Simulation of Anticipatory Postural Adjustments

Team Members

• Michelle Joyce
• Hannah Heigold

Project Video

Simulation of Anticipatory Postural Adjustments Video

Project Files

Background

Anticipatory postural adjustments (APA) are the postural changes that occur prior to the initiation of voluntary movement, which often involve measurable muscle activations and a shift in center of pressure (COP) [1]. This feedforward mechanism is critical for balance since it counteracts destabilizing forces that arise from movement and may assist in movement initiation by destabilizing the center of mass (COM) in the direction of intended motion (i.e. gait initiation) [2,3]. It has been shown that magnitude and timing of APAs are impaired in certain neuromuscular conditions, for example Parkinson’s [4], and reduced APAs are associated with poor balance control [5,6]. While APAs are reflective of balance abilities, they are not routinely tested in clinic. This is because they are not observable by human eye and otherwise require a lab set-up (EMG, force plates) to measure. OpenCap has been proposed as a tool for quantitative balance assessment that can translate to a clinical setting. However, it is currently unknown whether APAs can be predicted from OpenCap motion data. 

Therefore, the objective of this project is to assess the feasibility of predicting anticipatory postural adjustments using OpenCap motion data and dynamic optimization tools. While the future goal of this work is to assess APAs in a diverse set of balance assessment tasks, this project will focus on APAs during rise-to-toes to motivate the future work [2,7]. There is a well-characterized APA for the rise to toes task that involves a posterior shift in center of pressure prior to the anterior shift in center of mass [7, 8]. This is demonstrated in Figure 1.

Figure 1: Typical anterior-posterior (A-P) center of pressure (COP) and center of mass (COM) profiles for a rise to toes task. Adapted from [7]

Research Question(s)

What cost function is required in tracking and predictive simulations of a rise to toes task to elicit a physiological anticipatory postural adjustment?

Methods

Part 1: Predictive Simulation

A predictive simulation using direct collocation (OpenSim Moco [10]) was used to explore which cost function is required to elicit a physiological APA response without input data. This simulation used the planar muscle-driven 2D_gait.osim model included in the example2Dwalking Moco example. This simplified model has 10 degrees of freedom and a contact model with two contact spheres per foot. Since the predicted rise to toes was found to be sensitive to the initial state of the model, a standing simulation was performed which minimized effort over 0.5 seconds. The state bounds can be found in Figure 2 below. The final state from the standing solution was extracted and set to the initial state for the rise to toes simulation. The coordinates were loosely bound, as in the standing problem, to maintain a rise to toes solution but given freedom to explore coordination strategies. The model was constrained to start at the standing solution and finish with 20-25 degrees of plantar flexion. The knees were constrained to finish fully extended and the hips between 5 degrees extension to 15 degrees flexion to ensure the intended task. This mimics participant instructions to ‘keep legs straight’ and helps find a solution where the legs are kept together. Next, we explored how modifying the time bounds affected the simulated rise to toes, by incrementally decreasing the final time bound. Additional cost terms were added to the problem goal to determine which cost terms elicit reported physiological APAs [7]. It was hypothesized that COM acceleration is controlled for balance and stability; therefore, minimizing the integral of squared anterior-posterior and vertical acceleration was added as a goal, with varying weights. The resulting anterior-posterior COP and COM displacements were validated against reported values in Adkin, 2002 [7].

Figure 2: OpenSim Moco problem description for standing and rise to toes prediction

Part 2: Tracking Simulation

A tracking simulation in OpenSim Moco [10] was also used to investigate the simulated APA response in a rise to toes task with input experimental data from OpenCap [9]. Our simulations tracked 1-2 seconds of OpenCap kinematic data, with an initial posture of standing upright with feet flat on the ground and ending on the toes with approximately 8 degrees of plantar flexion. The 2D muscle driven model used in the predictive simulation and a 3D torque driven model were used in parallel simulations. From these simulations, we can evaluate the motion, center of pressure changes, and center of mass position. 

2D tracking simulation: 

The model used in this problem was a planar muscle driven model, “2D_gait.osim”, which was included in the Moco example “example2Dwalking” and used in the predictive simulation. It contains 10 degrees of freedom, 9 muscles per leg, and 2 contact spheres per foot. The input kinematic data to be tracked was from the file “posture_2D_tracking.mot”, from 13.4 to 14.4 seconds. This file was slightly adjusted from the original 3D OpenCap data file to make it suitable for tracking with this 2D model by renaming “lumbar_extension” to “lumbar” and changing the signs of  “knee_angle_r” and “knee_angle_l” to correct for the difference in flexion/extension direction between the models. 

To improve performance, this problem was set with the same initial states as the predictive simulation. The states bounds from the predictive solution were also included, with a change in the knee angle coordinates to allow up to 10 degrees of knee flexion, which was more representative of the experimental data. All final states were removed and only the experimental data provided input for the rest of the trajectory. This problem was first set with 2 goals, minimizing effort with a weight of 1, and minimizing tracking error with a weight of 100. Then, an additional goal to minimize center of mass acceleration was added with a weight of 2. Results of these simulations were validated by comparing anterior-posterior center of pressure and center of mass positions with the results in Adkin, 2007 [7] and plotting the kinematic results with the OpenCap kinematic data. 

3D tracking simulation:

Next, we reframed the problem for 3D tracking. The scaled model used here was the output model from our OpenCap data, modified to include foot contact spheres (“LaiArnoldModified2017_poly_withArms_weldHand_scaled_addContacts.osim”). It contains 33 degrees of freedom, 40 muscles per leg, and 6 contact spheres per foot. For this simulation, each muscle was removed and replaced with a 250 Nm torque actuator. Additionally, the coordinates in the upper body were locked and the subtalar joint welded. The input kinematic OpenCap data used is from 13 to 15 seconds in the file “posture_3D_tracking.mot”. In this version of the problem, we did not set initial states, but instead provided an initial guess of the previous solution so that we could repeatedly iterate on solutions. Similar to the 2D problem, there were 3 goals, minimizing tracking error, effort, and center of mass acceleration. Here the weights were set at 100 for tracking, 0.01 for effort, and 1 for acceleration. Results of these simulations were validated by comparing anterior-posterior center of pressure and center of mass positions with the results in Adkin, 2007 [7] and plotting the kinematic results with the OpenCap kinematic data.

Results

Part 1: Predictive Solution

The predictive simulations revealed that dorsiflexion is required to complete a rise to toes task, even though the dominant movement during a rise to toes is plantar flexion. Simulations which constrained the ankle coordinates to only plantar flexion could not converge. This agrees with the notion of an APA where the subject must move in a way that destabilizes the COM in the direction of intended motion, in this case dorsiflexing to destabilize the COM forward.

The problem defined in Figure 2 resulted in a minimal effort solution that produced a realistic rise to toes motion. The COP and COM anterior posterior (A-P) displacements are shown below in Figure 3 for the minimum effort solution with varying final time constraints. An APA (ie posterior shift in COP) is present in all of the solutions. As the time to complete the task decreases, the APA magnitude and duration also increases. This could indicate that APAs play a role in movement or task efficiency. Completing the task in 1.0 to 1.1 seconds, is closest in timing to what has been reported in literature, but has a smaller APA than what has been shown during a healthy, confident rise to toes task [7]. Therefore, it was worth exploring what other goals, in addition to minimizing effort, may be present to elicit the physiological APA response. 

Figure 3: Anterior-posterior COM (dashed lines) and COP (solid lines) displacement during a predicted rise to toes task with varying final time constraints. 

Figure 4a demonstrates the results for increasing the weight of a cost term which minimizes the integral of squared anterior-posterior acceleration. These results demonstrate that increasing the weight of an A-P acceleration penalty resulted in a smaller posterior shift and more gradual anterior shift in COP during the rise-to-toes. Slightly rewarding A-P acceleration increased the COP posterior shift. The COP displacement demonstrated higher variability compared to the COM displacement when adjusting the weight of the  A-P acceleration goal. 

As seen in Figure 4b, increasing the weight of a vertical acceleration goal (minimizing the integral of vertical acceleration squared)  resulted in a larger APA response, in both magnitude and duration. In fact, the largest weight resulted in a solution that most closely followed reported physiological APAs [7]. This result was surprising, but could reveal insight to the priority of the nervous system to reduce vertical accelerations for stability. It could also be a result of minimizing the integral of acceleration squared, rather than the peak acceleration during the task.

Figure 4: Anterior-posterior COM (dashed lines) and COP (solid lines) displacement during a predicted rise to toes task. The cost function included an effort term (weight = 1) and COM acceleration terms with increasing weight. The left figure (a) shows anterior-posterior COM acceleration squared and on the right (b) is vertical COM acceleration squared. 

The predicted rise to toes were compared against reported APAs [7], as shown in Figure 5 below. Figure 5a has the reported LOW AWAY response [7] which is a rise to toes performed on a low platform far from the edge. This is a ‘confident’ rise to toes. In contrast, the rise to toes shown in Figure 5c is the reported HIGH EDGE response which is a rise to toes performed on a high platform close to the edge. This is a ‘fear of falling’ rise to toes. 

Figure 5: Validation of predicted rise-to-toes against reported values [7]. The A-P COP and COM displacement from a predicted rise to toes with an effort weight of 1 and vertical acceleration squared weight of 2 (b) closely matches the reported ‘confident’ LOW AWAY rise to toes (a) Figure from [7].  The A-P COP and COM displacement from a predicted rise to toes with an effort weight of 1 and anterior-posterior acceleration squared weight of 2 (d) closely matches the reported ‘fear of falling’ HIGH EDGE rise to toes (c) Figure from [7]. 

When comparing results to those reported, we found the solution which minimized the integral of vertical acceleration squared with a weight of 2 (effort weight of 1) resulted in a COP and COM trajectory which matched the confident rise to toes, in overall shape, APA magnitude, and duration. In contrast, the solution which minimized the integral of anterior-posterior acceleration squared with a weight of 2 (effort weight of 1) resulted in a COP and COM trajectory which matched the fear of falling rise to toes, in overall shape, APA magnitude, and duration. This makes sense as someone at the edge of a high platform would avoid large forward accelerations. 

Various properties of the COP and COM trajectories were estimated from plots in the literature [7] and our predicted solutions, as shown in Table 1. While there are some discrepancies in magnitude, the values are overall in similar ranges to those reported in the literature, thereby increasing confidence in the prediction solution. Also, the trend from anterior-posterior acceleration cost to vertical acceleration cost followed the trend from the fear of falling (HIGH EDGE) to confident (LOW AWAY) response, further emphasizing the role of cost function terms in eliciting a unique APA response. 

Table 1: Comparison of reported rise-to-toes APA properties to predicted rise-to-toes properties. Note: these values are estimates taken from plots for the purpose of general comparison

The APA muscle activations during the rise-to-toes was also compared to the literature [7]. Shown in Figure 6a below is the left and right lower limb muscle activations during the confident rise to toes and in Figure 6b is the right lower limb muscle activations from the predicted rise to toes, along with the right COP trajectory. The solution correctly predicts tibialis anterior (dorsiflexor) muscle activation onset prior to peak COP posterior displacement. It also shows gastrocnemius and soleus (plantar flexors) muscle activation onset after peak COP posterior displacement. 

Figure 6: (a) Experimental tibialis anterior (TA), soleus (SO) and gastrocnemius (GA) profiles for left (L) and right (R) limbs for LOW AWAY condition. Figure from [7]. (b) Muscle activations of the right leg during predicted rise-to-toes with effort (weight = 1) and vertical acceleration squared (weight = 2). 

Part 2: Tracking Solution

Despite having kinematic data to track, the 2D tracking simulation was still sensitive to initial position. In this problem, without the initial states and bounds similar to those used in the predictive problem, this simulation had difficulty converging to a rise to toes motion in contact with the ground. However, the differences between the set initial position and the position it was trying to track may have influenced the results. Figure 7 below shows the anterior-posterior COP and COM positions for simulations with and without a center of mass acceleration cost term. We obtain similar results for both of these simulations, including an asymmetric response between the left and right legs. The motion tracking for these two versions of the simulation have only subtle differences, so for clarity, the tracked kinematics from the simulation with all three cost function terms (tracking, effort, and COM acceleration) is compared to those from OpenCap in Figure 8. 

Figure 7: Anterior-posterior COM (dashed lines) and COP (solid lines) displacement during a 2D muscle driven tracked rise to toes task. The cost function included an effort term (weight = 1), and a tracking term (weight = 100). The green lines, labeled ‘With Accel’, also included a COM acceleration term (weight = 2), while the purple lines, labeled ‘No Accel’, do not have this term. 

Figure 8: OpenCap kinematics compared to 2D muscle driven tracking results of the simulation including a  tracking term (weight = 100), effort term (weight = 1), and a COM acceleration term (weight = 2). Positive angles indicate flexion and negative angles indicate extension.

By looking only at the COP plot (Figure 7), it may seem like there is an APA response from the left leg. However, evaluating this plot in conjunction with the kinematic results in Figure 8, we see that the posterior shift in COP occurs during a rapid adjustment of hip flexion. This change in hip flexion angle may occur as the simulation moves from the set initial position in an attempt to more closely match the data it’s tracking. The differences between the COP change with and without an acceleration cost term may also be attributed to this kinematic change. The COP of the left leg in the simulation with the acceleration term (light green line) does not fall as quickly as the other values, perhaps due to minimizing its acceleration change. Additionally, the plots of kinematics in Figure 8, show that the first 0.4 seconds have a greater tracking error than the latter 0.6 seconds, but the beginning segment is the time period in which an expected APA would occur. Therefore, it is unclear if the COP response plotted here is physiological or created through kinematic changes that do not match the experimental data. Future work including adjusting starting times and positions of the simulation and collecting force plate data for validation would help to answer this question. 

The 3D torque driven tracking simulation did not require a set initial position to converge to a realistic rise to toes motion. The final solution was obtained through an iterative process in which the previous solution was set as the next initial guess. Results for the COP and COM positions and motion tracking are shown in Figures 9 and 10 below. 

Figure 9: Left) Anterior-posterior COM (dashed line) and COP (solid lines) displacement during a 3D torque driven tracked rise to toes task. The cost function included an effort term (weight = 0.01), a tracking term (weight = 100), and a COM acceleration term (weight = 1). The COP result can be compared to Right) the result reported in Adkin, 2007 [7]. 

Figure 10: OpenCap kinematics compared to 3D torque driven tracking results of the simulation including a  tracking term (weight = 100), effort term (weight = 0.01), and a COM acceleration term (weight = 1). Positive angles indicate flexion and negative angles indicate extension.

Similar to the 2D solution, this tracking problem displays asymmetry between the left and right legs. Contrary to the 2D solution, the tracked solution in this simulation is almost identical to the input OpenCap data. The right leg does elicit a response with a shape similar to the expected physiological APA as reported in Adkin, 2007 [7]. However, the posterior shift is approximately 2 cm instead of the reported 4 cm, and its duration of 0.6 s is double the expected duration of 0.3 s. 

As the results from the predictive simulation indicate, APA response in a rise to toes task may depend on the time in which the task is performed and the initial starting position. It is possible that in the segment of data tracked here, the person performing the toe rise began the movement with their center of pressure already shifted backwards. Additionally, this toe rise was completed slowly, which may contribute to the extended posterior shift in center of pressure in the 3D tracking results. 

Conclusion

Overall, a predictive minimal effort toe rise elicits the expected posterior shift in COP in a predictive rise to toes simulation. Unique APAs are produced by minimizing center of mass anterior-posterior and vertical accelerations, and these results match closely with ‘fearful’ and ‘confident’ rise to toes APAs as reported in Adkin, 2007 [7]. Tracking simulations of rise to toes with effort and center of mass acceleration goals may also elicit a similar shift in COP, but more investigation is needed. 

Limitations

While the A-P and vertical acceleration goals generated solutions with similar characteristics to the confident and fear of falling rise to toes, conclusions regarding the intent or goal of the nervous system while completing the task must be made with caution due to the complexity of the system. There are many aspects of motor control that were ignored or simplified in this approach. However, these results provide a framework for which we can study and understand APAs at a deeper level. Both the predictive and tracking simulations use a 2D model that does not have a metatarsophalangeal (MTP) joint, which is likely important for simulation of a rise to toes task which relies on foot and ankle kinematics. For this project, the main limitation was the lack of experimental ground reaction force data for validation. As previously described, the analysis of the tracking solutions was limited without being able to characterize the GRF errors.

Future Work

As mentioned previously in the results and limitations, validating our results against force plate data is an important next step for the tracking solutions. Working towards a 3D-muscle drive model, including an MTP joint, will also be important, particularly for capturing asymmetries. Collecting data at various speeds of rise to toes would allow for interesting comparisons of APA response and validation of the predictive simulation time results. Future work will also include the development of custom Moco goals specific to balance, including whole-body angular momentum. It will also be interesting to extend this framework to a larger range of movement tasks where APAs are clinically important.

Acknowledgments

We would like to thank the entire BIOE 485 teaching team, Scott Delp, Nick Bianco, Carmichael Ong, Reed Gurchiek, Jon Stingel, and Nicos Haralabidis, for their invaluable support in problem formulation and technical support using OpenSim Moco.

References

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