Wangdo Kim

Role of plantar fascia in the load bearing capacity of the human foot

Plantar fascia release is an accepted and widely used surgical way to reduce heel pain, however its effect of the load bearing characteristics of the foot is not well studied. A simple biomechanical model is developed here to analyze load bearing mechanism of the foot during the stance phase of the gait cycle. Quasilinearization is used for the system identification, and all models parameters are determined from the in vivo tests. The model is used to compare the load bearing mechanism of different pathological situations. The results of the study suggest that the plantar fascia carries as much as 14% of the total load on the foot. Its surgical release decreases dynamic loading on the ankle by only 10%. It is also found that the lowering of the arch degenerates the load bearing capacity of the foot. Thus, the plantar fascia plays an important part in the load bearing by the foot and its surgical release should be carefully considered.

Measurement of the Impulsive Bone Motion by Skin-Mounted Accelerometers

A measurement system was designed to investigate longitudinal wave propagation through the lower extremity generated from foot strikes. The principal goal of the design was to eliminate measurement time lag and amplitude reduction, such that the acceleration measured by Skin Mounted Accelerometer--SMA is equal to the actual acceleration of the bone measured by Bone Mounted Accelerometer--BMA. For accurate dynamic measurement, it is important that the gain and phase of the measurement system are as close as possible to a constant and zero, respectively, for the frequency range being covered. An in vitro experiment was carried out to simultaneously measure skin and bone accelerations. The obtained information was used for identification of a linear spring/damper model representing the interface between the BMA and the SMA. The present work showed that the SMA overestimated the BMA by 12 percent in the signals between 15-30 Hz.

Modeling of heel strike transients during running

Abstract The goal of this study is to develop a mathematical model that can describe the dissipation and attenuation of the shock wave initiated during the impact of the foot striking the ground. A three-degree-of-freedom spring-damper-mass system was conceived as an equivalent model of the lower extremity. The mathematical model that was developed was used to investigate the shock absorption phenomena of the human body. The model and solution procedure were verified by a drop test. The instant of the impact of landing was assumed to be equivalent to foot strike transients. The results showed that the quasilinearization technique can identify the spring and damping constants of the system at the instant of impact fairly accurately. The acceleration pattern as predicted from the proposed model was very close to the measured one. The model was used to analyze the effect of the ground and footwear damping and spring constants on the dynamic loading on the human musculoskeletal system. It was shown that changes in the spring constant do not have a significant effect on the ground reaction forces, while increase of the damping constant resulted in decrease of this force. Thus, the damping constant is the dominant factor in controlling the impact on the human musculoskeletal system.

Wound measurement by curvature maps: a feasibility study

A non-contact wound measurement method by laser scanner and curvature maps is presented. A patients foot ulcer is scanned by FastSCAN ten times over a three-week period. With the surfaces 3D coordinates, curvature maps of the ulcerous area are calculated. Utilizing a specified rim curvature value, the wound edge is detected and processed via cubic spline smoothing, which is qualitatively verified by a photograph. Subsequently, the depth, area and volume of the wound can be calculated. The results indicate that laser scanning followed by curvature analysis might be a potential clinical tool for non-contact measurement of wounds.

An inverse method for predicting tissue-level mechanics from cellular mechanical input

Extracellular matrix (ECM) provides a dynamic three-dimensional structure which translates mechanical stimuli to cells. This local mechanical stimulation may direct biological function including tissue development. Theories describing the role of mechanical regulators hypothesize the cellular response to variations in the external mechanical forces on the ECM. The exact ECM mechanical stimulation required to generate a specific pattern of localized cellular displacement is still unknown. The cell to tissue inverse problem offers an alternative approach to clarify this relationship. Developed for structural dynamics, the inverse dynamics problem translates measurements of local state variables (at the cell level) into an unknown or desired forcing function (at the tissue or ECM level). This paper describes the use of eigenvalues (resonant frequencies), eigenvectors (mode shapes), and dynamic programming to reduce the mathematical order of a simplified cell-tissue system and estimate the ECM mechanical stimulation required for a specified cellular mechanical environment. Finite element and inverse numerical analyses were performed on a simple two-dimensional model to ascertain the effects of weighting parameters and a reduction of analytical modes leading toward a solution. Simulation results indicate that the reduced number of mechanical modes (from 30 to 14 to 7) can adequately reproduce an unknown force time history on an ECM boundary. A representative comparison between cell to tissue (inverse) and tissue to cell (boundary value) modeling illustrates the multiscale applicability of the inverse model.

Using dual Euler angles for the analysis of arm movement during the badminton smash

Camera techniques are typically used in the study of human movement. However, as the number of joints and markers involved in a study increases, data extraction and calculation become increasingly tedious and complicated. To overcome this challenge, we propose a method of study that simplifies data extraction and calculation by using an electrogoniometer and dual Euler angles. The contribution of the rotation of each arm segment to produce a racket head’s speed was identified in the context of a badminton smash. The contribution of each segment rotation was computed using dual velocity analysis. A set of orthogonal Cartesian frames was established for computing the anatomical rotational velocities for each of the three segments of the upper arm. Electrogoniometers were attached to the subjects during the execution of the smash to obtain measurements of joint angles throughout the motion. To test the algorithm, the calculated velocity of the racket head was compared to the measured velocity. The calculated velocity was derived from an algorithm, while the measured velocity was obtained from a video image. The results are similar, indicating that the dual velocity method is suitable for determining segmental velocities in such kinematic situations.

The Stationary Configuration of the Knee

BACKGROUND Ligaments and cartilage contact contribute to the mechanical constraints in the knee joints. However, the precise influence of these structural components on joint movement, especially when the joint constraints are computed using inverse dynamics solutions, is not clear. METHODS We present a mechanical characterization of the connections between the infinitesimal twist of the tibia and the femur due to restraining forces in the specific tissue components that are engaged and responsible for such motion. These components include the anterior cruciate, posterior cruciate, medial collateral, and lateral collateral ligaments and cartilage contact surfaces in the medial and lateral compartments. Their influence on the bony rotation about the instantaneous screw axis is governed by restraining forces along the constraints explored using the principle of reciprocity. RESULTS Published kinetic and kinematic joint data (American Society of Mechanical Engineers Grand Challenge Competition to Predict In Vivo Knee Loads) are applied to define knee joint function for verification using an available instrumented knee data set. We found that the line of the ground reaction force (GRF) vector is very close to the axis of the knee joint. It aligns the knee joint with the GRF such that the reaction torques are eliminated. The reaction to the GRF will then be carried by the structural components of the knee instead. CONCLUSIONS The use of this reciprocal system introduces a new dimension of foot loading to the knee axis alignment. This insight shows that locating knee functional axes is equivalent to the static alignment measurement. This method can be used for the optimal design of braces and orthoses for conservative treatment of knee osteoarthritis.

An informational framework to predict reaction of constraints using a reciprocally connected knee model

Researchers have used screw theory to describe the motion of the knee in terms of instantaneous axes of the knee (IAK). However, how geometric change to the dynamic alignment of IAK may affect stance phase of foot loading has not yet been fully explained. We have tested our informational framework through readily accessible benchmark data (Fregly et al. 2012): muscle contraction and ground reaction force are compounded into a wrench that is reciprocal to the IAK and resolved into component wrenches belonging to the reciprocal screw system. This revealed the special screw system that defines the freedom available to the knee and more precisely revealed how to measure this first order of freedom. After this step, we determined the reciprocal screw system, which involves the theory of equilibrium. Hence, a screw system of the first order will have a screw system of the fifth order as its reciprocal. We established a framework the estimation of reaction of constraints about the knee using a process that is simplified by the judicious generation of IAK for the first order of freedom in equilibrium.

An Informational Algorithm as the Basis for Perception-Action Control of the Instantaneous Axes of the Knee

Traditional locomotion studies emphasize an optimization of the desired movement trajectories while ignoring sensory feedback. We propose an information based theory that locomotion is neither triggered nor commanded but controlled. The basis for this control is the information derived from perceiving oneself in the world. Control therefore lies in the human-environment system. In order to test this hypothesis, we derived a mathematical foundation characterizing the energy that is required to perform a rotational twist, with small amplitude, of the instantaneous axes of the knee (IAK). We have found that the joint’s perception of the ground reaction force may be replaced by the co-perception of muscle activation with appropriate intensities. This approach generated an accurate comparison with known joint forces and appears appropriate in so far as predicting the effect on the knee when it is free to twist about the IAK.

Tracking Knee Joint Functional Axes through Tikhonov Filtering and Plűcker Coordinates

Researchers have reported several compensation methods to estimate bone and joint position from a cluster of skin-mounted markers as influenced by Soft Tissue Artifacts (STA). Tikhonov Regularization Filtering (TRF) as a means to estimate Instantaneous Screw Axes (ISA) was introduced here as a means to reduce the displacement of a rigid body to its simplest geometric form. Recent studies have suggested that the ISA of the knee, i.e., Knee Functional Axes (KFA), might be closely connected to the estimation of constraint forces such as those due to medial and lateral connective tissues. The estimations of ISAs were known to be highly sensitive to noisy data, which may be mathematically ill-posed, requiring smoothing such as that conducted by regularization. The main contribution in this work was to establish the reciprocal connection between the KFA and Ground Reaction Forces (GRF) as a means to estimate joint constraint forces. Presented results compare the computational performance with published kinetic and kinematic joint data generated from an instrumented total knee replacement. Implications of these preliminary findings with respect to dynamic alignment as a functional anatomic metric are discussed.