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      A Dynamic Finite Element Analysis of Human Foot Complex in the Sagittal Plane during Level Walking

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          Abstract

          The objective of this study is to develop a computational framework for investigating the dynamic behavior and the internal loading conditions of the human foot complex during locomotion. A subject-specific dynamic finite element model in the sagittal plane was constructed based on anatomical structures segmented from medical CT scan images. Three-dimensional gait measurements were conducted to support and validate the model. Ankle joint forces and moment derived from gait measurements were used to drive the model. Explicit finite element simulations were conducted, covering the entire stance phase from heel-strike impact to toe-off. The predicted ground reaction forces, center of pressure, foot bone motions and plantar surface pressure showed reasonably good agreement with the gait measurement data over most of the stance phase. The prediction discrepancies can be explained by the assumptions and limitations of the model. Our analysis showed that a dynamic FE simulation can improve the prediction accuracy in the peak plantar pressures at some parts of the foot complex by 10%–33% compared to a quasi-static FE simulation. However, to simplify the costly explicit FE simulation, the proposed model is confined only to the sagittal plane and has a simplified representation of foot structure. The dynamic finite element foot model proposed in this study would provide a useful tool for future extension to a fully muscle-driven dynamic three-dimensional model with detailed representation of all major anatomical structures, in order to investigate the structural dynamics of the human foot musculoskeletal system during normal or even pathological functioning.

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          The spring in the arch of the human foot.

          Large mammals, including humans, save much of the energy needed for running by means of elastic structures in their legs and feet. Kinetic and potential energy removed from the body in the first half of the stance phase is stored briefly as elastic strain energy and then returned in the second half by elastic recoil. Thus the animal runs in an analogous fashion to a rubber ball bouncing along. Among the elastic structures involved, the tendons of distal leg muscles have been shown to be important. Here we show that the elastic properties of the arch of the human foot are also important.
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            Kinematic analysis of a multi-segment foot model for research and clinical applications: a repeatability analysis.

            An unbiased understanding of foot kinematics has been difficult to achieve due to the complexity of foot structure and motion. We have developed a protocol for evaluation of foot kinematics during barefoot walking based on a multi-segment foot model. Stereophotogrammetry was used to measure retroreflective markers on three segments of the foot plus the tibia. Repeatability was evaluated between-trial, between-day and between-tester using two subjects and two testers. Subtle patterns and ranges of motion between segments of the foot were consistently detected. We found that repeatability between different days or different testers is primarily subject to variability of marker placement more than inter-tester variability or skin movement. Differences between inter-segment angle curves primarily represent a shift in the absolute value of joint angles from one set of trials to another. In the hallux, variability was greater than desired due to vibration of the marker array used. The method permits objective foot measurement in gait analysis using skin-mounted markers. Quantitative and objective characterisation of the kinematics of the foot during activity is an important area of clinical and research evaluation. With this work we hope to have provided a firm basis for a common protocol for in vivo foot study.
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              Whole body inverse dynamics over a complete gait cycle based only on measured kinematics.

              This paper presents a three-dimensional (3D) whole body multi-segment model for inverse dynamics analysis over a complete gait cycle, based only on measured kinematic data. The sequence of inverse dynamics calculations differs significantly from the conventional application of inverse dynamics using force plate data. A new validated "Smooth Transition Assumption" was used to solve the indeterminacy problem in the double support phase. Kinematic data is required for all major body segments and, hence, a whole body gait measurement protocol is presented. Finally, sensitivity analyses were conducted to evaluate the effects of digital filtering and body segment parameters on the accuracy of the prediction results. The model gave reasonably good estimates of sagittal plane ground forces and moment; however, the estimates in the other planes were less good, which we believe is largely due to their small magnitudes in comparison to the sagittal forces and moment. The errors observed are most likely caused by errors in the kinematic data resulting from skin movement artefact and by errors in the estimated body segment parameters. A digital filtering cut-off frequency of 4.5 Hz was found to produce the best results. It was also shown that errors in the mass properties of body segments can play a crucial role, with changes in properties sometimes having a disproportionate effect on the calculated ground reactions. The implication of these results is that, even when force plate data is available, the estimated joint forces are likely to suffer from similar errors.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, USA )
                1932-6203
                2013
                11 November 2013
                : 8
                : 11
                : e79424
                Affiliations
                [1 ]Key Laboratory of Bionic Engineering, Jilin University, Changchun, P.R. China
                [2 ]School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester, United Kingdom
                [3 ]Editorial Department of Journal of Bionic Engineering, Jilin University, Changchun, P.R. China
                [4 ]Structure and Motion Laboratory, The Royal Veterinary College, University of London, Hatfield, United Kingdom
                German Cancer Research Center, Germany
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Conceived and designed the experiments: LR. Performed the experiments: ZHQ LR. Contributed reagents/materials/analysis tools: YD JRH LQR. Wrote the paper: ZHQ LR. Finite Element Modelling: ZHQ LR.

                Article
                PONE-D-13-04052
                10.1371/journal.pone.0079424
                3823660
                24244500
                d298fff0-be67-4f0d-95bc-acfc5afafb61
                Copyright @ 2013

                This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 23 January 2013
                : 23 September 2013
                Page count
                Pages: 10
                Funding
                This work was supported by the International Cooperation Project of National Natural Science Foundation of China (No. 50920105504), a Biotechnology and Biological Sciences Research Council Grant (No.BB/H002782/1), the Project of National Natural Science Foundation of China (No. 51105167), the Fundamental Research Founds of China (No. Z201105), the Key project of National Science Foundation of China (No, 51290290 & 51290292)? the postdoctoral project (No, 2013M530985) and the scientific and technological development planning project of Jilin Province (No, 20130522187JH). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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