J Biomech Eng. 1996;118(3):273-279. doi:10.1115/1.2796007.

A realistic model experiment on hemodynamics was performed to study correlations between wall shear stresses measured in a cast model of the aortic bifurcation and intimal thickness at each corresponding site of the native blood vessel from which the cast had been made. An elastic model of a 54 year old human aortic bifurcation was made of a polyurethane elastomer using a dipping method, and was perfused with Newtonian or non-Newtonian fluid under physiologic pulsatile flow condition. Local flow velocities were measured with an optical-fibered, 3-dimensional laser Doppler anemometer (3D-LDA) to determine wall shear stresses. Distribution of intimal thickness was determined using histological specimens of the native blood vessel. The results obtained are: 1) Non-Newtonian fluid rheology increased wall shear stresses; 2) Positive correlations were observed between intimal thickness and the maximum instantaneous wall shear stress, and 3) However, if we take only the data from the circumference at the level of the flow divider tip, there were negative correlations between them.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):280-286. doi:10.1115/1.2796008.

Laminar and turbulent numerical simulations of steady flow in an aneurysm model were carried out over Reynolds numbers ranging from 300 to 3600. The numerical simulations are validated with Digital Particle Image Velocimetry (DPIV) measurements, and used to study the fluid dynamic mechanisms that characterize aneurysm deterioration, by correlating them to in vitro blood platelet deposition results. It is shown that the recirculation zone formed inside the aneurysm cavity creates conditions that promote thrombus formation and the viability of rupture. Wall shear stress values in the recirculation zone are around one order of magnitude less than in the entrance zone. The point of reattachment at the distal end of the aneurysm is characterized by a pronounced wall shear stress peak. As the Reynolds number increases in laminar flow, the center of the recirculation region migrates toward the distal end of the aneurysm, increasing the pressure at the reattachment point. Under fully turbulent flow conditions (Re = 3600) the recirculation zone inside the aneurysm shrinks considerably. The wall shear stress values are almost one order of magnitude larger than those for the laminar cases. The fluid dynamics mechanisms inferred from the numerical simulation were correlated with measurements of blood platelet deposition, offering useful explanations for the different morphologies of the platelet deposition curves.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):287-294. doi:10.1115/1.2796009.

Experimental results are reported for the low Reynolds number flow of a suspension of spherical particles through a divergent capillary bifurcation consisting of a straight tube of circular cross-section that splits to form two tubes of equal diameter. The partitioning of particles between the downstream branches of the bifurcation is measured as a function of the partitioning of total volume (particles + suspending fluid) between the branches. Two bifurcation geometries are examined: a symmetric Y-shaped bifurcation and a nonsymmetric T-shaped bifurcation. This experiment focuses on the role of hydrodynamic interactions between particles on the partitioning of particles at the bifurcation. The particle diameter, made dimensionless with respect to the diameter of the branch tubes, ranges from 0.4 to 0.8. Results show that hydrodynamic interactions among the particles are significant at the bifurcation, even for conditions where interactions are unimportant in the straight branches away from the bifurcation. As a result of hydrodynamic interactions among particles at the bifurcation, the partitioning of particles between the branches is affected for particle volume fractions as small as 2 percent. The experimental results show that the effect of particle volume fraction is to diminish the inhomogeneity of particle partitioning at the bifurcation. However, the magnitude of this effect depends strongly on the overall shape of the bifurcation geometry, and, in particular on the angles between the branches.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):295-301. doi:10.1115/1.2796010.

A new separation technique has been developed to determine the forward and backward running arterial pressure wave components. It takes into account friction as well as nonlinear effects due to convective acceleration and to the pressure dependence of the arterial compliance. The new method is a combination of two methods treating friction and nonlinearities separately. The method requires the measurements of pressure and flow at one location as well as the knowledge of the area-pressure relationship. The validity of the method was tested by a simulation experiment in which the forward and backward waves were known a priori. It was shown that the new method is significantly more accurate in the predictions of the forward and backward waves when compared to the classical method assuming linearity and no dissipation. The new wave separation method was also applied to simulated aortic waves for (a) a healthy subject and (b) a subject with decreased compliance. Comparison with the classical linear method showed that neglecting nonlinearities leads to an overestimation of the forward and backward pressure wave amplitudes. The errors, however, were in the order of 5 to 10 percent. We concluded that, for most clinical purposes, the improvement using the nonlinear method is of the same magnitude as experimental errors, and thus the linear method would suffice.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):302-310. doi:10.1115/1.2796011.

Steady flows in model proximal and distal end-to-side bypass anastomoses were simulated numerically. The predictions were compared to whole field measurements of the flow in in vitro models, and were shown to match well the general features of the measured flows. The predictions confirmed that the flows in end-to-side anastomoses are complex and three dimensional, and contain areas that could allow long residence times. Careful examination of the predictions revealed certain features of the flows not seen easily in the experiments. Shear stress and pressure on the vessel walls were predicted, and areas known to be prone to intimal hyperplasia were shown to correspond to areas of high spatial gradient of shear stress. Two anastomosis angles, 30 and 45 deg, were considered, and it was shown that the more acute angle may have some benefit in terms of the levels of shear gradients and the power required to drive the flow through the anastomosis.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):311-317. doi:10.1115/1.2796012.

The fully developed periodic laminar flow of incompressible Newtonian fluids through a pipe of circular cross section, which is coiled in a circle, was simulated numerically. The flow patterns are characterized by three parameters: the Womersley number Wo, the Dean number De, and the amplitude ratio β. The effect of these parameters on the flow was studied in the range 2.19 ≤ Wo ≤ 50.00, 15.07 ≤ De ≤ 265.49 and 0.50 ≤ β ≤ 2.00, with the curvature ratio δ fixed to be 0.05. The way the secondary flow evolved with increasing Womersley number and Dean number is explained. The secondary flow patterns are classified into three main groups: the viscosity-dominated type, the inertia-dominated type, and the convection-dominated type. It was found that when the amplitude ratio of the volumetric flow rate is equal to 1.0, four to six vortices of the secondary flow appear at high Dean numbers, and the Lyne-type flow patterns disappear at β ≥ 0.50.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):318-325. doi:10.1115/1.2796013.

Blood flow turbulence downstream of a concentric 86 percent area reduction stenosis was characterized using absolute and relative Doppler spectral broadening measurements, relative Doppler velocity fluctuation, and Doppler backscattered power. Bidi-mensional mappings of each Doppler index were obtained using a 10 MHz pulsed-wave Doppler system. Calf red cells suspended in a saline solution were used to scatter ultrasound and were circulated in an in vitro steady flow loop model. Results showed that the absolute spectral broadening was not a good index of turbulence because it was strongly affected by the deceleration of the jet and by the shear layer between the jet and the recirculation zones. Relative Doppler spectral broadening (absolute broadening divided by the frequency shift), velocity fluctuation, and Doppler power indices provided consistent mapping of the centerline axial variation of turbulence evaluated by hot-film anemometry. The best agreement between the hot-film and Doppler ultrasound methods was however obtained with the Doppler back-scattered power. The most consistent bidimensional mapping of the flow characteristics downstream of the stenosis was also observed with the Doppler power index. The relative broadening and the velocity fluctuation produced artifacts in the shear layer and in the recirculation zones. Power Doppler imaging is a new emerging technique that may provide reliable in vivo characterization of blood flow turbulence.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):326-332. doi:10.1115/1.2796014.

Presence of a small abdominal aortic aneurysm (AAA) often presents a difficult clinical dilemma—a reparative operation with its inherent risks versus monitoring the growth of the aneurysm, with the accompanying risk of rupture. The risk of rupture is conventionally believed to be a function of the AAA bulge diameter. In this work, we hypothesized that the risk of rupture depends on AAA shape. Because rupture is inevitably linked to stress, membrane theory was used to predict the stresses in the walls of an idealized AAA, using a model which was axisymmetric and fusiform, with the ends merged into straight open-ended tubes. When the stresses for many different shapes of model AAAs were examined, a number of conclusions became evident: (i) maximum hoop stress typically exceeded maximum meridional stress by a factor of 2 to 3 (ii) the shape of an AAA had a small effect on the meridional stresses and a rather dramatic effect on the hoop stresses, (iii) maximum stress typically occurred near the inflection point of a curve drawn coincident with the AAA wall, and (iv) the maximum stress was a function—not of the bulge diameter—but of the curvatures (i.e. shape) of the AAA wall. This last result suggested that rupture probability should be based on wall curvatures, not on AAA bulge diameter, Because curvatures are not much harder to measure than bulge diameter, this concept may be useful in a clinical setting in order to improve prediction of the likelihood of AAA rupture.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):333-340. doi:10.1115/1.2796015.

The dispersion of a bolus of soluble contaminant in a curved tube during volume-cycled oscillatory flows is studied. Assuming a small value of δ (the ratio of tube radius to radius of curvature), the Navier-Stokes equations are solved by using a perturbation method. The convection-diffusion equation is then solved by expanding the local concentration in terms of the cross-sectionally averaged concentration and its axial derivatives. The time-averaged dimensionless effective diffusivity, 〈Deff /D〉, is calculated for a range of Womersley number α and different values of stroke amplitude A and Schmidt number Sc, where D is the molecular diffusivity of contaminant. For the parameter values considered, the results show that axial dispersion in a curved tube is greater than that in a straight tube, and that it has a local maximum near α = 5 for given fixed values of Sc = 1, A = 5 and δ = 0.3. Finally it is demonstrated how the time history of concentration at a fixed axial position can be used to determine the effective diffusivity.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):341-348. doi:10.1115/1.2796016.

An axisymmetric elastic shell deformation model has been created to predict the conformity of a soft contact lens when pressed against the eye. Regions of contact and gap may be predicted, and the nonuniform reaction pressure between the lens and eye may also be found. This is important for issues like abrasion and comfort. Bending, membrane and transverse shear loads within the lens are also computed. Commercial soft contact lenses and a representative eye shape are used for the examples. We find that the uniformity of loading against the eye is strongly affected by the degree to which the lens is shaped to fit the eye, and relatively unaffected by the thickness of the lens.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):349-356. doi:10.1115/1.2796017.

This paper presents a simplified dynamical model for the control of one-degree-of-freedom synovial joints considered as pure trochlean joints. This model considers the joint dynamics, the dynamics of the corresponding muscles and their calcium balance dynamics, as well as position and force feedbacks provided by the spindles and the Golgi tendon organs. Delays in the transmission of information are also taken into account as they proved to be of critical importance for the dynamical behavior of the considered systems. The linearized version of this model, which is valid for a rather wide range of movements, also allows us to investigate the stability of the system, as well as its stability robustness with respect to the feedback gains. Further, particular behaviors such as tremor are described.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):357-366. doi:10.1115/1.2796018.

The objective of this paper was to propose a mathematical model for the fatigue and recovery phases of a paraplegic’s quadriceps muscle subjected to intermittent functional electrical stimulation (FES). The model is based on in vivo, noninvasive, recording of fatigue related metabolic parameters recorded during stimulation and recovery. Records of the time variations of the muscle’s phosphorus metabolites, particularly the phosphocreatine (PCr) and inorganic phosphorus (Pi), obtained from 31 P magnetic resonance spectroscopy (MRS), were used to calculate the intracellular pH level in the muscle and this latter parameter was incorporated in a musculo-tendon model. The fatigue-recovery model allows the transition from the fatiguing phase to the recovery phase as soon as the stimulation terminates and vice versa. This model was incorporated into a Huxley type muscle model expressing the dynamics of the muscle. Two ordinary differential equations describing the musculo-tendon dynamics and the dynamics of the activation were solved simultaneously and records of the force trajectory during intermittent stimulations were obtained. Study cases ranging from 5 to 30 s for each of the stimulation and recovery alternating phases were stimulated. The force and the total impulse in the modeled quadriceps muscle were computed. It was found that the greatest impulse was produced in intermittent stimulation of 40-50 s duty cycle, with a 50 percent ratio between the stimulation and recovery intervals. An additional series of six runs, including two contractions, one of 3 min and one of 1 min, separated by rest periods of 3, 6, 9, 12, 15, and 30 min was performed. From the predicted force trajectories obtained, the maximal force values served for comparison with measured values made on one patient.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):367-376. doi:10.1115/1.2796019.

In this study, we had subjects voluntarily generate various forces in a transverse plane just above their ankles. The contributions of their muscles and soft tissues to the support of the total external knee joint moment were determined by analyzing the experimental data using a biomechanical model of the knee. In this model, muscle forces were estimated using the recorded EMGs. To account for subject variability, various muscle parameters were adjusted using a nonlinear least-squares fit of the model’s estimated flexion and extension joint moments to those recorded externally. Using the estimated muscle forces, the contributions from the muscles and other soft tissues to the total joint moment were obtained. The results showed that muscles were primarily used to support flexion and extension loads at the knee, but in so doing, were able to support some part of the varus or valgus loads. However, soft tissue loading was still required. Soft tissues supported up to an average maximum of 83 percent of the external load in pure varus and valgus. Soft tissue loading in pure varus and valgus was less than 100 percent of the external load as the muscles, on average, were able to support 17 percent of the external load. This muscle support was by virtue of muscle cocontraction and/or specific muscle activation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):377-386. doi:10.1115/1.2796020.

To understand the wear mechanism of the ultrahigh molecular weight polyethylene (UHMWPE) articular plate used in artificial knee joints, the cyclic contact behavior of the plate during gait movement was analyzed using the constitutive equation for cyclic plasticity. In this study, two-dimensional plane strain model was employed and the contact behavior of femoral and tibial components was simulated by translating the contact stress distribution which was calculated from elasto-plastic indentation analysis of two components. For analytical model, the anatomical type artificial knee joint was employed and the effect of the shape of contact surface on the wear behavior of the plate was investigated. As a result, it was clarified that the wear of the plate should occur both from the surface and the subsurface of the plate and the wear behavior of the plate should be closely related with the shape of contact surface. Then the optimum shape of contact surface could be designed using this method.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):387-390. doi:10.1115/1.2796021.

The creation of 3-D finite element (FE) models of bone and implant-bone systems is a labor-intensive task due to the need to model different cases and variations, to perform patch tests and to account for the nonhomogeneous material properties with an acceptable amount of work. In this study, we developed an interface between a precision QCT and a FE system and applied it to a specimen bone. With the new method, the time necessary for model generation was reduced substantially. Furthermore, the elastic properties for each element were automatically derived from the corresponding CT-values. In order to demonstrate the importance of taking into account inhomogeneity, a comparison between the nonhomogeneous model and a homogeneous, “averaged” model was performed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):391-398. doi:10.1115/1.2796022.

Screws placed into cancellous bone in orthopedic surgical applications, such as fixation of fractures of the femoral neck or the lumbar spine, can be subjected to high loads. Screw pullout is a possibility, especially if low density osteoporotic bone is encountered. The overall goal of this study was to determine how screw thread geometry, tapping, and cannulation affect the holding power of screws in cancellous bone and determine whether current designs achieve maximum purchase strength. Twelve types of commercially available cannulated and noncannulated cancellous bone screws were tested for pullout strength in rigid unicellular polyurethane foams of apparent densities and shear strengths within the range reported for human cancellous bone. The experimentally derived pullout strength was compared to a predicted shear failure force of the internal threads formed in the polyurethane foam. Screws embedded in porous materials pullout by shearing the internal threads in the porous material. Experimental pullout force was highly correlated to the predicted shear failure force (slope = 1.05, R2 = 0.947) demonstrating that it is controlled by the major diameter of the screw, the length of engagement of the thread, the shear strength of the material into which the screw is embedded, and a thread shape factor (TSF) which accounts for screw thread depth and pitch. The average TSF for cannulated screws was 17 percent lower than that of noncannulated cancellous screws, and the pullout force was correspondingly less. Increasing the TSF, a result of decreasing thread pitch or increasing thread depth, increases screw purchase strength in porous materials. Tapping was found to reduce pullout force by an average of 8 percent compared with nontapped holes (p = 0.0001). Tapping in porous materials decreases screw pullout strength because the removal of material by the tap enlarges hole volume by an average of 27 percent, in effect decreasing the depth and shear area of the internal threads in the porous material.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):399-404. doi:10.1115/1.2796023.

A tapered femoral total hip stem with a debonded stem-cement interface and an unsupported distal tip subjected to constant axial load was evaluated using two-dimensional (2D) axisymmetric finite element analysis. The analysis was performed to test if the mechanical condition suggest that a “taper-lock” with a debonded viscoelastic bone cement might be an alternative approach to cement fixation of stem type cemented hip prosthesis. Effect of stem-cement interface conditions (bonded, debonded with and without friction) and viscoelastic response (creep and relaxation) of acrylic bone cement on cement mantle stresses and axial displacement of the stem was also investigated. Stem debonding with friction increased maximum cement von Mises stress by approximately 50 percent when compared to the bonded stem. Of the stress components in the cement mantle, radial stresses were compressive and hoop stresses were tensile and were indicative of mechanical taper-lock. Cement mantle stress, creep and stress relaxation and stem displacement increased with increasing load level and with decreasing stem-cement interface friction. Stress relaxation occur predominately in tensile hoop stress and decreased from 1 to 46 percent over the conditions considered. Stem displacement due to cement mantle creep ranged from 614 μm to 1.3 μm in 24 hours depending upon interface conditions and load level.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):405-411. doi:10.1115/1.2796024.

The study reported in this article was conducted to propose a set graphical and analytical tools and assess their clinical utility by analyzing gait kinematics and dynamics of polio survivors. Phase-plane portraits and first return maps were used as graphical tools to detect abnormal patterns in the sagittal kinematics of post-polio gait. Two new scalar measures were introduced to assess the bilateral kinematic symmetry and dynamic stability of human locomotion. Nine healthy subjects and seventeen post-polio patients were involved in the project. Significant increases in the knee extension and ankle plantar flexion of post-polio patients were observed during the weight acceptance phases of their gait. Polio patients also exhibited highly noticeable excessive hip flexion during the swing phase of their ambulation. Using the proposed symmetry measure, we concluded that post-polio patients walked less symmetrically than normals. Our conclusion, however, was based on the bilateral symmetry in the sagittal plane only. Finally, we observed that post-polio patients walked significantly less stably than normals. In addition, weaknesses in lower extremity muscles of polio patients were found to be an important factor that affected stable ambulation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(3):412-419. doi:10.1115/1.2796025.

A side airbag system comprising a 12 liter bag to cover the BioSid chest and the abdomen down to the arm rest level, and 75 mm of padding to cover the pelvic/thigh area was evaluated by a series of sled tests at two different velocities, 10 m/s and 12 m/s. The initial bag (over) pressure was varied from 0 to 80 kPa and the bag ventilation area was varied from zero to 1500 mm2 . Compressed air was used to fill the bag. It was found that the ventilation of the bag reduced the maximum chest deflection by 30 percent and the maximum viscous criterion, VC, by 50 percent (comparison was made with the same bag without ventilation). A suitable initial bag (over) pressure was found to be about 40 kPa, when the loading of the abdomen was also taken into consideration. The results indicate that the chest deflection is proportional to the door average velocity (during the first 20 ms of deflection) to the power of about 2 and that the VC is proportional to the same velocity to the power of about 4. It was also found that a 12 liter ventilated side airbag resulted in 30–40 percent lower chest deflection and about 60 percent lower VC than 50 mm of chest padding (Ethafoam 220).

Commentary by Dr. Valentin Fuster


J Biomech Eng. 1996;118(3):423-425. doi:10.1115/1.2796027.

Pedicle screws are commonly used in spinal reconstruction, and failure of pedicle screws due to bending is a significant clinical problem. To measure the moments typically placed on pedicle screws in situ we instrumented 7 mm Cotrel-Dubousset (CD) pedicle screws with internally mounted strain gauges. The screws were designed to measure flexion-extension moments at a single cross-section as dictated by strain gauge placement. It is possible to measure moments of up to 12 Nm at any location along the length of the screw by constructing transducers with varying strain gauge placements. These transducers are capable of measuring moments at points located within the vertebra including the pedicle, which is where failure usually occurs clinically. Transducer output was both linear and reproducible. These transducers are being used to investigate the load transfer characteristics between the pedicle screw and the vertebra. This technique could be applied to investigations of load sharing in reconstruction plates, lag-screws, and cross-locked intra-medullary nails.

Commentary by Dr. Valentin Fuster

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