Disclosure: The authors declared no conflict of interest.
Funding agencies: No funding was received for the present study. The authors declare that they have no conflict of interest. The experiments in this study were performed in accordance with the laws of the country in which the study was conducted.
To compare the mechanical external work (Wext) and pendular energy transduction (Rstep) at spontaneous walking speed (Ss) in individuals with Prader–Willi syndrome (PWS) versus subjects with nonsyndromal obesity (OB) to investigate whether the early onset of obesity allows PWS subjects to adopt energy conserving gait mechanics.
Design and Methods
Wext and Rstep were computed using kinematic data acquired by an optoelectronic system and compared in 15 PWS (BMI = 39.5 ± 1.8 kg m−2; 26.7 ± 1.5 year) and 15 OB (BMI = 39.3 ± 1.0 kg m−2; 28.7 ± 1.9 year) adults matched for gender, age and BMI and walking at Ss.
Ss was significantly lower in PWS (0.98 ± 0.03 m s−1) than in OB (1.20 ± 0.02 m s−1; P < 0.001). There were no significant differences in Wext per kilogram between groups (PWS: 0.37 ± 0.04 J kg−1 m−1; OB: 0.40 ± 0.05 J kg−1 m−1; P = 0.66) and in Rstep (PWS: 69.9 ± 2.9%; OB: 67.7 ± 2.4%; P = 0.56). However, Rstep normalized to Froude number (Rstep/Fr) was significantly greater in PWS (6.0 ± 0.6) than in OB (3.8 ± 0.2; P = 0.001). Moreover, Rstep/Fr was inversely correlated with age of obesity onset (r = −0.49; P = 0.006) and positively correlated with obesity duration (r = 0.38; P = 0.036).
Individuals with PWS seem to alter their gait to improve pendular energy transduction as a result of precocious and chronic adaptation to loading.
Obesity has been recognized as one of the most serious public health challenges. Strategies for the prevention and treatment of obesity are high on the public health agenda. As the most common mode of physical activity, walking may contribute significantly to weight management in overweight and obese individuals . Spontaneous walking speed (Ss), also known as preferred or self-selected speed, is the speed normally used during daily living activities. This appears to be an appropriate walking intensity for weight reduction programs aimed at inducing negative energy balance . Ss is normally slower in obese individuals than in individuals of normal body mass [3, 4]. At this speed, obese subjects walk with a more erect pattern with reduced hip and knee flexion, increased ankle plantar flexion, lower absolute knee torque (N m−1) and power values [i.e., mechanical plasticity ] as compared to normal body mass subjects . Especially in class III obesity [body mass index (BMI) > 40 kg m−2], this may represent an active strategy to increase dynamic balance  and minimize knee loads , mechanical work  and energy cost during walking . Testing individuals at Ss may also provide insight into the adaptive changes in gait behavior  in response to obesity , weight loss , and aging . As recently suggested by Hortobàgyi et al. , behavioral adaptations such as changes in walking speed, provide a means to investigate the interaction between the effects of obesity and an individual's control of gait pattern.
From a biomechanical perspective, level walking can be modelled as an inverted pendulum. This is characterized by pendular transduction of potential into kinetic energy, due to the vertical shift of the body mass center (CM) and its forward speed, respectively . This mechanism seems to reduce the work done by the muscles to translate CM with respect to the ground (Wext) and thus minimize the energy cost of walking . Recently, several studies on obese subjects have reported higher absolute Wext (J m−1) with similar relative Wext (J kg−1 m−1) at fixed [10, 11] and spontaneous walking speed  as compared to normal body mass individuals. This suggests that body mass is the main determinant of Wext and that pendular energy transduction is not impaired in obese subjects [4, 10, 11].
The pendular mechanism in human walking is not innate but acquired through walking experience during childhood. In toddlers, the pendular energy transduction is 50% lower as compared to children and adults, indicating that this mechanism is not implemented at the onset of unsupported walking, but requires active neural control and an appropriate pattern of inter-segmental coordination . Unsupported walking (i.e., gait experience) associated with neural maturation seems to act as a “functional trigger of gait maturation”  to improve the pendular energy transduction while walking. Therefore, early obesity onset associated with walking experience may induce specific pattern changes and modify the pendular energy transduction in gait during childhood (i.e., the key period for the development of gait pattern). So far, however, no studies have investigated the effect of early onset of obesity on pendular energy transduction. Adults with Prader–Willi syndrome (PWS) who develop morbid obesity during early childhood (i.e., between 1 and 6 years of age) as a consequence of their hyperphagia , may allow us to investigate this issue.
PWS is a complex disorder associated with multiple anomalies resulting from a failure of expression of paternally inherited genes in the PWS region of chromosome 15 (15q11.2-q13). The major manifestations of PWS include severe neonatal hypotonia, life-threatening obesity, dysmorphic features, mild mental retardation, behavioral disturbance, hypogonadism, and short stature. Hypotonia and excessive body mass are believed to be major determinants of the typical gait alterations associated with this syndrome. Adult individuals with PWS walk slower with a shorter stride length, a lower cadence and a longer stance phase as compared to both body mass index—matched obese and healthy subjects .
The aim of this study was to compare the mechanical external work and the pendular energy transduction at spontaneous walking speed in PWS subjects and individuals with nonsyndromic obesity. It was hypothesized that slower Ss (i.e., behavioral adaptation) in adults with PWS would be associated with similar mechanical work and pendular energy recovery (i.e., mechanical plasticity) as compared to gender-, age-, and BMI-matched adults with nonsyndromic obesity. Therefore, early obesity might favor modulation of gait pattern in adults with PWS to improve pendular energy transduction during walking.
Two groups of subjects participated in the study: an obese (OB) group [BMI = 39.3 ± 1.0 kg m−2 (mean ± standard error of the mean); n = 15, 8 females and 7 males; 28.7 ± 1.9, range 19-39 years] and a PWS group (BMI = 39.5 ± 1.8 kg m−2; n = 15, 8 females and 7 males; 26.7 ± 1.5, range 19-40 years). The two groups were matched for gender, age, and BMI. All PWS subjects showed the typical clinical phenotype . Cytogenetic analysis was performed in the PWS subjects: nine of them had interstitial deletion of the proximal long arm of chromosome 15 (del15q11–q13) and six had uniparental maternal disomy for chromosome 15 (UPD15). All PWS subjects showed mild mental retardation. Subjects participating in the study had to score over the cut-off value of 24 in the Mini Mental State Examination (MMSE) Italian version . MMSE scores over the cut-off value indicate the absence of widespread acquired cognitive disorders in adult people and specifically that our PWS participants were able to understand the experimental instructions. All subjects were otherwise healthy and free of clinically significant orthopedic, neurological, cardiovascular, or respiratory conditions. The study was approved by the Ethical Committee of the “Istituto Auxologico Italiano” and informed written consent was obtained from the patients and, whenever necessary, their parents or guardians.
Each subject completed two test sessions, as previously described . In the first session, a physician took the medical history and performed a physical examination, and each subject was then introduced to the experimental procedures. The second session was dedicated to gait pattern evaluation using an optoelectronic system with six cameras (460 Vicon, UK) recording at 100 Hz. Passive markers were placed on the subjects’ feet and posterior superior iliac spines according to the Vicon Plug-In Gait marker set (modified Helen-Hayes marker set) . The bony landmark was identified by the same operator by means of palpatory examination in the prone position and then again in the standing position and subsequently using Martin pelvimeter to identify in a precise and repeatable procedure the anatomical landmark as previously described . The subjects were asked to walk on a 10-m walkway at Ss. Biomechanical data from three trials were collected for further analysis.
Anthropometric measurements and obesity onset and duration
Standing height was measured using a Harpenden stadiometer and limb length was assessed as the distance between the great trochanter and the ground in the right limb. The identification of the greater trochanter was performed by anthropometric measures and according to the Vicon Plug-In Gait marker set as follows: the same expert operator manually located the bony landmark in the supine, side and standing position and with the markers of the pelvis and knee. Body mass was measured to the nearest 0.1 kg on a precision digital scale with the subject wearing shorts and a T-shirt. Body composition was assessed using a tetrapolar bioelectrical impedance method (BIA 101/S, Akern, Florence, Italy). Information on the age of obesity onset was gathered by retrospectively reviewing all medical charts of patients. Obesity duration could then be calculated in absolute (yrs) and relative (% of age) values.
Step duration, frequency, length and duration of single and double support were computed defining the gait cycle by kinematic data of foot markers. Six passive markers were placed on the participants’ feet on the second metatarsus, the lateral malleolus and the lateral heel . To take into account the difference in size between the two groups, the dimensionless Froude number (Fr) was computed as the ratio between Ss2 and the acceleration of gravity (g = 9.81 m s−2) multiplied by the limb length (l) [Ss2 (g l−1)−1] .
Mechanical external work and potential-kinetic energy transduction
CM was approximated as the midpoint between the markers positioned on the subject's posterior superior iliac spine, according to previous studies [4, 11]. Coordinate data were filtered using Woltring's general crossvalidatory quintic smoothing spline. The displacement of CM was analyzed in vertical (y), horizontal (x), and medio-lateral (z) components. During walking at Ss, the potential (Ep) and the kinetic energy (Ek) fluctuations of CM within each step can be calculated as previously described . The instantaneous Ep was computed from y, body mass (m) and g (Eq. (1)). The first-order finite difference of the 3D displacements of CM provided the velocity changes of the CM in the vertical (Vy), horizontal (Vx), and medio-lateral (Vz) directions. From the instantaneous Vy, Vx and Vz and m, we computed the instantaneous vertical, horizontal and lateral kinetic energies of the CM (Ekv, Ekh, Ekl, respectively; Eq. (3)).
All calculations were performed for each step. The beginning and the end of a step were defined as the instant when Ep reached the minimum value . A step was selected for analysis when the sum of the increments in Vy, Vx, and Vz changes did not differ by more than 25% from the sum of the decrements, thus revealing a relatively constant average height and speed per step . The average steps analyzed for each subject were 12.5 ± 0.6 and 13.9 ± 0.6 for OB and PWS, respectively. As in previous studies [4, 9, 20], the increments in Ek and Ep were added to obtain the total mechanical energy of CM (Etot = Ek + Ep = Ekh + Ekv + Ekl+ Ep). The work performed per step was calculated as the sum of the positive increments in the total mechanical energy (Etot). The positive increments of Etot were equal to the total external work performed per step (Wext). The vertical work per step (Wv) was equal to the positive increments in vertical energy (Ev= Ekv+ Ep). The forward work (Wf) was equal to the positive increments in kinetic horizontal energy (Ekh). The lateral work (Wl) per step was equal to the positive increment in kinetic lateral energy (Ekl). In this article, mechanical work (i.e., Wext, Wv, Wf, and Wl) is expressed in J kg−1 m−1 (i.e., mechanical work per unit mass and unit distance). In walking, Wext is always less than the sum of Wv, Wf, and Wl, since mechanical energy is recovered within each step by the pendular transduction of potential to kinetic energy and vice versa . The fraction of mechanical energy recovered (Rstep), due to this transduction, was calculated according to previous studies [4, 19]:
The magnitude of Wext, and thus Rstep depends on: (i) the relative amplitude of the potential and kinetic energy curves, (ii) the relative phase of the fluctuations in the potential and kinetic energy curves, and (iii) the rates of fluctuation of Ek and Ep (shape of the curves) . We then calculated the relative magnitude of the mechanical kinetic work (Wk: the positive increments in Ek) and the potential work (Wp: the positive increments in Ep) as the ratio Wk/Wp for each step. Chemical energy is expended to perform positive and, to a lesser extent, negative work, and, therefore, the latter was neglected. To reduce energy expenditure, the mechanical energy changes of CM should be reduced to a minimum.
Data are expressed as means ± standard error of the mean (SEM) for all variables. An unpaired (independent group) t test was used to determine differences in the physical characteristics (i.e., height, limb length, body mass, obesity onset, and duration) and in biomechanical data (i.e., spatio-temporal and kinetic parameters). When the assumption of normality of distribution was violated, a Mann–Whitney U test for nonparametric values was used to compare the two groups. As the assumption of normality of distribution was violated, correlations between Rstep and the age of obesity onset and duration were performed using the Spearman correlation coefficient (r). The level of significance was set at P < 0.05.
The anthropometric characteristics of the study participants are presented in the Table 1. The height, fat-free and body mass were significantly lower in PWS than OB (P = 0.001, P = 0.001, and P = 0.03, respectively). In contrast, body fat percentage was significantly higher in PWS than in OB (P < 0.001). There was no significant difference in limb length between the two groups (P = 0.21). A significant earlier obesity onset was found in PWS than in OB (P < 0.001). Obesity duration in absolute and relative terms was significantly longer in PWS as compared to OB (P = 0.016 and P < 0.001, respectively).
Table 1. Subject characteristics
PWG (n = 15)
OBG (n = 15)
Means values ± SEM are reported. F, female; M, male; BMI, Body Mass Index. *Significant difference between Prader–Willi group (PWG) and obese group (OBG) (P < 0.05).
7 M, 8 F
7 M, 8 F
26.7 ± 1.5
28.7 ± 1.9
1.52 ± 0.02*
1.66 ± 0.03
Limb length, m
0.78 ± 0.01
0.81 ± 0.02
Body mass, kg
91.8 ± 5.1*
108.4 ± 4.9
39.5 ± 1.8
39.3 ± 1.0
Body fat (%)
53.2 ± 1.2*
41.8 ± 1.5
Fat free mass (kg)
42.7 ± 2.3*
54.1 ± 2.2
Obesity onset, yr
2.2 ± 0.1*
11.4 ± 0.5
Obesity duration, yr
24.6 ± 1.5*
17.3 ± 2.4
Obesity duration, %age
91.5 ± 0.3*
58.7 ± 1.6
Spatio-temporal parameters and vertical and lateral displacements of CM
Ss, Fr and step length were significantly lower in PWS than in OB (P < 0.001 for all; Table 2). There were no significant differences in step duration and frequency or in double and single support durations (P ≥ 0.18; Table 2). The vertical displacement of CM was similar in the two groups (P = 0.09; Table 2). The lateral displacements of CM were significantly higher in PWS than in OB (P < 0.001; Table 2).
Table 2. Spatio-temporal parameters at spontaneous walking speed
Means values ± SEM are reported. Ss, spontaneous walking speed; Fr, Froude number; CM: center of body mass. *Significant difference between Prader–Willi group (PWG) and obese group (OBG) (P < 0.05).
Ss, m s−1
0.98 ± 0.03*
1.20 ± 0.02
0.13 ± 0.01*
0.18 ± 0.01
Step duration, s
0.53 ± 0.01
0.53 ± 0.01
Step length, m
0.51 ± 0.01*
0.63 ± 0.01
Step frequency, Hz
1.92 ± 0.04
1.92 ± 0.03
Double support duration, %
25.9 ± 1.4
24.0 ± 0.6
Single support duration, %
73.7 ± 1.5
76.0 ± 0.6
Vertical displacement of CM, cm
3.1 ± 0.1
3.5 ± 0.2
Lateral displacements of CM, cm
5.0 ± 0.2*
3.7 ± 0.2
Mechanical external work and potential-kinetic energy transduction
There were no significant differences in the relative Wext and Wf (J kg−1 m−1) between the two groups (P = 0.66 and P = 0.25, respectively; Table 3). The relative Wv and Wl were significantly higher in PWS as compared to OB (P = 0.03 and P = 0.009, respectively; Table 3). Wk/Wp tended to be lower in PWS than OB (P = 0.08; Table 3).
Table 3. Mechanical works at spontaneous walking speed (Ss)
Means values ± SEM are reported. Wext, mechanical external work; Wf, mechanical forward work; Wv, mechanical vertical work; Wl, mechanical lateral work. Wk, mechanical kinetic work; Wp, mechanical potential work. *Significant difference between Prader–Willi group (PWG) and obese group (OBG) (P < 0.05). §P = 0.08 for difference between PWG and OBG.
Wext, J kg−1 m−1
0.37 ± 0.04
0.40 ± 0.05
Wf, J kg−1 m−1
0.54 ± 0.04
0.62 ± 0.05
Wv, J kg−1 m−1
0.59 ± 0.02*
0.53 ± 0.02
Wl, J kg−1 m−1
0.07 ± 0.00*
0.94 ± 0.06§
1.12 ± 0.08
Rstep was similar in the two groups (P = 0.56; Figure 1A), whereas Rstep normalized to Fr (Rstep/Fr) was significantly higher in PWS than in OB (P = 0.001; Figure 1B). Rstep/Fr was significantly and inversely correlated with age of obesity onset (r = −0.49; P = 0.006) and positively correlated with obesity duration (r = 0.38; P = 0.036) and lateral displacements (r = 0.44; P = 0.016).
The main finding of this study was that slower spontaneous walking speed (i.e., behavioral adaptation) in PWS subjects was associated with similar mechanical external work per unit mass and fraction of mechanical energy recovery (i.e., mechanical plasticity) as compared to obese individuals matched for gender, age, and BMI. The fraction of mechanical energy recovered normalized to Froude number was higher in PWS than OB and was correlated with the age of obesity onset and the duration of obesity. These findings suggest that gait pattern may have been influenced by the early onset (2-3 years of age) of obesity, which is a feature of PWS. Therefore, as a result of precocious and chronic adaptation to loading, individuals with PWS appear to modulate their gait to improve pendular energy transduction.
Ss was ∼18% slower in PWS as compared to OB. This result is in line with previous measurements in PWS [14, 21] and obese individuals [3, 4]. At Ss, step length was ∼19% shorter in PWS than in OB, whereas all other spatio-temporal parameters were similar. Fr (i.e., walking speed normalized to limb length) was ∼28% lower in PWS as compared to OB, suggesting that the decreased Ss cannot be fully explained by limb length. The reduced push-off capacity in PWS , secondary to reduced maximal muscle strength  and muscle mass , may partly explain their slower Ss compared to BMI-matched obese individuals with higher fat-free body mass (Table 1). Other spatio-temporal parameters seem to indicate that individuals with PWS and OB subjects modulate their step characteristics to minimize single support duration and reduce muscular work and Wext while walking, in line with previous findings . Moreover, shorter steps associated with similar step frequency may indicate that PWS individuals elect to reduce the mechanical work required to redirect CM during double support phase (i.e., step-to-step transition) . Because PWS individuals are characterized by decreased fat-free body mass (Table 1) and physical activity levels  and therefore supposedly by lower maximal oxygen uptake  as compared to nonsyndromic obese subjects, they may select a slower Ss than OB subjects to achieve the same relative effort (i.e., energy expenditure at Ss, expressed as % of maximal oxygen uptake) . Even though relative effort was not measured in this study, Ss is the result of competing demands from multiple rather than from single constraints based on the mechanical and energy cost of coordination and control of human bipedal locomotion  (i.e., behavioral adaptations). Therefore, PWS might select a Ss that simultaneously reduces muscular effort, mechanical work and the energy cost of walking.
Walking at Ss PWS and OB showed similar relative Wext. Our Wext values are in line with those reported in obese adolescents  and obese adults . Another study on obese adults  reported higher values. Methodological differences in the assessment of Wext may explain this discrepancy. In the present study, we used an optoelectronic system to quantify CM motion, as assessed by the displacements of a single anatomical point. Browning et al.  used force platforms. Our methodology may have overestimated the Wf induced by tilting of the trunk . However, it has been reported that Wext was significantly correlated between the two methods  [our methodological limitations have been previously described in detail ]. In this study, the two groups were compared using the same methodology, which has already been used to assess Wext in obese individuals [4, 11].
Rstep was similar in the two groups and to values previously reported in obese individuals [4, 11]. Although gait behavioral adaptations induced by obesity onset [5, 8] can be investigated by testing subjects during walking at two different Ss, Rstep depends on walking speed . Thus, the comparison of biomechanical variables of gait at different Ss represents a methodological limitation of our study. However, PWS individuals, walking at slower Ss, had similar Rstep values to OB subjects and these values are typically reported at faster walking speeds . Based on previous findings  for the speed rage of our groups (1–1.2 m s−1), Rstep would increase as PWS individuals increased walking speed, giving them higher Rstep at the same speed as OB subjects. This demonstrates therefore that Rstep in PWS individuals is improved compared with nonsyndromic obese subjects. Further support for this important finding is that Rstep normalized to Fr was found to be ∼58% higher in PWS as compared to OB. This normalization is possible only for the narrow Fr range (0.13–0.18) used for the two groups in this study. In fact, within this range, the relationship between Rstep and Fr may be considered linear [12, 29]. Furthermore, Rstep/Fr was inversely correlated with the age of obesity onset and positively correlated with obesity duration. Altogether these findings support our hypothesis that as a result of their early-onset obesity, PWS individuals seem to adopt changes in gait that improve the pendular mechanism. The excessive body mass may interact with the experience of walking inducing a specific development of the pendulum mechanism during the first months of independent locomotion in PWS toddlers. This development may continue throughout childhood, parallel to greater stability  and improvements in other kinematic and kinetic gait parameters , and then reach a plateau in adulthood. Optimizing the pendular mechanism may be considered an adaptive mechanism to load to minimize Wext and metabolic rate during walking, as previously observed in African women carrying loads on their head [18, 31]. In fact, the improvement in pendular mechanical energy transduction in PWS could be a mechanism to reduce the metabolic cost of walking. This may be a compensatory mechanism to minimize muscle work so as to economize on energy and counterbalance low mechanical efficiency during walking at Ss as previously shown in patients with ankle osteoarthritis Ss . Although early onset of obesity may favor modulation of gait pattern in adult PWS, we can not completely exclude the possibility that other factors associated with PWS and the anthropometry of the participants (e.g., reduced lean body mass) may also have contributed to the observed gait differences between individuals with PWS and OB subjects. To confirm our results and isolate the effect of obesity onset on gait pattern, future studies should compare Wext and Rstep at fixed and spontaneous walking speeds in PWS and nonsyndromic obese children.
A possible explanation of these changes in mechanical energy may be that Wv and Wl were ∼11 and ∼25% higher in PWS than OB, respectively. The increases in Wv and especially in Wl optimize the relative magnitude of the kinetic and potential energies and improve Rstep in PWS. In fact, the ratio Wk/Wp tended to be lower and close to 1 in PWS as compared to OB. PWS individuals may adopt a “waddling” walking strategy, which allows them to use the higher Wl to compensate the lower Wf (nonstatistically significant), due to slower Ss, and thus increase the kinetic energy available to convert into gravitational potential energy, as previously shown in penguin waddling . Higher Wl in PWS is due to the greater lateral displacements of CM (∼35%) in PWS than in OB. This is indirect evidence that PWS individuals take wider steps as compared to OB subjects, who in turn have a wider-based gait than normal body mass individuals [4, 11]. Increased lateral CM displacement in PWS may be explained by their greater postural instability as compared to non-syndromic obese individuals . It has been suggested that the increased step width may represent an active strategy to increase dynamic balance during walking or may simple reflect the greater girth of thigh and lower limb in this population . In PWS, increased fat mass and decreased lean mass in all body regions and especially in the lower limbs as compared to OB  may also be implicated in greater lateral CM displacements while walking at Ss. Lateral displacements were significantly and positively correlated to Rstep/Fr, suggesting that “waddling” gait is mainly involved in improving energy recovery through the pendulum mechanism in PWS.
Although the body is capable of adapting to the increased mass and of optimizing walking efficiency, a slower walking speed may hinder a range of daily activities, inducing a certain degree of disability in PWS children and adults. Previous research  points to body mass reduction and gait training as means to elicit an effective ambulatory pattern and minimize disability in PWS adults and several studies have shown that physical training in PWS individuals confers beneficial effects [see for a review ]. Treadmill walking at a faster speed than Ss with a real-time feedback of CM  and with PWS individuals asked to reduce lateral CM displacements may represent an important part of a multicomponent training program including walking, postural, and lower limb strength exercises associated with diet. In fact, this type of treadmill walking training may be effective to increase Ss and Wk through an enhanced Wf and decreased Wl to preserve the improved Rstep that characterizes gait in PWS individuals.
In conclusion, the results of this study show that, at slower Ss, individuals with PWS walk with similar Wext and Rstep and higher Rstep/Fr compared to matched nonsyndromic obese subjects. Moreover, Rstep/Fr was correlated with the age of obesity onset and duration. Therefore, individuals with PWS seem to improve pendular energy transduction (i.e., mechanical plasticity) using the increased Wv and Wl to optimize the relative magnitude of kinetic and potential energy during walking at slower Ss (i.e., behavioral adaptation). Precocious and chronic adaptation to loading appears to be involved in the specific gait alterations in PWS by enhancing the pendulum-like mechanism at spontaneous walking speeds.