Dynamics of the aortic arch submitted to a shock loading: Parametric study with fluid-structure models.

This work aims to present some fluid-structure models for analyzing the dynamics of the aorta during a brusque loading. Indeed, various lesions may appear at the aortic arch during car crash or other accident such as brusque falling. Aortic stresses evolution are simulated during the shock at the cross section and along the aorta. One hot question was that if a brusque deceleration can generate tissue tearing, or a shock is necessary to provoke such a damage. Different constitutive laws of blood are then tested whereas the aorta is assumed linear and elastic. The overall shock model is inspired from an experimental jig. We show that the viscosity has strong influence on the stress and parietal moments and forces. The nonlinear viscosity has no significant additional effects for healthy aorta, but modifies the stress and parietal loadings for the stenotic aorta.

Mechanical interaction between cells and fluid for bone tissue engineering scaffold: modulation of the interfacial shear stress.

An analytical model of the fluid/cell mechanical interaction was developed. The interfacial shear stress, due to the coupling between the fluid and the cell deformation, was characterized by a new dimensionless number N(fs). For N(fs) above a critical value, the fluid/cell interaction had a damping effect on the interfacial shear stress. Conversely, for N(fs) below this critical value, interfacial shear stress was amplified. As illustration, the role of the dynamic fluid/cell mechanical coupling was studied in a specific biological situation involving cells seeded in a bone scaffold. For the particular bone scaffold chosen, the dimensionless number N(fs) was higher than the critical value. In this case, the dynamic shear stress at the fluid/cell interface is damped for increasing excitation frequency. Interestingly, this damping effect is correlated to the pore diameter of the scaffold, furnishing thus target values in the design of the scaffold. Correspondingly, an efficient cell stimulation might be achieved with a scaffold of pore size larger than 300 microm as no dynamic damping effect is likely to take place. The analytical model proposed in this study, while being a simplification of a fluid/cell mechanical interaction, brings complementary insights to numerical studies by analyzing the effect of different physical parameters.

Targeted mechanical properties for optimal fluid motion inside artificial bone substitutes.

Our goal was to develop a method to identify the optimal elastic modulus, Poisson's ratio, porosity, and permeability values for a mechanically stressed bone substitute. We hypothesized that a porous bone substitute that favors the transport of nutriments, wastes, biochemical signals, and cells, while keeping the fluid-induced shear stress within a range that stimulates osteoblasts, would likely promote osteointegration. Two optimization criteria were used: (i) the fluid volume exchange between the artificial bone substitute and its environment must be maximal and (ii) the fluid-induced shear stress must be between 0.03 and 3 Pa. Biot's poroelastic theory was used to compute the fluid motion due to mechanical stresses. The impact of the elastic modulus, Poisson's ratio, porosity, and permeability on the fluid motion were determined in general and for three different bone substitute sizes used in high tibial osteotomy. We found that fluid motion was optimized in two independent steps. First, fluid transport was maximized by minimizing the elastic modulus, Poisson's ratio, and porosity. Second, the fluid-induced shear stress could be adjusted by tuning the bone substitute permeability so that it stayed within the favorable range of 0.03 to 3 Pa. Such method provides clear guidelines to bone substitute developers and to orthopedic surgeons for using bone substitute materials according to their mechanical environment.

Peri-implant bone remodeling after total hip replacement combined with systemic alendronate treatment: a finite element analysis.

In order to decrease the peri-implant bone loss during the life-time of the implant, oral use of anti-osteoporosis drugs (like bisphosphonates) has been suggested. In this study, bone remodeling parameters identified from clinical trials of alendronate were used to simulate the effect of those drugs used after total hip arthroplasty on the peri-implant bone density. Results of the simulation show that the oral administrated drugs increase bone density around the implant and decreases, at the same time, the micromovements between the implant and the surrounding bone tissue. Incorporation of drug effect in numerical studies of bone remodeling is a promising tool especially to predetermine safe bisphosphonate doses that could be used with orthopedic implants.

Biphasic constitutive laws for biological interface evolution.

A model of tissue differentiation at the bone-implant interface is proposed. The basic hypothesis of the model is that the mechanical environment determines the tissue differentiation. The stimulus chosen is related to the bone-implant micromotions. Equations governing the evolution of the interfacial tissue are proposed and combined with a finite element code to determine the evolution of the fibrous tissue around prostheses. The model is applied to the case of an idealized hip prosthesis.

Virtual power based algorithm for decoupling large motions from infinitesimal strains: application to shoulder joint biomechanics.

New trends of numerical models of human joints require more and more computation of both large amplitude joint motions and fine bone stress distribution. Together, these problems are difficult to solve and very CPU time consuming. The goal of this study is to develop a new method to diminish the calculation time for this kind of problems which include calculation of large amplitude motions and infinitesimal strains. Based on the Principle of Virtual Power, the present method decouples the problem into two parts. First, rigid body motion is calculated. The bone micro-deformations are then calculated in a second part by using the results of rigid body motions as boundary conditions. A finite element model of the shoulder was used to test this decoupling technique. The model was designed to determine the influence of humeral head shape on stress distribution in the scapula for different physiological motions of the joint. Two versions of the model were developed: a first version completely deformable and a second version based on the developed decoupling method. It was shown that biomechanical variables, as mean pressure and von Mises stress, calculated with the two versions were sensibly the same. On the other hand, CPU time needed for calculating with the new decoupled technique was more than 6 times less than with the completely deformable model.

A finite element model of the shoulder: application to the comparison of normal and osteoarthritic joints.

OBJECTIVE: The objective of the present study was to develop a numerical model of the shoulder able to quantify the influence of the shape of the humeral head on the stress distribution in the scapula. The subsequent objective was to apply the model to the comparison of the biomechanics of a normal shoulder (free of pathologies) and an osteoarthritic shoulder presenting primary degenerative disease that changes its bone shape. DESIGN: Since the stability of the glenohumeral joint is mainly provided by soft tissues, the model includes the major rotator cuff muscles in addition to the bones. BACKGROUND: No existing numerical model of the shoulder is able to determine the modification of the stress distribution in the scapula due to a change of the shape of the humeral head or to a modification of the glenoid contact shape and orientation. METHODS: The finite element method was used. The model includes the three-dimensional computed tomography-reconstructed bone geometry and three-dimensional rotator cuff muscles. Large sliding contacts between the reconstructed muscles and the bone surfaces, which provide the joint stability, were considered. A non-homogenous constitutive law was used for the bone as well as non-linear hyperelastic laws for the muscles and for the cartilage. Muscles were considered as passive structures. Internal and external rotations of the shoulders were achieved by a displacement of the muscle active during the specific rotation (subscapularis for internal and infrapinatus for external rotation). RESULTS: The numerical model proposed is able to describe the biomechanics of the shoulder during rotations. The comparison of normal vs. osteoarthritic joints showed a posterior subluxation of the humeral head during external rotation for the osteoarthritic shoulder but no subluxation for the normal shoulder. This leads to important von Mises stress in the posterior part of the glenoid region of the pathologic shoulder while the stress distribution in the normal shoulder is fairly homogeneous. CONCLUSION: This study shows that the posterior subluxation observed in clinical situations for osteoarthritic shoulders may also be cause by the altered geometry of the pathological shoulder and not only by a rigidification of the subscapularis muscle as often postulated. This result is only possible with a model including the soft tissues provided stability of the shoulder. RELEVANCE: One possible cause of the glenoid loosening is the eccentric loading of the glenoid component due to the translation of the humeral head. The proposed model would be a useful tool for designing new shapes for a humeral head prosthesis that optimizes the glenoid loading, the bone stress around the implant, and the bone/implant micromotions in a way that limits the risks of loosening.

Determination of orthotropic bone elastic constants using FEA and modal analysis.

Finite element models have been widely employed in an effort to quantify the stress and strain distribution around implanted prostheses and to explore the influence of these distributions on their long-term stability. In order to provide meaningful predictions, such models must contain an appropriate reflection of mechanical properties. Detailed geometrical and density information is now readily available from CT scanning. However, despite the use of phantoms, a method of determining mechanical properties (or elastic constants) from bone density has yet to be made available in a usable form. In this study, a cadaveric bone was CT scanned and its natural frequencies were measured using modal analysis. Using the geometry obtained from the CT scan data, a finite element mesh was created with the distribution of density established by matching the mass of the FE bone model with the mass of the cadaveric bone. The maximum values of the orthotropic elastic constants were then established by matching the predictions from FE modal analyses to the experimental natural frequencies, giving a maximum error of 7.8% over 4 modes of vibration. Finally, the elastic constants of the bone derived from the analyses were compared with those measured using ultrasound techniques. This produced a difference of <1% for both the maximum density and axial Young's Modulus. This study has thereby produced an orthotropic finite element model of a human femur. More importantly, however, is the implication that it is possible to create a valid FE model by simply comparing the FE results with the measured resonant frequency of the CT scanned bone.

[Noncemented total hip arthroplasty: influence of extramedullary parameters on initial implant stability and on bone-implant interface stresses]. / Arthroplastie totale non cimentée de la hanche: influence des paramètres extra-médullaires sur la stabilité primaire de l'implant et sur les contraintes à l'interface os/implant.

PURPOSE OF THE STUDY: After total hip replacement, the initial stability of the cementless femoral stem is a prerequisite for ensuring bone ingrowth and therefore long term fixation of the stem. For custom made implants, long term success of the replacement has been associated with reconstruction of the offset, antero/retro version of the neck orientation and its varus/valgus orientation angle. The goals of this study were to analyze the effects of the extra-medullary parameters on the stability of a noncemented stem after a total hip replacement, and to evaluate the change of stress transfer. MATERIAL AND METHODS: The geometry of a femur was reconstructed from CT-scanner data to obtain a three-dimensional model with distribution of bone density. The intra-medullary shape of the stem was based on the CT-scanner. Seven extra-medullary stem designs were compared: 1) Anatomical case based on the reconstruction of the femoral head position from the CT data; 2) Retroverted case of - 15 degrees with respect to the anatomical reconstruction; 3) Anteverted case with an excessive anteversion angle of + 15 degrees with respect to the anatomical case; 4) Medial case: shortened femoral neck length (- 10 mm) inducing a medial shift of the femoral head offset; 5) Lateral case: elongated femoral neck length (+ 10 mm) inducing lateral shift of the femoral head offset 6) Varus case with CCD angle 127 degrees; 7) Valgus case with CCD angle 143 degrees. The plasma sprayed stem surface was modeled with a frictional contact between bone and implant (friction coefficient: 0.6). The loading condition corresponding to the single limb stance phase during the gait cycle was used for all cases. Applied loads included major muscular forces (gluteus maximus, gluteus medius, psoas). RESULTS: Micromotions (debonding and slipping) of the stems relative to the femur and interfacial stresses (pressure and friction) were different according to the extra-medullary parameters. However, the locations of peak stresses and micromotions were not modified. The highest micromotions and stresses corresponded to the lateral situation and to the anteverted case (micro-slipping and pressure were increased up to 35 p.100). High peak pressure was observed for all designs, ranging from anatomical case (34 MPa) to anteverted case (44 MPa). The peak stresses and micromotions were minimal for the anatomical case. The maximal micro-debonding was not significantly modified by the extra-medullary design of the femoral stem. DISCUSSION: The extra-medullary stem design has been shown to affect the primary stability of implant and the stress transfer after THR. Most interfacial regions present small micro-slipping which normally allows the occurrence of bone ingrowth. The anatomical design presents the lowest micromotions and the lowest interfacial stresses. The worst cases correspond to the anteverted and lateralized cases. Probably, the anteverted situation involves higher torsion torque, which in turn may induce high torsion shear micromotions and higher stress at the interface. Moreover, the lever arm of the weight bearing force on the femoral head is augmented for the augmented neck length situation. This increases the bending moment, and therefore may increase the stresses as well as the stem shear micromotions. In summary, the present results could be taken as biomechanical arguments for the requirement of anatomical reconstruction of not only the intra-medullary shape but also the extra-medullary parameters (reconstruction of the normal hip biomechanics).

On the independence of time and strain effects in the stress relaxation of ligaments and tendons.

The hypothesis of variables separation, namely the time and the strain separation in the relaxation function, is widely used in soft tissue biomechanics. Although this hypothesis is central to several biomechanical models, only few experimental works have tried to verify it. From these studies, contradictory results have been found. Moreover, it has recently been noted that no such experimental verification has been performed for ligament tissues. In this paper, an experimental method is developed to test the hypothesis of variables separation. This method is then used with human cruciate ligaments and patellar tendons. It is shown that the use of the variables separation hypothesis is justified at least for strain values lower than 16% for anterior cruciate ligament, lower than 12% for posterior cruciate ligament and lower than 6% for patellar tendon. The method presented in this paper could be used to verify the validity of variables separation for other tissues.

The fixation of the cemented femoral component. Effects of stem stiffness, cement thickness and roughness of the cement-bone surface.

After cemented total hip arthroplasty (THA) there may be failure at either the cement-stem or the cement-bone interface. This results from the occurrence of abnormally high shear and compressive stresses within the cement and excessive relative micromovement. We therefore evaluated micromovement and stress at the cement-bone and cement-stem interfaces for a titanium and a chromium-cobalt stem. The behaviour of both implants was similar and no substantial differences were found in the size and distribution of micromovement on either interface with respect to the stiffness of the stem. Micromovement was minimal with a cement mantle 3 to 4 mm thick but then increased with greater thickness of the cement. Abnormally high micromovement occurred when the cement was thinner than 2 mm and the stem was made of titanium. The relative decrease in surface roughness augmented slipping but decreased debonding at the cement-bone interface. Shear stress at this site did not vary significantly for the different coefficients of cement-bone friction while compressive and hoop stresses within the cement increased slightly.

Strain rate effect on the mechanical behavior of the anterior cruciate ligament-bone complex.

Traction tests were performed on the bovine anterior cruciate ligament-bone complex at seven strain rates (0.1, 1, 5, 10, 20, 30, 40%/s). Corresponding stress-strain curves showed that, for a given strain level, the stress increased with the augmentation of the strain rate. This phenomenon was important since the stress increased by a factor of three between the tests performed at the lowest and highest strain rates. The influence of the strain rate was quantified with a new variable called the "supplemental stress". This variable represented the percentage of total stress due to the effect of strain rate. It was observed that at a strain rate of 40%/s, more than 70% of the stress in the ligament was due to the strain rate effect. In fact, the strain rate strongly affected the toe region, but did not influence the linear part of the stress-strain curves. The use of the linear tangent moduli was then not adequate to describe the strain rate effect in the anterior cruciate ligament-bone complex. This study showed that the "supplemental stress" was a synthetic and convenient variable to quantify the effect of the strain rate on the entire stress-strain curves. This quantification is especially important when comparing the mechanical behavior between anterior cruciate ligament and tissues used as ligament graft.

Viscoelastic constitutive law in large deformations: application to human knee ligaments and tendons.

Traction tests on soft tissues show that the shape of the stress strain curves depends on the strain rate at which the tests are performed. Many of the constitutive models that have been proposed fail to properly consider the effect of the strain rate when large deformations are encountered. In the present study, a framework based on elastic and viscous potentials is developed. The resulting constitutive law is valid for large deformations and satisfies the principles of thermodynamics. Three parameters -- two for the elasticity and one for the viscosity -- were enough to precisely fit the non-linear stress strain curves obtained at different strain rates with human cruciate ligaments and patellar tendons. The identification results then in a realistic, three-dimensional viscoelastic constitutive law. The developed constitutive law can be used regardless of the strain or rotation values. It can be incorporated into a finite element program to model the viscoelastic behavior of ligaments and tendons under dynamic situations.

Displacements of the tibial tuberosity. Effects of the surgical parameters.

A three-dimensional computer model is used, based on the finite element method, to investigate the effects of 1-, 1.5-, and 2-cm tibial tubercle elevations and of 0.5- and 1-cm medial displacements of the tuberosity, performed with different bone shingles. Patellar kinematics and patellofemoral interface peak pressure, between 45 degrees and 135 degrees of passive knee flexion, are compared for these different surgical parameters with those of a normal knee not surgically treated. The shingle lengths of 3, 5, 7, and 10 cm have little influence on the results. Augmenting tubercle medializations decrease the lateral peak pressure but result in an overpressure of the medial facet that is 154% of the normal peak value. With knee flexion between 45 degrees and 60 degrees, increasing tubercle elevations decreases later and medial peak pressures. With flexion of more than 60 degrees, increasing elevations decrease the lateral peak pressure, but they augment and even cause overpressure on the medial facet. An overpressure on the lateral facet also is seen in midrange knee flexion (75 degrees-90 degrees) for all tubercle elevation values. Increasing tubercle elevations and medializations appear to be the predominant parameters from a biomechanical point of view.

The biomechanics of the human patella during passive knee flexion.

The fundamental objectives of patello-femoral joint biomechanics include the determination of its kinematics and of its dynamics, as a function of given control parameters like knee flexion or applied muscle forces. On the one hand, patellar tracking provides quantitative information about the joint's stability under given loading conditions, whereas patellar force analyses can typically indicate pathological stress distributions associated for instance with abnormal tracking. The determination of this information becomes especially relevant when facing the problem of evaluating surgical procedures in terms of standard (i.e. non-pathological) knee functionality. Classical examples of such procedures include total knee replacement (TKR) and elevation of the tibial tubercle (Maquet's procedure). Following this perspective, the current study was oriented toward an accurate and reliable determination of the human patella biomechanics during passive knee flexion. To this end, a comprehensive three-dimensional computer model, based on the finite element method, was developed for analyzing articular biomechanics. Unlike previously published studies on patello-femoral biomechanics, this model simultaneously computed the joint's kinematics, associated tendinous and ligamentous forces, articular contact pressures and stresses occurring in the joint during its motion. The components constituting the joint (i.e. bone, cartilage, tendons) were modeled using objective forms of non-linear elastic materials laws. A unilateral contact law allowing for large slip between the patella and the femur was implemented using an augmented Lagrangian formulation. Patellar kinematics computed for two knee specimens were close to equivalent experimental ones (average deviations below 0.5 degrees for the rotations and below 0.5 mm for the translations) and provided validation of the model on a specimen by specimen basis. The ratio between the quadriceps pulling force and the patellar tendon force was less than unity throughout the considered knee flexion range (30-150 degrees), with a minimum near 90 degrees of flexion for both specimens. The contact patterns evolved from the distal part of the retropatellar articular surface to the proximal pole during progressive flexion. The lateral facet bore more pressure than the medial one, with corresponding higher stresses (hydrostatic) in the lateral compartment of the patella. The forces acting on the patella were part of the problem unknowns, thus leading to more realistic loadings for the stress analysis, which was especially important when considering the wide range of variations of the contact pressure acting on the patella during knee flexion.

Influence of soft structures on patellar three-dimensional tracking.

During knee flexion, the human patella moves along a complex path resulting from the combined actions of articular contact and soft-tissue stabilization. The current study is an attempt to characterize the role of these soft structures on patellar kinematics. To this end, the three-dimensional patellar motion during full knee flexion was accurately measured before and after partial dissection of the joint. The guiding role of the femoral groove prevailed over soft-tissue action through most of the range of motion. At full extension, however, when the patella and the femur were not in contact, the influence of the retinaculi was most noticeable, highlighting the unstable behavior of the patella near extension. The differences between the intact and dissected knee kinematics suggested that control over patellar motion is ensured by the transverse soft-tissue structures near extension and by the patellofemoral joint geometry during further flexion.