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TECHNICAL PAPERS: Bone/Orthopedics

J Biomech Eng. 2006;128(4):473-480. doi:10.1115/1.2205370.

The present study examines the viscoelastic behavior of cancellous bone at low strains and the effects of damage on this viscoelastic behavior. It provides experimental evidence of interaction between stress relaxation behavior and the effect of accumulated damage. The results suggest that damage is at least orthotropic in trabecular bone specimens under uniaxial loading. Simple linear models of viscoelasticity described the time-dependent stress-strain behavior at low strains before and after specimen damage, although better fits of these models were obtained prior to damage. Modeling the observed changes in relaxation times with damage accumulation appears necessary to successfully predict the post-damage viscoelastic response.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(4):481-486. doi:10.1115/1.2205373.

Articulating cervical disk implants have been proposed as an alternative to disk fusion in the treatment of cervical disk disease. To examine the mechanical effect of articulating cervical disk implants (ACDI) versus simulated cervical disk fusion, a mechanical test device was constructed and cadaveric tests were carried out. While results show little effect on the pressures above and below the treatment level, the percent hysteretic behavior of the specimens trended to be higher for the ACDI, indicating that these implants retain more of the natural energy absorption capability of the cervical spine.

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Cell

J Biomech Eng. 2005;128(4):487-495. doi:10.1115/1.2205867.

In an attempt to understand the role of structural rearrangement onto the cell response during imposed cyclic stresses, we simulated numerically the frequency-dependent behavior of a viscoelastic tensegrity structure (VTS model) made of 24 elastic cables and 6 rigid bars. The VTS computational model was based on the nonsmooth contact dynamics (NSCD) method in which the constitutive elements of the tensegrity structure are considered as a set of material points that mutually interact. Low amplitude oscillatory loading conditions were applied and the frequency response of the overall structure was studied in terms of frequency dependence of mechanical properties. The latter were normalized by the homogeneous properties of constitutive elements in order to capture the essential feature of spatial rearrangement. The results reveal a specific frequency-dependent contribution of elastic and viscous effects which is responsible for significant changes in the VTS model dynamical properties. The mechanism behind is related to the variable contribution of spatial rearrangement of VTS elements which is decreased from low to high frequency as dominant effects are transferred from mainly elastic to mainly viscous. More precisely, the elasticity modulus increases with frequency while the viscosity modulus decreases, each evolution corresponding to a specific power-law dependency. The satisfactorily agreement found between present numerical results and the literature data issued from in vitro cell experiments suggests that the frequency-dependent mechanism of spatial rearrangement presently described could play a significant and predictable role during oscillatory cell dynamics.

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Fluids/Heat/Transport

J Biomech Eng. 2006;128(4):496-504. doi:10.1115/1.2205372.

Comprehensive understanding of the biomechanical performance of the lamina cribrosa (LC) and the optic nerve head is central to understanding the role of elevated intraocular pressures (IOP) in chronic open angle glaucoma. In this paper, six closed-from mathematical models based on different idealizations of the LC are developed and compared. This approach is used to create further understanding of the biomechanical behavior by identifying the LC features and properties that have a significant effect on its performance under elevated IOP. The models developed are based on thin circular plate and membrane theories, and consider influences such as in-plane pretension caused by scleral expansion and large deflections. Comparing the results of the six models against a full ocular globe finite element model suggests the significance of the in-plane pretension and the importance of assuming that the sclera provides the LC with a clamped edge. The model that provided the most accurate representation of the finite element model was also used to predict the behavior of a number of LC experimental tests presented in the literature. In addition to the deflections under elevated IOP, the model predictions include the distributions of stress and strain, which are shown to be compatible with the progression of visual field loss experienced in glaucoma.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(4):505-515. doi:10.1115/1.2205375.

Hyperthermia is a cancer treatment modality in which body tissue is exposed to elevated temperatures to destroy cancerous cells. Hyperthermia treatment planning refers to the use of computational models to optimize the heating protocol with the goal of isolating thermal damage to predetermined treatment areas. This paper presents an algorithm to optimize a hyperthermia treatment protocol using the conjugate gradient method with the adjoint problem. The output of the minimization algorithm is a heating protocol that will cause a desired amount of thermal damage. The transient temperature distribution in a cylindrical region is simulated using the bioheat transfer equation. Temperature and time are integrated to calculate the extent of thermal damage in the region via a first-order rate process based on the Arrhenius equation. Several validation experiments are carried out by applying the results of the minimization algorithm to an albumen tissue phantom. Comparisons of metrics describing the damage region (the height and radius of the volume of thermally ablated phantom) show good agreement between the desired extent of damage and the measured extent of damage. The sensitivity of the bioheat transfer model and the Arrhenius damage model to their constituent parameters is calculated to create a tolerable range of error between the desired and measured extent of damage. The measured height and radius of the ablated region fit well within the tolerable range of error found in the sensitivity analysis.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(4):516-526. doi:10.1115/1.2205377.

Blood flow dynamics under physiologically realistic pulsatile conditions plays an important role in the growth, rupture, and surgical treatment of intracranial aneurysms. The temporal and spatial variations of wall pressure and wall shear stress in the aneurysm are hypothesized to be correlated with its continuous expansion and eventual rupture. In addition, the assessment of the velocity field in the aneurysm dome and neck is important for the correct placement of endovascular coils. This paper describes the flow dynamics in two representative models of a terminal aneurysm of the basilar artery under Newtonian and non-Newtonian fluid assumptions, and compares their hemodynamics with that of a healthy basilar artery. Virtual aneurysm models are investigated numerically, with geometric features defined by $β=0deg$ and $β=23.2deg$, where $β$ is the tilt angle of the aneurysm dome with respect to the basilar artery. The intra-aneurysmal pulsatile flow shows complex ring vortex structures for $β=0deg$ and single recirculation regions for $β=23.2deg$ during both systole and diastole. The pressure and shear stress on the aneurysm wall exhibit large temporal and spatial variations for both models. When compared to a non-Newtonian fluid, the symmetric aneurysm model $(β=0deg)$ exhibits a more unstable Newtonian flow dynamics, although with a lower peak wall shear stress than the asymmetric model $(β=23.2deg)$. The non-Newtonian fluid assumption yields more stable flows than a Newtonian fluid, for the same inlet flow rate. Both fluid modeling assumptions, however, lead to asymmetric oscillatory flows inside the aneurysm dome.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(4):527-539. doi:10.1115/1.2205863.

A new mechanism for quantifying the filling energetics in the left ventricle (LV) and past mechanical heart valves (MHV) is identified and presented. This mechanism is attributed to vortex formation dynamics past MHV leaflets. Recent studies support the conjecture that the natural healthy left ventricle (LV) performs in an optimum, energy-preserving manner by redirecting the flow with high efficiency. Yet to date, no quantitative proof has been presented. The present work provides quantitative results and validation of a theory based on the dynamics of vortex ring formation, which is governed by a critical formation number (FN) that corresponds to the dimensionless time at which the vortex ring has reached its maximum circulation content, in support of this hypothesis. Herein, several parameters (vortex ring circulation, vortex ring energy, critical FN, hydrodynamic efficiencies, vortex ring propagation speed) have been quantified and presented as a means of bridging the physics of vortex formation in the LV. In fact, the diastolic hydrodynamic efficiencies were found to be 60, 41, and 29%, respectively, for the porcine, anti-anatomical, and anatomical valve configurations. This assessment provides quantitative proof of vortex formation, which is dependent of valve design and orientation, being an important flow characteristic and associated to LV energetics. Time resolved digital particle image velocimetry with kilohertz sampling rate was used to study the ejection of fluid into the LV and resolve the spatiotemporal evolution of the flow. The clinical significance of this study is quantifying vortex formation and the critical FN that can potentially serve as a parameter to quantify the LV filling process and the performance of heart valves.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(4):540-553. doi:10.1115/1.2206198.

Efficacy of topical microbicidal drug delivery formulations against HIV depends in part on their ability to coat, distribute, and be retained on epithelium. Once applied to the vagina, a formulation is distributed by physical forces including: gravity, surface tension, shearing, and normal forces from surrounding tissues, i.e., squeezing forces. The present study focused on vaginal microbicide distribution due to squeezing forces. Mathematical simulations of squeezing flows were compared with squeezing experiments, using model vaginal gel formulations. Our objectives were: (1) to determine if mathematical simulations can accurately describe squeezing flows of vaginal gel formulations; (2) to find the best model and optimized parameter sets to describe these gels; and (3) to examine vaginal coating due to squeezing using the best models and summary parameters for each gel. Squeezing flow experiments revealed large differences in spreadability between formulations, suggesting different coating distributions in vivo. We determined the best squeezing flow models and summary parameters for six test gels of two compositions, cellulose and polyacrylic acid (PAA). We found that for some gels it was preferable to deduce model input parameters directly from squeezing flow experiments. For the cellulose gels, slip conditions in squeezing flow experiments needed to be evaluated. For PAA gels, we found that in the absence of squeezing experiments, rotational viscometry measurements (to determine Herschel-Bulkley parameters) led to reasonably accurate predictions of squeezing flows. Results indicated that yield stresses may be a strong determinant of squeezing flow mechanics. This study serves as a template for further investigations of other gels and determination of which sources of rheological data best characterize potential microbicidal formulations. These mathematical simulations can serve as useful tools for exploring drug delivery parameters, and optimizing formulations, prior to costly clinical trials.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(4):554-563. doi:10.1115/1.2206200.

We have utilized a computational model of the expansion of a microbubble in a liquid-filled flexible tube to investigate the potential for acoustic vaporization of perfluorocarbon droplets to damage blood vessels during a novel gas embolotherapy technique for the potential treatment of tumors. This model uses a fixed grid, multi-domain, interface tracking, direct numerical simulation method that treats all interfaces and boundaries as sharp discontinuities for high accuracy. In the current work, we examined effects of initial bubble size on the flows and wall stresses that result from droplet vaporization. The remaining dimensionless parameters that govern the system response (Reynolds, Weber, and Strouhal numbers, initial bubble pressure, and wall stiffness and tension) were selected to model an arteriole. The results for a flexible tube are significantly different from those for a rigid tube. Two major flow regimes occur due to the combined effect of bubble and tube deformation: in flow at the tube ends and out flow near the bubble surface. The flexibility of the tube largely dissipates the extreme pressure that develops in the rigid tube model. Both the magnitude and the overall expansion time of the rapidly changing pressure are greatly reduced in the flexible tube. Smaller initial bubble diameters, relative to the vessel diameter, result in lower wall stresses. This study indicates that wall flexibility can significantly influence the wall stresses that result from acoustic vaporization of intravascular perfluorocarbon droplets, and suggests that acoustic activation of droplets in larger, more flexible vessels may be less likely to damage or rupture vessels than activation in smaller and stiffer vessels.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(4):564-572. doi:10.1115/1.2206202.

Clinical imaging methods are highly effective in the diagnosis of vascular pathologies, but they do not currently provide enough detail to shed light on the cause or progression of such diseases, and would be hard pressed to foresee the outcome of surgical interventions. Greater detail of and prediction capabilities for vascular hemodynamics and arterial mechanics are obtained here through the coupling of clinical imaging methods with computational techniques. Three-dimensional, patient-specific geometric reconstructions of the pediatric proximal pulmonary vasculature were obtained from x-ray angiogram images and meshed for use with commercial computational software. Two such models from hypertensive patients, one with multiple septal defects, the other who underwent vascular reactivity testing, were each completed with two sets of suitable fluid and structural initial and boundary conditions and used to obtain detailed transient simulations of artery wall motion and hemodynamics in both clinically measured and predicted configurations. The simulation of septal defect closure, in which input flow and proximal vascular stiffness were decreased, exhibited substantial decreases in proximal velocity, wall shear stress (WSS), and pressure in the post-op state. The simulation of vascular reactivity, in which distal vascular resistance and proximal vascular stiffness were decreased, displayed negligible changes in velocity and WSS but a significant drop in proximal pressure in the reactive state. This new patient-specific technique provides much greater detail regarding the function of the pulmonary circuit than can be obtained with current medical imaging methods alone, and holds promise for enabling surgical planning.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(4):573-578. doi:10.1115/1.2206203.

Motivated by the physiological problem of pulmonary airway reopening, we study the steady propagation of an air finger into a buckled elastic tube, initially filled with viscous fluid. The system is modeled using geometrically non-linear, Kirchhoff-Love shell theory, coupled to the free-surface Navier-Stokes equations. The resulting three-dimensional, fluid-structure-interaction problem is solved numerically by a fully coupled finite element method. Our study focuses on the effects of fluid inertia, which has been neglected in most previous studies. The importance of inertial forces is characterized by the ratio of the Reynolds and capillary numbers, $Re∕Ca$, a material parameter. Fluid inertia has a significant effect on the system’s behavior, even at relatively small values of $Re∕Ca$. In particular, compared to the case of zero Reynolds number, fluid inertia causes a significant increase in the pressure required to drive the air finger at a given speed.

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Joint/Whole Body

J Biomech Eng. 2006;128(4):579-587. doi:10.1115/1.2205864.
OPEN ACCESS

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(4):588-595. doi:10.1115/1.2205865.

This study presents an optimized matching algorithm for a dual-orthogonal fluoroscopic image system used to determine six degrees-of-freedom total knee arthroplasty (TKA) kinematics in-vivo. The algorithm was evaluated using controlled conditions and standard geometries. Results of the validation demonstrate the algorithm’s robustness and capability of realizing a pose from a variety of initial poses. Under idealized conditions, poses of a TKA system were recreated to within 0.02±0.01 mm and 0.02±0.03 deg for the femoral component and 0.07±0.09 mm and 0.16±0.18 deg for the tibial component. By employing a standardized geometry with spheres, the translational accuracy and repeatability under actual conditions was found to be 0.01±0.06 mm. Application of the optimized matching algorithm to a TKA patient showed that the pose of in-vivo TKA components can be repeatedly located, with standard deviations less than ±0.12 mm and ±0.12 deg for the femoral component and ±0.29 mm and ±0.25 deg for the tibial component. This methodology presents a useful tool that can be readily applied to the investigation of in-vivo motion of TKA kinematics.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(4):596-603. doi:10.1115/1.2205866.

The locations of the joint axes of the ankle complex vary considerably between subjects, yet no noninvasive method with demonstrated accuracy exists for locating these axes. The moments of muscle and ground reaction forces about the joint axes are dependent on axis locations, making knowledge of these locations critical to accurate musculoskeletal modeling of the foot and ankle. The accuracy of a computational optimization method that fits a two-revolute model to measured motion was assessed using computer-generated data, a two-revolute mechanical linkage, and three lower-leg cadaver specimens. Motions were applied to cadaver specimens under axial load while bone-mounted markers attached to the tibia, talus, and calcaneus were tracked using a video-based motion analysis system. Estimates of the talocrural and subtalar axis locations were computed from motions of the calcaneus relative to the tibia using the optimization method. These axes were compared to mean helical axes computed directly from tibia, talus, and calcaneus motions. The optimization method performed well when the motions were computer-generated or measured in the mechanical linkage, with angular differences between optimization and mean helical axes ranging from $1deg$ to $5deg$. In the cadaver specimens, however, these differences exceeded $20deg$. Optimization methods that locate the anatomical joint axes of the ankle complex by fitting two revolute joints to measured tibia-calcaneus motions may be limited because of problems arising from non-revolute behavior.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(4):604-609. doi:10.1115/1.2206199.

Shoulder motion is complex and significant research efforts have focused on measuring glenohumeral joint motion. Unfortunately, conventional motion measurement techniques are unable to measure glenohumeral joint kinematics during dynamic shoulder motion to clinically significant levels of accuracy. The purpose of this study was to validate the accuracy of a new model-based tracking technique for measuring three-dimensional, in vivo glenohumeral joint kinematics. We have developed a model-based tracking technique for accurately measuring in vivo joint motion from biplane radiographic images that tracks the position of bones based on their three-dimensional shape and texture. To validate this technique, we implanted tantalum beads into the humerus and scapula of both shoulders from three cadaver specimens and then recorded biplane radiographic images of the shoulder while manually moving each specimen’s arm. The position of the humerus and scapula were measured using the model-based tracking system and with a previously validated dynamic radiostereometric analysis (RSA) technique. Accuracy was reported in terms of measurement bias, measurement precision, and overall dynamic accuracy by comparing the model-based tracking results to the dynamic RSA results. The model-based tracking technique produced results that were in excellent agreement with the RSA technique. Measurement bias ranged from $−0.126to0.199mm$ for the scapula and ranged from $−0.022to0.079mm$ for the humerus. Dynamic measurement precision was better than $0.130mm$ for the scapula and $0.095mm$ for the humerus. Overall dynamic accuracy indicated that rms errors in any one direction were less than $0.385mm$ for the scapula and less than $0.374mm$ for the humerus. These errors correspond to rotational inaccuracies of approximately $0.25deg$ for the scapula and $0.47deg$ for the humerus. This new model-based tracking approach represents a non-invasive technique for accurately measuring dynamic glenohumeral joint motion under in vivo conditions. The model-based technique achieves accuracy levels that far surpass all previously reported non-invasive techniques for measuring in vivo glenohumeral joint motion. This technique is supported by a rigorous validation study that provides a realistic simulation of in vivo conditions and we fully expect to achieve these levels of accuracy with in vivo human testing. Future research will use this technique to analyze shoulder motion under a variety of testing conditions and to investigate the effects of conservative and surgical treatment of rotator cuff tears on dynamic joint stability.

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Soft Tissue

J Biomech Eng. 2006;128(4):610-622. doi:10.1115/1.2205371.

The development of methods to predict the strength and stiffness of biomaterials used in tissue engineering is critical for load-bearing applications in which the essential functional requirements are primarily mechanical. We previously quantified changes in the effective stiffness $(E)$ of needled nonwoven polyglycolic acid (PGA) and poly-L-lactic acid (PLLA) scaffolds due to tissue formation and scaffold degradation under three-point bending. Toward predicting these changes, we present a structural model for $E$ of a needled nonwoven scaffold in flexure. The model accounted for the number and orientation of fibers within a representative volume element of the scaffold demarcated by the needling process. The spring-like effective stiffness of the curved fibers was calculated using the sinusoidal fiber shapes. Structural and mechanical properties of PGA and PLLA fibers and PGA, PLLA, and 50:50 PGA/PLLA scaffolds were measured and compared with model predictions. To verify the general predictive capability, the predicted dependence of $E$ on fiber diameter was compared with experimental measurements. Needled nonwoven scaffolds were found to exhibit distinct preferred (PD) and cross-preferred (XD) fiber directions, with an $E$ ratio (PD/XD) of $∼3:1$. The good agreement between the predicted and experimental dependence of $E$ on fiber diameter $(R2=0.987)$ suggests that the structural model can be used to design scaffolds with $E$ values more similar to native soft tissues. A comparison with previous results for cell-seeded scaffolds (Engelmayr, G. C., Jr., , 2005, Biomaterials, 26(2), pp. 175–187) suggests, for the first time, that the primary mechanical effect of collagen deposition is an increase in the number of fiber-fiber bond points yielding effectively stiffer scaffold fibers. This finding indicated that the effects of tissue deposition on needled nonwoven scaffold mechanics do not follow a rule-of-mixtures behavior. These important results underscore the need for structural approaches in modeling the effects of engineered tissue formation on nonwoven scaffolds, and their potential utility in scaffold design.

Topics: Fibers , Stiffness
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(4):623-630. doi:10.1115/1.2206201.

Very limited information is currently available on the constitutive modeling of the tensile response of articular cartilage and its dynamic modulus at various loading frequencies. The objectives of this study were to (1) formulate and experimentally validate a constitutive model for the intrinsic viscoelasticity of cartilage in tension, (2) confirm the hypothesis that energy dissipation in tension is less than in compression at various loading frequencies, and (3) test the hypothesis that the dynamic modulus of cartilage in unconfined compression is dependent upon the dynamic tensile modulus. Experiment 1: Immature bovine articular cartilage samples were tested in tensile stress relaxation and cyclical loading. A proposed reduced relaxation function was fitted to the stress-relaxation response and the resulting material coefficients were used to predict the response to cyclical loading. Adjoining tissue samples were tested in unconfined compression stress relaxation and cyclical loading. Experiment 2: Tensile stress relaxation experiments were performed at varying strains to explore the strain-dependence of the viscoelastic response. The proposed relaxation function successfully fit the experimental tensile stress-relaxation response, with $R2=0.970±0.019$ at 1% strain and $R2=0.992±0.007$ at 2% strain. The predicted cyclical response agreed well with experimental measurements, particularly for the dynamic modulus at various frequencies. The relaxation function, measured from 2% to 10% strain, was found to be strain dependent, indicating that cartilage is nonlinearly viscoelastic in tension. Under dynamic loading, the tensile modulus at $10Hz$ was $∼2.3$ times the value of the equilibrium modulus. In contrast, the dynamic stiffening ratio in unconfined compression was $∼24$. The energy dissipation in tension was found to be significantly smaller than in compression (dynamic phase angle of $16.7±7.4deg$ versus $53.5±12.8deg$ at $10−3Hz$). A very strong linear correlation was observed between the dynamic tensile and dynamic compressive moduli at various frequencies $(R2=0.908±0.100)$. The tensile response of cartilage is nonlinearly viscoelastic, with the relaxation response varying with strain. A proposed constitutive relation for the tensile response was successfully validated. The frequency response of the tensile modulus of cartilage was reported for the first time. Results emphasize that fluid-flow dependent viscoelasticity dominates the compressive response of cartilage, whereas intrinsic solid matrix viscoelasticity dominates the tensile response. Yet the dynamic compressive modulus of cartilage is critically dependent upon elevated values of the dynamic tensile modulus.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEF

J Biomech Eng. 2006;128(4):631-635. doi:10.1115/1.2206204.

A study of mechanical heart valve behavior in the pulmonary position as a function of pulmonary vascular resistance is reported for the St. Jude Medical bileaflet (SJMB) valve and the MedicalCV Omnicarbon (OTD) tilting disk valve. Tests were conducted in a pulmonic mock circulatory system and impedance was varied in terms of system pulmonary vascular resistance (PVR). An impedance spectrum was found using instantaneous pulmonary artery pressure and flow rate curves. Both valves fully opened and closed at and above a nominal PVR of $3.0mmHg∕L∕min$. The SJMB valve was prone to leaflet bounce at closure, but otherwise completely closed, at settings above and below this nominal setting. At PVR values at and below $2.0mmHg∕L∕min$, the SJMB valve exhibited two types of leaflet aberrant behavior: single leaflet only closure while the other leaflet fluttered, and incomplete closure where both leaflets flutter but neither remain fully closed. The OTD valve fully opened and closed to a PVR value of $1.6mmHg∕L∕min$. At lower values, the valve did not close. Valves designed for the left heart can show aberrant behavior under normal conditions as pulmonary valves.

Commentary by Dr. Valentin Fuster