The applicability of the time/temperature superposition principle to brain tissue.

This paper deals with the mechanical characterization of brain tissue which behaves as a viscoelastic material. We focus on the linear viscoelastic behavior, which should apply for small strains at any strain rate, and demonstrate the applicability of the time/temperature superposition principle. This principle allows the opportunity to extend the range of shear rates for which the material is characterized, and makes the results applicable to impact conditions. This characterization of the linear behavior forms the basis for a further nonlinear characterization of the tissue.

The influence of different boundary conditions on the response of the head to impact: a two-dimensional finite element study.

The objective of the present study is to gain a better understanding of the possible importance of skull-brain interface conditions, boundary conditions at the head-neck junction, and brain material properties when modeling the response of the human head to transient loadings. To that end, a two-dimensional plane strain finite element model of a para-sagittal section of a human head has been developed. The model comprises the brain and the skull, with the foramen magnum represented by a force-free opening. The model geometry was obtained from MRI data. The material properties used were adopted from the literature and are homogeneous and isotropic. In all analyses the skull bone was modeled as a linearly elastic material. First, to enable a comparison between simulation results and experiments reported in the literature, the loading conditions, realized in experiments reported in literature, were used as input to the completely linearly elastic model without a kinematic constraint at the head-neck junction. This was done for both rigid coupling and no coupling at the skull-brain interface. Next, various versions of the model were constructed by using different combinations of the following features: linear elastic or viscoelastic brain material properties, different contact conditions at the skull-brain interface, and incorporation of a neck constraint. The results show that both coup and contrecoup pressures are much more sensitive to the type of skull-brain interface condition than to the presence or absence of a force-free foramen magnum. A neck constraint proves to be an important modeling assumption, because of its effect upon the deformation of the brain. The use of different time-dependent deviatoric material parameters for the brain did not significantly change the head's response.

A note on the reduced creep function corresponding to the quasi-linear visco-elastic model proposed by Fung.

For description of the visco-elastic behavior of soft biological tissues, Fung proposed a visco-elastic model formulated in terms of a relaxation function and corresponding relaxation spectrum. For the corresponding creep function, Fung proposed an expression which needs correction to obtain a consistent formulation. This creep function and the corresponding creep spectrum are derived in this note.

A model of force transmission in the tibio-femoral contact incorporating fluid and mixtures.

An axisymmetric finite element model is formulated which comprises a rigid spherical indentor, a meniscal ring and an articular cartilage layer, both considered as mixture materials which are interacting with an ideal fluid sub-system. From parameter studies it is concluded that the application of the mixture theory in comparison with solid modelling only leads to significant effects when the outer surfaces of the components are not sealed. The load distribution appears to change enormously during relaxation of the models. Initially the largest fraction of the load is borne by the fluid in the cavity, while at the end, when the system has reached its final configuration, the meniscal ring bears the major part of the load. Further, the length of the relaxation period appears to depend on the magnitude of the step change of the load. Finally, the curvature of the spherical indentor appears to have significant effects on the loading of the meniscal ring, only immediately after the step changes of load are applied, and these effects disappear as soon as the fluid starts to exude from the models.

A numerical model of the load transmission in the tibio-femoral contact area.

An axisymmetric finite element model is applied to the analysis of the force transmission between the tibia-meniscus-femur. The model assumes linear elastic material properties, static loading and sliding contact between the components. The study explores the effects of (a) tibial surface geometry (plane, convex, concave), (b) inclusion of soft layers on the bony components and (c) anisotropic properties of the meniscus. When soft layers are absent, tibial surface geometry is found to affect the total axial stiffness of the model, the radial displacement of the meniscal ring as well as the meniscal share in load transmission. Inclusion of soft layers yields qualitatively the same results for the different geometries, under the understanding that axial stiffness decreases while meniscal radial displacements increase. However, the effect of tibial geometry on the meniscal share in load transmission almost disappears as soon as soft layers are applied, while at the same time a significant increase of this share is observed. Increased circumferential stiffness of the meniscal ring raises this share even more.

An experimental setup for the measurement of forces on a human cadaveric foot during inversion.

An experimental setup was developed for statically measuring seven vertical and three horizontal reaction forces on the foot. In the setup, the leg can be simultaneously loaded (1) by a vertical force, (2) by an externally applied axial moment, and (3) by simulated muscle forces. The foot is free to invert under influence of the external loads. Statical analysis and test experiments were used for evaluation. The setup can be used in combination with Roentgen photogrammetry to measure bone positions simultaneously with forces.

An experimental approach to evaluate the dynamic behavior of the human knee.

An experimental approach for an in vitro investigation of some aspects of dynamic force transmission through the human knee joint is presented. Essentially, the behavior of the joint was analyzed by measuring the responses to low level random excitation of the tibia while the femur was clamped. A global equilibrium position of the joint was attained by exerting static forces on the tibia via three tendinous muscle attachments. The responses to the applied dynamic loads were measured using a multi-channel dynamic measuring system and quantified by means of transfer function analysis techniques. Some preliminary experimental results are presented to illustrate the effects of variation of the direction and the magnitude of the applied dynamic and static loads.

Parameter estimation using the quasi-linear viscoelastic model proposed by Fung.

Using the quasi-linear viscoelastic model proposed by Fung for the description of the viscoelastic properties of soft biological tissues, the parameters governing their time-dependent behavior are commonly estimated from relaxation experiments. Exact quantification is possible from the response to a step change in the strain. Since it is physically impossible to realize a true step change in the strain, in practice the response to a steplike strain change is used. In the present study the discrepancies between the exact and the estimated parameter values are investigated using a hypothetical quasi-linear viscoelastic material. The parameter tau 1, governing the fast viscous phenomena, is found to be subject to the largest errors. Methods for obtaining better estimates of tau 1 are outlined in a number of special cases.

The mechanical properties of porcine aortic valve tissues.

In uniaxial tensile experiments in vitro mechanical properties of the different parts of porcine aortic valves, i.e. the leaflets, the sinus wall and the aortic wall, have been dealt with. Tissue strips cut in different directions were investigated. The collagen bundles in the leaflets show a stiffening effect and cause a marked anisotropy: within the physiological range of strains the largest slopes of the stress-strain curves of leaflet specimens in the bundle direction are a factor of about 20 larger than those of specimens taken along the perpendicular direction. For the sinus and aortic tissues, these values are 50-200 times smaller than those obtained from the leaflet specimens in the bundle direction. Two aspects of viscoelastic behaviour were examined: the strain rate sensitivity of the stress-strain curves and the relaxation behaviour. The stress-strain curves of the different valve parts appeared to be rather insensitive to the strain rate: the most pronounced sensitivity observed in our experiments, was a doubling of the stress at the same strain caused by a hundredfold increase of the strain rate. In analyzing the relaxation behaviour, use was made of the relaxation model proposed by Fung (1972, in Biomechanics, its Foundations and Objectives; Fung, Perrone and Anliker. Prentice Hall). In the leaflets, about 45% stress relaxation was found whereas this amounted to 30% in the sinus and aortic walls. Predictions based upon the model indicate that on cyclic loading the larger viscous losses have to be expected in the leaflets.