Mechanical Advantages and Disadvantages of a Lower Limb Using Forefoot to Heel Strike Landing ^†

Abstract

A previous study reported that habitually barefoot Kenyan distance runners tend to use a mid-foot strike or a forefoot-heel strike (FHS). Current findings indicate FHS helps enhance Kenyans’ running performance. However, no study has investigated how FHS modulates leg stiffness (k_leg) and altered running velocity with changes in k_leg. Because vertical displacement of the centre of mass and k_leg during hopping are applicable to the running process, this study investigated how FHS affects k_leg and hopping frequency (f_hopping) during hopping. Subjects hopped at 2.2 Hz with normal hopping (NH-2.2Hz) and at a comfortable frequency with FHS (FHS-CF). According to each subject’s comfortable frequency at FHS-CF, they were divided into higher (HG, 2.49 ± 0.11 Hz) and lower (LG, 2.16 ± 0.19 Hz) groups. With FHS-CF, the flight duration in HG was significantly shorter than that in LG. k_leg in HG was greater than that in LG. Negative work in the first half of the stance phase and positive work in the second half of the stance phase at all three joints were smaller in HG than in LG. The touchdown angle was larger and angular displacements at the joints were smaller in HG than in LG. The findings indicate that when hoppers used FHS, they increased their preferred f_hopping by stiffening their leg joints during the stance phase and jumping with a lower height than in normal hopping; additionally, it is important to increase the touchdown joint angle for a stiffened joint.

1. Introduction

A recent anthropometrical study reports that Kenyan distance runners who live in the Rift Valley Province and habitually run barefoot tend to use either a forefoot-heel strike (FHS) or a mid-foot strike, while habitually shod runners use a heel–toe strike (HTS) [1]. This indicates that habitual differences in footwear influence foot-strike skills, FHS is used to dissipate impact force during barefoot running, and Kenyan habitual barefoot runners change from HTS to FHS to attain high-speed running. Consequently FHS may be a reason to achieve high-speed running. However, although previous studies [2] investigated the relationship between the foot strike patterns and waveforms of the ground reaction force (GRF), there is no study investigating how FHS affects kinetic variables in the whole leg during running or running velocities obtained from the centre of mass of the body (COM).

Previous studies investigated the relationship between running velocities and kinetic variables using a spring–mass model using body mass on a linear leg spring [3,4], with leg stiffness (k_leg) representing the relationship between internal forces, such as muscular force, and external forces, such as GRF. The optimal k_leg determines preferred hopping frequencies (f_hopping) as 2.2 Hz [5] and stride frequencies during running as 1.16 steps/sec [6]. When both frequencies increase by 65%, k_leg for both increases twofold [6], indicating that findings obtained for hopping are applicable to running. The relationship between k_leg and f_hopping is also reported in other studies [5,7]. However, there is no study investigating how k_leg is modulated during FHS-hopping and consequently, how it affects the preferred f_hopping. This study aimed to investigate how hoppers change their preferred f_hopping with changes in k_leg when using FHS.

Previous studies have investigated the relationship between k_leg and f_hopping under normal hopping (NH) in which the foot is plantarflexed at touchdown [5], showing that k_leg increases with increased ankle stiffness (k_ankle) and joint stiffness (k_joint) increases with increased touchdown joint angle [7,8]. k_leg during hopping while wearing a spring-loaded ankle-foot orthosis with plantarflexion resistance is similar to that obtained while wearing the orthosis with no resistance; moreover, knee joint stiffness (k_knee) increased to compensate for the decrease in biological k_ankle due to the plantar flexion resistance [9]. Furthermore, since the displacements of leg spring and joint decrease as k_leg and k_joint increase, there is negative and positive work at each joint (W_joint⁻ and W_joint⁺, respectively), calculated by integrating the negative and positive periods of instantaneous joint power over each landing, indicating the work in each joint (W_joint) indirectly considered k_joint in each joint. This study will provide several interesting findings that differ from the previous studies because foot orientation in FHS is more dorsiflexed than in NH. Therefore, in the present study, it was hypothesized (1) that k_leg will increase with increases in preferred f_hopping and (2) that this would be due to increased and decreased k_knee and mechanical work to compensate for decreases and increases in k_ankle and mechanical work, respectively, during FHS hopping.

2. Methods

2.1. Subjects and Measurements

Thirteen healthy subjects (seven men, six women, mean age 22.1 ± 1.4 [standard deviation, SD] years) gave informed consent prior to participation according to our institutional review board. One male subject was excluded due to an inability to match f_hopping to the metronome beat. Subjects were instructed to perform NH and FHS hopping tasks with their arms akimbo on a force platform (AMTI, Watertown, MA, USA), which measures GRF and ground reaction moments, and matching the metronome beat set at 2.2 Hz in NH, which is considered as comfort hopping frequency in NH [4,7] (NH-2.2 Hz). Further, during FHS hopping, each subject was instructed to hop at a comfortable frequency (FHS-CF). The duration of the hopping tasks was 60 s; kinetic and kinematic data were measured from 10 to 15 s for data analysis. GRF and moments were sampled at 1000 Hz and stored in a PC via an Analog–Digital converter (Kyowa, Tokyo, Japan). GRF data were low pass filtered at 25 Hz using a fourth order Butterworth filter. Sagittal plane kinematics in right halves of lower limbs and the trunk were captured using a high-speed camera (120 fps, Photron, Tokyo, Japan). The kinematic data were synchronized with vertical GRF (Fz) higher than 20 N when the subject initially landed on the platform. Digitized reflective markers were mounted on the right halves of the subject’s body using digitization software [10].

2.2. Data Analysis and Statisitical Analysis

The digitized and transformed 2-D coordinates of each marker were used to calculate the centre of mass for each segment and COM by an anthropometric parameter and to estimate joint torque (τ_joint) using standard inverse dynamics [11]. To precisely calculate τ_joint and k_leg in each stance phase, GRF and kinematic data in each stance phase of hopping were extracted. k_leg and k_joint were estimated by the slope of the curve between the vertical displacement of COM and Fz and the curve between angular displacement and torque in each joint during the first half of the stance phase (left hand of Figure 1). k_leg was calculated using the following equation:

k_leg = Fz_max/ΔCOM_max

(1)

where Fz_max indicates the maximum value of Fz and ΔCOM_max indicates the maximum value of vertical displacements in COM. k_joint was calculated using the following equation:

k_joint = Δτ_joint/Δθ_joint

(2)

where Δτ_joint indicates the maximum value of extensor torque and Δθ_joint indicates the angular displacement in each joint. Kinetic variables, such as k_leg, Fz and τ_joint, were normalized by dividing by the subject’s body mass, thus removing the influence of body mass on the kinetic variables.

As mentioned in the introduction, the work in each joint (W_joint) indirectly considered the stiffness in each joint. The work was calculated using the following equation:

$$W_{joint}=\underset{T1}{\overset{T2}{{\displaystyle \int }}}{\tau }_{joint}\times {\omega }_{joint} dt$$

(3)

where ω_joint indicates the angular velocity of a joint and T1 and T2 indicate intervals of integrating joint power. τ_joint in the three joints exerted extensor torque, while ω_joint showed flexor and extensor direction in the first and second periods, respectively, of the stance phase. Negative and positive powers were obtained in the first and second halves of the stance phase. Therefore, negative and positive works (W_joint⁻ and W_joint⁺, respectively) were obtained in each joint by integrating the negative and positive powers, respectively.

One-way analysis of variables with repeated measures with the two hopping tasks was applied to test for significant difference for each individual variable, with an α of 0.05. Based on each subject’s preferred hopping frequency in FHS-CF, subjects were equally divided into higher and lower groups (see details in results); the Friedman test was applied to compare the hopping trials and the groups. Significant main effects were followed by the Mann–Whitney test.

3. Results

Table 1. Individual mean and SD values of temporal parameters during FHS-CF.

Subject Number	1	3	4	5	6	7	8	9	10	11	12	13
f(hops/sec)	2.479 ± 0.265	2.157 ± 0.075	2.169 ± 0.057	2.485 ± 0.089	2.156 ± 0.179	2.636 ± 0.167	2.338 ± 0.055	1.906 ± 0.066	2.401 ± 0.067	2.557 ± 0.111	2.031 ± 0.078	2.310 ± 0.161
Group	H	L	L	H	L	H	H	L	H	H	L	L

‘f’ means hopping frequency, ‘H’ and ‘L’ mean that hoppers hopped with frequencies above and below 2.2 hops/sec, respectively.

shows kinematic and kinetic variables including preferred f_hopping and k_leg in FHS-CF. Since there were individual differences in the preferred f_hopping, subjects were divided into a higher frequency group (Higher GP), which was > 2.2 Hz as determined by the mean – SD of the frequency, and lower frequency group (Lower GP), with a mean – SD values < 2.2 Hz. Consequently, as shown in

Table 2. Kinematics and kinetics summary obtained from Higher and Lower groups.

	NH-2.2 Hz				FHS-CF
Variables	Higher Group		Lower Group		Higher Group		Lower Group
Hopping frequency (hops/sec)					2.49 ± 0.15		2.16 ± 0.13
1st Peak Fz (N/BW) **	0 ± 0.00		0 ± 0.00		0.81 ± 1.38		1.33 ± 1.49
2nd Peak Fz (N/BW)	3.24 ± 0.29		3.44 ± 0.47		3.09 ± 0.38		3.24 ± 0.66	*
Contact duration (sec)	0.30 ± 0.03		0.29 ± 0.03		0.28 ± 0.03		0.28 ± 0.04
Aerial times (sec)	0.16 ± 0.03		0.18 ± 0.03	*	0.13 ± 0.04	1	0.20 ± 0.05	*
COM downward displacement (m)	0.13 ± 0.01		0.12 ± 0.02		0.11 ± 0.01	1	0.13 ± 0.01	*
Ankle displacement (rad)	0.59 ± 0.10		0.57 ± 0.07		0.45 ± 0.08	1	0.54 ± 0.07	*
Knee displacement (rad)	0.42 ± 0.07		0.39 ± 0.09		0.36 ± 0.07	1	0.50 ± 0.08	1,*
Hip displacement (rad)	0.18 ± 0.05		0.16 ± 0.06		0.17 ± 0.06		0.25 ± 0.06
Ankle angle at touchdown (rad)	2.20 ± 0.12		2.16 ± 0.12		2.08 ± 0.09	1	2.06 ± 0.12
Knee angle at touchdown (rad)	2.79 ± 0.08	*	2.68 ± 0.12		2.78 ± 0.09	*	2.72 ± 0.13
Hip angle at touchdown (rad)	3.08 ± 0.13		3.00 ± 0.12		3.08 ± 0.13	*	2.99 ± 0.14

“1” means significant difference from NH-2.2 Hz in same group (p < 0.05). * an asterisk means that the value was significantly larger than the other group. BW means subjkect’s body weight, Fz means vetical ground reaction force. ** two asterisks mean that no statistical comparison was conducted because of a lower number of samples.

, while the frequency obtained from all subjects was 2.31 ± 0.11 Hz, the frequency in the Higher and Lower GPs was 2.49 ± 0.15 Hz and 2.19 ± 0.13 Hz, respectively. The contact duration for Higher GPs at FHS-CF was the same as that at NH-2.2Hz. In addition, the flight duration of Higher GP at FHS-CF was significantly shorter than that at NH-2.2 Hz. k_leg, k_ankle, and k_knee were also compared between Higher GP and Lower GP. In the Higher GP, k_leg in FHS-CF significantly increased compared to that at NH-2.2 Hz and that in FHS-CF in Lower GP (Figure 1). However, there were no significant changes in k_ankle or k_knee between differences in hopping task or groups. Figure 2 shows W_joint⁺ and W_joint⁻ at the ankle, knee, and hip joints. In Higher GP, although W_ankle⁺ and W_ankle⁻ in FHS-CF was significantly lower than at NH-2.2 Hz, no significant difference in the mechanical work between FHS-CF and NH-2.2 Hz was found for the other joints. In FHS-CF, both W_joint⁺ and W_joint⁻ were significantly lower in Higher GP than in Lower GP.

Table 2 shows the mean and SD value of the two peaks in Fz. At FHS-CF, the first peak of Fz at touchdown in Higher GP was smaller than that in Lower GP, although there were no significant differences in the peak between the groups. The second peak of Fz at mid-stance was significantly smaller in Higher GP than in Lower GP. In both Higher and Lower GPs, the touchdown angle at the ankle joint at FHS-CF was significantly smaller than that at NH-2.2 Hz. At FHS-CF, the touchdown angle at the knee and hip joints in Higher GP was significantly greater than that in Lower GP. For the Higher GP, angular displacements at the ankle and knee joints at FHS-CF were significantly decreased compared to that at NH-2.2 Hz. The displacement of FHS-CF obtained from Higher GP was significantly lower than that in Lower GP.

4. Discussion

The main findings of this study were that, based on the preferred hopping frequency f_hopping at FHS-CF, when subjects were divided into Higher GP and Lower GP, in the Higher GP, the f_hopping obtained at FHS-CF was higher than that obtained at NH-2.2 Hz. k_leg at FHS-CF was higher than that at NH-2.2Hz in higher GP, and at FHS-CF, k_leg in Higher GP was also lower than that in Lower GP. The results support the hypothesis of this study and correspond with previous studies stating leg stiffness k_leg increases with f_hopping [5,7]. While the previous studies reported that downward displacement of COM decreased and contact duration shortened as f_hopping increased with k_leg, the current study showed that although the displacement decreased, the flight duration also decreased. However, in Lower GP, the flight duration increased as the displacement increased. The facts indicate that hoppers are able to increase the f_hopping by decreasing the hopping height when using FHS.

When hoppers use a spring-loaded ankle-foot orthosis with plantar flexion resistance, their k_leg increased by increasing k_knee to compensate for the decreases in biological k_ankle due to the orthosis; consequently, f_hopping increased [3]. Hence, it was hypothesized that preferred f_hopping is enhanced by increasing k_knee. However, this hypothesis was rejected because, in Higher GP, k_knee did not vary in other hopping trials. This may be explained by a previous study which showed that k_knee increased by antagonistic activation between the plantar flexor, which is antagonistically activated against the spring for plantar flexor resistance, and the knee extensor [9]; in the current study, antagonistic activation may not have occurred because the muscular force in plantar flexion was decreased due to dorsiflexion movement that stretches the plantar flexor muscles and reciprocally deactivates them.

Furthermore, the W_joint⁺ and W_joint⁻ at the lower extremity that indirectly represents modulation of joint stiffness showed that, in FHS-CF, W_ankle⁺ and W_ankle⁻ decreased; however, work in Higher GP, with the exception of W_knee⁻, was smaller than that in Lower GP. The reductions in the W_joint were caused by the decreases in extensor torque and/or angular displacement at the joints. Therefore, subjects in Higher GP hopped with their leg joints stiffened during the stance phase. The findings not only suggest that FHS enables increased f_hopping with increasing k_leg by stiffening the ankle joint during the whole stance phase but also support the findings of previous studies that k_leg during hopping primarily depends on k_ankle [5].

In addition, the W_joint at the leg joints explains muscular activation and work at the leg extensor muscles across joints. Thus, the decreased or unchanged W_joint suggests the force for jumping exerted by leg extensor muscles is decreased. The 2nd peak of Fz occurred mid-stance during FHS-CF in Higher GP and was lower than that in Lower GP; indicating that the muscular force required for jumping exerted by subjects in Higher GP was lower than that in Lower GP. Meanwhile, in Lower GP at FHS-CF, the peak value of the impact force was larger, and furthermore, W_joint⁺ and W_joint⁻ were greater compared with Higher GP. Concerning the exerting force and leg work, when humans hop on damped surfaces that absorb impact force, positive work for exerting jumping force is increased, and thus the peak value of Fz is increased as damping coefficients increase [12]. The authors explained this was due to humans compensating for the absorbed impact force, essentially used for jumping, by increasing their positive work for exerting a jumping force. The findings showing increases in W_joint⁺ and W_joint⁻ at the leg joints in Lower GP at FHS-CF indicate it is difficult for subjects to increase their f_hopping because they absorb the impact force by softening their leg joints and then exerted the force for leg extension for jumping; thus, this is consistent with earlier studies. Hence, stiffening the leg joints to utilize the impact force for jumping is enhanced at the preferred f_hopping at FHS-CF.

The findings of this study may explain why distance runners that use FHS such as Kenyan runners are able to run with higher speed. We found that when subjects use FHS and stiffen their leg joint during the whole stance phase, it enables them to hop with a low jumping height, reducing W_joint of three leg joints and consequently, increase their preferred f_hopping. The findings are consistent with earlier studies investigating not only the higher stride frequency in Kenyan runners compared to others [13], but also that k_leg is increased with increases in stride frequency [6]. Therefore, Kenyan runners stiffen the leg joint and reduce W_joint during the stance phase.

In summary, when hoppers use FHS, a lower hopping height is needed to increase their preferred hopping frequency. To attain the low hopping height, it is necessary to stiffen the leg joint and exert less mechanical work during the stance phase, and the knee and hip joints are extended at touchdown. Furthermore, Kenyan runners run with a higher stride frequency by stiffening their leg joints during the stance phase.