Characterization of the mechanical properties of skin by inverse analysis combined with the indentation test

This study proposes a new method to determine the mechanical properties of human skin by the use of the indentation test [Pailler-Mattei, 2004. Caractérisation mécanique et tribologique de la peau humaine in vivo, Ph.D. Thesis, ECL-no. 2004-31; Pailler-Mattei, Zahouani, 2004. Journal of Adhesion Science and Technology 18, 1739-1758]. The principle of the measurements consists in applying an in vivo compressive stress [Zhang et al., 1994. Proceedings of the Institution of Mechanical Engineers 208, 217-222; Bosboom et al., 2001. Journal of Biomechanics 34, 1365-1368; Oomens et al., 1984. Selected Proceedings of Meetings of European Society of Biomechanics, pp. 227-232; Oomens et al., 1987. Journal of Biomechanics 20(9), 877-885] on the skin tissue of an individual's forearm. These measurements show an increase in the normal contact force as a function of the indentation depth. The interpretation of such results usually requires a long and tedious phenomenological study. We propose a new method to determine the mechanical parameters which control the response of skin tissue. This method is threefold: experimental, numerical, and comparative. It consists combining experimental results with a numerical finite elements model in order to find out the required parameters. This process uses a scheme of extended Kalman filters (EKF) [Gu et al., 2003. Materials Science and Engineering A345, 223-233; Nakamura et al., 2000. Acta Mater 48, 4293-4306; Leustean and Rosu, 2003. Certifying Kalman filters. RIACS Technical Report 03.02, 27pp. http://gureni.cs.uiuc.edu/~grosu/download/luta + leo.pdf; Welch and Bishop, An introduction to Kalman filter, University of North Carolina at Chapel Hill, 16p. http://www.cs.unc.edu/~welch/kalman/]. The first results presented in this study correspond to a simplified numerical modeling of the global system. The skin is assumed to be a semi-infinite layer with an isotropic linear elastic mechanical behavior [Zhang et al., 1994. Proceedings of the Institution of Mechanical Engineers 208, 217-222] This analysis will be extended to more realistic models in further works.     

Validation of net joint loads calculated by inverse dynamics in case of complex movements: application to balance recovery movements

The joint forces and moments driving the motion of a human subject are classically computed by an inverse dynamic calculation. However, even if this process is theoretically simple, many sources of errors may lead to huge inaccuracies in the results. Moreover, a direct comparison with in vivo measured loads or with "gold standard" values from literature is only possible for very specific studies. Therefore, assessing the inaccuracy of inverse dynamic results is not a trivial problem and a simple method is still required. This paper presents a simple method to evaluate both: (1) the consistency of the results obtained by inverse dynamics; (2) the influence of possible modifications in the inverse dynamic hypotheses. This technique concerns recursive calculation performed on full kinematic chains, and consists in evaluating the loads obtained by two different recursive strategies. It has been applied to complex 3D whole body movements of balance recovery. A recursive Newton-Euler procedure was used to compute the net joint loads. Two models were used to represent the subject bodies, considering or not the upper body as a unique rigid segment. The inertial parameters of the body segments were estimated from two different sets of scaling equations [De Leva, P., 1996. Adjustments to Zatsiorsky-Suleyanov's segment inertia parameters. Journal of Biomechanics 29, 1223-1230; Dumas, R., Chèze, L., Verriest, J.-P., 2006b. Adjustments to McConville et al. and Young et al. Body Segment Inertial Parameters. Journal of Biomechanics, in press]. Using this comparison technique, it has been shown that, for the balance recovery motions investigated: (1) the use of the scaling equations proposed by Dumas et al., instead of those proposed by De Leva, improves the consistency of the results (average relative influence up to 30% for the transversal moment); (2) the arm motions dynamically influence the recovery motion in a non negligible way (average relative influence up to 15% and 30% for the longitudinal force and the transversal moment, respectively).     

Comparison of three standard anatomical reference frames for the tibia-fibula complex

Definition of anatomical reference frames is necessary both for in vitro biomechanical testing, and for in vivo human movement analyses. Different reference frames have been proposed in the literature for the lower limb, and in particular for the tibia–fibula complex. The scope of this work was to compare the three most commonly referred proposals (proposed by [Ruff, C.B., Hayes, W.C., 1983. Cross-sectional geometry at Pecos Pueblo femora and tibiae —A biomechanical investigation: I. method and general patterns of variation. American Journal of Physical Anthropology 60, pp. 359–381.], by [Cappozzo, A., Catani, F., Della Croce, U., Leardini, A., 1995. Position and orientation in space of bones during movement: anatomical frame definition and determination. Clinical Biomechanics (Bristol, Avon) 10, pp. 171–178.], and by the Standardization and Terminology Committee of the International Society of Biomechanics, [Wu, G., Siegler, S., Allard, P., Kirtley, C., Leardini, A., Rosenbaum, D., Whittle, M., D'Lima, D.D., Cristofolini, L., Witte, H., Schmid, O., Stokes, I., 2002. ISB recommendation on definitions of joint coordinate system of various joints for reporting of human joint motion—part I: ankle, hip and spine. International Society of Biomechanics. Journal of Biomechanics 35, pp. 543–548.]). These three frames were identified on six cadaveric tibia–fibula specimens based on the relevant anatomical landmarks, using a high-precision digitizer. The intra-operator (ten repetitions) and inter-operator (three operators) repeatability were investigated in terms of reference frame orientation. The three frames had similar intra-operator repeatability. The reference frame proposed by Ruff et al. had a better inter-operator repeatability (this must be put in relation with the original context of interest, i.e. in vitro measurements on dissected bones). The reference frames proposed by Ruff et al. and by ISB had a similar alignment; the frame proposed by Cappozzo et al. was considerably externally rotated and flexed with respect to the other two. Thus, the reference frame proposed by Ruff et al. is preferable when the full bone surface is accessible (typically during in vitro tests). Conversely, no advantage in terms of repeatability seems to exist between the reference frames proposed by Cappozzo et al. and ISB.     

Assessment of mechanobiological models for the numerical simulation of tissue differentiation around immediately loaded implants

Nowadays, there is a growing consensus on the impact of mechanical loading on bone biology. A bone chamber provides a mechanically isolated in vivo environment in which the influence of different parameters on the tissue response around loaded implants can be investigated. This also provides data to assess the feasibility of different mechanobiological models that mathematically describe the mechanoregulation of tissue differentiation. Before comparing numerical results to animal experimental results, it is necessary to investigate the influence of the different model parameters on the outcome of the simulations. A 2D finite element model of the tissue inside the bone chamber was created. The differentiation models developed by Prendergast, et al. ["Biophysical stimuli on cells during tissue differentiation at implant interfaces", Journal of Biomechanics, 30(6), (1997), 539-548], Huiskes et al. ["A biomechanical regulatory model for periprosthetic fibrous-tissue differentiation", Journal of Material Science: Materials in Medicine, 8 (1997) 785-788] and by Claes and Heigele ["Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing", Journal of Biomechanics, 32(3), (1999) 255-266] were implemented and integrated in the finite element code. The fluid component in the first model has an important effect on the predicted differentiation patterns. It has a direct effect on the predicted degree of maturation of bone and a substantial indirect effect on the simulated deformations and hence the predicted phenotypes of the tissue in the chamber. Finally, the presence of fluid also causes time-dependent behavior. Both models lead to qualitative and quantitative differences in predicted differentiation patterns. Because of the different nature of the tissue phenotypes used to describe the differentiation processes, it is however hard to compare both models in terms of their validity.     

Estimation of the axis of a screw motion from noisy data--a new method based on Plücker lines

The problems of estimating the motion and orientation parameters of a body segment from two n point-set patterns are analyzed using the Plücker coordinates of a line (Plücker lines). The aim is to find algorithms less complex than those in conventional use, and thus facilitating more accurate computation of the unknown parameters. All conventional techniques use point transformation to calculate the screw axis. In this paper, we present a novel technique that directly estimates the axis of a screw motion as a Plücker line. The Plücker line can be transformed via the dual-number coordinate transformation matrix. This method is compared with Schwartz and Rozumalski [2005. A new method for estimating joint parameters from motion data. Journal of Biomechanics 38, 107-116] in simulations of random measurement errors and systematic skin movements. Simulation results indicate that the methods based on Plücker lines (Plücker line method) are superior in terms of extremely good results in the determination of the screw axis direction and position as well as a concise derivation of mathematical statements. This investigation yielded practical results, which can be used to locate the axis of a screw motion in a noisy environment. Developing the dual transformation matrix (DTM) from noisy data and determining the screw axis from a given DTM is done in a manner analogous to that for handling simple rotations. A more robust approach to solve for the dual vector associated with DTM is also addressed by using the eigenvector and the singular value decomposition.     

A passive dynamic walking robot that has a deterministic nonlinear gait

There is a growing body of evidence that the step-to-step variations present in human walking are related to the biomechanics of the locomotive system. However, we still have limited understanding of what biomechanical variables influence the observed nonlinear gait variations. It is necessary to develop reliable models that closely resemble the nonlinear gait dynamics in order to advance our knowledge in this scientific field. Previously, Goswami et al. [1998. A study of the passive gait of a compass-like biped robot: symmetry and chaos. International Journal of Robotic Research 17(12)] and Garcia et al. [1998. The simplest walking model: stability, complexity, and scaling. Journal of Biomechanical Engineering 120(2), 281-288] have demonstrated that passive dynamic walking computer models can exhibit a cascade of bifurcations in their gait pattern that lead to a deterministic nonlinear gait pattern. These computer models suggest that the intrinsic mechanical dynamics may be at least partially responsible for the deterministic nonlinear gait pattern; however, this has not been shown for a physical walking robot. Here we use the largest Laypunov exponent and a surrogation analysis method to confirm and extend Garcia et al.'s and Goswami et al.'s original results to a physical passive dynamic walking robot. Experimental outcomes from our walking robot further support the notion that the deterministic nonlinear step-to-step variations present in gait may be partly governed by the intrinsic mechanical dynamics of the locomotive system. Furthermore the nonlinear analysis techniques used in this investigation offer novel methods for quantifying the nature of the step-to-step variations found in human and robotic gait.     

Subunit positioning and transmembrane helix organisation in the core dimer of photosystem II

Recently 3D structural models of the photosystem II (PSII) core dimer complexes of higher plants (spinach) and cyanobacteria (Synechococcus elongatus) have been derived by electron [Rhee et al. (1998) Nature 396, 283-286; Hankamer et al. (2001) J. Struct. Biol., in press] and X-ray [Zouni et al. (2001) Nature 409, 739-743] crystallography respectively. The intermediate resolutions of these structures do not allow direct identification of side chains and therefore many of the individual subunits within the structure are unassigned. Here we review the structure of the higher plant PSII core dimer and provide evidence for the tentative assignment of the low molecular weight subunits. In so doing we highlight the similarities and differences between the higher plant and cyanobacterial structures.     

Calculating the 2D motion of lumbar vertebrae using splines

In this study we investigate the use of splines and the ICP method [Besl, P., McKay, N., 1992. A method for registration of 3d shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence 14, 239-256.] for calculating the transformation parameters for a rigid body undergoing planar motion parallel to the image plane. We demonstrate the efficacy of the method by estimating the finite centre of rotation and angle of rotation from lateral flexion/extension radiographs of the lumbar spine. In an in vitro error study, the method displayed an average error of rotation of 0.44 +/- 0.45 degrees, and an average error in FCR calculation of 7.6 +/- 8.5 mm. The method was shown to be superior to that of Crisco et al. [Two-dimensional rigid-body kinematics using image contour registration. Journal of Biomechanics 28(1), 119-124.] and Brinckmann et al. [Quantification of overload injuries of the thoracolumbar spine in persons exposed to heavy physical exertions or vibration at the workplace: Part i - the shape of vertebrae and intervertebral discs - study of a yound, healthy population and a middle-aged control group. Clinical Biomechanics Supplement 1, S5-S83.] for the tests performed here. In general, we believe the use of splines to represent planar shapes to be superior to using digitised curves or landmarks for several reasons. First, with appropriate software, splines require less effort to define and are a compact representation, with most vertebra outlines using less than 30 control points. Second, splines are inherently sub-pixel representations of curves, even if the control points are limited to pixel resolutions. Third, there is a well-defined method (the ICP algorithm) for registering shapes represented as splines. Finally, like digitised curves, splines are able to represent a large class of shapes with little effort, but reduce potential segmentation errors from two dimensions (parallel and perpendicular to the image gradient) to just one (parallel to the image gradient). We have developed an application for performing all the necessary computations which can be downloaded from http://www.claritysmart.com.     

The effect of uphill and downhill walking on gait parameters: A self-paced treadmill study

It has been shown that gait parameters vary systematically with the slope of the surface when walking uphill (UH) or downhill (DH) (Andriacchi et al., 1977; Crowe et al., 1996; Kawamura et al., 1991; Kirtley et al., 1985; McIntosh et al., 2006; Sun et al., 1996). However, gait trials performed on inclined surfaces have been subject to certain technical limitations including using fixed speed treadmills (TMs) or, alternatively, sampling only a few gait cycles on inclined ramps. Further, prior work has not analyzed upper body kinematics. This study aims to investigate effects of slope on gait parameters using a self-paced TM (SPTM) which facilitates more natural walking, including measuring upper body kinematics and gait coordination parameters.Gait of 11 young healthy participants was sampled during walking in steady state speed. Measurements were made at slopes of +10°, 0° and −10°. Force plates and a motion capture system were used to reconstruct twenty spatiotemporal gait parameters. For validation, previously described parameters were compared with the literature, and novel parameters measuring upper body kinematics and bilateral gait coordination were also analyzed.Results showed that most lower and upper body gait parameters were affected by walking slope angle. Specifically, UH walking had a higher impact on gait kinematics than DH walking. However, gait coordination parameters were not affected by walking slope, suggesting that gait asymmetry, left-right coordination and gait variability are robust characteristics of walking. The findings of the study are discussed in reference to a potential combined effect of slope and gait speed. Follow-up studies are needed to explore the relative effects of each of these factors.     

A mathematical model of the optokinetic reflex

The role of the optokinetic reflex (OKR) is that of cooperating with the vestibulo-ocular reflex (VOR) in the task of image stabilization on the retina during head rotations in a stationary visual surround. Since the dynamics of VOR was already well established, it has been possible to make a broad estimation of what the dynamics of OKR should be in order to obtain the performances observed in normal subjects. A mathematical model of OKR has been presented, and the experimental results obtained by Raphan et al. (1977) in the monkey and by Collins et al. (1970) in man were used to validate the model and to obtain a precise estimation of its parameters.Work supported by CNR, Special Project on Biomedical Engineering, grant No. 78.00512.86     

In vivo age- and sex-related creep of human lumbar motion segments and discs in pure centric tension

In vivo creep of human lumbar motion segments and discs subject to pure centric tension is presented, in terms of aging, sex and disc level. Time-related elongations of segments L3-4, L4-5 and L5-S1 were measured during the usual 20 min long traction hydrotherapy of patients, by using a computerized subaqual ultrasound measuring method [Kurutz et al., 2002a. Orvosi Hetilap 143 (13), 673-684; Kurutz et al., 2003. Journal of Bioengineering and Biomechanics 5 (1), 67-92]. Elongation of segments was considered as a change of the distance between two adjacent spinous processes. Based on these experiments, in vivo creep of human lumbar FSUs was investigated in centric tension, in terms of sex, age and disc level. Three-parameter rheological models were used to determine viscoelastic tensile moduli of human lumbar FSUs and discs. From three time-related measured elongation values, in vivo damping constants with creep functions were calculated for each segment, in terms of sex, aging and disc level. It has been demonstrated that initial elastic elongations decrease, concerning stiffness increase with aging. Similarly, tensile creep elongations decrease, damping properties increase with aging. Former observations concerning the difference in deformation propagation of men and women in time, have been verified by means of creep analysis: although males have higher initial elastic deformability, due to a smaller damping of females, the deformation propagation of women overtakes men in creep process. This tendency is more significant with aging. Increasing damping was observed in distal direction, both for males and females.     

Evaluation of the global optimisation method within the upper limb kinematics analysis

The aim of this study is to assess the performances of the global optimisation (GO) method (Bone position estimation from skin marker co-ordinates using GO with joint constraints. Journal of Biomechanics 32, 129-134) within the upper limb kinematics analysis. First the model of the upper limb is presented. Then we apply GO method in order to reduce skin movement artefacts that imply relative movement between markers and bones. The performances of the method are then evaluated with the help of simulated movements of the upper limb. Results show a significant reduction of the errors and of the variability due to skin movement.     

Linear poroelastic cancellous bone anisotropy: trabecular solid elastic and fluid transport properties

The mechanical performance of cancellous bone is characterized using experiments which apply linear poroelasticity theory. It is hypothesized that the anisotropic organization of the solid and pore volumes of cancellous bone can be physically characterized separately (no deformable boundary interactive effects) within the same bone sample. Due to its spongy construction, the in vivo mechanical function of cancellous or trabecular bone is dependent upon fluid and solid materials which may interact in a hydraulic, convective fashion during functional loading. This project provides insight into the organization of the tissue, ie., the trabecular connectivity, by defining the separate nature of this biphasic performance. Previous fluid flow experiments [Kohles et al., 2001, Journal of Biomechanics, 34(11), pp. 1197-1202] describe the pore space via orthotropic permeability. Ultrasonic wave propagation through the trabecular network is used to describe the solid component via orthotropic elastic moduli and material stiffness coefficients. The linear poroelastic nature of the tissue is further described by relating transport (fluid flow) and elasticity (trabecular load transmission) during regression analysis. In addition, an empirical relationship between permeability and porosity is applied to the collected data. Mean parameters in the superior-inferior (SI) orientation of cubic samples (n=20) harvested from a single bovine distal femur were the largest (p<0.05) in comparison to medial-lateral (ML) and anterior-posterior (AP) orientations: Apparent elastic modulus (2,139 MPa), permeability (4.65x10(-10) m2), and material stiffness coefficient (13.6 GPa). A negative correlation between permeability as a predictor of structural elastic modulus supported a parametric relationship in the ML (R2=0.4793), AP (R2=0.3018), and SI (R2=0.6445) directions (p<0.05).     

Reliability of upper and lower extremity anthropometric measurements and the effect on tissue mass predictions

Accurate modeling of soft tissue motion effects relative to bone during impact requires knowledge of the mass of soft and rigid tissues in living people. Holmes et al., [2005. Predicting in vivo soft tissue masses of the lower extremity using segment anthropometric measures and DXA. Journal of Applied Biomechanics, 21, 371–382] developed and validated regression equations to predict the individual tissue masses of lower extremity segments of young healthy adults, based on simple anthropometric measurements. However, the reliability of these measurements and the effect on predicted tissue mass estimates from the equations has yet to be determined. In the current study, two measurers were responsible for collecting two sets of unilateral measurements (25 male and 25 female subjects) for the right upper and lower extremities. These included 6 lengths, 6 circumferences, 8 breadths, and 4 skinfold thicknesses. Significant differences were found between measurers and between sexes, but these differences were relatively small in general (75–80% of between-measurer differences were <1 cm). Within-measurer measurement differences were smaller and more consistent than those between measurers in most cases. Good to excellent reliability was demonstrated for all measurement types, with intra-class correlation coefficients of 0.79, 0.86, 0.85 and 0.86 for lengths, circumferences, breadth and skinfolds, respectively. Predicted tissue mass magnitudes were moderately affected by the measurement differences. The maximum mean errors between measurers ranged from 3.2% to 24.2% for bone mineral content and fat mass, for the leg and foot, and the leg segments, respectively.     

A nonlinear biphasic viscohyperelastic model for articular cartilage

Experiments on articular cartilage have shown nonlinear stress-strain curves under finite deformations as well as intrinsic viscous effects of the solid phase. The aim of this study was to propose a nonlinear biphasic viscohyperelastic model that combines the intrinsic viscous effects of the proteoglycan matrix with a nonlinear hyperelastic constitutive equation. The proposed equation satisfies objectivity and reduces for uniaxial loading to a solid type viscous model in which the actions of the springs are represented by the hyperelastic function proposed by Holmes and Mow [1990. J. Biomechanics 23, 1145-1156.]. Results of the model, that were efficiently implemented in an updated Lagrangian algorithm, were compared with experimental infinitesimal data reported by DiSilverstro and Suh [2001. J. Biomechanics 34, 519-525.] and showed acceptable fitting for the axial force (R(2)=0.991) and lateral displacement (R(2)=0.914) curves in unconfined compression as well as a good fitting of the axial indentation force curve (R(2)=0.982). In addition, the model showed an excellent fitting of finite-deformation confined compression stress relaxation data reported by Ateshian et al. [1997. J. Biomechanics 30, 1157-1164.] and Huang et al. [2005. J. Biomechanics 38, 799-809.] (R(2)=0.993 and R(2)=0.995, respectively). The constitutive equation may be used to represent the mechanical behavior of the proteoglycan matrix in a fiber reinforced model of articular cartilage.     

Proposal of a thorax segment coordinate system for the 3D kinematical analysis of the cervical spine

The International Society of Biomechanics detailed the recommendations for 3D kinematics of intervertebral movements (Wu, et al. 2002. J Biomech. 35:543–548), but does not specify how to adapt this proposal to describe the kinematics of the cervical spine, between the head and the thorax. The analysis of the literature shows that no consensus exists at the present time on this subject. The objective of our study was to identify the reference points that formed the most rigid triplet allowing building an optimal thorax segment coordinate system (SCS). We thus measured the variations of distances between markers placed on various anatomical landmarks, and then the deformations of the combinations of three markers on different cervical movements of a sample of 10 asymptomatic subjects. The results show that the triplet formed by the sternum and both acromions undergoes less deformation on the flexion–extension movement. For all the other movements (lateral bending, axial rotation and complex movements), the triplet formed by sternum, T3 and TH (positioned on the thoracic spinal column, in a horizontal plane containing the sternal marker), undergoes less deformation. As a conclusion, the optimal triplet to define the thorax SCS for 3D kinematical analysis of the cervical spine is that formed by the markers: sternum, T3 and TH. This triplet makes it possible to define an orthonormal SCS, the axes of which coincide with anatomical directions, i.e. with the functional axes of the movement.     

Proposal of a thorax segment coordinate system for the 3D kinematical analysis of the cervical spine

The International Society of Biomechanics detailed the recommendations for 3D kinematics of intervertebral movements (Wu, et al. 2002. J Biomech. 35:543-548), but does not specify how to adapt this proposal to describe the kinematics of the cervical spine, between the head and the thorax. The analysis of the literature shows that no consensus exists at the present time on this subject. The objective of our study was to identify the reference points that formed the most rigid triplet allowing building an optimal thorax segment coordinate system (SCS). We thus measured the variations of distances between markers placed on various anatomical landmarks, and then the deformations of the combinations of three markers on different cervical movements of a sample of 10 asymptomatic subjects. The results show that the triplet formed by the sternum and both acromions undergoes less deformation on the flexion-extension movement. For all the other movements (lateral bending, axial rotation and complex movements), the triplet formed by sternum, T3 and TH (positioned on the thoracic spinal column, in a horizontal plane containing the sternal marker), undergoes less deformation. As a conclusion, the optimal triplet to define the thorax SCS for 3D kinematical analysis of the cervical spine is that formed by the markers: sternum, T3 and TH. This triplet makes it possible to define an orthonormal SCS, the axes of which coincide with anatomical directions, i.e. with the functional axes of the movement.