Effects of simulated reduced gravity and walking speed on ankle, knee, and hip quasi-stiffness in overground walking.

Quasi-stiffness characterizes the dynamics of a joint in specific sections of stance-phase and is used in the design of wearable devices to assist walking. We sought to investigate the effect of simulated reduced gravity and walking speed on quasi-stiffness of the hip, knee, and ankle in overground walking. 12 participants walked at 0.4, 0.8, 1.2, and 1.6 m/s in 1, 0.76, 0.54, and 0.31 gravity. We defined 11 delimiting points in stance phase (4 each for the ankle and hip, 3 for the knee) and calculated the quasi-stiffness for 4 phases for both the hip and ankle, and 2 phases for the knee. The R2 value quantified the suitability of the quasi-stiffness models. We found gravity level had a significant effect on 6 phases of quasi-stiffness, while speed significantly affected the quasi-stiffness in 5 phases. We concluded that the intrinsic muscle-tendon unit stiffness was the biggest determinant of quasi-stiffness. Speed had a significant effect on the R2 of all phases of quasi-stiffness. Slow walking (0.4 m/s) was the least accurately modelled walking speed. Our findings showed adaptions in gait strategy when relative power and strength of the joints were increased in low gravity, which has implications for prosthesis and exoskeleton design.

Introduction

Quantifying the quasi-stiffness of the human lower limb joints during locomotion can provide insight to gait biomechanics and be valuable for the design of robotic exoskeletons and prostheses. Quasi-stiffness, sometimes referred to as dynamic stiffness, is a linear model of the relationship between joint moment and angle during particular phases of the gait cycle [1,2]. The joint is modelled as a torsional spring with the external or negative internal joint moment proportional to the joint angle. Past studies have quantified joint quasi-stiffness for the hip, knee, and ankle during human walking [2-6]. Quasi-stiffness during the power absorption phase of the biological joint can provide an indication of potential absorbed energy that may be recovered later in the gait cycle. Ankle quasi-stiffness has been the most investigated of the lower limb joints with findings showing the quasi-stiffness changes with gait speed, added mass, and bodyweight [5-8]. Studies have also shown changes in quasi-stiffness under external perturbations [9].

Joint quasi-stiffness during human walking has been useful in control systems of robotic exoskeletons, prostheses, and bipedal robots which mimic the normal biomechanical behaviour of the human lower limb [10-12]. A common control method for wearable robotics is to set the relative impedances (e.g. stiffness and damping) and equilibrium points of the mechanical joints for different phases of the gait cycle. Biological quasi-stiffness provides information on suitable robot impedances. This technique of finite state machine control allows for smooth walking assistance without directly coupling the user’s neural commands to the exoskeleton. For people who are unable to generate sufficient resistance to ground reaction forces, an exoskeleton/prosthesis with finite state machine controlled stiffness can provide appropriate resistance at a biological joint to prevent limb collapse during stance phase. Although joint quasi-stiffness is a simplified model of joint dynamics, it provides an approximation that has practical engineering applications.

Study of joint quasi-stiffness during different gait conditions may also provide insight into human neural control [13,14]. Joint quasi-stiffness is determined by the state of all passive and active tissues that cross the joint [15,16]. The biggest factor influencing joint quasi-stiffness is the stiffness of the muscle-tendon units actuating the joint. Muscle-tendon stiffness is comprised of the stiffness of the tendon and the stiffness of the muscles which attach to the tendon [17]. Joint quasi-stiffness should theoretically increase with muscle force and with increases in tendon stiffness that occur when a tendon is stretched. The former is an active mechanism and the latter a passive mechanism, but both are related to muscle force. A biological question of interest is if the preferred joint quasi-stiffness is dependent on muscle force. Although past studies have been able to examine quasi-stiffness over a small range of joint torques via changing walking speed and added mass, they have not studied a large range of peak torque values [7,18,19].

Used as a gait rehabilitation therapy, simulated reduced gravity reduces the joint torques and muscle forces required to produce gait [20,21]. One technique to simulate reduced gravity is to apply a constant upwards force to the torso with a harness, counteracting gravity without altering body mass [22]. The effect of gravity on the arms and legs when not in contact with the ground is unchanged. The reduced ground reaction forces from simulated reduced gravity can be very useful for gait rehabilitation, allowing people to practice walking if they normally struggle to walk independently. Supporting bodyweight contributes a large portion of the energetic cost of walking [22-25]. Reducing the effective bodyweight also decreases joint contact forces and net muscle moments during walking, essentially making it easier to walk [20,21,26]. In rehabilitation, simulated reduced gravity is often referred to as bodyweight support and has been used for gait rehabilitation of people with spinal cord injury, post-stroke hemiparesis, traumatic leg injury, and other neurological disabilities [27-32]. Practicing walking in simulated reduced gravity can improve muscle strength, limb and muscle coordination, and bone density [33,34]. To the best of our knowledge, there has been no investigation of joint quasi-stiffness in clinical populations in normal or reduced gravity. To parse out the effects and interactions of gravity level, walking speed, and underlying pathological physiology on quasi-stiffness, we first need an understanding of the relationship between gravity level, walking speed, and joint quasi-stiffness in a healthy population.

Biomechanists use simulated reduced gravity to test hypotheses about how gravity and bodyweight affect human movement. Past studies have shown that simulated reduced gravity alters the kinematic, kinetic, and electromyographic components of gait in able-bodied humans [20]. For example, the walk to run transition speed decreases, stance phase duration decreases, energetic cost decreases, joint contact forces and net muscle moments decrease, and electromyographic activity of some leg muscles decrease in stance phase [24,35-42]. These papers have made it clear that the force due to gravity acting on the torso plays a large role in determining how humans control the motion of their bodies during locomotion.

The purpose of this study was to understand the effect of simulated reduced gravity on ankle, knee, and hip quasi-stiffness walking overground at a range of speeds. Simulated reduced gravity will reduce joint moments during the stance phase of walking. If there is a relationship between joint moment and quasi-stiffness, it should be noticeable with a three-fold range of gravity levels. We hypothesized that joint quasi-stiffness would decrease with simulated reduced gravity as it is likely dependent on the intrinsic muscle-tendon unit stiffness which scales with muscle and tendon force [15,43-45].

Methods

Data collection

12 able bodied individuals with no history of neuromuscular conditions participated in the study (6 female, 26±4 years old, body mass 70±8 kg, height 1.74±0.07 m, mean±s.d.). Participant demographics are detailed in S1 Table. Each participant signed an informed consent form approved by the University of Florida’s institutional review board. The bodyweight support system used in this study (described in detail in [46]) uses constant force springs to provide a constant upwards force on the participant via a harness. Fluctuations in support force were less than ±5% bodyweight at normal gravity (1 G). Participants wore the harness and walked over an 8m overground walkway at 0.4, 0.8, 1.2, and 1.6 m/s in 1, 0.76, 0.54, and 0.31 gravity (G).

The walkway had 3 embedded force plates (AMTI, Watertown, MA, USA) to measure ground reaction forces at 1000 Hz and we used a visual motion capture system (Optitrack, Corvallis, OR, USA) to measure joint kinematics at 100 Hz. We palpated for and placed 22 reflective markers on the following anatomical landmarks: Ilium anterior superior, ilium posterior superior, greater trochanter of the femur, femoral lateral epicondyle, femoral medial epicondyle, fibula apex of the lateral malleolus, tibia apex of medial malleolus, the posterior of the calcaneus, heads of the 1st and 5th metatarsals, and the hallux. In addition to the anatomical markers, participants wore rigid bodies with 4 reflective markers on each shank and thigh. To control for walking speed, we used infra-red timing gates set-up before and after the force plates.

Participants completed all speed conditions for a level of simulated reduced gravity, rested for 5–15 minutes, then moved onto walking at the next level of reduced gravity. For each participant, we randomized the order of gravity levels and the order of the speed conditions for each simulated gravity level. To ensure the subjects’ biomechanics adapted to simulated reduced gravity, participants practiced walking for 3 minutes at each gravity level before data were collected. Participants received no specific instructions on how to walk in reduced gravity, although we did request that they do their best to not include a flight phase in the highest walking speed and lowest gravity condition. We collected kinematic and kinetic data for 4 trials wherein the participant’s right foot struck a single force plate, and the left foot landed on a subsequent force plate or straddled the remaining two force plates.

Data processing

We attained joint angles and net internal moments from Visual 3D (C-Motion, Germantown, MD, USA) and determined quasi-stiffness with custom MATLAB (Mathworks, Natick, MA, USA) scripts. We first filtered motion capture and force plate data with a zero lag, 6 Hz lowpass 4th order Butterworth filter and then cut the data to stance phase (right foot initial contact to right foot toe off). An 18 N threshold on the vertical ground reaction force identified initial contact and toe off. To build our anthropometric model for joint angle and moment calculations in Visual3D, we used default segment definitions and estimated the hip joint location with the Coda pelvis model [47]. To facilitate averaging across participants, we normalized the net internal moment to body mass. We will refer to normalized joint internal net moment as joint moment in this paper.

We defined and calculated 4 phases of quasi-stiffness for both the hip and ankle, and 2 phases of quasi-stiffness for the knee (Figs 1–3 and Table 1). We chose phases of quasi-stiffness delimited by points of interest (Table 2) with reference to previous studies [1-6,17]. We calculated the quasi-stiffness as the slope between joint angle (degrees) and normalized joint internal net moment (Nm/kg).

Fig 1

Ankle angle, moment, and moment-angle relationships during stance phase overlaid with points of interest and phases of quasi-stiffness.

The smaller subplots on the left show ankle angle and moment during stance phase. The dashed vertical lines represent the timings of each point of interest, while the open circles identify the point of interest itself. The phases of quasi-stiffness are identified at the bottom of these plots, with the arrows indicating their onset and termination. The large, right figure shows the moment-angle relationship with the quasi-stiffness overlayed as dashed lines and the points of interests as “+”. Data for visualization were normalized to 60 data points and averaged across all participants walking in normal gravity at 1.6 m/s. Direction of internal joint moment and joint angle are indicated with arrows on the rightmost plot.

Fig 3

Hip angle, moment, and moment-angle relationships during stance phase overlaid with points of interest and phases of quasi-stiffness.

The smaller subplots on the left show hip angle and moment during stance phase. The dashed vertical lines represent the timings of each point of interest, while the open circles identify the point of interest itself. The phases of quasi-stiffness are identified at the bottom of these plots, with the arrows indicating their onset and termination. The large, right figure shows the moment-angle relationship with the quasi-stiffness overlayed as dashed lines and the points of interests as “+”. Data for visualization were normalized to 60 data points and averaged across all participants walking in normal gravity at 1.6 m/s. Direction of internal joint moment and joint angle are indicated with arrows on the rightmost plot.

Table 1

All quasi-stiffness phases, their acronym, and the points of interest between which they were found.

	Quasi-Stiffness		Point of Interest
			Starting	Ending
Ankle	Early dorsi-flexion	KAnD1	P1 An	P2 An
	Late dorsi-flexion	KAnD2	P2 An	P3 An
	Total dorsi-flexion	KAnDF	P1 An	P3 An
	Plantar-flexion	KAnPF	P3 An	P4 An
Knee	Knee flexion	KKnF	P1 Kn	P2 Kn
	Knee extension	KKnE	P2 Kn	P3 Kn
Hip	Early hip extension	KHiE1	P1 Hi	P2 Hi
	Late hip extension	KHiE2	P2 Hi	P3 Hi
	Total hip extension	KHiE	P1 Hi	P3 Hi
	Hip flexion	KHiF	P3 Hi	P4 Hi

Table 2

All points of interest for finding quasi-stiffness phases and their description.

Point of interest	Descriptor
P1 An	Minimum local ankle plantarflexion moment (in early stance)
P2 An	Temporal mid-point of stance
P3 An	Maximum plantar flexion moment
P4 An	Toe-off
P1 Kn	Local minimum knee extension moment (in early stance)
P2 Kn	Maximum knee extension moment
P3 Kn	Local minimum knee extension moment (after P2Kn)
P1 Hi	Local minimum hip flexion moment (in early stance)
P2 Hi	Transition of hip moment from extension to flexion
P3 Hi	Local maximum hip flexion moment (in late stance)
P4 Hi	Local minimum hip flexion moment before toe-off (if no local minimum, toe-off was used)

Ankle

The 4 points of interest for the ankle were the: minimum local ankle plantarflexion moment at the start of stance phase (P1), temporal mid-point of stance (P2), maximum plantar flexion moment (P3), and toe-off (P4). At normal (1.2 m/s) to fast (1.6 m/s) speeds, the mid-point of stance typically coincided with the low point of the “m”-shaped vertical ground reaction force and the point where the anterior-posterior force crossed from positive to negative. The quasi-stiffness phases defined by the consecutive points of interest were: early dorsi-flexion (KAnD1) from P1 to P2, late dorsi-flexion (KAnD2) from P2 to P3, and plantar-flexion (KAnPF) from P3 to P4. We defined an additional ankle quasi-stiffness phase as total dorsi-flexion (KAnDF) which we found between P1 and P3. We did not calculate quasi-stiffness in the early and late dorsi-flexion phases if the temporal mid-point of stance (P2) occurred after the point of maximum plantar-flexion moment (P3). If the duration between P2 and P3 was less than 0.05 s, we did not calculate quasi-stiffness of the late dorsi-flexion phase for that trial. Fig 1 visualizes the points of interest and quasi-stiffness phases for the ankle.

Knee

For the knee, we defined the 3 points of interest as the: local minimum knee extension moment at the beginning of stance (P1), maximum knee extension moment (P2), and local minimum knee extension moment occurring after P2 (P3). We calculated the quasi-stiffness phases of knee flexion (KKnF) and knee extension (KKnE) between P1 and P2, and P2 and P3 respectively. The points of interest and quasi-stiffness phases of the knee are displayed in Fig 2.

Fig 2

Knee angle, moment, and moment-angle relationships during stance phase overlaid with points of interest and phases of quasi-stiffness.

The smaller subplots on the left show knee angle and moment during stance phase. The dashed vertical lines represent the timings of each point of interest, while the open circles identify the point of interest itself. The phases of quasi-stiffness are identified at the bottom of these plots, with the arrows indicating their onset and termination. The large, right figure shows the moment-angle relationship with the quasi-stiffness overlayed as dashed lines and the points of interests as “+”. Data for visualization were normalized to 60 data points and averaged across all participants walking in normal gravity at 1.6 m/s. Direction of internal joint moment and joint angle are indicated with arrows on the rightmost plot.

Hip

The hip moment-angle relationship had 4 points of interest: local minimum hip flexion moment at the beginning of stance (P1), when the hip moment transitioned from extension to flexion (P2), local maximum hip flexion moment occurring near the end of stance (P3), and local minimum hip flexion moment before toe-off, or if there was no local minimum, toe-off (P4). At normal to fast speeds (1.2 & 1.6 m/s) in normal gravity, the transition of hip moment from extension to flexion coincided with a local maximum hip flexion moment before the temporal mid-point of stance. We defined the 3 consecutive quasi-stiffness phases of the hip as: early extension (KHiE1) between P1 and P2, late extension (KHiE2) between P2 and P3, and flexion (KHiF) between P3 and P4. Between P1 and P3, we defined a 4th phase of quasi-stiffness (KHiE) encapsulating the total phase of hip extension. In trials where the hip moment did not transition from extension to flexion, we did not calculate KHiE1 and KHiE2. If the time between 2 consecutive points of interest was less than 0.05 seconds, we did not calculate quasi-stiffness for that phase of gait. Fig 3 illustrates the points of interest and quasi-stiffness phases of the hip.

Calculating quasi-stiffness

We found the 11 points of interest for each walking trial, then calculated the stiffness of each quasi-stiffness phase using a least squares linear model. For each walking trial, we applied the linear model as a function of joint angle (i.e. predicted joint moment from given joint angles). To determine the fit of the model for each phase of quasi-stiffness in each trial, we calculated the R2 value. We also calculated the duration of each phase of quasi-stiffness as a percentage of the total stance time. Finally, we averaged quasi-stiffness values, R2, and phase durations across each walking trial in a condition for every participant, and then averaged across participants.

Statistics

To evaluate if speed and gravity had a significant effect on quasi-stiffness and quality of fit, we used a linear mixed model with simulated gravity level and speed as repeated factors, and participants as a random factor. We performed the statistical tests with SPSS (IBM Corp. Armonk, NY, USA). Due to data missing in our final dataset, a mixed linear model was deemed more suitable than an ANOVA. We used the Benjamini-Hochberg technique to make post-hoc comparisons (significance value of 0.05) [48,49].

Results

The moment-angle loops for the hip, knee, and ankle changed shape with both level of reduced gravity and speed (Fig 4). In some walking conditions, particularly at the slower speeds (0.4 & 0.8 m/s) or high levels of reduced gravity, certain points of interest were not present in the moment-angle relationship. For example, 2 participants exhibited no hip flexion moment during the stance phase of walking in 0.31 G at 0.4 m/s, so P2 did not occur. Furthermore, we did not use the data of 2 participants in the 0.31 G, 1.6 m/s condition as they were unable to walk without a flight phase. Additionally, data were lost for 1 participant at normal gravity, 1.2 m/s walking. S2 Table indicates the number of participants data from which we calculated each quasi-stiffness phase for every walking condition. Table 3 reports the significance of gravity level and speed on quasi-stiffness values and quality of the fit from the linear mixed model. We list the mean quasi-stiffness and R2 values in S3 and S4 Tables respectively.

Fig 4

Moment-angle loops in stance phase for the hip, knee, and ankle walking in 1, 0.76, 0.54, and 0.31 G at 0.4, 0.8, 1.2, and 1.6 m/s.

Data for visualization were normalized to 60 data points and averaged across all participants in each condition. Every x-axis displays joint angle of the respective joint.

Table 3

Post-hoc significance of gravity level and speed on quasi-stiffness and fits.

Joint	Quasi-stiffness	P value		Quality of fit	P value
		Gravity	Speed		Gravity	Speed
Ankle	KAnD1	>0.99	>0.99	R2 of KAnD1	0.741	<0.001*
	KAnD2	<0.001*	>0.99	R2 of KAnD2	<0.001*	<0.001*
	KAnDF	<0.001*	>0.99	R2 of KAnDF	<0.001*	<0.001*
	KAnPF	<0.001*	<0.001*	R2 of KAnPF	>0.99	<0.001*
Knee	KKnF	<0.001*	<0.001*	R2 of KKnF	>0.99	<0.001*
	KKnE	>0.99	<0.001*	R2 of KKnE	0.837	<0.001*
Hip	KHiE1	0.004*	<0.001*	R2 of KHiE1	>0.99	<0.001*
	KHiE2	>0.99	>0.99	R2 of KHiE2	0.030*	0.020*
	KHiE	>0.99	>0.99	R2 of KHiE	>0.99	<0.001*
	KHiF	0.001*	<0.001*	R2 of KHiF	0.332	<0.001*

Significant results are bolded and denoted with an asterisk.

Ankle

Ankle quasi-stiffness tended to decrease with reduced gravity level (Fig 5). Level of simulated gravity significantly reduced quasi-stiffness of late dorsi-flexion (KAnD2), total dorsiflexion (KAnDF), and plantar-flexion (KAnPF) (all p < 0.001). The quality of fit for KAnD2 and KAnDF was significantly reduced with gravity level (p<0.001). We found a significant effect of speed on KAnPF (p<0.001) and walking speed was a significant factor for the quality of fit for all 4 linear models of stiffness (all p<0.001). The effect of speed on fit was not consistent across quasi-stiffness phases and gravity levels. Gravity level and speed appeared to impact the duration spent in each phase of quasi-stiffness. Duration of late dorsi-flexion and all dorsi-flexion tended to decrease with reduced gravity and increased speed. Plantar-flexion duration tended to increase with reduced gravity and slower speeds.

Fig 5

Quasi-stiffness of the ankle in stance phase at different levels of simulated reduced gravity and speeds.

Top row shows stiffness values, middle row is the quality of fit of the linear quasi-stiffness model, and bottom row is the duration of the quasi-stiffness phase as percent of stance phase. Each column of plots is a different quasi-stiffness phase for the ankle: KAnD1 is early dorsi-flexion, KAnD2 is Ankle late dorsi-flexion, KAnDF is overall Ankle dorsi-flexion, and KAnPF is Ankle plantar-flexion. The error bars represent standard deviation.

Knee

Simulated reduced gravity significantly decreased the quasi-stiffness of the knee in the flexion phase (KKnF) across speeds (p<0.001), but had no significant effect on quasi-stiffness in the knee extension phase (KKnF) (p>0.99) (Fig 6). Gravity level had no significant effect on the R2 fits of the models. Duration of both flexion and extension stages tended to decrease with reduced gravity. Speed had a significant effect on the quasi-stiffness values and fits for knee flexion and extension (all p<0.001). There were no instances where P1, P2, or P3 could not be identified.

Fig 6

Quasi-stiffness of the knee in stance phase at different levels of simulated reduced gravity and speeds.

Top row shows stiffness values, middle row is the quality of fit of the linear quasi-stiffness model, and bottom row is the duration of the quasi-stiffness phase as percent of stance phase. Each column of plots is a different quasi-stiffness phase for the knee: KKnF is flexion, and KKnE is knee extension. The error bars show standard deviation.

Hip

Reduced gravity significantly reduced the quasi-stiffness of the hip in the early extension (KHiE1) and the flexion stage (KHiF) (p = 0.004 and p<0.001 respectively) (Fig 7). Reduced gravity also significantly impacted the fit of the quasi-stiffness model in the late phase of hip extension (p = 0.03). Increased walking speed significantly increased KHiE1 and KHiF (all p<0.001). The fit of the linear model was significantly affected by walking speed for all 4 phases of quasi-stiffness (p<0.001 for R2 of KHiE1, KHiF, and KHiE. p = 0.02 for R2 of KHiE2). Percent of stance spent in each quasi-stiffness phase appeared to be affected by both gravity and speed. The proportion of time spent in the early hip extension phase increased with reduced gravity, while the late phase of hip extension was decreased. Reduced gravity also decreased the proportion of time spent in the hip flexion phase. Faster walking speeds tended to increase time spent in the late phase of hip extension and in the phase of hip flexion. The quasi-stiffness of hip flexion was often not calculable at 0.31 G as either i) the point of maximum hip flexion moment (P3) occurred at toe-off (P4), or ii) the time between maximum hip flexion moment (P3) and local minimum flexion moment (P4) was less than 0.05 s.

Fig 7

Quasi-stiffness of the hip in stance phase at different levels of simulated reduced gravity and speeds.

Top row shows stiffness values, middle row is the quality of fit of the linear quasi-stiffness model, and bottom row is the duration of the quasi-stiffness phase as percent of stance phase. Each column of plots is a different quasi-stiffness phase for the hip: KHiE1 is early hip extension, KHiE2 is hip late extension, KHiE is overall hip extension, and KHiF is knee flexion. The error bars illustrate standard deviation.

Discussion

Simulated reduced gravity substantially modified joint moment-angle relationships in stance phase, prompting changes in quasi-stiffness values and linearity. In agreement with our hypothesis, artificially reducing gravity generally decreased the quasi-stiffness of the hip, knee, and ankle. Speed was a significant factor in determining the R2 fit of the linear quasi-stiffness models, while gravity level had a smaller effect on R2. Our results confirmed previous research which found speed to cause morphological changes in the moment-angle relationship of the ankle [7] and to be a predictor of stiffness [3-5].

Biomechanical principles underlying joint quasi-stiffness

Joint quasi-stiffness tended to decrease with gravity level, which is in agreement with the supposition that quasi-stiffness is modulated by the inherent properties of the muscle-tendon units. Simulated reduced gravity reduced the load through the joints and moments about the leg joints, and reduced the muscle activation amplitudes during stance [21]. At lower muscle forces, there is less stretch of the tendon which moves the tendon stiffness into the short range stiffness known as the toe region. The toe region occurs at low levels of tendon stretch and incurs a smaller stiffness than in the subsequent linear phase of tendon length-force relationship. However, an alternative possibility is that subjects actively adjusted their muscle activation patterns to achieve close to normal joint displacements at reduced gravity. This approach would also produce a reduced joint quasi-stiffness at reduced gravity, completely independent of underlying muscle-tendon unit mechanical properties. Future research could use ultrasound imaging [45] to provide a better indication of intrinsic muscle-tendon displacements and stiffnesses during walking under simulated reduced gravity.

Our implementation of a rigid foot model may have led to an underestimation of the true ankle quasi-stiffness. We modelled the foot as a single rigid body, assuming no rotation or translation within the joints of the foot. Investigation of ankle quasi-stiffness in hopping found that modelling the ankle and foot separately, allowing for deformation of the arch of the foot, resulted in a substantially higher ankle quasi-stiffness than when the foot was modelled as a single rigid body [50].

Ankle quasi-stiffness and selection of points of interest

Ankle quasi-stiffness decreased with reduced gravity but exhibited large variations at extreme speeds. The variation in KAnD1 was very large during slow walking (0.4 m/s) although the variation decreased with reduced gravity. The individual trial data showed substantial variation in angle-moment loops in 0.4 m/s walking both within and between participants. This is reflected in large variations across bodyweight conditions for the R2 fit and percent of stance spent in early dorsiflexion. We determined quasi-stiffness to be a good model for early-dorsiflexion (KAnD1) and plantarflexion (KAnPF) in all conditions (R2>0.74 and R2>0.79 respectively). Our statistical results confirm that gravity level is a greater predictor of ankle quasi-stiffness value, but that across quasi-stiffness phases, speed is the most influential factor for R2 fit.

Quasi-stiffness provided an acceptable approximation of the moment-angle relationship in late-dorsiflexion (KAnD2) and total dorsiflexion (KAnDF) phases, but the quality of fit was decreased with reduced gravity and faster walking speeds (R2~ = 0.5 at 1.6 m/s for KAnD2 and KAnDF in 0.55G and 0.31 G respectively). The poor linearity of the late and total dorsiflexion phases at 1.6 m/s (and 1.2 m/s to a lesser extent) was related to the peak plantarflexion moment occurring after peak dorsiflexion angle. In normal gravity walking, the ankle angle continued to increase in dorsiflexion until the peak plantarflexion moment was reached, at which point the ankle dorsiflexion angle began to decrease. In fast and normal walking (1.6 & 1.2 m/s), particularly at low gravity, the moment-angle loop changed direction, with the ankle dorsiflexion angle decreasing before peak plantarflexion moment occurred. Therefore, the late dorsiflexion and total dorsiflexion phases exhibited non-linear behaviour and were not closely modelled by a linear model of quasi-stiffness.

We defined phases of quasi-stiffness and delimiting points of interest with reference to past literature and consideration of changes in moment-angle relationship across speeds and gravity levels. Previous studies used 4 points of interest to examine ankle quasi-stiffness in 3 distinct and approximately linear phases: early dorsiflexion, late dorsiflexion, and plantarflexion. The plantarflexion moment above a threshold [6,51,52], and minimum dorsiflexion angle [5] were used in separate studies to define point P1. We chose to use the minimum plantarflexion moment as the ankle angle profile changed substantially with gravity. In some low gravity conditions, the minimum dorsiflexion angle occurred close to the temporal mid-point of stance and no local minimum existed close to the beginning of stance. Although minimum ankle angle could have been a more suitable P1 at normal-fast walking speeds (1.2 & 1.6 m/s) in normal gravity, the point of minimum ankle plantarflexion moment was much more robust at capturing the onset of the linear early dorsiflexion phase of the ankle across all speeds and levels of simulated gravity. Our findings agreed with previous studies that determined P3 and P4 were suitably defined by maximum plantarflexion moment and toe-off respectively [5,7,19].

Whereas our definitions of P1, P3, and P4 were shared with previous works, we found that previously established definitions of P2 were not suitable due to the large variety of morphologies in moment-angle relationships across gravity and speed levels. Shamaei et al. and Krupenevich et al. identified the point of change between early and late dorsiflexion as ~30% of the gait cycle [5,17]. Crenna et al. used a 1.7x increase in the incremental ratio between moment and angle (the local slope of the relationship) to identify the transition between early and late dorsiflexion [6]. We initially considered the local minimum of vertical ground reaction force to determine P2 but found no local minimum in slow walking (0.4 m/s) and in medium walking (0.8 m/s) with high levels of reduced gravity. The wide range of moment-angle relationships meant that there was not an obvious change in slope or quasi-stiffness during the dorsiflexion stage for some walking conditions. For the reasons stated prior, we chose to define the transition between early and late dorsiflexion as the temporal mid-point (50%) of stance-phase. At normal and fast walking speeds (1.2 & 1.6 m/s) in gravity levels close to normal, the mid-point of stance coincided with the local minimum ground reaction force and visual change in moment-angle relationship. At slow-medium speeds (0.4 & 0.8 m/s) and medium levels of gravity, the mid-point of stance was able to consistently partition the dorsi-flexion phase. At low gravity and slow-medium speeds (0.4 & 0.8 m/s), the temporal mid-point of stance occasionally occurred very close to or after the peak moment. In these circumstances, initial and/or later dorsiflexion quasi-stiffness were not applicable and dorsi-flexion was only modelled as a single linear phase (KAnDF). Previous studies have evaluated quasi-stiffness over the entire period of dorsi-flexion, making a linear approximation of the often non-linear phase of dorsiflexion [2,19]. Benefits to modelling quasi-stiffness for the entire dorsiflexion phase, instead of 2 discrete phases, include model simplicity and ability to identify the start and end of the dorsiflexion phase in real time. Because P2 was dependant on stance duration, it could only be found in post-processing or approximated in real-time.

Knee quasi-stiffness and selection of points of interest

Our model of knee joint quasi-stiffness was in close agreement with previous studies which considered quasi-stiffness for the knee flexion and extension phases occurring in early and mid-stance [1,4]. All 3 points of interest (P1, P2, and P3) were easily identifiable across levels of simulated gravity and speeds. The quasi-stiffness during knee flexion (KKnF) significantly reduced with gravity level (P<0.001), but the quasi-stiffness of the extension stage (KKnE) was not affected (P>0.99). KKnF exhibited a R2 > 0.85 across all gravity and speed levels, indicating that quasi-stiffness was a good model of the knee during power absorption. In addition to a smaller peak knee extension moment, reducing gravity reduced the peak knee extension angle in early-mid stance. A smaller extension moment in combination with a more flexed knee created a rounded moment-angle profile, thus reducing linearity of the extension phase and ability of the quasi-stiffness model to accurately capture knee dynamics. In the lowest gravity condition, R2 of KKnE was less than 0.7. KKnE also had a poor fit (R2 ~ = 0.5) at 0.4 m/s in normal gravity. We therefore concluded that KKnE was a suitable model in normal (1 G) to 0.54 G at 0.8–1.6 m/s, but was unsuitable in the lowest gravity level (0.31 G) across speeds and for 0.4 m/s walking speed in all gravity levels. Previous studies averaged KKnF and KKnE to find the knee quasi-stiffness throughout early-mid stance [4]. However, a single quasi-stiffness model of the knee would be unsuitable and inaccurate at low gravities due to the widening of the moment-angle loop.

The duration spent in the knee flexion and extension phase typically only accounted for ~60% of the stance phase, suggesting that a substantial proportion of the knee dynamics are not modelled by our quasi-stiffness parameters. Future studies on knee joint quasi-stiffness may choose to consider a 3rd phase of quasi stiffness between local minimum knee extension moment (P3) and the local maxima of knee extension before toe-off. We identified a local extension moment maxima at ~80% of stance in all speeds and gravity conditions. Linear quasi-stiffness may be a suitable model for this extension phase and a 4th phase of quasi-stiffness could also approximate the moment-angle relationship between the local extension moment maxima and toe-off.

Hip quasi-stiffness and selection of points of interest

Quasi-stiffness provided a good model of hip dynamics throughout stance and we found the quasi-stiffness of the early extension (KHiE1) and flexion (KHiF) phases were dependant on gravity level (p = 0.004 and p<0.001 respectively). Although KHiF decreased with gravity, the percent of stance spent in the flexion phase also decreased with gravity. At each walking speed in the lowest gravity condition, at least 2 subjects did not exhibit a hip flexion phase, with the proportion of subjects increasing with walking speed (S2 Table). The lack of hip flexion at low gravity across speeds was further evidence of the subjects adopting different gait strategies when ground reaction forces are reduced. In normal gravity, KHiF closely approximates hip moment-angle relationship, except for 0.4 m/s walking. Therefore, KHiF was a suitable model for gravity levels 0.54, 0.76, and 1 G for walking speeds between 0.8 and 1.6 m/s.

In general, the R2 fit of each phase of hip quasi-stiffness was good across all levels of gravity, but 0.4 m/s had both the lowest R2 values and the largest variation in standard deviation. Due to the large variation in mean R2 at 0.4 m/s, we found that quasi-stiffness was not a suitable model for walking at slow speeds (0.4 m/s). Quasi-stiffness control is therefore not a suitable assistance strategy for wearable devices to assist slow walkers.

We developed a new hip quasi-stiffness model with reference to two previously established models. An earlier model of hip quasi-stiffness, developed by Frigo et al., identified 4 phases of quasi-stiffness for the hip: 3 phases of extension in stance phase separated by different slopes, and 1 phase of extension during the swing phase [1]. Shamaei et al. modelled an extension and flexion phase of quasi-stiffness using maximum hip flexion moment as the transition point between them and local deflection points as the onset of the extension and termination of the flexion phase [3]. The local deflection was defined as the point where the double derivative of moment with respect to angle showed a local discontinuity. To ensure our model was robust to a wide range of gait speeds and gravity levels, we chose to model 2 distinct phases of extension, an overall extension phase, and a flexion stage. Our model agreed with previous studies in that the peak hip flexion moment defined the termination of the extension stage. Our delimiting point between the 2 phases of extension was the transition of hip moment from extension to flexion as this metric was relatively easy to measure in real time, and could be found across almost all gravity levels and gait speeds. Our R2 results showed that the extension phases were able to reasonably approximate hip quasi-stiffness. Unique to our model, we calculated KHiE (from minimum to maximum hip flexion moment) and found this to be a good model (R2 > 0.74) of the moment-angle relationship at speeds greater than 0.4 m/s. This single quasi-stiffness value was able to model hip dynamics for up to 80% of stance across gravity levels. We were unable to calculate early and late extension stages for some walking conditions as the hip moment remained in extension for the duration of stance. The single quasi-stiffness model of the hip extension phase is a more robust model than a 2-phase extension model of hip dynamics at a wide range of speeds and gravity levels.

Implications of findings

Our quasi-stiffness models of the ankle, knee, and hip have implications for robotic control of finite-state machine controlled bipedal robots, prosthetics, and exoskeletons. Exoskeletons and prosthetics can emulate quasi-stiffness during a phase of gait by using finite-state machine controllers to identify phases of gait and modify effective stiffness of the robotic joint [10,53-57]. All of the current biomimetic exoskeletons and prostheses that assist gait by adjusting device quasi-stiffness are designed for walking at normal gravity. Our findings suggest that similar devices with reduced stiffness values would be able to assist gait in reduced gravity overground walking, which is a therapy often used for gait rehabilitation. We also identified specific linear phases in the joint moment-angle relationships during stance where robotic quasi-stiffness assistance would be beneficial and reported the biological measurements that indicate beginning and end of these phases.

Gravity level and joint quasi-stiffness had a linear but non-proportional relationship. Due to the complexity of the relationship and the interplay of walking speed, the quasi-stiffness of a leg joint at normal gravity cannot be multiplied by the gravity level to predict quasi-stiffness of the joint in reduced gravity.

Passive or quasi-passive exoskeletons use springs to assist locomotion and our results could be valuable in determining optimal spring stiffnesses and period of engagement. Passive running ankle prostheses most-commonly use a spring-leaf spring with specific stiffness to aid in ankle plantarflexion energy storage and return [58,59]. Some knee prostheses also use quasi-passive mechanisms to assist gait [60,61]. Passive or quasi-passive exoskeletons also use passive stretch and relax of springs in parallel with the legs to assist gait [62-67]. Our results showed that 6 phases of quasi-stiffness were significantly decreased by gravity level and therefore a single spring stiffness would not be optimal for multiple gravity levels. Previous research found that walking speed impacts quasi-stiffness of joints [51,52,68] and mechanisms have been developed to vary spring stiffness across gaits. We conclude that similar adjustments are needed for walking in low gravity.

Quasi-stiffness of leg joints in reduced gravity may also have design implications for extra-vehicular space suits. Space suits are pressurized, which makes the suit stiff. Increased suit stiffness makes it harder or more energetically expensive to bend leg joints as the joint must overcome the stiffness imposed by the suit. Integration of exoskeletons in space-suits could assist movement in low-gravity environments like Mars or the Moon [69,70]. The integrated exoskeleton could be designed to assist walking by mimicking the biological joint quasi stiffness at low gravity in non-pressurized conditions. Our results detail the relationship between gravity and joint-quasi stiffness and could be used to design a gait assisting exoskeleton integrated into a space suit.

Limitations

There were a few limitations to our study. The first is that we controlled for speed using the average speed over a 4 m section of the walk-way, centered around the forceplates. Participants completed 1–3 strides during the period we controlled for speed and their gait speed may have varied at different points of the walkway. We asked participants to maintain an even walking pace throughout the walkway and post-processing confirmed that walking speeds were close to the target walking speed. It should be noticed that participants struggled to walk very slowly (0.4 m/s) in normal gravity. We chose to include 0.4 m/s as a testing condition because people with walking difficulties, who would benefit from walking with an exoskeleton in reduced gravity environments, have a slower preferred and maximal speed. It is also worth noting that we tested with only healthy-able bodied participants. Joint quasi-stiffness of people with physical limitations may be different to that of able-bodied people and could react differently in response to altered gravity. If the neuromuscular control of quasi-stiffness was a property of inherent muscle stiffness as supported by our findings, then it would stand to reason that joint quasi-stiffness of people with gait disabilities would also decrease with gravity. The statistical power of our results could have been improved with more subjects. The number of subjects in this study is comparable to previous studies on bodyweight supported walking or joint quasi-stiffness [38,39].

Conclusion

Quasi-stiffness tended to decrease with simulated reduced gravity and supported the theory that joint quasi-stiffness is determined by the inherent stiffness properties of the muscle-tendon units. We identified 4 phases of quasi-stiffness in both the ankle and hip, and 2 phases of quasi-stiffness in the knee that approximated moment-angle loops across different levels of gravity and walking speeds. At low levels of gravity, the relative power and strength of the joints were increased and subjects could choose from a wide selection of gait strategies. Our findings on quasi-stiffness in reduced gravity have implications for passive, quasi-passive, and finite-state machine controlled prostheses, and exoskeletons.

Participant descriptive data.

(DOCX)

Click here for additional data file.

Walking conditions and number of subjects for which phases of quasi-stiffness could not be calculated.

Numbers in bold indicate conditions where data were lost.

(DOCX)

Click here for additional data file.

Mean quasi-stiffness values with standard deviations for all conditions.

(DOCX)

Click here for additional data file.

Mean R2 for each quasi-stiffness linear model with standard deviations for all conditions.

(DOCX)

Click here for additional data file.

31 Mar 2022

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Reviewer #1: This study aims at investigating the effect of simulated reduced gravity (provided by a bodyweight support system) and speed on quasi-stiffness of the hip, knee and ankle during overground walking. Quantifying quasi-stiffness during simulated reduced gravity may have important implications for the design of prosthetics and exoskeletons when external bodyweight support is provided. The authors found that quasi-stiffness decrease with simulated reduced gravity and speed is a main factor in determining quasi-stiffness. They concluded that joint quasi-stiffness is determined by the inherent stiffness properties of the muscle tendon units. The manuscript is well written and the quality of the data, analysis and figures provide enough evidence to support the conclusions.

Minor comment:

The proposed hypothesis (“We hypothesized that joint quasi-stiffness would decrease with simulated reduced gravity as it is likely dependent on peak muscle and tendon force”) is a prediction of the results given the relationship between joint net moments and quasi-stiffness. I would suggest to reformulating the hypothesis in relation to the proposed biomechanical principles underlying the modulation of quasi-stiffness.

Reviewer #2: The current paper aimed to determine how joint quasi-stiffness changes in response to different levels of simulated reduced gravity at a range of walking speeds. Quasi-stiffness is a useful tool for controlling robotic devices and has yet to be studied at different gravity levels. Twelve healthy, young participants completed the protocol, which involved overground walking over a force plate at prescribed speeds and gravity levels. The results support the authors’ hypothesis that quasi-stiffness would decrease with reductions in simulated gravity. The discussion compares and contrasts the quasi-stiffness parameters to that of previous literature and proposes explanations for the mechanism behind the changes in quasi-stiffness.

While the paper is well-written, there are a handful of typos and omissions (some of which I have pointed out below). In addition, I have suggested some more impactful revisions pertaining to clarifying the methodology and focusing the intro and discussion.

The most important revisions deal with ensuring that the framing of the conclusions is appropriate for the scope of this study.

Intro:

Throughout the intro, please include citations to back up statements of known phenomena. For example, page 9, line 23-24, multiple studies have shown a decrease in GRF due to simulated reduced gravity many of which are referenced elsewhere in this manuscript.

The section on simulated reduced gravity as a gait rehabilitation therapy is lacking a clear, concise message. In the current study, gait rehabilitation appears to have motivated the use of the slowest walking speed, and in the discussion the idea of rehabilitative devices is touched on. As is, the paragraph does not appear to add meaningfully to the introduction, other than to state that body-weight support is used as a therapeutic tool. Perhaps joint quasi-stiffness has been studied in these populations and could be added to this section?

Method:

Page 12, lines 5-7: I think this sentence is incomplete, and may be intended to provide references for the quasi-stiffness phases, which would be helpful.

Figure 1: These figures help quite a bit with visualizing and understanding the quasi-stiffness calculation and results. However, there are quite a few elements and acronyms, which make the figure difficult to understand quickly: it needs to be studied while referencing Tables 1 & 2. I recommend adding a figure that shows joint moment over time and indicates the phases over which quasi-stiffness was calculated, which will allow readers to more easily understand when the points of interest occur in the gait cycle

Page 13, line 5: I assume ‘mid-point of stance’ refers to the temporal mid-point. Is this correct? Or is it based on a spatial metric? Please clarify.

Page 13, line 5: planter > plantar

Page 14, line12: Please specify which speeds you mean by ‘normal’.

Page 14, line 22: Please add some more specifics to this section. It is not clear when the analysis is being run on a single stride, single condition, single subject, etc. For example, as written, it seems that you calculated quasi-stiffness using a least squares model for a given phase within a single stride. Then you used the resulting model to predict the joint moment from the joint angle for that same phase. It is not clear to me how that is different from the R^2 of the linear model, unless different strides or subjects were compared.

Results:

Figure 3: I recommend swapping the positions of the Kanpf column and Kandf column, so that the columns are more chronological from left to right. Also, the data labels for each speed level (x vs o vs triangle etc) are very clear in the legend, but not clear in the figure itself, which may make this figure hard to read for a person with color-blindness. Please make the data labels more visible. Lastly, please indicate in the figure caption which measure of error the error bars are indicating (likely standard deviation).

Page 17, line 9: This appears to be the first and only use of these acronyms, so please state with words instead of acronyms.

Figure 5: Similar to Figure 3, I recommend swapping the positions of Khif and Khie.

Discussion:

Section: Biomechanical Principles Underlying Joint Quasi-Stiffness

While I agree with the sentiment of this section, I think it should be slightly reframed. The conclusion that ‘…quasi-stiffness is modulated by the inherent properties of the muscle-tendon units” is perhaps a stretch beyond the scope of the current study. The section could be strengthened by including discussion on how the interaction between tendon and muscle dynamics are impacted by different loads and how these changes could contribute to explaining the results of the current study. Additionally, I was unable to find/access a complete reference for citation 41, which appears to be important for this argument.

Page 20, line 6 & throughout: The authors make several references to ‘normal’ walking speed. There are four speeds, and it is unclear which speed or speeds they are referring to as normal. Please be more specific when referencing results. One solution would be to use a parenthetical such as ‘…normal walking (1.2 m/s)…’ or to define what constitutes ‘normal’ at first mention.

Page 21, line 14: ‘liner’ > ‘linear’

Page 22, line 23: Could the change in hip kinematics be related to how the participants are interacting with the body-weight support system? According to the 2020 Maclean paper, slower speeds saw higher forward pulling forces. Perhaps it would be worthwhile to investigate trunk angle to determine how the lack of hip flexion could come about.

Page 23, line 2: ‘worst’ > ‘lowest’

Page 24, line 10: ‘liner’ > ‘linear’

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31 May 2022

Reviewer #1:

This study aims at investigating the effect of simulated reduced gravity (provided by a bodyweight support system) and speed on quasi-stiffness of the hip, knee and ankle during overground walking. Quantifying quasi-stiffness during simulated reduced gravity may have important implications for the design of prosthetics and exoskeletons when external bodyweight support is provided. The authors found that quasi-stiffness decrease with simulated reduced gravity and speed is a main factor in determining quasi-stiffness. They concluded that joint quasi-stiffness is determined by the inherent stiffness properties of the muscle tendon units. The manuscript is well written and the quality of the data, analysis and figures provide enough evidence to support the conclusions.

We thank the reviewer for their feedback and are happy to hear that the paper is well-written.

Minor comment:

The proposed hypothesis (“We hypothesized that joint quasi-stiffness would decrease with simulated reduced gravity as it is likely dependent on peak muscle and tendon force”) is a prediction of the results given the relationship between joint net moments and quasi-stiffness. I would suggest to reformulating the hypothesis in relation to the proposed biomechanical principles underlying the modulation of quasi-stiffness.

Hypothesis has been modified to include the intrinsic muscle-tendon unit stiffness and some references to back up our hypothesis.

“We hypothesized that joint quasi-stiffness would decrease with simulated reduced gravity as it is likely dependent on the intrinsic muscle-tendon unit stiffness which scales with muscle and tendon force [15,43-45].”

Reviewer #2:

The current paper aimed to determine how joint quasi-stiffness changes in response to different levels of simulated reduced gravity at a range of walking speeds. Quasi-stiffness is a useful tool for controlling robotic devices and has yet to be studied at different gravity levels. Twelve healthy, young participants completed the protocol, which involved overground walking over a force plate at prescribed speeds and gravity levels. The results support the authors’ hypothesis that quasi-stiffness would decrease with reductions in simulated gravity. The discussion compares and contrasts the quasi-stiffness parameters to that of previous literature and proposes explanations for the mechanism behind the changes in quasi-stiffness.

While the paper is well-written, there are a handful of typos and omissions (some of which I have pointed out below). In addition, I have suggested some more impactful revisions pertaining to clarifying the methodology and focusing the intro and discussion.

The most important revisions deal with ensuring that the framing of the conclusions is appropriate for the scope of this study.

We thank the reviewer for their detailed feedback and suggestions to improve manuscript quality. We’re also happy to hear that the review found the paper well-written. We have endeavoured to incorporate your feedback to improve the manuscript.

Intro:

Throughout the intro, please include citations to back up statements of known phenomena. For example, page 9, line 23-24, multiple studies have shown a decrease in GRF due to simulated reduced gravity many of which are referenced elsewhere in this manuscript.

We have added some references to back up statements of known phenomena. The sentences with new references in the introduction are:

“Study of joint quasi-stiffness during different gait conditions may also provide insight into human neural control [13,14].”

“Joint quasi-stiffness is determined by the state of all passive and active tissues that cross the joint [15,16].”

“Used as a gait rehabilitation therapy, simulated reduced gravity reduces the joint torques and muscle forces required to produce gait [20,21].”

“One technique to simulate reduced gravity is to apply a constant upwards force to the torso with a harness, counteracting gravity without altering body mass [22].”

“Reducing the effective bodyweight also decreases joint contact forces and net muscle moments during walking, essentially making it easier to walk [20,21,26].”

“We hypothesized that joint quasi-stiffness would decrease with simulated reduced gravity as it is likely dependent on the intrinsic muscle-tendon unit stiffness which scales with muscle and tendon force [15,43-45].”

The references used are:

13. Wind AM, Rouse EJ. Neuromotor Regulation of Ankle Stiffness is Comparable to Regulation of Joint Position and Torque at Moderate Levels. Sci Rep. 2020;10. doi:10.1038/S41598-020-67135-X

14. Rouse EJ, Hargrove LJ, Perreault EJ, Kuiken TA. Estimation of Human Ankle Impedance During the Stance Phase of Walking. IEEE Trans Neural Syst Rehabil Eng. 2014;22: 870. doi:10.1109/TNSRE.2014.2307256

15. Whittington B, Silder A, Heiderscheit B, Thelen DG. The contribution of passive-elastic mechanisms to lower extremity joint kinetics during human walking. Gait Posture. 2008;27: 628–634. doi:10.1016/J.GAITPOST.2007.08.005

16. Silder A, Heiderscheit B, Thelen DG. Active and passive contributions to joint kinetics during walking in older adults. J Biomech. 2008;41: 1520–1527. doi:10.1016/J.JBIOMECH.2008.02.016

20. MacLean MK, Ferris DP. Human muscle activity and lower limb biomechanics of overground walking at varying levels of simulated reduced gravity and gait speeds. PLoS One. 2021;16. doi:10.1371/JOURNAL.PONE.0253467

21. Goldberg SR, Stanhope SJ. Sensitivity of joint moments to changes in walking speed and body-weight-support are interdependent and vary across joints. J Biomech. 2013;46: 1176–1183. doi:10.1016/J.JBIOMECH.2013.01.001

22. Farley CT, McMahon TA. Energetics of walking and running: insights from simulated reduced-gravity experiments. J Appl Physiol. 1992;73: 2709–2712. doi:10.1152/jappl.1992.73.6.2709

26. Apte S, Plooij M, Vallery H. Influence of body weight unloading on human gait characteristics: a systematic review. J Neuroeng Rehabil. 2018;15. doi:10.1186/s12984-018-0380-0

43. Rack PMH, Westbury DR. The short range stiffness of active mammalian muscle and its effect on mechanical properties. J Physiol. 1974;240: 331. doi:10.1113/JPHYSIOL.1974.SP010613

44. Walmsley B, Proske U. Comparison of stiffness of soleus and medial gastrocnemius muscles in cats. J Neurophysiol. 1981;46: 250–259. doi:10.1152/JN.1981.46.2.250

45. Krupenevich RL, Beck ON, Sawicki GS, Franz JR. Reduced Achilles Tendon Stiffness Disrupts Calf Muscle Neuromechanics in Elderly Gait. Gerontology. 2022;68: 241–251. doi:10.1159/000516910

The section on simulated reduced gravity as a gait rehabilitation therapy is lacking a clear, concise message. In the current study, gait rehabilitation appears to have motivated the use of the slowest walking speed, and in the discussion the idea of rehabilitative devices is touched on. As is, the paragraph does not appear to add meaningfully to the introduction, other than to state that body-weight support is used as a therapeutic tool. Perhaps joint quasi-stiffness has been studied in these populations and could be added to this section?

In this section, we introduce and discuss the concept of simulated reduced gravity. Specifically, we highlight that the technique can reduce joint torque, which links back to the previous paragraph of exploring quasi-stiffness under such conditions. We think it is important to dedicate some of the introduction to an overview of bodyweight supported walking. To the best of our knowledge, joint quasi-stiffness has not been studied in a clinical population. To improve the relevancy of the discussion of gait rehabilitation, we have explained the benefit of understanding the effect of gravity level in a healthy population as it pertains to understanding if pathological gait has an interaction with gravity level.

“To the best of our knowledge, there has been no investigation of joint quasi-stiffness in clinical populations in normal or reduced gravity. To parse out the effects and interactions of gravity level, walking speed, and underlying pathological physiology on quasi-stiffness, we first need an understanding of the relationship between gravity level, walking speed, and joint quasi-stiffness in a healthy population.”

Method:

Page 12, lines 5-7: I think this sentence is incomplete, and may be intended to provide references for the quasi-stiffness phases, which would be helpful.

This sentence was incomplete, thank you for catching that. We have completed it and added the 5 references relevant to building our quasi-stiffness models.

We chose phases of quasi-stiffness delimited by points of interest (Table 2) with reference to previous studies [1-6,17].

Figure 1: These figures help quite a bit with visualizing and understanding the quasi-stiffness calculation and results. However, there are quite a few elements and acronyms, which make the figure difficult to understand quickly: it needs to be studied while referencing Tables 1 & 2. I recommend adding a figure that shows joint moment over time and indicates the phases over which quasi-stiffness was calculated, which will allow readers to more easily understand when the points of interest occur in the gait cycle

We agree that there’s a lot of information on these figures and they required some time to be fully understood. We have endeavoured to improve clarity and split the figure into 3, with each joint moment-angle loop accompanied by the moment and angle during stance. We hope the consistency in colours and labelling between the figures, will help improve clarity. The text from each new figure is a small variation of the following:

“Figure X. Joint angle, moment, and moment-angle relationships during stance phase overlaid with points of interest and phases of quasi-stiffness. The smaller subplots on the left show joint angle and moment during stance phase. The dashed vertical lines represent the timings of each point of interest, while the open circles identify the point of interest itself. The phases of quasi-stiffness are identified at the bottom of these plots, with the arrows indicating their onset and termination. The large, right figure shows the moment-angle relationship with the quasi-stiffness overlayed as dashed lines and the points of interests as “+”. Data for visualization were normalized to 60 data points and averaged across all participants walking in normal gravity at 1.6 m/s. Direction of internal joint moment and joint angle are indicated with arrows on the rightmost plot.”

Page 13, line 5: I assume ‘mid-point of stance’ refers to the temporal mid-point. Is this correct? Or is it based on a spatial metric? Please clarify.

You assume correctly. We have clarified the mid-point is “temporal” at multiple points in the manuscript for clarity.

Page 14, line12: Please specify which speeds you mean by ‘normal’.

Page 20, line 6 & throughout: The authors make several references to ‘normal’ walking speed. There are four speeds, and it is unclear which speed or speeds they are referring to as normal. Please be more specific when referencing results. One solution would be to use a parenthetical such as ‘…normal walking (1.2 m/s)…’ or to define what constitutes ‘normal’ at first mention.

We agree that the speeds were somewhat confusing as they were originally were presented and have clarified walking speeds throughout the paper. Generally speaking, slow = 0.4 m/s, medium = 0.8 m/s, normal = 1.2 m/s, and fast = 1.6 m/s.

Page 14, line 22: Please add some more specifics to this section. It is not clear when the analysis is being run on a single stride, single condition, single subject, etc. For example, as written, it seems that you calculated quasi-stiffness using a least squares model for a given phase within a single stride. Then you used the resulting model to predict the joint moment from the joint angle for that same phase. It is not clear to me how that is different from the R^2 of the linear model, unless different strides or subjects were compared.

We appreciate ethe feedback and have added additional information for clarity. In short, for every walking trial, the linear model was used to predict moment from angle and we found the R^2 for that trial. Stiffness and R^2 values were then averaged within conditions for each participants, and then averaged across participants.

“We found the 11 points of interest for each walking trial, then calculated the stiffness of each quasi-stiffness phase using a least squares linear model. For each walking trial, we applied the linear model as a function of joint angle (i.e. predicted joint moment from given joint angles). To determine the fit of the model for each phase of quasi-stiffness in each trial, we calculated the R2 value. We also calculated the duration of each phase of quasi-stiffness as a percentage of the total stance time. Finally, we averaged quasi-stiffness values, R2, and phase durations across each walking trial in a condition for every participant, and then averaged across participants.”

Results:

Figure 3: I recommend swapping the positions of the Kanpf column and Kandf column, so that the columns are more chronological from left to right. Also, the data labels for each speed level (x vs o vs triangle etc) are very clear in the legend, but not clear in the figure itself, which may make this figure hard to read for a person with color-blindness. Please make the data labels more visible. Lastly, please indicate in the figure caption which measure of error the error bars are indicating (likely standard deviation).

We have reordered the columns to be ordered as suggested. They were originally ordered in strict chronological order, as Kandf does not follow on from Kand2, but we can see the benefit to grouping all the dorsi-flexion QS together and have implemented this in the figures and tables.

We chose the colours such that they would be discernible in greyscale and for several colour-blindness types. We used an online tool (link to tool with our colours pre-loaded) to visualize the colours for different colour-blindness types and converted the figures to greyscale to check for clarity. The 0.4 and 0.8 m/s colours are the closest in greyscale, so we chose the label markers that are most visually different (cross and open circle). Unfortunately, increasing the size of the markers makes the plots too noisy and the data more difficult to read. We have included that the error bars represent standard deviation. The new figure caption reads:

“Figure 5. Quasi-stiffness of the ankle in stance phase at different levels of simulated reduced gravity and speeds. Top row shows stiffness values, middle row is the quality of fit of the linear quasi-stiffness model, and bottom row is the duration of the quasi-stiffness phase as percent of stance phase. Each column of plots is a different quasi-stiffness phase for the ankle: KAnD1 is early dorsi-flexion, KAnD2 is Ankle late dorsi-flexion, KAnDF is overall Ankle dorsi-flexion, and KAnPF is Ankle plantar-flexion. The error bars represent standard deviation.”

Page 17, line 9: This appears to be the first and only use of these acronyms, so please state with words instead of acronyms.

Thank you for bringing our attention to this! The PKn, QKn, and RKn acronyms were accidental hold-outs of an older set of acronyms used when drafting the manuscript. These acronyms have been updated to P1Kn, P2Kn, and P3Kn respectively. The text in the manuscript reads as:

“There were no instances where P1Kn, P2Kn, or P3Kn could not be identified.”

Figure 5: Similar to Figure 3, I recommend swapping the positions of Khif and Khie.

We have swapped the order of the appearance for this figure and relevant table. The final 2 sentences of the figure caption reads:

“Each column of plots is a different quasi-stiffness phase for the hip: KHiE1 is early hip extension, KHiE2 is hip late extension, KHiE is overall hip extension, and KHiF is knee flexion. The error bars illustrate standard deviation.”

Discussion:

Section: Biomechanical Principles Underlying Joint Quasi-Stiffness

While I agree with the sentiment of this section, I think it should be slightly reframed. The conclusion that ‘…quasi-stiffness is modulated by the inherent properties of the muscle-tendon units” is perhaps a stretch beyond the scope of the current study. The section could be strengthened by including discussion on how the interaction between tendon and muscle dynamics are impacted by different loads and how these changes could contribute to explaining the results of the current study. Additionally, I was unable to find/access a complete reference for citation 41, which appears to be important for this argument.

We have softened this section so our discussion stays within the scope of this study. Citation 41 is still in review, so we have removed it from this manuscript. The section now reads as:

“Joint quasi-stiffness tended to decrease with gravity level, which is in agreement with the supposition that quasi-stiffness is modulated by the inherent properties of the muscle-tendon units. Simulated reduced gravity reduced the load through the joints and moments about the leg joints, and reduced the muscle activation amplitudes during stance [21]. At lower muscle forces, there is less stretch of the tendon which moves the tendon stiffness into the short range stiffness known as the toe region. The toe region occurs at low levels of tendon stretch and incurs a smaller stiffness than in the subsequent linear phase of tendon length-force relationship. However, an alternative possibility is that subjects actively adjusted their muscle activation patterns to achieve close to normal joint displacements at reduced gravity. This approach would also produce a reduced joint quasi-stiffness at reduced gravity, completely independent of underlying muscle-tendon unit mechanical properties. Future research could use ultrasound imaging [45] to provide a better indication of intrinsic muscle-tendon displacements and stiffnesses during walking under simulated reduced gravity.

“Our implementation of a rigid foot model may have led to an underestimation of the true ankle quasi-stiffness. We modelled the foot as a single rigid body, assuming no rotation or translation within the joints of the foot. Previous research has found that modelling the ankle and foot separately, allowing for deformation of the arch of the foot, underestimated quasi-stiffness of the ankle in hopping [50]. “

Page 22, line 23: Could the change in hip kinematics be related to how the participants are interacting with the body-weight support system? According to the 2020 Maclean paper, slower speeds saw higher forward pulling forces. Perhaps it would be worthwhile to investigate trunk angle to determine how the lack of hip flexion could come about.

Thank-you for your insights. We do not think the pulling forces would have impacted the lack of hip flexion. The pulling forces at all gravity levels rarely exceeded 1% of the person’s bodyweight (in normal gravity). We suggest the lack of hip flexion is an adoption of a new walking strategy. We did not have any markers above the hips, so we cannot retroactively examine trunk angle.

Page 13, line 5: planter > plantar

Page 21, line 14: ‘liner’ > ‘linear’

Page 24, line 10: ‘liner’ > ‘linear’

Thank you for pointing out these spelling errors. We have corrected them in the revision.

Page 23, line 2: ‘worst’ > ‘lowest’

We agree that ‘lowest’ is a better choice than ‘worst’ and have updated the word choice in the revision.

We have tracked changes in the manuscript revision, and highlighted yellow any changes we made which could not be tracked (i.e. referencing or table formatting)

Submitted filename: Response to Reviewers QuasiStiffness.docx

Click here for additional data file.

11 Jul 2022

Effects of simulated reduced gravity and walking speed on ankle, knee, and hip quasi-stiffness in overground walking

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29 Jul 2022

PONE-D-21-38355R1

Effects of simulated reduced gravity and walking speed on ankle, knee, and hip quasi-stiffness in overground walking

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