Stability in a frontal plane model of balance requires coupled changes to postural configuration and neural feedback control.

Postural stability depends on interactions between the musculoskeletal system and neural control mechanisms. We present a frontal plane model stabilized by delayed feedback to analyze the effects of altered stance width on postural responses to perturbations. We hypothesized that changing stance width alters the mechanical dynamics of the body and limits the range of delayed feedback gains that produce stable postural behaviors. Surprisingly, mechanical stability was found to decrease as stance width increased due to decreased effective inertia. Furthermore, due to sensorimotor delays and increased leverage of hip joint torque on center-of-mass motion, the magnitudes of the stabilizing delayed feedback gains decreased as stance width increased. Moreover, the ranges of the stable feedback gains were nonoverlapping across different stance widths such that using a single neural feedback control strategy at both narrow and wide stances could lead to instability. The set of stable feedback gains was further reduced by constraints on foot lift-off and perturbation magnitude. Simulations were fit to experimentally measured kinematics, and the identified feedback gains corroborated model predictions. In addition, analytical gain margin of the linearized system was found to predict step transitions without the need for simulation. In conclusion, this model offers a method to dissociate the complex interactions between postural configuration, delayed sensorimotor feedback, and nonlinear foot lift-off constraints. The model demonstrates that stability at wide stances can only be achieved if delayed neural feedback gains decrease. This model may be useful in explaining both expected and paradoxical changes in stance width in healthy and neurologically impaired individuals.

Neuromechanical tuning of nonlinear postural control dynamics.

Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.

Validation of a non-invasive fluoroscopic imaging technique for the measurement of dynamic knee joint motion.

The accurate measurement of the in vivo knee joint kinematics in six degrees-of-freedom (6DOF) remains a challenge in biomedical engineering. We have adapted a dual fluoroscopic imaging system (DFIS) to investigate the various in vivo dynamic knee joint motions. This paper presents a thorough validation of the accuracy and repeatability of the DFIS system when used to measure 6DOF dynamic knee kinematics. First, the validation utilized standard geometric spheres made from different materials to demonstrate the capability of the DFIS technique to determine the object positions under changing speeds. The translational pose of the spheres could be recreated to less than 0.15+/-0.09 mm for velocities below 300 mm/s. Next, tantalum beads were inserted into the femur and tibia of two fresh frozen cadaver knees to compare the dynamic kinematics measured by matching knee models to the kinematics from the tantalum bead matching-a technique similar to Roentgen stereophotogrammetric analysis (RSA). Each cadaveric knee was attached to the crosshead of a tensile testing machine and vertically translated at a rate of 16.66 mm/s while images were captured with the DFIS. Subsequently, the tibia was held fixed and the femur manually flexed from full extension to 90 degrees of flexion, as the DFIS acquired images. In vitro translation of the cadaver knee using the tensile testing machine deviated from predicted values by 0.08+/-0.14 mm for the matched knee models. The difference between matching the knee and tantalum bead models during the dynamic flexion-extension motion of the knee was 0.1+/-0.65 degrees /s in flexion speed; 0.24+/-0.16 mm in posterior femoral translation; and 0.16+/-0.61 degrees in internal-external tibial rotation. Finally, we applied the method to investigate the knee kinematics of a living subject during a step ascent and treadmill gait. High repeatability was demonstrated for the in vivo application. Thus, the DFIS provides an easy and powerful tool for accurately determining 6DOF positions of the knee when performing daily functional activities.

Accuracy of force and center of pressure measures of the Wii Balance Board.

The Nintendo Wii Balance Board (WBB) is increasingly used as an inexpensive force plate for assessment of postural control; however, no documentation of force and COP accuracy and reliability is publicly available. Therefore, we performed a standard measurement uncertainty analysis on 3 lightly and 6 heavily used WBBs to provide future users with information about the repeatability and accuracy of the WBB force and COP measurements. Across WBBs, we found the total uncertainty of force measurements to be within ± 9.1N, and of COP location within ± 4.1mm. However, repeatability of a single measurement within a board was better (4.5 N, 1.5mm), suggesting that the WBB is best used for relative measures using the same device, rather than absolute measurement across devices. Internally stored calibration values were comparable to those determined experimentally. Further, heavy wear did not significantly degrade performance. In combination with prior evaluation of WBB performance and published standards for measuring human balance, our study provides necessary information to evaluate the use of the WBB for analysis of human balance control. We suggest the WBB may be useful for low-resolution measurements, but should not be considered as a replacement for laboratory-grade force plates.

Stability radius as a method for comparing the dynamics of neuromechanical systems.

Robust motor behaviors emerge from neuromechanical interactions that are nonlinear, have delays, and contain redundant neural and biomechanical components. For example, in standing balance a subject's muscle activity (neural control) decreases as stance width (biomechanics) increases when responding to a lateral perturbation, yet the center-of-mass motion (behavior) is nearly identical regardless of stance width. We present stability radius, a technique from robust control theory, to overcome the limitations of classical stability analysis tools, such as gain margin, which are insufficient for predicting how concurrent changes in both biomechanics (plant) and neural control (controller) affect system behavior. We first present the theory and then an application to a neuromechanical model of frontal-plane standing balance with delayed feedback. We show that stability radius can quantify differences in the sensitivity of system behavior to parameter changes, and predict that narrowing stance width increases system robustness. We further demonstrate that selecting combinations of stance width (biomechanics) and feedback gains (neural control) that have the same stability radius produce similar center-of-mass behavior in simulation. Therefore, stability radius may provide a useful tool for understanding neuromechanical interactions in movement and could aid in the design of devices and therapies for improving motor function.

Neuromechanic: a computational platform for simulation and analysis of the neural control of movement.

Neuromusculoskeletal models solve the basic problem of determining how the body moves under the influence of external and internal forces. Existing biomechanical modeling programs often emphasize dynamics with the goal of finding a feed-forward neural program to replicate experimental data or of estimating force contributions or individual muscles. The computation of rigid-body dynamics, muscle forces, and activation of the muscles are often performed separately. We have developed an intrinsically forward computational platform (Neuromechanic, www.neuromechanic.com) that explicitly represents the interdependencies among rigid body dynamics, frictional contact, muscle mechanics, and neural control modules. This formulation has significant advantages for optimization and forward simulation, particularly with application to neural controllers with feedback or regulatory features. Explicit inclusion of all state dependencies allows calculation of system derivatives with respect to kinematic states and muscle and neural control states, thus affording a wealth of analytical tools, including linearization, stability analyses and calculation of initial conditions for forward simulations. In this review, we describe our algorithm for generating state equations and explain how they may be used in integration, linearization, and stability analysis tools to provide structural insights into the neural control of movement.

Analysis of tibiofemoral cartilage deformation in the posterior cruciate ligament-deficient knee.

BACKGROUND: Degeneration of the tibiofemoral articular cartilage often develops in patients with posterior cruciate ligament deficiency, yet little research has focused on the etiology of this specific type of cartilage degeneration. In this study, we hypothesized that posterior cruciate ligament deficiency changes the location and magnitude of cartilage deformation in the tibiofemoral joint. METHODS: Fourteen patients with a posterior cruciate ligament injury in one knee and the contralateral side intact participated in the study. First, both knees were imaged with use of a specific magnetic resonance imaging sequence to create three-dimensional knee models of the surfaces of the bone and cartilage. Next, each patient performed a single leg lunge as images were recorded with a dual fluoroscopic system at 0 degrees, 30 degrees, 60 degrees, 75 degrees, 90 degrees, 105 degrees, and 120 degrees of knee flexion. Finally, the three-dimensional knee models and fluoroscopic images were used to reproduce the in vivo knee position at each flexion angle with use of a previously described image-matching method. With use of these series of knee models, the location and magnitude of peak tibiofemoral cartilage deformation at each flexion angle were compared between the intact contralateral and posterior cruciate ligament-deficient knees. RESULTS: In the medial compartment of the posterior cruciate ligament-deficient knees, the location and magnitude of peak cartilage deformation were significantly changed, compared with those in the intact contralateral knees, between 75 degrees and 120 degrees of flexion, with a more anterior and medial location of peak cartilage deformation on the tibial plateau as well as increased deformation of the cartilage. In the lateral compartment, no significant differences in the location or magnitude of peak cartilage deformation were found between the intact and posterior cruciate ligament-deficient knees. CONCLUSIONS: The altered kinematics associated with posterior cruciate ligament deficiency resulted in a shift of the tibiofemoral contact location and an increase in cartilage deformation in the medial compartment beyond 75 degrees of knee flexion. The magnitude of the medial contact shift in the posterior cruciate ligament-deficient knee was on the same order as that of the anterior contact shift.

Increased tibiofemoral cartilage contact deformation in patients with anterior cruciate ligament deficiency.

OBJECTIVE: To investigate the in vivo cartilage contact biomechanics of the tibiofemoral joint following anterior cruciate ligament (ACL) injury. METHODS: Eight patients with an isolated ACL injury in 1 knee, with the contralateral side intact, participated in the study. Both knees were imaged using a specific magnetic resonance sequence to create 3-dimensional models of knee bone and cartilage. Next, each patient performed a lunge motion from 0 degrees to 90 degrees of flexion as images were recorded with a dual fluoroscopic system. The three-dimensional knee models and fluoroscopic images were used to reproduce the in vivo knee position at each flexion angle. With this series of knee models, the location of the tibiofemoral cartilage contact, size of the contact area, cartilage thickness at the contact area, and magnitude of the cartilage contact deformation were compared between intact and ACL-deficient knees. RESULTS: Rupture of the ACL changed the cartilage contact biomechanics between 0 degrees and 60 degrees of flexion in the medial compartment of the knee. Compared with the contralateral knee, the location of peak cartilage contact deformation on the tibial plateaus was more posterior and lateral, the contact area was smaller, the average cartilage thickness at the tibial cartilage contact area was thinner, and the resultant magnitude of cartilage contact deformation was increased. Similar changes were observed in the lateral compartment, with increased cartilage contact deformation from 0 degrees to 30 degrees of knee flexion in the presence of ACL deficiency. CONCLUSION: ACL deficiency alters the in vivo cartilage contact biomechanics by shifting the contact location to smaller regions of thinner cartilage and by increasing the magnitude of the cartilage contact deformation.