Mechanical model of the recovery from stumbling

Biol. Cybern. 3, 1 9 (2004) DOI 10.1007/s00422-004-0508-0 Springer-Verlag 2004 Mechanical model of the recovery from stumbling A. Forner Cordero 1,2, H. J. F. M. Koopman 1, F. C. T. van der Helm 1 1 Institute for Biomedical Technology (BMTI), Biomedische Werktuigbouwkunde, CTW Gebouw, Universiteit Twente, P.B. 217, 7500 AE Enschede, The Netherlands 2 Motor Control Laboratory, Department of Kinesiology, Group Biomedical Sciences, K.U. Leuven. Tervuursevest 101, 3001 Leuven, Belgium Received: 9 April 2003 / Accepted: 8 July 2004 / Published online: Abstract. Several strategies have been described as a reaction to a stumble during gait. The elevating strategy, which tries to proceed with the perturbed step, was executed as a response to a perturbation during early swing. The lowering strategy, bringing the perturbed leg to the ground and overtaking the obstacle with the contralateral limb, was executed more frequently when the perturbation appeared at mid or late swing. The goal of this paper is to analyze which mechanical factors determine the most advantageous strategy. In order to determine these factors, a mechanical model of the recovery was developed and used to analyze a series of perturbation experiments. It was assumed that the goal of the recovery reaction was to control the trunk as an inverted pendulum during the double-stance phase. In order to be able to control the trunk angle, one foot should be up front and one foot should be behind the hips; otherwise it would be impossible to generate the required trunk torques. The trunk dynamics were expressed in terms of the ground reaction forces and their application point. A larger step (elevation strategy) gives the opportunity to dissolve the perturbation in one step. A small step (lowering strategy) necessarily results in a second quick step, after which the perturbation energy can be dissipated in the second double-stance phase. If a recovery step is too slow, it becomes impossible to counteract the forward flexion of the trunk. It is suggested that a measure of the ability to recover from a stumble could be based on the ability to perform quick steps. 1 Introduction Falling during gait is one of the most serious problems in the elderly. Many falls occur when the subject is unable to recover from a perturbation like a slip, an accidental slide of the landing foot, or a stumble, when the swinging foot strikes an obstacle (Winter 1995). Each person has certain Correspondence to: F. Cordero (e-mail: Arturo.FornerCordero@faber.kuleuven.ac.be) mechanical limitations in reacting to a perturbation. The identification of these limitations that compromise balance in frail populations would be useful to design specific therapeutic interventions aimed at reducing the risk of falling. Experimental work over the last two decades has shown three main groups of recovery strategies to a stumble, either on the floor (Eng et al. 1994) or on a treadmill (Dietz et al. 1986, 1987; Schillings et al. 1996; Forner Cordero et al. 2003): elevating, lowering, and delayed lowering. The elevating strategy, which tries to proceed with the perturbed step, was executed as a response to a perturbation during early swing. The lowering strategy, bringing the perturbed leg to the ground and overtaking the obstacle with the contralateral limb, was executed more frequently when the perturbation appeared at mid or late swing. The delayed lowering reflected the failure to execute an elevating strategy after a perturbation at early swing (Schillings et al. 2000). These strategies refer only to the lower limb motion during the perturbed step. However, the control of the trunk flexion appears to be crucial for the recovery (Grabiner et al. 1993; Grabiner and Kasprisin 1994). In addition, the recovery reaction affects several steps after the perturbation (Forner Cordero et al. 2003). Perturbations induced on a treadmill trigger the same response mechanisms as on the ground (Owings et al. 2001), whereas a treadmill allows measuring multiple steps until complete recovery is accomplished (Forner Cordero et al. 2003). It is important to determine which factors determine the choice of each strategy and relate them to the success of the recovery. A logistic regression model to classify the different strategies showed that the strategy choice was almost completely determined by the percentage of the stride length when the perturbation occurred (Pavol et al. 2001). The factors that affect the lowering strategy in the elderly were analyzed with a model and experimental data (van den Bogert et al. 2002). It was found that the body tilt angle should be less than 25 to allow a successful recovery within the step and this tilt angle was more sensitive to the time of response than to the gait speed. However, the tilt angle did not predict falls that occurred in the 4 2 2 0 0 5 0 8 Journal No. Article No. B Despatch: 31/8/2004 Journal : BCYB No. of Pages : 9 Author s Disk received Used Corrupted Mismatch Keyed

422/00508/2 recovery steps, indicating that other mechanisms might play an important role in the recovery. In this paper, the results from stumbling experiments are analyzed with a mechanical model of the recovery. Each strategy results in a certain foot placement that determines the ability to control the trunk. In this model, assuming that the goal of the recovery is to control the forward flexion of the trunk (van den Bogert et al. 2002), the trunk torques are expressed in terms of the ground reaction forces (GRF) and their point of application. Considering that the point of application of the GRF depends on the foot placement, the mechanical limitations of each recovery strategy can be identified. 2 Materials and methods 2.1 Experiments Four healthy young male subjects participated in the stumbling experiments (Table 1). The Medical Ethical Committee of the local rehabilitation hospital approved the experimental protocol and the subjects signed an informed consent. While the subjects were walking at 1.1 m/s (4 km/h) on a treadmill, an unexpected perturbation was applied and recorded. The perturbation consisted of blocking a rope attached to the left lower leg, thus braking the forward swing phase. The perturbation onset and the duration of the blockage were set at early, mid, and late swing with short (250 ms) or long (450 ms) durations for early swing and short duration for the perturbations in mid or late swing. The gait cycle was monitored online by means of a footswitch under the footwear sole in order to synchronize the perturbation instant. The order of the perturbation types and the time between them was random, and the subject was not informed if a perturbation was going to be applied (Forner Cordero et al. 2003). A safety frame attached by a rope to a chest harness prevented the subject from falling. The rope was loose enough so that the subject could lean without tensing it. If the rope were tensed, this would be considered a fall. The motion of the body was measured by means of a five-camera VICON system (VICON 370). The joint and segment angles were calculated following the procedure described by Koopman (Koopman et al. 1995). The same steps were recorded at 50 Hz with plantar pressure insoles (Pedar, Novel GmbH) placed inside of the subject s footwear. With the motion data, plus the vertical GRF and the centers of pressure, total (CoP), right (CoPR), and left (CoPL) foot, obtained from the insoles, it is possible to compute the inverse dynamics following an optimization procedure described elsewhere (Forner Cordero et al. 2004a). In this way, the joint forces and moments were computed for an eight-segment model (Koopman et al. 1995). 2.2 Model The model of the double stance was aimed at relating the foot placement, which resulted from different strategies and can be regarded as the model input, to the trunk control margins, i.e., maximal trunk torques (model output). This model consisted of three links in the sagittal plane (Fig. 1). The trunk was connected by two hip joints, located at the same position, to the legs. Each leg was defined as a variable-length link between the centers of pressure under each foot (x CoPR and x CoPL ) and the hip joints. The trunk motion resembles an inverted pendulum rotating around the hip joint. The hip torque M z hip can be written as: M z hip = (I CT + at 2 m T ) θ T +m T a T ((ÿ ) hip + g) cos θ T ẍ hip sin θ T, (1) with m T the mass of the trunk, I CT the inertia moment of the trunk with respect to the center of mass, a T the distance between the hip joint and the center of mass (COM) of the trunk, x hip, y hip anteroposterior and vertical position of the hip joint (Fig. 1) respectively, g the acceleration term due to gravity (9.81 m/s 2 ), and θ T the segment angle of the trunk with respect to the horizontal (Fig. 1). With L being the leading limb, R the trailing limb, and x CoPR, x CoPL the positions of the centers of pressure, CoPR Table 1. Subject characteristics and recovery strategy chosen Subject Height Weight Age Eleva- Lowe- De- Fall (cm) (Kg) (years) ting ring layed lowering A 167 84 28 2 4 1 1 B 183 80 40 2 4 3 C 181 67 22 2 4 7 D 181 83 24 6 1 Mean 179 78 26 (SD) (7) (7) (3) Total 6 18 12 1 Fig. 1. Three-link model used for the interpretation and simulation of the recovery

422/00508/3 and CoPL, under each foot, the hip moment is expressed in terms of the GRF as: M z hip = F gr x L R sin θ R + FgL x L L sin θ L F y gr L R cos θ R F y gl L L cos θ L +m L g (b R cos θ R + b L cos θ L ). (2) In these equations m L is the mass of the leg (assuming that both legs have the same mass); b R and b L are the distances between the hip joint and, respectively, the COM of the right and left leg; L R and L L are the lengths of the modeled legs between the hip joint and the CoP of each foot; θ R and θ L are the segment angles of the right and left leg, respectively, with respect to the horizontal; Fg x and F g y are the anteroposterior and vertical GRF acting on the CoP; F x gr, F y gr and F gl x, F y gl are the anteroposterior and vertical GRF, respectively, acting on CoPR and CoPL. Equation (2) is equivalent to (3) when the leg angles are expressed in terms of the positions of the hip and the centers of pressure of the right (CoPR) and left (CoPL) foot: M z hip = F gr x y hip + FgL x y hip F y gr (x hip x CoPR ) +F y gl (x CoPL x hip ) +m L g (b R cos θ R + b L cos θ L ). (3) These equations show that, during double stance, the maximal hip torques depend on the relative positions of the hip and the centers of pressure CoPR and CoPL. The vertical force must be positive (except on sticky floors) and is limited by the subject s weight and the maximal vertical acceleration of the center of mass. The horizontal force under each foot is a fraction of the vertical force for each foot limited by the friction coefficient between foot and floor. 2.2.1 Maximal torques during normal double stance. It must be noted that the hip is between the centers of pressure. The leading limb is ahead of the trailing limb, and the hip moves between CoPL and CoPR [(4)]: x CoPR x hip 0 and x CoPL x hip 0 F y gr 0, Fy gl 0. (4) Equations (3) and (4) show that the maximal and minimal hip extension torques occur when all the vertical force is applied at the leading and trailing limb, respectively. If we assume that the horizontal GRF on each foot act in the direction of the line that joins each CoP with x hip, this force can only contribute to reduce the maximal flexion or extension torques at the hip. Therefore, the maximal torques can be written as: Maximal flexion torque: M z hip = F g y (x CoPR x hip ) (5a) Maximal extension torque: M z hip = F g y (x CoPL x hip ), (5b) where the left leg is the leading limb and Fg y represents the maximal vertical force. Given the step length and the hip trajectory, it is possible to calculate the maximal hip torque that a subject can apply to control the trunk flexion during double stance. The model is further simplified assuming that during double stance CoPL and CoPR do not move and the distance between them defines the step length. 2.2.2 False double stance. If the hip is ahead of the leading limb CoP, only the horizontal forces and the weight of the legs can contribute to an extension torque [(3)]. However, the horizontal forces have an effect on the anteroposterior acceleration of the COM. Therefore, the horizontal forces result in an extension moment at the hip joint but at the cost of a forward acceleration of the hip. It is named a false double stance because it is not possible to control the trunk independently of accelerating the COM anteroposteriorly. 2.3 Simulation of the recovery double stance This model was used to evaluate the effect of the step length in controlling the trunk forward flexion. First, using an inverse dynamics approach, the maximal and minimal hip torques were computed with (5a) and (5b). With these torques, a forward dynamics calculation of the maximal possible trunk extension and flexion angles was performed [(1)]. Secondly, the effect of changes in the swing speed, resulting in different step lengths, was simulated using experimental data. The input parameters were the swing speed and the swing time, which define the step length. The initial conditions for the trunk angle and angular acceleration were obtained from experimental data, and the hip was considered to move forward at the gait speed (1.1 m/s in all the trials). The inertial parameters of the trunk were taken from Winter (1990). The model describes the hip torques as a function of the CoP positions, the GRF, and the hip trajectory. The effect of the different step lengths resulting from the elevating, lowering, and delayed lowering strategies was simulated with the model. 2.4 Data analysis The variables obtained from the experimental data were: step length and time, angle, angular velocity, and angular acceleration of trunk at heel strike, at toe-off, and at onset and end of perturbation; hip position with respect to the center of pressure of trailing foot and hip velocity and acceleration at the same instants. The choice of these variables was justified by the model equations. The recovery strategies were classified into three groups according to the step length and time normalized to the normal gait values for each subject using cluster analysis (K-means clusters, SPSS from SPSS Inc.). The mean and standard deviations of the hip positions relative to CoPR and CoPL in the anteroposterior direction were calculated at heel strike, toe-off, and, for the perturbed trials, perturbation instants. An analysis of variance (ANOVA), considering the strategy as a factor, of the relative hip position and trunk angles at the end of the perturbation and heel strike left and toe-off right was aimed at establishing whether these variables determine the strategy choice. The significance (at a 0.05 level) of the difference was examined with a post hoc test (assuming that the variances were not equal; Tahmane s T2, SPSS from SPSS Inc.).

422/00508/4 3 Results 3.1 Experimental results Table 1 presents the characteristics of the subjects and the number of recovery strategies that were chosen. Only one subject fell once at the first perturbed trial. The step length and the body configuration at the double stance that followed the perturbation of the left leg were dependent on the strategy (Fig. 2). Each strategy has different mechanisms to cope with the perturbation. The classification of strategies as a factor of the left step length and time are illustrated in Fig. 3. XCoPL Toe-off left L R L R Xhip XCoPR XCoPR Perturbation during left swing R XCoPR R Xhip L L XCoPL Heel-strike left XCoPR Xhip XCoPL Heel-strike left Fig. 2. Stick diagram representation of the perturbation and the possible recovery reactions The hip positions relative to CoPR and CoPL at the beginning (heel strike left) and end (toe-off right) of the double-stance phase next to the perturbation were significantly different for each strategy (Table 2). In most cases, the landing occurs with the hip between both CoP (Table 2). In the case of the fall, the hip is ahead of the CoP. The hip positions are referred to the position of each CoP (CoPR and CoPL). Thus, a positive value indicates that the hip is ahead of the center of pressure. The hip positions relative to each CoP are plotted in Fig. 4. Most hip positions are behind the left foot (CoPL) and ahead of the right foot (CoPR) at foot contact (hsl). The ANOVA of the trunk angles at the end of the perturbed swing (hsl) revealed that it was significantly smaller for the delayed lowering strategy (mean value of 82 ) than for the elevating and lowering strategies (mean values of 87 and 86, respectively). The mean trunk angular velocity at hsl is positive (extension velocity) for the elevating strategy (mean value of 19 /s), although there were some negative values that correspond to a flexion velocity (Fig. 5). There were significant differences in the angular velocity of the trunk between the elevating and lowering strategies (mean = 21 /s) with respect to the delayed lowering (mean = 30 /s) that had larger negative (flexion) values. At the beginning of the recovery stride, starting at heel strike right after the perturbation, it was shown that the relative positions of the hip depended on the strategy. The hip position with respect to the trailing limb (CoPL) was too advanced in the lowering (mean = 0.32 m) and delayed lowering (mean = 0.41 m) strategies. The hip position was significantly less advanced in the elevating strategy (mean = 0.17 m)..4.2 Normalized left step length 1.2 1.0.8.6.4.2 Strategy step 0.0 Delayed.6.7.8.9 1.0 1.1 1.2 1.3 Normalized left step time Fig. 3. Normalized step length and step time with the corresponding classification according to the strategy Hip pos. respect CoPL at hsl (m) -.0 -.2 -.4 Strategy No Pert -.6 Delayed -.1 0.0.1.2.3.4 Hip pos. respect CoPR at hsl (m) Fig. 4. Hip positions with respect to the left (CoPL) and right (CoPR) limbs at the heel strike left after the perturbation. The normal gait values (No pert) are also included. In the fall, the hip was ahead of the CoPL (0.29 m) and behind the CoPR ( 0.08 m). The step length was negative; thus CoPL was the trailing limb in this case. There are several trials where the hip was ahead of the leading limb but with values smaller than 0.035 m Fall

422/00508/5 Table 2. Means and standard deviations of the hip positions with respect to each CoP at the heel strike left (hsl) and toe-off right (tor) after the perturbation and at the beginning and end of the perturbation for each strategy and normal gait (No pert) Strategy Hip position with respect to CoPR at Hip position with respect to CoPL at Perturbation on (m) Perturbation off (m) hsl (m) tor (m) hsl (m) tor (m) n = 6 Mean 0.26 0.05 0.21 0.33 0.32 0.20 SD 0.03 0.1 0.04 0.05 0.04 0.04 n = 18 Mean 0.13 0.05 0.10 0.15 0.12 0.05 SD 0.07 0.06 0.06 0.10 0.08 0.08 Delayed n = 12 Mean 0.21 0.08 0.1 0.15 0.04 0.01 SD 0.07 0.04 0.03 0.06 0.03 0.05 Fall n = 1 Mean 0.26 0.03 0.08 0.11 0.26 0.29 No pert n = 79 Mean 0.18 0.33 0.39 0.26 SD 0.04 0.05 0.04 0.02 Trunk angular velocity at hsl (deg/s) 60 40 20 0-20 -40-60 Strategy No Pert -80 Delayed 76 78 80 82 84 86 88 90 Trunk angle at hsl (deg) Fig. 5. Trunk angle and angular velocity at the heel strike left after the perturbation. Responses are classified according to the strategy. According to the model conventions, negative values correspond to flexion 3.2 Simulation of the recovery double stance Fall The experimental results showed that the hip positions with respect to CoPR and CoPL were different in each strategy. The maximal hip torque is a function of the step length according to (5a) and (5b), and, for a normal step length, it should be larger than the required torques during normal walking. Under normal gait conditions, the step length is such that the hip torque is guaranteed to always be within the maximum flexion and maximum extension values (Fig. 6). As the swing phase is perturbed, the step speed is reduced while the hip continues its forward movement. In the delayed lowering strategy case presented in Fig. 7, the hip is ahead of the leading center of pressure (CoPL) in the double stance after the perturbation. The whole body is flexed forward. The hip at heel strike was about to overtake the leading limb CoP. At this instant the maximal Joint torque (N m) 400 300 200 100 0-100 -200-300 Maximal hip torque (extension) Measured hip torque Minimal hip torque (flexion) -400 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time (s) Fig. 6. Maximal hip torques versus the hip torques during a normal double-stance phase. Heel strike occurs at 0 s and toe-off at 0.16 s (dashed vertical line). The measured moments correspond to the torque calculated with the model presented here (solid) and to the moment calculated with the eight-segment model used only for the measurements torque given by (5a) is not valid, and the maximal torque is given by the horizontal GRF as described in (3). With the hip ahead of both CoPL and CoPR, the horizontal GRF under each foot should be positive, resulting from an extensor moment at the hip. This means that the landing foot does not produce a negative horizontal force. At the end of the double stance after the perturbation (right toeoff), the horizontal GRF were positive when the hip was ahead of CoPL (Fig. 8). For normal walking and elevating strategy the horizontal forces were negative. When the hip margin with respect to the CoPL was very small, the horizontal force became positive. This implies an extensor moment contribution at the hip joint. If the horizontal GRF was positive during the double-stance phase, the hip joint and the body COM were

422/00508/6 Joint torques (N m) 0-50 -100-150 -200 Maximal hip torque (extension) Minimal hip torque (flexion) Measured hip torque 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time (s) Fig. 7. Maximal hip torques versus the hip torques during the double-stance phase after a perturbation with a delayed lowering strategy. Heel strike occurs at 0 s and toe-off at 0.125 s (dashed vertical line). The measured moments correspond to the torque calculated with the model presented here (solid) and to the moment calculated with the eight-segment model used only for the measurements. The configuration of the body exceeds the model predictions accelerated forward, reducing the double-stance time. The key point was determining if the next step would be quick enough to overtake the hip and provide enough margins to compensate the forward flexion of the trunk. A measured trial showing a delayed lowering strategy (Fig. 9a) was simulated introducing small changes in the swing speed, as if the subject could not perform a quick step (Fig. 9b,c). The gait speed was 1.1 m/s. The measured recovery step had a swing time of 0.38 s and a step length of 0.74 m. In the simulation of the speed of response, the swing speed (ratio of step length to swing time) was reduced from 1.9 m/s (measured) to 1.7 m/s (simulated) with a swing time of 0.3 s. Total horizontal GRF at tor (N) 200 100 0-100 -200 Strategy No Pert -300 Delayed -.4 -.3 -.2 -.1 0.0.1.2.3 Hip pos. respect CoPL at tor (m) Fig. 8. Scatter plot of the hip position with respect to the leading limb (CoPL) and the total horizontal GRF at the end of the double stance after the perturbation (tor). The responses are classified according to the strategy. Normal walking (No pert) and the falling case (Fall) are also included Fall With the maximal torques determined by the feet placement [(5a)] it was impossible to extend the trunk, and with the minimal torques [(5b)] the trunk fell forward (Fig. 9). 4 Discussion 4.1 Experiments The strategies observed on a treadmill were similar to those found on the ground, as has been reported by several authors (Schillings et al. 1996; Owings et al. 2001; Forner Cordero et al. 2003). Despite their mechanical differences, the human balance control mechanisms remained basically the same. Performing the experiments on a treadmill permitted the analysis of multiple steps until recovery was accomplished either from a kinematic (Forner Cordero et al. 2003) or an energetic (Forner Cordero et al. 2004b) point of view. 4.2 Strategies to control the trunk The recovery from the perturbation was described as an effort to control the forward flexion of the trunk. The limitations to apply a certain moment on the trunk are given by physical constraints, such as the position of the front foot ahead of the hip, the hip position and trunk angle, and by subject conditions, like the maximal force of the trunk flexors and extensors. Describing the trunk dynamics in terms of the GRF and the CoP, which are determined by the relative position of the feet with respect to the trunk, it is possible to investigate the effect of the different strategies on the maximal trunk torques. In addition, the model presented here reveals the importance of the double-stance phase for the recovery from a stumble, as pointed out previously (Forner Cordero et al. 2004b). The model showed that, for normal step lengths, the range of hip torques given by the step length was much larger than the measured values. The trunk could be controlled with the vertical GRF independently of the horizontal GRF, and thus independently of body center of mass acceleration. The elevating strategy resulted in step of sufficient length to control the trunk and recover from the disturbance during the first double-stance phase after the perturbation. The lowering and delayed lowering strategies resulted in shorter step lengths and had lower hip torques, in either flexion or extension, constrained by the limits defined in (5a) and (5b). If the step is too slow, and thus too short, it is not possible to compensate the forward trunk motion in the first double-stance phase; one or several quick compensation steps are needed. This reasoning agrees with previous results that pointed to the time of response as a major factor in the recovery from stumbling (van den Bogert et al. 2002). In addition, the worst perturbation would cause the larger reduction in the step speed, implying that stumbles with longer durations would be more difficult to handle. Hypothetically, it would be impossible to recover from perturbations beyond a certain duration. This was confirmed in experiments that

422/00508/7 Fig. 9a c. Stick diagrams of two consecutive double-stance phases after a perturbation with delayed lowering strategy. The measured recovery response (a) had a swing speed of 1.94 m/s. The effect of the reduction of this speed to 1.7 m/s with a swing time of 0.3 s resulted increased the duration of a stumble (Smeesters et al. 2001). Furthermore, the model suggests that the correct perception of the CoP under the foot is crucial in controlling the trunk and maintaining balance in agreement with recent literature that has identified changes in gait patterns due to loss of plantar sensation (Perry et al. 2001; Eils et al. 2004). The hip-cop tolerance can be considered as a measure of the recovery. For the short-step strategies (lowering and delayed lowering), the range of possible hip torques in a shorter step. The motion of the trunk during the second doublestance phase after the perturbation was simulated for the maximal (b) and minimal (c) hip torques given by (5a) and (5b) is smaller, explaining why more steps are needed to regain the normal trunk position after the perturbation in these cases (Forner Cordero et al. 2003). 4.3 Falling during the experiments There was only one fall in these experiments. At the end of the double stance after the perturbation, the hip was too

422/00508/8 far ahead of the CoP of the weight-accepting limb (Fig. 4). The model suggests that it was impossible to stop the forward rotation of the trunk in the double-stance phase, and the subsequent step was not quick enough to recover. This resembled the mechanism of an after-step fall (Pavol et al. 2001). It was described that the subjects performed one or more recovery steps that were not enough to counteract the forward trunk flexion. With the step speed relationship presented here, it appears that falling after one quick step and falling after multiple steps belong to the same category. The differences in the responses would be due to the time of response, or the quickest step that a certain subject was able to perform. 4.4 Role of the horizontal forces and the hip-cop distance According to (3), the horizontal and vertical forces under each foot contribute to hip torques in opposing directions influencing the stability of the trunk. The horizontal GRF under each foot have a kind of synchrony : while the trail limb pushes forward, the lead limb is braking (Donelan et al. 2002; Kuo 2002). The resultant force, during a normal gait double-stance phase, varies from initial positive to negative values at the end of the double stance (Fig. 9). The maximal horizontal forces are a factor of the vertical force, given by the friction coefficient µ with the ground. The forces under each foot are related to the maximal hip torque, according to (3); if µ is very small (as walking on ice), the steps must be very short and the weight transfer between each foot must be done very quickly. In normal gait the hip was between the limits defined by the CoPR and CoPL during double stance,allowing a wide range of hip flexion and extension moments with the single intervention of the vertical GRF under each foot. The horizontal forces had little influence on the maximum torque when the hip was between both CoP, and its influence increased as the hip margins to the CoP decreased with shorter steps (Fig. 8). A false double stance occurs if the hip is ahead of the leading CoP. From (3) it follows that in this case it is impossible to control the trunk movement without applying horizontal forces. In our experiments, when the hip was ahead of the CoP, the only possibility to obtain an extensor trunk moment resulted from a positive anteroposterior horizontal force that would accelerate forward the body COM, i.e., a jump to recover. The experimental results supported this inference based on the model (Fig. 8). 4.5 Is the maximal step speed the limitation to recover? During a stumble, the forward leg swing is stopped while the hip continues moving forward, resulting in a double stance with too small distance between hip and CoP. The immediate goal is to perform a quick step, i.e., to place one foot ahead of the hip. The ability to perform quick steps is a limitation on recovery from a perturbation. These results reveal the importance of a sufficient step length and the relation of the distance from the hip to the center of pressure to control the trunk and underscore the role of the horizontal forces when the hip is outside of the CoP limits. 5 Conclusions In a double-stance-phase model it was shown that the position of the front foot determines the ability to keep the trunk upright, which is the main objective in preventing a fall. This model provides insight into the strategy choice in order to control the trunk forward flexion in terms of strategies: elevating, lowering, and delayed lowering. To control the trunk forward flexion after a stumble, a necessary condition is adequate foot placement. These results support the hypothesis that the speed of response, as the step speed, is crucial for the recovery. 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