Effects of mechanical forces on maintenance and adaptation of form in trabecular bone.

The architecture of trabecular bone, the porous bone found in the spine and at articulating joints, provides the requirements for optimal load transfer, by pairing suitable strength and stiffness to minimal weight according to rules of mathematical design. But, as it is unlikely that the architecture is fully pre-programmed in the genes, how are the bone cells informed about these rules, which so obviously dictate architecture? A relationship exists between bone architecture and mechanical usage--while strenuous exercise increases bone mass, disuse, as in microgravity and inactivity, reduces it. Bone resorption cells (osteoclasts) and bone formation cells (osteoblasts) normally balance bone mass in a coupled homeostatic process of remodelling, which renews some 25% of trabecular bone volume per year. Here we present a computational model of the metabolic process in bone that confirms that cell coupling is governed by feedback from mechanical load transfer. This model can explain the emergence and maintenance of trabecular architecture as an optimal mechanical structure, as well as its adaptation to alternative external loads.

Accurate assessment of in situ isometric contractile properties of hindlimb plantar and dorsal flexor muscle complex of intact mice.

An isometric torque sensor for measuring in situ contractions of plantar or dorsal flexors of intact mouse hindlimb has been developed and evaluated. With this device, muscle torque can be accurately measured within the range of -14 mN.m to +14 mN.m. Special attention was paid to fixation of the mouse hindlimb to the measurement device. Halothane-anaesthetized Swiss wild-type mice were positioned on the thermostatic measurement platform, and fixated with a hip and foot fixation system. The novel fixation unit was evaluated by measuring knee and ankle displacements during a contraction. A mathematical muscle model was used to quantify the effects of these displacements on the contractile parameters. Measured ankle and knee displacement, due to non-absolute fixation. resulted in a calculated muscle fibre shortening of 2.5%. Simulations of a contraction with this degree of fibre shortening, using the mathematical muscle model, showed only minor effects on maximal torque generation and the temporal parameters (half-relaxation time and 10-50% rise time). Furthermore, we showed that muscle torque in our set-up is hardly affected by eccentricity between ankle and measurement axis. Measured tetanic muscle torques of intact dorsal and plantar flexors were 3.2+/-0.4 mN.m and 11.8+/-1.6 mN.m, respectively. The half-relaxation time of plantar flexors was significantly higher than that of dorsal flexors (12.9+/-2.7 ms versus 8.8+/-1.2 ms), whereas the 10-50% rise time was longer in plantar (14.9+/-0.6 ms) than in dorsal (11.8+/-2.0 ms) flexors.

A Finite Element Approach for Skeletal Muscle using a Distributed Moment Model of Contraction.

The present paper describes a geometrically and physically nonlinear continuum model to study the mechanical behaviour of passive and active skeletal muscle. The contraction is described with a Huxley type model. A Distributed Moments approach is used to convert the Huxley partial differential equation in a set of ordinary differential equations. An isoparametric brick element is developed to solve the field equations numerically. Special arrangements are made to deal with the combination of highly nonlinear effects and the nearly incompressible behaviour of the muscle. For this a Natural Penalty Method (NPM) and an Enhanced Stiffness Method (ESM) are tested. Finally an example of an analysis of a contracting tibialis anterior muscle of a rat is given. The DM-method proved to be an efficient tool in the numerical solution process. The ESM showed the best performance in describing the incompressible behaviour.

The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90 degrees curved tube.

A numerical and experimental investigation of unsteady entry flow in a 90 degrees curved tube is presented to study the impact of the non-Newtonian properties of blood on the velocity distribution. The time-dependent flow rate for the Newtonian and the non-Newtonian blood analog fluid were identical. For the numerical computation, a Carreau-Yasuda model was employed to accommodate the shear thinning behavior of the Xanthan gum solution. The viscoelastic properties were not taken into account. The experimental results indicate that significant differences between the Newtonian and non-Newtonian fluid are present. The numerical results for both the Newtonian and the non-Newtonian fluid agree well with the experimental results. Since viscoelasticity was not included in the numerical code, shear thinning behavior of the blood analog fluid seems to be the dominant non-Newtonian property, even under unsteady flow conditions. Finally, a comparison between the non-Newtonian fluid model and a Newtonian fluid at a rescaled Reynolds number is presented. The rescaled Reynolds number, based on a characteristic rather than the high-shear rate viscosity of the Xanthan gum solution, was about three times as low as the original Reynolds number. Comparison reveals that the character of flow of the non-Newtonian fluid is simulated quite well by using the appropriate Reynolds number.

The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model.

Laser Doppler anemometry experiments and finite element simulations of steady flow in a three dimensional model of the carotid bifurcation were performed to investigate the influence of non-Newtonian properties of blood on the velocity distribution. The axial velocity distribution was measured for two fluids: a non-Newtonian blood analog fluid and a Newtonian reference fluid. Striking differences between the measured flow fields were found. The axial velocity field of the non-Newtonian fluid was flattened, had lower velocity gradients at the divider wall, and higher velocity gradients at the non-divider wall. The flow separation, as found with the Newtonian fluid, was absent. In the computations, the shear thinning behavior of the analog blood fluid was incorporated through the Carreau-Yasuda model. The viscoelastic properties of the fluid were not included. A comparison between the experimental and numerical results showed good agreement, both for the Newtonian and the non-Newtonian fluid. Since only shear thinning was included, this seems to be the dominant non-Newtonian property of the blood analog fluid under steady flow conditions.

Diffusion tensor imaging in biomechanical studies of skeletal muscle function.

In numerical simulations of skeletal muscle contractions, geometric information is of major importance. The aim of the present study was to determine whether the diffusion tensor imaging (DTI) technique is suitable to obtain valid input with regard to skeletal muscle fibre direction. The accuracy of the DTI method was therefore studied by comparison of DTI fibre directions in the rat tibialis anterior muscle with fascicle striation patterns visible on high-resolution magnetic resonance imaging (MRI) and with fibre directions in an actual longitudinal section (ALS) through the same muscle. The results showed an excellent qualitative agreement between high-resolution MRI and DTI. Despite less accurate quantitative comparison with ALS, it was concluded that DTI does indeed measure skeletal muscle fibre direction. After the experiment, it was possible to determine an appropriate voxel size (0.9 mm3) that provided enough resolution and acceptable accuracy (5 degrees) to use DTI fibre directions in biomechanical analyses. Muscle deformation during contraction, resulting from a finite element simulation with a mesh that was directly generated from the experimental data, has been presented.

Mechanical blood-tissue interaction in contracting muscles: a model study.

A finite element (FE) model of blood perfused biological tissue has been developed. Blood perfusion is described by fluid flow through a series of 5 intercommunicating vascular compartments that are embedded in the tissue. Each compartment is characterized by a blood flow permeability tensor, blood volume fraction and vessel compliance. Local non-linear relationships between intra-extra vascular pressure difference and blood volume fraction, and between blood volume fraction and the permeability tensor, are included in the FE model. To test the implementation of these non-linear relations, FE results of blood perfusion in a piece of tissue that is subject to increased intramuscular pressure, are compared to results that are calculated with a lumped parameter (LP) model of blood perfusion. FE simulation of blood flow through a contracting rat calf muscle is performed. The FE model used in this simulation contains a transversely isotropic, non-linearly elastic description of deforming muscle tissue, in which local contraction stress is prescribed as a function of time. FE results of muscle tension, total arterial inflow and total venous outflow of the muscle during contraction, correspond to experimental results of an isometrically and tetanically contracting rat calf muscle.

Wall shear stress in backward-facing step flow of a red blood cell suspension.

An experimental investigation of the wall shear stress distribution downstream of a backward-facing step is carried out. The wall shear stress distribution was determined by measuring the deformation of a gel layer, attached to the wall downstream of the step. Speckle pattern interferometry was applied to measure the deformation of the gel layer. The measured deformation, combined with the properties of the gel layer, served as an input for a finite element solid mechanics computation to determine the stress distribution in the gel layer. The wall shear stress, required to generate the measured deformation of the gel layer, was determined from these computations. A Newtonian buffer solution and a non-Newtonian red blood cell suspension were used as measuring fluids. The deformation of the gel layer was determined for a Newtonian buffer solution to evaluate the method and to obtain the properties of the gel layer. Subsequently, the wall shear stress distribution for the non-Newtonian red blood cell suspension was determined for three different flow rates. The inelastic non-Newtonian Carreau-Yasuda model served as constitutive model for the red blood cell suspension. Using this model, the velocity and wall shear stress distribution were computed by means of a finite element fluid mechanics computation. From the comparison between the numerical and the experimental results, it can be concluded that wall shear stresses, induced by the red blood cell suspension, can be modeled accurately by employing a Carreau-Yasuda model.

Finite-element simulation of blood perfusion in muscle tissue during compression and sustained contraction.

Mechanical interaction between tissue stress and blood perfusion in skeletal muscles plays an important role in blood flow impediment during sustained contraction. The exact mechanism of this interaction is not clear, and experimental investigation of this mechanism is difficult. We developed a finite-element model of the mechanical behavior of blood-perfused muscle tissue, which accounts for mechanical blood-tissue interaction in maximally vasodilated vasculature. Verification of the model was performed by comparing finite-element results of blood pressure and flow with experimental measurements in a muscle that is subject to well-controlled mechanical loading conditions. In addition, we performed simulations of blood perfusion during tetanic, isometric contraction and maximal vasodilation in a simplified, two-dimensional finite-element model of a rat calf muscle. A vascular waterfall in the venous compartment was identified as the main cause for blood flow impediment both in the experiment and in the finite-element simulations. The validated finite-element model offers possibilities for detailed analysis of blood perfusion in three-dimensional muscle models under complicated loading conditions.

Effects of four different methods of sampling arterial blood and storage time on gas tensions and shunt calculation in the 100% oxygen test.

At the present time, plastic syringes are most commonly used for collecting arterial blood. The oxygen tension of the arterial blood (Pa,O2) in these syringes may fall. We studied the effect of the type of syringe, metabolism, and storage time on the arterial oxygen pressures measured and on the pulmonary shunt calculated. In 10 patients, 2-3 h after aortacoronary bypass surgery, a 100% oxygen test was performed. Four arterial blood gas samples were withdrawn from each patient in random order, two in glass syringes and two in plastic syringes. One glass and one plastic syringe were stored at room temperature (RT), and the others were stored in ice-water (IW). Each sample was analysed as soon as possible, and repeated 15, 30, 60 and 120 min after sampling. The Pa,O2 measurement in blood in the glass syringe in IW measured as soon as possible after sampling was considered the "gold standard". Pulmonary shunt calculations were performed using the results of the various blood gas analyses. Compared with the "gold standard", all of the other methods showed significant deterioration in the Pa,O2 measurement. The effect due to diffusion was 0.05 kPa x min(-1), and that due to metabolism 0.11 kPa x min(-1). The Pa,O2 in the glass syringes stored in IW remained stable with time. The pulmonary shunt was significantly overestimated when the "gold standard" blood gas results were not used (range 0.8-9.9%). Glass (not plastic) syringes should be used in the 100% oxygen test. The syringe should be cooled immediately, even when the sample is analysed as soon as possible.

A triaxial accelerometer and portable data processing unit for the assessment of daily physical activity.

The present study describes the development of a triaxial accelerometer (TA) and a portable data processing unit for the assessment of daily physical activity. The TA is composed of three orthogonally mounted uniaxial piezoresistive accelerometers and can be used to register accelerations covering the amplitude and frequency ranges of human body acceleration. Interinstrument and test-retest experiments showed that the offset and the sensitivity of the TA were equal for each measurement direction and remained constant on two measurement days. Transverse sensitivity was significantly different for each measurement direction, but did not influence accelerometer output (< 3% of the sensitivity along the main axis). The data unit enables the on-line processing of accelerometer output to a reliable estimator of physical activity over eight-day periods. Preliminary evaluation of the system in 13 male subjects during standardized activities in the laboratory demonstrated a significant relationship between accelerometer output and energy expenditure due to physical activity, the standard reference for physical activity (r = 0.89). Shortcomings of the system are its low sensitivity to sedentary activities and the inability to register static exercise. The validity of the system for the assessment of normal daily physical activity and specific activities outside the laboratory should be studied in free-living subjects.

Nonhomogeneous permeability of canine anulus fibrosus.

STUDY DESIGN: This report examines the permeability coefficient and aggregate modulus of slices of anulus cut from canine lumbar intervertebral discs. OBJECTIVES: To examine the influence of radial position on the properties of these materials, including outer samples with intact anulus edge. SUMMARY OF BACKGROUND DATA: The outer edge of anulus fibrosus shows radial bulge during axial compression of motion segments. The radial bulge increases monotonically when the axial compression is sustained for several hours, until a plateau is reached. Triphasic modeling of axial compression shows that this time course of radial bulge can not be obtained using a uniform permeability coefficient according to values in the literature. METHODS: Confined consolidation experiments (controlled load) were designed to measure the time course of uniaxial deformation of samples of anulus that were 4 mm in diameter and 1 mm tall. The rotation symmetry axis of the samples was defined in the radial direction of the disc. The radial permeability coefficient and the aggregate modulus were determined using the consolidation data and the linear biphasic theory. RESULTS: The permeability coefficient was lower at the periphery than in deeper layers of the anulus. Outer samples with outer surfaces that were 0.0-0.5 mm from the anulus edge had an average permeability coefficient of (1.02 +/- 0.57) x 10(-16) m4/Ns (n = 24). Inner samples that were 2.0-2.5 mm from the anulus edge had an average permeability coefficient of (2.81 +/- 0.98) x 10(-16) m4/Ns (n = 13). The aggregate modulus HA of outer samples was significantly higher (HA = 1.56 +/- 0.34 MPa) than that of inner samples (HA = 1.31 +/- 0.47 MPa). CONCLUSIONS: The fact that the outer anulus is less permeable than the inner anulus may explain why radial bulge of anulus fibrosus increases monotonically in time to an equilibrium value during sustained axial compression of a motion segment.

Analysis of the axial flow field in stenosed carotid artery bifurcation models--LDA experiments.

Laser Doppler anemometer (LDA) experiments were performed to gain quantitative information on the differences between the large-scale flow phenomena in a non-stenosed and a stenosed model of the carotid artery bifurcation. The influence of the presence of the stenosis was compared to the effect of flow pulse variation to evaluate the feasibility of early detection of stenosis in clinical practice. Three-dimensional Plexiglass models of a non-stenosed and a 25% stenosed carotid artery bifurcation were perfused with a Newtonian fluid. The flow conditions approximated physiological flow. The results of the velocity measurements in the non-stenosed model agreed with the results from previous hydrogen-bubble visualization. A shear layer separated the low-velocity area near the non-divider wall from the high-velocity area near the divider wall. In this shear layer, vortex formation occurred during the deceleration phase of the flow pulse. The instability of this shear layer dictated the flow disturbances. The influences of the mild stenosis, located at the non-divider wall, was mainly limited to the stability of the shear layer. No disturbances were found downstream of the stenosis near the non-divider wall. Using a pulse wave with an increased systolic deceleration time, the velocity distribution showed an extended region with reversed flow, a more pronounced shear layer and increased vortex strength. From these measurements it is obvious that the influence of the presence of a mild stenosis, mainly limited to the stability of the shear layer, can hardly be distinguished from the effects of a variation of the flow pulse. From this it can be concluded that methods for detection of mild stenosis, using solely the large-scale flow phenomena, as can be measured by ultrasound or MRI techniques, will hardly have any clinical relevance.

Strain distribution on rat medial gastrocnemius (MG) during passive stretch.

Deformation of the surface of passive medial gastrocnemius muscle (MG) was measured in vivo while performing a hysteresis test. The gastrocnemius muscle of male rats were dissected free and the distal tendon was cut. The lateral head was separated from the medial head. The muscle origins were left intact. 60-70 fluorescent, polystyrene spheres (diameter 0.7 mm) were attached to the surface of the MG. During the experiment, two-dimensional video recordings of the movements of the MG were made. The coordinates of the marker centroids were obtained by computer processing of digitized images and marker displacements as a function of time were calculated. Green-Lagrange strains in two principal directions were calculated (epsilon 1, epsilon 2) for three specimens. epsilon 1 had approximately the same direction as the muscle fibers. The longitudinal strain of the fibers (20-30%) was larger than the strain of the aponeurosis (1-5%); p < 0.001. No significant difference was found between the values of the transverse strains of muscle fibers and aponeurosis; the value of epsilon 2 was -6 to -9% for both tissue structures.

Daily physical activity assessment: comparison between movement registration and doubly labeled water.

The use of movement registration for daily physical activity assessment was evaluated during a 7-day period in 30 free-living subjects. Body movement was registered with a Tracmor motion sensor consisting of a triaxial accelerometer and a data unit for on-line processing of accelerometer output over 1-min intervals. Average Tracmor output was correlated against four different energy estimates: 1) average daily metabolic rate (ADMR), determined with doubly labeled water; 2) ADMR-sleeping metabolic rate (SMR; determined in a respiration chamber); 3) (ADMR-SMR) per kilogram of body mass; and 4) the overall physical activity level (PAL = ADMR/SMR). The highest correlation was found for the relationship between Tracmor output and PAL (r = 0.58). After correction for Tracmor values arising from vibrations produced by transportation means, this correlation was improved to 0.73. There was no difference between Tracmor output and PAL in discriminating between overall activity levels with "low" (PAL < 1.60), "moderate" (1.60 < or = PAL < or = 1.85), and "high" (PAL > 1.85) intensity. It is concluded that the Tracmor can be used in free-living subjects to distinguish among interindividual as well as intraindividual levels of daily physical activity.

Determination of muscle fibre orientation using Diffusion-Weighted MRI.

Biomechanical studies have shown that the distribution of stress and strain in biological tissue is strongly dependent on fibre orientation. Therefore, to analyze the local mechanical load, accurate data on muscle fibre orientation are needed. Traditional techniques to determine fibre orientation are inherently invasive. Here we used Diffusion Weighted MRI to non-invasively determine, in each image voxel of 0.23 x 0.23 mm, the diffusion tensor of water in the cat semimembranosus muscle. The direction corresponding to the largest eigenvector of this tensor was calculated. This direction was found to correspond qualitatively to the muscular fibre direction, as determined by visual inspection.

A 3-D finite element model of blood perfused rat gastrocnemius medialis muscle.

A finite element description of blood perfusion has been developed, and is applied to skeletal muscles. Three-dimensional distributions of blood pressures and flows in deforming muscles are calculated. The muscle tissue is considered as a fluid-saturated porous solid. The blood is modeled as a series of five intercommunicating compartmental fluids, representing arterial, arteriolar, capillary, venular and venous blood, that reside in the pores (blood vessels) of the muscle tissue. The blood vessels are modeled as distensible tubes, embedded in the muscle tissue. A 3-D finite element mesh has been mapped on a reconstructed geometry of a gastrocnemius medialis muscle of the rat. Blood perfused linear elastic muscle material behaviour has been assigned to this mesh. A simulation of blood perfusion, resulting from a constant arterio-venous pressure difference, through the reconstructed muscle has been performed. Calculated blood pressure and flow distributions were within physiological range.

Three-dimensional reconstruction of the rat triceps surae muscle and finite element mesh generation of the gastrocnemius medialis muscle.

In order to simulate blood flow in skeletal muscle, our group has developed a finite element description of perfused skeletal muscle. This model requires input parameters concerning the vascular system, muscle contraction and the geometry of a muscle, including its aponeuroses. The objective of the present paper is to create a geometrical reconstruction of the rat gastrocnemius medialis muscle that can be incorporated in the finite element model. Since this muscle is connected to the plantaris and the gastrocnemius lateralis muscle, a detailed computer graphical reconstruction of the triceps surae muscle, based on histological cross-sections, has been accomplished first. Using this reconstruction, relevant sections were selected to create the finite element mesh of the gastrocnemius medialis muscle. Special attention was payed to the location of the aponeuroses. The mesh can be used in finite element simulations of perfused skeletal muscle.

Confined compression of canine annulus fibrosus under chemical and mechanical loading.

Uniaxial confined compression and swelling experiments on cylindrical specimens taken either in an axial or in a radial direction from a canine lumbar annulus fibrosus are presented. The loading protocol consisted of a combination of stepwise mechanical and chemical loading. Swelling and consolidation curves of normalized displacement versus square root of normalized time did not show a dependence on site or orientation of the specimen. All stages in which height increases, namely, conditioning, swelling, and desolidation show only slight differences in these normalized curves. Consolidation is initially faster, and later slower. The transport coefficient for axial specimens is higher than for radial specimens, for consolidation e.g., 3.14 +/- 1.56 10(-10) m2s(-1) and 1.11 +/- 0.33 10(-10) m2s(-1) respectively, the biphasic aggregate moduli are 1.01 +/- 0.31 MPa and 0.66 +/- 0.30 MPa, respectively.