H.J. Grootenboer

Articular contact in a three-dimensional model of the knee

This study is aimed at the analysis of articular contact in a three-dimensional mathematical model of the human knee-joint. In particular the effect of articular contact on the passive motion characteristics is assessed in relation to experimentally obtained joint kinematics. Two basically different mathematical contact descriptions were compared for this purpose. One description was for rigid contact and one for deformable contact. The description of deformable contact is based on a simplified theory for contact of a thin elastic layer on a rigid foundation. The articular cartilage was described either as a linear elastic material or as a non-linear elastic material. The contact descriptions were introduced in a mathematical model of the knee. The locations of the ligament insertions and the geometry of the articular surfaces were obtained from a joint specimen of which experimentally determined kinematic data were available, and were used as input for the model. The ligaments were described by non-linear elastic line elements. The mechanical properties of the ligaments and the articular cartilage were derived from literature data. Parametric model evaluations showed that, relative to rigid articular contact, the incorporation of deformable contact did not alter the motion characteristics in a qualitative sense, and that the quantitative changes were small. Variation of the elasticity of the elastic layer revealed that decreasing the surface stiffness caused the ligaments to relax and, as a consequence, increased the joint laxity, particularly for axial rotation. The difference between the linear and the non-linear deformable contact in the knee model was very small for moderate loading conditions. The motion characteristics simulated with the knee model compared very well with the experiments. It is concluded that for simulation of the passive motion characteristics of the knee, the simplified description for contact of a thin linear elastic layer on a rigid foundation is a valid approach when aiming at the study of the motion characteristics for moderate loading conditions. With deformable contact in the knee model, geometric conformity between the surfaces can be modelled as opposed to rigid contact which assumed only point contact.

A multisensory integration model of human stance control.

Abstract. A model is presented to study and quantify the contribution of all available sensory information to human standing based on optimal estimation theory. In the model, delayed sensory information is integrated in such a way that a best estimate of body orientation is obtained. The model approach agrees with the present theory of the goal of human balance control. The model is not based on purely inverted pendulum body dynamics, but rather on a three-link segment model of a standing human on a movable support base. In addition, the model is non-linear and explicitly addresses the problem of multisensory integration and neural time delays. A predictive element is included in the controller to compensate for time delays, necessary to maintain erect body orientation. Model results of sensory perturbations on total body sway closely resemble experimental results. Despite internal and external perturbations, the controller is able to stabilise the model of an inherently unstable standing human with neural time delays of 100 ms. It is concluded, that the model is capable of studying and quantifying multisensory integration in human stance control. We aim to apply the model in (1) the design and development of prostheses and orthoses and (2) the diagnosis of neurological balance disorders.

An inverse dynamics model for the analysis, reconstruction and prediction of bipedal walking

Walking is a constrained movement which may best be observed during the double stance phase when both feet contact the floor. When analyzing a measured movement with an inverse dynamics model, a violation of these constraints will always occur due to measuring errors and deviations of the segments model from reality, leading to inconsistent results. Consistency is obtained by implementing the constraints into the model. This makes it possible to combine the inverse dynamics model with optimization techniques in order to predict walking patterns or to reconstruct non-measured rotations when only a part of the three-dimensional joint rotations is measured. In this paper the outlines of the extended inverse dynamics method are presented, the constraints which define walking are defined and the optimization procedure is described. The model is applied to analyze a normal walking pattern of which only the hip, knee and ankle flexions/extensions are measured. This input movement is reconstructed to a kinematically and dynamically consistent three-dimensional movement, and the joint forces (including the ground reaction forces) and joint moments of force, needed to bring about this movement are estimated.

Effects of fit and bonding characteristics of femoral stems on adaptive bone remodeling

Bone atrophy caused by stress-shielding may cause serious complications for the long-term fixation of hip stems. In particular, uncemented total hip arthroplasty is threatened by this problem, because the stems are usually larger and, as a consequence, stiffer than those of cemented implants. In the present study, the effects of fit and bonding characteristics of femoral hip stems were investigated, using the (nonlinear) finite element method in combination with adaptive bone remodeling theory to predict the bone density distribution in a bone or bone/implant configuration. Unknown parameters used in the theory, such as a reference equilibrium loading stimulus and a threshold (dead) zone of this stimulus, were established (triggered) by using the method to predict the density distributions in the natural femur and around fully coated uncemented implants. The computer simulation method can provide long term predictions of remodeling patterns around various implant configurations. Several cases were analyzed, whereby the coating conditions (fully, partly, or noncoated) and the fit characteristics (press fitted or overreamed) were varied. The computer predictions showed that partly coating can only significantly reduce bone atrophy relative to fully coated stems, when the coating is applied at a small region at the utmost proximal part of the stem. For smooth press-fit stems the predicted amount of bone loss (35 percent in the proximal medial region) was less than for a one-third proximally coated or a fully coated stem (50 to 54 percent predicted bone loss in the proximal medial region).(ABSTRACT TRUNCATED AT 250 WORDS)

Trends of mechanical consequences and modeling of a fibrous membrane around femoral hip prostheses

In the present study, the effects of a fibrous membrane between cement and bone in a femoral total hip replacement were investigated. The study involved the problem of modeling this fibrous membrane in finite-element analyses, and its global consequences for the load-transfer mechanism and its resulting stress patterns. A finite-element model was developed, suitable to describe nonlinear contact conditions in combination with nonlinear material properties of the fibrous membrane. The fibrous tissue layer was described as a highly compliant material with little resistance against tension and shear. The analysis showed that the load transfer mechanism from stem to bone changes drastically when such a membrane is present. These effects are predominantly caused by tensile loosening and slip at the interface, and are enhanced by the nonlinear membrane characteristics. Using parametric analysis, it was shown that these effects on the load-transfer mechanism cannot be described satisfactorily with linear elastic models. Most importantly, the fibrous tissue interposition causes excessive stress concentrations in bone and cement, and relatively high relative displacements between these materials.

A Hill type model of rat medial gastrocnemius muscle that accounts for shortening history effects

The aim of the present study was to develop a Hill type muscle model that accounts for the effects of shortening history. For this purpose, a function was derived that relates force depression to starting length, shortening amplitude and contraction velocity. History parameters were determined from short-range isokinetic experiments on rat medial gastrocnemius muscle (GM). Simulations of isokinetic as well as isotonic experiments were performed with the new model and a standard Hill type model. The simulation results were compared with experimental results of rat GM to evaluate if incorporation of history effects leads to improvements in model predictions. In agreement with the experimental results, the new model qualitatively described force reduction during and after isokinetic shortening as well as the experimental observation that isometric endpoints of isotonic contractions are attained at higher muscle lengths than is expected from the fully isometric length-force curve. Consequently, the new model gave a better quantitative prediction of the experimental results compared to the standard model. It was concluded that incorporation of history effects can improve the predictive power of a Hill type model considerably. The applicability of the model to conditions other than those described in the present paper is discussed.

The relative position of EDL muscle affects the length of sarcomeres within muscle fibers: experimental results and finite-element modeling.

BACKGROUND Effects of extramuscular connective tissues on muscle force (experimentally measured) and lengths of sarcomeres (modeled) were investigated in rat. It was hypothesized that changes of muscle-relative position affect the distribution of lengths of sarcomeres within muscle fibers. METHOD OF APPROACH The position of extensor digitorum longus muscle (EDL) relative to intact extramuscular connective tissues of the anterior crural compartment was manipulated without changing its muscle-tendon complex length. RESULTS Significant effects of EDL muscle relative position on proximal and distal EDL forces were found, indicating changes of extramuscular myofascial force transmission. EDL isometric force exerted at its proximal and distal tendons differed significantly. Finite-element modeling showed that the distribution of lengths of sarcomeres is altered by changes of muscle-relative position. CONCLUSIONS It is concluded that forces exerted on a muscle via extramuscular myofascial pathways augment distributions of lengths of sarcomeres within that muscle.

Stiffness and hysteresis properties of some prosthetic feet

A prosthetic foot is an important element of a prosthesis, although it is not always fully recognized that the properties of the foot, along with the prosthetic knee joint and the socket, are in part responsible for the stability and metabolic energy cost during walking. The stiffness and the hysteresis, which are the topics of this paper, are not properly prescribed, but could be adapted to improve the prosthetic walking performance. The shape is strongly related to the cosmetic appearance and so can not be altered to effect these improvements. Because detailed comparable data on foot stiffness and hysteresis, which are necessary to quantify the differences between different types of feet, are absent in literature, these properties were measured by the authors in a laboratory setup for nine different prosthetic feet, bare and with two different shoes. One test cycle consisted of measurements of load deformation curves in 66 positions, representing the range from heel strike to toe-off. The hysteresis is defined by the energy loss as a part of the total deformation energy. Without shoes significant differences in hysteresis between the feet exist, while with sport shoes the differences in hysteresis between the feet vanish for the most part. Applying a leather shoe leads to an increase of hysteresis loss for all tested feet. The stiffness turned out to be non-constant, so mean stiffness is used. Because very little is known about the optimal values of stiffness and hysteresis, and substantial differences in stiffness between different feet and shoes exist, further investigation into the importance of stiffness and hysteresis to the walking quality of a foot is necessary. Footwear counts too for this quality because it modifies the variation in stiffness among the feet.

Pre-Strained Epimuscular Connections Cause Muscular Myofascial Force Transmission to Affect Properties of Synergistic EHL and EDL Muscles of the Rat

BACKGROUND Myofascial force transmission occurs between muscles (intermuscular myofascial force transmission) and from muscles to surrounding nonmuscular structures such as neurovascular tracts and bone (extramuscular myofascial force transmission). The purpose was to investigate the mechanical role of the epimuscular connections (the integral system of inter- and extramuscular connections) as well as the isolated role of extramuscular connections on myofascial force transmission and to test the hypothesis, if such connections are prestrained. METHOD OF APPROACH Length-force characteristics of extensor hallucis longus (EHL) muscle of the rat were measured in two conditions: (I) with the neighboring EDL muscle and epimuscular connections of the muscles intact: EDL was kept at a constant muscle tendon complex length. (II) After removing EDL, leaving EHL with intact extramuscular connections exclusively. RESULTS (I) Epimuscular connections of the tested muscles proved to be prestrained significantly. (1) Passive EHL force was nonzero for all isometric EHL lengths including very low lengths, increasing with length to approximately 13% of optimum force at high length. (2) Significant proximodistal EDL force differences were found at all EHL lengths: Initially, proximal EDL force = 1.18 +/- 0.11 N, where as distal EDL force = 1.50 +/- 0.08 N (mean +/- SE). EHL lengthening decreased the proximo-distal EDL force difference significantly (by 18.4%) but the dominance of EDL distal force remained. This shows that EHL lengthening reduces the prestrain on epimuscular connections via intermuscular connections; however; the prestrain on the extramuscular connections of EDL remains effective. (II) Removing EDL muscle affected EHL forces significantly. (1) Passive EHL forces decreased at all muscle lengths by approximately 17%. However, EHL passive force was still non-zero for the entire isometric EHL length range, indicating pre-strain of extramuscular connections of EHL. This indicates that a substantial part of the effects originates solely from the extramuscular connections of EHL. However, a role for intermuscular connections between EHL and EDL, when present, cannot be excluded. (2) Total EHL forces included significant shape changes in the length-force curve (e.g., optimal EHL force decreased significantly by 6%) showing that due to myofascial force transmission muscle length-force characteristics are not specific properties of individual muscles. CONCLUSIONS The pre-strain in the epimuscular connections of EDL and EHL indicate that these myofascial pathways are sufficiently stiff to transmit force even after small changes in relative position of a muscle with respect to its neighboring muscular and nonmuscular tissues. This suggests the likelihood of such effects also in vivo.

Modelling functional effects of muscle geometry.

Muscle architecture is an important aspect of muscle functioning. Hence, geometry and material properties of muscle have great influence on the force-length characteristics of muscle. We compared experimental results for the gastrocnemius medialis muscle (GM) of the rat to model results of simple geometric models such as a planimetric model and three-dimensional versions of this model. The capabilities of such models to adequately calculate muscle geometry and force-length characteristics were investigated. The planimetric model with elastic aponeurosis predicted GM muscle geometry well: maximal differences are 6, 1, 4 and 6% for fiber length, aponeurosis length, fiber angle and aponeurosis angle respectively. A slanted cylinder model with circular fiber cross-section did not predict muscle geometry as well as the planimetric model, whereas the geometry results of a second slanted cylinder model were identical to the planimetric model. It is concluded that the planimetric model is capable of adequately calculating the muscle geometry over the muscle length range studied. However, for modelling of force-length characteristics more complex models are needed, as none of the models yielded results sufficiently close to experimental data. Modelled force-length characteristics showed an overestimation of muscle optimum length by 2 mm with respect to experimental data, and the force at the ascending limb of the length force curve was underestimated. The models presented neglect important aspects such as non-linear geometry of muscle, certain passive material properties and mechanical interactions of fibers. These aspects may be responsible for short-comings in the modelling. It is argued that, considering the inability to adequately model muscle length-force characteristics for an isolated maximally activated (in situ) muscle, it is to be expected that prediction will fail for muscle properties in conditions of complex movement with many interacting factors. Therefore, modelling goals should be limited to the heuristic domain rather than expect to be able to predict or even approach medical or biological reality. However, the increased understanding about muscular mechanisms obtained from heuristic use of such simple models may very well be used in creating progress in, for example, clinical applications.