Knee joint angles and displacements, U = [<i>θ</i>_<i>1</i> <i>θ</i>_<i>2</i> <i>θ</i>_<i>3</i> <i>d</i>_<i>1</i> <i>d</i>_<i>2</i> <i>d</i>_<i>3</i>]^<i>T</i> for both subjects.

<p>Model-derived kinematics estimated with the four knee joint models: no joint model (N, red), spherical model (S, yellow), parallel mechanism (P, green), and stiffness matrix (M, cyan) plotted against fluoroscopy-based kinematics (Ref, black). Sensitivity analysis results are represented by the mean of the kinematics estimation over the 511 runs of MBO embedding perturbed stiffness matrices (, dark blue), with corridor representing the variation in the estimation for one standard deviation (light grey, ) and 1.96 standard deviation (, dark grey) around the mean value.</p

Bland-Altman plot for subject S2.

<p>Bland-Altman plot with reference kinematics (absissas) and difference (ordinates) between model-derived and reference fluoroscopy-based kinematics. From left to right Bland-Altman plots for models N, S, P, M respectively, corresponding to joint angles and displacements, from top to bottom EF, AA, IER, and LM, AP and PD, respectively. Differences between model-derived kinematics and fluoroscopy-based kinematics are plotted against reference amplitude of movement (angle or displacement). Thick black line represents the bias (mean of the differences) whose value is designated by b, thin black lines represent the limits of agreement whose value is designated by l = b ± 1.96 standard deviation. Squared Pearson’s correlation coefficient (r²), root mean square error (rmse) and standard deviation (sd) are displayed for each graph.</p

Model specifications.

<p>(A) Natural coordinates, <b>Q</b>_<i>i</i>, for shank (<i>i</i> = 2) and thigh (<i>i</i> = 3) and knee joint coordinate system. (B) Representation of the four different knee joint models, from top to bottom: no joint model (N), spherical model (S), parallel mechanism (P), and stiffness matrix (M).</p

Leg and Joint Stiffness in Children with Spastic Diplegic Cerebral Palsy during Level Walking

<div><p>Individual joint deviations are often identified in the analysis of cerebral palsy (CP) gait. However, knowledge is limited as to how these deviations affect the control of the locomotor system as a whole when striving to meet the demands of walking. The current study aimed to bridge the gap by describing the control of the locomotor system in children with diplegic CP in terms of their leg stiffness, both skeletal and muscular components, and associated joint stiffness during gait. Twelve children with spastic diplegia CP and 12 healthy controls walked at a self-selected pace in a gait laboratory while their kinematic and forceplate data were measured and analyzed during loading response, mid-stance, terminal stance and pre-swing. For calculating the leg stiffness, each of the lower limbs was modeled as a non-linear spring, connecting the hip joint center and the corresponding center of pressure, with varying stiffness that was calculated as the slope (gradient) of the axial force vs. the deformation curve. The leg stiffness was further decomposed into skeletal and muscular components considering the alignment of the lower limb. The ankle, knee and hip of the limb were modeled as revolute joints with torsional springs whose stiffness was calculated as the slope of the moment vs. the angle curve of the joint. Independent t-tests were performed for between-group comparisons of all the variables. The CP group significantly decreased the leg stiffness but increased the joint stiffness during stance phase, except during terminal stance where the leg stiffness was increased. They appeared to rely more on muscular contributions to achieve the required leg stiffness, increasing the muscular demands in maintaining the body posture against collapse. Leg stiffness plays a critical role in modulating the kinematics and kinetics of the locomotor system during gait in the diplegic CP.</p></div

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<p>Definitions of the abbreviations of the markers are given in Table.</p

Means (SD) of the initial values, total changes and normalized total changes of the inter-marker distances for each of the marker pairs of the mandible.

<p>The ‘group mean’ shows the mean of the normalized total changes over the whole group of markers. (unit: cm) Definitions of the abbreviations of the markers are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0096540#pone-0096540-t001" target="_blank">Table 1</a>.</p

Effective GRF and effective leg length.

<p>Stick figure of a lower limb during stance phase of gait showing the definitions of the effective GRF (thin vector, Fe(t)) and effective leg length (<i>L</i>_<i>e</i>(t)). The former is defined as the component of the measured GRF (thick vector) along the line joining the center of pressure (COP) and the hip joint center. The latter is defined as the distance between the COP and the hip joint center.</p

(a) Amount, (b) monthly change, and (c) percentage of change of the volume of the mandible over the monitoring period.

<p>(a) Amount, (b) monthly change, and (c) percentage of change of the volume of the mandible over the monitoring period.</p

Anatomical landmarks of the mandible considered in the current study as indicated on the 3D mandible model viewed from the right and from the top.

<p>Anatomical landmarks of the mandible considered in the current study as indicated on the 3D mandible model viewed from the right and from the top.</p

A schematic diagram illustrating the computer-based method for defining the GO point on the mandible: (a) oblique view, and (b) sagittal view.

<p>To determine GO, a plane (cyan, with cyan contact points) containing the posterior ramus borders (or tangent to the borders in mathematical terms), and a second plane (pink, with pink contact points) containing the inferior corpus borders (or tangent to the borders in mathematical terms) were established to form an obtuse angle. A third plane (green, with green contact points) passing through the intersection of the first two planes and bisecting their obtuse angle meets the curved gonial edge, and the red point on the intersected edge and closest to the intersection of the first two planes gives the GO (gonion). The axes of the local coordinate system are shown as arrows in red, blue and green.</p