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TECHNICAL PAPERS

J Biomech Eng. 1999;122(2):109-117. doi:10.1115/1.429648.

Aided by advancements in computer speed and modeling techniques, computational modeling of cardiac function has continued to develop over the past twenty years. The goal of the current study was to develop a computational model that provides blood–tissue interaction under physiologic flow conditions, and apply it to a thin-walled model of the left heart. To accomplish this goal, the Immersed Boundary Method was used to study the interaction of the tissue and blood in response to fluid forces and changes in tissue pathophysiology. The fluid mass and momentum conservation equations were solved using Patankar’s Semi-Implicit Method for Pressure Linked Equations (SIMPLE). A left heart model was developed to examine diastolic function, and consisted of the left ventricle, left atrium, and pulmonary flow. The input functions for the model included the pulmonary driving pressure and time-dependent relationship for changes in chamber tissue properties during the simulation. The results obtained from the left heart model were compared to clinically observed diastolic flow conditions for validation. The inflow velocities through the mitral valve corresponded with clinical values (E-wave=74.4 cm/s, A-wave=43 cm/s, and E/A=1.73). The pressure traces for the atrium and ventricle, and the appearance of the ventricular flow fields throughout filling, agreed with those observed in the heart. In addition, the atrial flow fields could be observed in this model and showed the conduit and pump functions that current theory suggests. The ability to examine atrial function in the present model is something not described previously in computational simulations of cardiac function. [S0148-0731(00)01302-9]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;122(2):118-124. doi:10.1115/1.429643.

This study was focused on a series of in vitro tests on the turbulent flow characteristics of three bileaflet aortic valves: St. Jude Medical (SJM), CarboMedics (CM), and Edwards Tekna (modified Duromedics, DM). The flow fields of the valves were measured in a pulsatile flow model with a laser-Doppler anemometer (LDA) at the aortic sinus area downstream of the valves. The heart rate was set at 70 beats per minute, the cardiac output was maintained at 5 liters per minute, and the aortic pressure wave forms were kept within the physiological range. Cycle-resolved analysis was applied to obtain turbulence data, including mean velocity, Reynolds stresses, autocorrelation coefficients, energy spectral density functions, and turbulence scales. The Reynolds shear stresses of all three valves induced only minor damage to red blood cells, but directly damaged the platelets, increasing the possibility of thrombosis. The smallest turbulence length scale, which offers a more reliable estimate of the effects of turbulence on blood cell damage, was three times the size of red blood cells and five times the size of platelets. This suggests that there is more direct interaction with the blood cells, thus causing more damage. [S0148-0731(00)00302-2]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;122(2):125-134. doi:10.1115/1.429634.

The high incidence of thromboembolic complications of mechanical heart valves (MHV) limits their success as permanent implants. The thrombogenicity of all MHV is primarily due to platelet activation by contact with foreign surfaces and by nonphysiological flow patterns. The latter include elevated flow stresses and regions of recirculation of blood that are induced by valve design characteristics. A numerical simulation of unsteady turbulent flow through a bileaflet MHV was conducted, using the Wilcox k–ω turbulence model for internal low-Reynolds-number flows, and compared to quantitative flow visualization performed in a pulse duplicator system using Digital Particle Image Velocimetry (DPIV). The wake of the valve leaflet during the deceleration phase revealed an intricate pattern of interacting shed vortices. Particle paths showed that platelets that were exposed to the highest flow stresses around the leaflets were entrapped within the shed vortices. Potentially activated, such platelets may tend to aggregate and form free emboli. Once formed, such free emboli would be convected downstream by the shed vortices, increasing the risk of systemic emboli. [S0148-0731(00)01202-4]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;122(2):135-142. doi:10.1115/1.429635.

The three dimensionally curved aortic arch is modeled as a portion of a helical pipe. Pulsatile blood flow therein is calculated assuming helical symmetry and an experimentally measured pressure pulse. Appropriate values for the Womersley and Reynolds numbers are taken from allometric scaling relations for a variety of body masses. The flow structure is discussed with particular reference to the wall shear, which is believed to be important in the inhibition of atheroma. It is found that nonplanar curvature limits the severity of flow separation at the inner bend, and reduces spatial variation of wall shear. [S0148-0731(00)00402-7]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;122(2):143-151. doi:10.1115/1.429644.

A study is conducted into the oscillatory behavior of a finite element model of an alveolar duct. Its load-bearing components consist of a network of elastin and collagen fibers and surface tension acting over the air–liquid interfaces. The tissue is simulated using a visco-elastic model involving nonlinear quasi-static stress–strain behavior combined with a reduced relaxation function. The surface tension force is simulated with a time- and area-dependent model of surfactant behavior. The model was used to simulate lung parenchyma under three surface tension cases: air-filled, liquid-filled, and lavaged with 3-dimethyl siloxane, which has a constant surface tension of 16 dyn/cm. The dynamic elastance (Edyn) and tissue resistance (Rti) were computed for sinusoidal tidal volume oscillations over a range of frequencies from 0.16–2.0 Hz. A comparison of the variation of Edyn and Rti with frequency between the model and published experimental data showed good qualitative agreement. Little difference was found in the model between Rti for the air-filled and lavaged models; in contrast, published data revealed a significantly higher value of Rti in the lavaged lung. The absence of a significant increase in Rti for the lavaged model can be attributed to only minor changes in the individual fiber bundle resistances with changes in their configuration. The surface tension was found to make an important contribution to both Edyn and Rti in the air-filled duct model. It was also found to amplify any existing tissue dissipative properties, despite exhibiting none itself over the small tidal volume cycles examined. [S0148-0731(00)00502-1]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;122(2):152-158. doi:10.1115/1.429636.

Deposition patterns and efficiencies of a dilute suspension of inhaled particles in three-dimensional double bifurcating airway models for both in-plane and 90 deg out-of-plane configurations have been numerically simulated assuming steady, laminar, constant-property air flow with symmetry about the first bifurcation. Particle diameters of 3, 5, and 7 μm were used in the simulation, while the inlet Stokes and Reynolds numbers varied from 0.037 to 0.23 and 500 to 2000, respectively. Comparisons between these results and experimental data based on the same geometric configuration showed good agreement. The overall trend of the particle deposition efficiency, i.e., an exponential increase with Stokes number, was somewhat similar for all bifurcations. However, the deposition efficiency of the first bifurcation was always larger than that of the second bifurcation, while in general the particle efficiency of the out-of-plane configuration was larger than that of the in-plane configuration. The local deposition patterns consistently showed that the majority of the deposition occurred in the carinal region. The distribution pattern in the first bifurcation for both configurations were symmetric about the carina, which was a direct result of the uniaxial flow at the inlet. The deposition patterns about the second carina showed increased asymmetry due to highly nonuniform flow generated by the first bifurcation and were extremely sensitive to bifurcation orientation. Based on the deposition variations between bifurcation levels and orientations, the use of single bifurcation models was determined to be inadequate to resolve the complex fluid–particle interactions that occur in multigenerational airways. [S0148-0731(00)01102-X]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;122(2):159-165. doi:10.1115/1.429637.

Numerous effects (e.g., airway wall buckling, gravity, airway curvature, capillary instabilities) give rise to nonuniformities in the depth of the liquid lining of peripheral lung airways. The effects of such thickness variations on the unsteady spreading of a surfactant monolayer along an airway are explored theoretically here. Flow-induced film deformations are shown to have only a modest influence on spreading rates, motivating the use of a simplified model in which the liquid-lining depth is prescribed and the monolayer concentration satisfies a spatially inhomogeneous nonlinear diffusion equation. Two generic situations are considered: spreading along a continuous annular liquid lining of nonuniform depth, and spreading along a rivulet that wets the airway wall with zero contact angle. In both cases, transverse averaging at large times yields a one-dimensional approximation of axial spreading that is valid for the majority of the monolayer. However, a localized monolayer remains persistently two dimensional in a region at its leading edge having axial length scales comparable to the length scale of transverse depth variation. It is also shown how the transverse spreading of a monolayer may be arrested as it approaches a static contact line at the edge of a rivulet. Implications for Surfactant Replacement Therapy are discussed. [S0148-0731(00)00202-8]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;122(2):166-172. doi:10.1115/1.429638.

Viscoelastic properties of wet and dry human compact bone were studied in torsion and in bending for both the longitudinal and transverse directions at frequencies from 5 mHz to 5 kHz in bending to more than 50 kHz in torsion. Two series of tests were done for different longitudinal and transverse specimens from a human tibia. Wet bone exhibited a larger viscoelastic damping tan δ (phase between stress and strain sinusoids) than dry bone over a broad range of frequency. All the results had in common a relative minimum in tan δ over a frequency range, 1 to 100 Hz, which is predominantly contained in normal activities. This behavior is inconsistent with an optimal “design” for bone as a shock absorber. There was no definitive damping peak in the range of frequencies explored, which could be attributed to fluid flow in the porosity of bone. [S0148-0731(00)00102-3]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;122(2):173-179. doi:10.1115/1.429639.

The anulus fibrosus (AF) is a lamellar, fibrocartilaginous component of the intervertebral disc, which exhibits highly anisotropic behaviors in tension. These behaviors arise from the material’s unique collagen structure. We have investigated the use of a linear, fiber-induced anisotropic model for the AF using a quadratic strain energy density formulation with an explicit representation of the collagen fiber populations. We have proposed a representative set of intrinsic material properties using independent datasets of the AF from the literature and appropriate thermodynamic constraints. The model was validated by comparing predictions with previous experimental data for AF behavior and its dependence on fiber angle. The model predicts that compressible effects may exist for the AF, and suggests that physical effects of the equivalent “matrix,” “fiber,” “fiber–matrix,” and “fiber–fiber,” interactions may be important contributors to the mechanical behavior of the AF. [S0148-0731(00)00802-5]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;122(2):180-188. doi:10.1115/1.429640.

A finite deformation mixture theory is used to quantify the mechanical properties of the annulus fibrosus using experimental data obtained from a confined compression protocol. Certain constitutive assumptions are introduced to derive a special mixture of an elastic solid and an inviscid fluid, and the constraint of intrinsic incompressibility is introduced in a manner that is consistent with results obtained for the special theory. Thirty-two annulus fibrosus specimens oriented in axial (n=16) and radial (n=16) directions were obtained from the middle-lateral portion of intact intervertebral discs from human lumbar spines and tested in a stress-relaxation protocol. Material constants are determined by fitting the theory to experimental data representing the equilibrium stress versus stretch and the surface stress time history curves. No significant differences in material constants due to orientation existed, but significant differences existed due to the choice of theory used to fit the data. In comparison with earlier studies with healthy annular tissue, we report a lower aggregate modulus and a higher initial permeability constant. These differences are explained by the choice of reference configuration for the experimental studies. [S0148-0731(00)01002-5]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;122(2):189-195. doi:10.1115/1.429641.

Mechanical behavior of articular cartilage was characterized in unconfined compression to delineate regimes of linear and nonlinear behavior, to investigate the ability of a fibril-reinforced biphasic model to describe measurements, and to test the prediction of biphasic and poroelastic models that tissue dimensions alter tissue stiffness through a specific scaling law for time and frequency. Disks of full-thickness adult articular cartilage from bovine humeral heads were subjected to successive applications of small-amplitude ramp compressions cumulating to a 10 percent compression offset where a series of sinusoidal and ramp compression and ramp release displacements were superposed. We found all equilibrium behavior (up to 10 percent axial compression offset) to be linear, while most nonequilibrium behavior was nonlinear, with the exception of small-amplitude ramp compressions applied from the same compression offset. Observed nonlinear behavior included compression-offset-dependent stiffening of the transient response to ramp compression, nonlinear maintenance of compressive stress during release from a prescribed offset, and a nonlinear reduction in dynamic stiffness with increasing amplitudes of sinusoidal compression. The fibril-reinforced biphasic model was able to describe stress relaxation response to ramp compression, including the high ratio of peak to equilibrium load. However, compression offset-dependent stiffening appeared to suggest strain-dependent parameters involving strain-dependent fibril network stiffness and strain-dependent hydraulic permeability. Finally, testing of disks of different diameters and rescaling of the frequency according to the rule prescribed by current biphasic and poroelastic models (rescaling with respect to the sample’s radius squared) reasonably confirmed the validity of that scaling rule. The overall results of this study support several aspects of current theoretical models of articular cartilage mechanical behavior, motivate further experimental characterization, and suggest the inclusion of specific nonlinear behaviors to models. [S0148-0731(00)00702-0]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;122(2):196-202. doi:10.1115/1.429642.

An investigation of the effects of laser irradiation with a wavelength of 532 nm and pulse duration of 10 ms on whole blood was performed in vitro. Threshold radiant exposures for coagulation were quantified and transient radiometric temperatures were measured. The progression of effects with increasing radiant exposure—from evaporation to coagulation-induced light scattering to aggregated coagulum formation to ablation—is described. Results indicate that coagulation and ablation occur at temperatures significantly in excess of those assumed in previous theoretical studies. An Arrhenius rate process analysis based on hemoglobin data indicates good agreement with experimental results. [S0148-0731(00)00902-X]

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEF

J Biomech Eng. 1999;122(2):203-207. doi:10.1115/1.429645.

Preclinical testing of orthopaedic implants is becoming increasingly important to eliminate inferior designs before animal experiments or clinical trials are begun. Preclinical tests can include both laboratory bench tests and computational modeling. One problem with bench tests is that variability in prosthesis insertion can significantly influence the failure rate; this makes comparison of prostheses more difficult. To solve this problem an insertion method is required that is both accurate and reproducible. In this work, a general approach to the insertion of hip prostheses into femoral bones is proposed based on physically replicating an insertion path determined using computer animation. As a first step, the seated prosthesis position is determined from templates and femur radiographs. Three-dimensional images of the prosthesis and bone are then imported into computer animation software and an insertion path in the coronal plane is determined. The insertion path is used to determine the profile of a cam. By attaching the prosthesis to a carriage, which is pneumatically moved along this cam, the required insertion motion of the prosthesis in the coronal plane can be achieved. This paper describes the design and validation of the insertion machine. For the validation study, a nonsymmetric hip prosthesis design (Lubinus SPII, Waldemar Link, Germany) is used. It is shown that the insertion machine has sufficient accuracy and reproducibility for preclinical mechanical testing. [S0148-0731(00)00602-6]

Commentary by Dr. Valentin Fuster

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