of Physiology, 6, 243–251. Cavagna, G. A., & Franzetti, P. (1986). The determinants of the step frequency in walking humans. Journal of Physiology (London), 373, 235–242. Cavagna, G. A., Franzetti, P., & Fuchimoto, T. (1983). The mechanics of walking in children. Journal of Physiology (London), 343, 332–339.

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