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IN THIS ISSUE

### Research Papers

J Biomech Eng. 2008;131(3):031001-031001-10. doi:10.1115/1.3005200.

Abdominal aortic aneurysm (AAA) rupture represents a major cardiovascular risk, combining complex vascular mechanisms weakening the abdominal artery wall coupled with hemodynamic forces exerted on the arterial wall. At present, a reliable method to predict AAA rupture is not available. Recent studies have introduced fluid structure interaction (FSI) simulations using isotropic wall properties to map regions of stress concentrations developing in the aneurismal wall as a much better alternative to the current clinical criterion, which is based on the AAA diameter alone. A new anisotropic material model of AAA that closely matches observed biomechanical AAA material properties was applied to FSI simulations of patient-specific AAA geometries in order to develop a more reliable predictor for its risk of rupture. Each patient-specific geometry was studied with and without an intraluminal thrombus (ILT) using two material models—the more commonly used isotropic material model and an anisotropic material model—to delineate the ILT contribution and the dependence of stress distribution developing within the aneurismal wall on the material model employed. Our results clearly indicate larger stress values for the anisotropic material model and a broader range of stress values as compared to the isotropic material, indicating that the latter may underestimate the risk of rupture. While the locations of high and low stresses are consistent in both material models, the differences between the anisotropic and isotropic models become pronounced at large values of strain—a range that becomes critical when the AAA risk of rupture is imminent. As the anisotropic model more closely matches the biomechanical behavior of the AAA wall and resolves directional strength ambiguities, we conclude that it offers a more reliable predictor of AAA risk of rupture.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2008;131(3):031002-031002-12. doi:10.1115/1.3005158.

The hinge region of a mechanical bileaflet valve is implicated in blood damage and initiation of thrombus formation. Detailed fluid dynamic analysis in the complex geometry of the hinge region during the closing phase of the bileaflet valve is the focus of this study to understand the effect of fluid-induced stresses on the activation of platelets. A fixed-grid Cartesian mesh flow solver is used to simulate the blood flow through a two-dimensional geometry of the hinge region of a bileaflet mechanical valve. Use of local mesh refinement algorithm provides mesh adaptation based on the gradients of flow in the constricted geometry of the hinge. Leaflet motion is specified from the fluid-structure interaction analysis of the leaflet dynamics during the closing phase from a previous study, which focused on the fluid mechanics at the gap between the leaflet edges and the valve housing. A Lagrangian particle tracking method is used to model and track the platelets and to compute the magnitude of the shear stress on the platelets as they pass through the hinge region. Results show that there is a boundary layer separation in the gaps between the leaflet ear and the constricted hinge geometry. Separated shear layers roll up into vortical structures that lead to high residence times combined with exposure to high-shear stresses for particles in the hinge region. Particles are preferentially entrained into this recirculation zone, presenting the possibility of platelet activation, aggregation, and initiation of thrombi.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(3):031003-031003-9. doi:10.1115/1.3002757.

This paper presents an extension of a recently developed low-dimensional modeling approach for normal human gait to the modeling of asymmetric gait. The asymmetric model is applied to analyze the gait dynamics of a transtibial prosthesis user, specifically the changes in joint torque and joint power costs that occur with variations in sagittal-plane alignment of the prosthesis, mass distribution of the prosthesis, and roll-over shape of the prosthetic foot being used. The model predicts an increase in cost with addition of mass and a more distal location of the mass, as well as the existence of an alignment at which the costs are minimized. The model’s predictions also suggest guidelines for the selection of prosthetic feet and suitable alignments. The results agree with clinical observations and results of other gait studies reported in the literature. The model can be a useful analytical tool for more informed design and selection of prosthetic components, and provides a basis for making the alignment process systematic.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(3):031004-031004-11. doi:10.1115/1.3005331.

The next generation of medical devices and engineered tissues will require development of scaffolds that mimic the structural and functional properties of the extracellular matrix (ECM) component of tissues. Unfortunately, little is known regarding how ECM microstructure participates in the transmission of mechanical load information from a global (tissue or construct) level to a level local to the resident cells ultimately initiating relevant mechanotransduction pathways. In this study, the transmission of mechanical strains at various functional levels was determined for three-dimensional (3D) collagen ECMs that differed in fibril microstructure. Microstructural properties of collagen ECMs (e.g., fibril density, fibril length, and fibril diameter) were systematically varied by altering in vitro polymerization conditions. Multiscale images of the 3D ECM macro- and microstructure were acquired during uniaxial tensile loading. These images provided the basis for quantification and correlation of strains at global and local levels. Results showed that collagen fibril microstructure was a critical determinant of the 3D global and local strain behaviors. Specifically, an increase in collagen fibril density reduced transverse strains in both width and thickness directions at both global and local levels. Similarly, collagen ECMs characterized by increased fibril length and decreased fibril diameter exhibited increased strain in width and thickness directions in response to loading. While extensional strains measured globally were equivalent to applied strains, extensional strains measured locally consistently underpredicted applied strain levels. These studies demonstrate that regulation of collagen fibril microstructure provides a means to control the 3D strain response and strain transfer properties of collagen-based ECMs.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(3):031005-031005-9. doi:10.1115/1.3005148.

Forward dynamic simulation provides a powerful framework for characterizing internal loads and for predicting changes in movement due to injury, impairment or surgical intervention. However, the computational challenge of generating simulations has greatly limited the use and application of forward dynamic models for simulating human gait. In this study, we introduce an optimal estimation approach to efficiently solve for generalized accelerations that satisfy the overall equations of motion and best agree with measured kinematics and ground reaction forces. The estimated accelerations are numerically integrated to enforce dynamic consistency over time, resulting in a forward dynamic simulation. Numerical optimization is then used to determine a set of initial generalized coordinates and speeds that produce a simulation that is most consistent with the measured motion over a full cycle of gait. The proposed method was evaluated with synthetically created kinematics and force plate data in which both random noise and bias errors were introduced. We also applied the method to experimental gait data collected from five young healthy adults walking at a preferred speed. We show that the proposed residual elimination algorithm (REA) converges to an accurate solution, reduces the detrimental effects of kinematic measurement errors on joint moments, and eliminates the need for residual forces that arise in standard inverse dynamics. The greatest improvements in joint kinetics were observed proximally, with the algorithm reducing joint moment errors due to marker noise by over 20% at the hip and over 50% at the low back. Simulated joint angles were generally within $1deg$ of recorded values when REA was used to generate a simulation from experimental gait data. REA can thus be used as a basis for generating accurate simulations of subject-specific gait dynamics.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(3):031006-031006-6. doi:10.1115/1.3005164.

Intervertebral disk degeneration results in alterations in the mechanical, chemical, and electrical properties of the disk tissue. The purpose of this study is to record spatially resolved streaming potential measurements across intervertebral disks exposed to cyclic compressive loading. We hypothesize that the streaming potential profile across the disk will vary with radial position and frequency and is proportional to applied load amplitude, according to the presumed fluid-solid relative velocity and measured glycosaminoglycan content. Needle electrodes were fabricated using a linear array of $Ag∕AgCl$ micro-electrodes and inserted into human motion segments in the midline from anterior to posterior. They were connected to an amplifier to measure electrode potentials relative to the saline bath ground. Motion segments were loaded in axial compression under a preload of $500N$, sinusoidal amplitudes of $±200N$ and $±400N$, and frequencies of $0.01Hz$, $0.1Hz$, and $1Hz$. Streaming potential data were normalized by applied force amplitude, and also compared with paired experimental measurements of glycosaminoglycans in each disk. Normalized streaming potentials varied significantly with sagittal position and there was a significant location difference at the different frequencies. Normalized streaming potential was largest in the central nucleus region at frequencies of $0.1Hz$ and $1.0Hz$ with values of approximately $3.5μV∕N$. Under $0.01Hz$ loading, normalized streaming potential was largest in the outer annulus regions with a maximum value of $3.0μV∕N$. Correlations between streaming potential and glycosaminoglycan content were significant, with $R2$ ranging from 0.5 to 0.8. Phasic relationships between applied force and electrical potential did not differ significantly by disk region or frequency, although the largest phase angles were observed at the outermost electrodes. Normalized streaming potentials were associated with glycosaminoglycan content, fluid, and ion transport. Results suggested that at higher frequencies the transport of water and ions in the central nucleus region may be larger, while at lower frequencies there is enhanced transport near the periphery of the annulus. This study provides data that will be helpful to validate multiphasic models of the disk.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(3):031007-031007-7. doi:10.1115/1.3005169.

Inconclusive findings regarding the collagen fiber architecture and the material properties of the glenohumeral capsule make it unclear whether the material symmetry of the glenohumeral capsule is isotropic or anisotropic. The overall objective of this work was to use a combined experimental and computational protocol to characterize the mechanical properties of the axillary pouch of the glenohumeral capsule and to determine the appropriate material symmetry. Two perpendicular tensile and finite simple shear deformations were applied to a series of tissue samples from the axillary pouch of the glenohumeral capsule. An inverse finite element optimization routine was then used to determine the material coefficients for an isotropic hyperelastic constitutive model by simulating the experimental conditions. There were no significant differences between the material coefficients obtained from the two perpendicular tensile deformations or finite simple shear deformations. Furthermore, stress-stretch relationships predicted by utilizing the material coefficients from one direction were able to predict the responses of the same tissue sample in the perpendicular direction. These similarities between the longitudinal and transverse material behaviors of the tissue imply that the capsule may be considered an isotropic material. However, differences did exist between the material coefficients obtained from the tensile and shear loading conditions. Therefore, a more advanced constitutive model is needed to predict both the tensile and shear responses of the material.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(3):031008-031008-9. doi:10.1115/1.3049478.

An investigation of collagen fiber reorientation, as well as fluid and matrix movement of equine articular cartilage and subchondral bone under compressive mechanical loads, was undertaken using small angle X-ray scattering measurements and optical microscopy. Small angle X-ray scattering measurements were made on healthy and diseased samples of equine articular cartilage and subchondral bone mounted in a mechanical testing apparatus on station ID18F of ESRF, Grenoble, together with fiber orientation analysis using polarized light and displacement measurements of the cartilage matrix and fluid using tracers. At surface pressures of up to approximately 1.5 MPa, there was reversible compression of the tangential surface fibers and immediately subjacent zone. As load increased, deformation in these zones reached a maximum and then reorientation propagated to the radial deep zone. Between surface pressures of 4.8 MPa and 6.0 MPa, fiber orientation above the tide mark rotated 10 deg from the radial direction, with an overall loss of alignment. With further increase in load, the fibers “crimped” as shown by the appearance of subsidiary peaks approximately $±10 deg$ either side of the principal fiber orientation direction. Failure at higher loads was characterized by a radial split in the deep cartilage, which propagated along the tide mark while the surface zone remained intact. In lesions, the fiber organization was disrupted and the initial response to load was consistent with early rupture of fibers, but the matrix relaxed to an organization very similar to that of the unloaded tissue. Tracer measurements revealed anisotropic solid and fluid displacement, which depended strongly on depth within the tissue.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(3):031009-031009-10. doi:10.1115/1.3049479.

In spite of impressive progress in developing general constitutive laws for soft tissues, there exists still no comprehensive model valid for any general deformation scheme. The present study focuses on the uniaxial response of the skin as a model for other multifibrous soft tissues. While the skin’s nonlinear viscoelastic constitutive response has been extensively studied and modeled, the phenomena associated with mechanical preconditioning have so far not been dealt with. Yet preconditioning is an inherent response feature in the skin, both in vitro and in vivo. It is hypothesized that by considering the structure of the elastic and collagen fibers and their individual rheological properties, it is possible to develop a reliable general constitutive law for the skin’s uniaxial response. A stochastic hybrid constitutive model was developed based on the collagen and elastic fiber morphologies and their rheological properties. The multiple protocol uniaxial data of Eshel and Lanir (“Effects of Strain Level and Proteoglycan Depletion on Preconditioning and Viscoelastic Responses of Rat Dorsal Skin  ,” 2001, Ann. Biomed. Eng., 29, pp. 164–172) served to estimate the model’s parameters and to validate its reliability. Parametric investigation was then used to test model parsimony (minimal form) and to elucidate the roles of response mechanism and the relative contribution of each constituent. The model predictions show a very close fit to the data and good predictive capability. The results are consistent with the quasilinear viscoelastic response of both elastic and collagen fibers and are likewise consistent with the notion (supported by published experimental observations) that preconditioning in collagen is probably due to an increase in the fiber reference length and is due to strain softening (Mullins effect) in elastic fibers. The predictions also agree with the observed predominance of elastic fibers at low strains and suggest that as strain increases, collagen becomes predominant, but the effect of elastic fibers is still significant. The parsimony analysis of the 22 model parameters (18 are nonlinear in the model) points to the predominant role of viscoelasticity and preconditioning in both fibers, followed in order of importance by collagen waviness and elastic fiber nonlinearity. A reliable and comprehensive uniaxial constitutive law for the rat skin was developed based on the tissue microstructure and on its constituents’ rheological properties.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(3):031010-031010-16. doi:10.1115/1.3049481.

The inhalation of micron-sized aerosols into the lung’s acinar region may be recognized as a possible health risk or a therapeutic tool. In an effort to develop a deeper understanding of the mechanisms responsible for acinar deposition, we have numerically simulated the transport of nondiffusing fine inhaled particles ($1 μm$ and $3 μm$ in diameter) in two acinar models of varying complexity: (i) a simple alveolated duct and (ii) a space-filling asymmetrical acinar branching tree following the description of lung structure by Fung (1988, “A Model of the Lung Structure and Its Validation  ,” J. Appl. Physiol., 64, pp. 2132–2141). Detailed particle trajectories and deposition efficiencies, as well as acinar flow structures, were investigated under different orientations of gravity, for tidal breathing motion in an average human adult. Trajectories and deposition efficiencies inside the alveolated duct are strongly related to gravity orientation. While the motion of larger particles $(3 μm)$ is relatively insensitive to convective flows compared with the role of gravitational sedimentation, finer $1 μm$ aerosols may exhibit, in contrast, complex kinematics influenced by the coupling between (i) flow reversal due to oscillatory breathing, (ii) local alveolar flow structure, and (iii) streamline crossing due to gravity. These combined mechanisms may lead to twisting and undulating trajectories in the alveolus over multiple breathing cycles. The extension of our study to a space-filling acinar tree was well suited to investigate the influence of bulk kinematic interaction on aerosol transport between ductal and alveolar flows. We found the existence of intricate trajectories of fine $1 μm$ aerosols spanning over the entire acinar airway network, which cannot be captured by simple alveolar models. In contrast, heavier $3 μm$ aerosols yield trajectories characteristic of gravitational sedimentation, analogous to those observed in the simple alveolated duct. For both particle sizes, however, particle inhalation yields highly nonuniform deposition. While larger particles deposit within a single inhalation phase, finer $1 μm$ particles exhibit much longer residence times spanning multiple breathing cycles. With the ongoing development of more realistic models of the pulmonary acinus, we aim to capture some of the complex mechanisms leading to deposition of inhaled aerosols. Such models may lead to a better understanding toward the optimization of pulmonary drug delivery to target specific regions of the lung.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(3):031011-031011-12. doi:10.1115/1.3005332.

A model of the upper extremity is developed in which the forearm is constrained to lie in a horizontal plane and electrical stimulation is applied to the triceps muscle. Identification procedures are described to estimate the unknown parameters using tests that can be performed in a short period of time. Examples of identified parameters obtained experimentally are presented for both stroke patients and unimpaired subjects. A discussion concerning the identification’s repeatability, together with results confirming the accuracy of the overall representation, is given. The model has been used during clinical trials in which electrical stimulation is applied to the triceps muscle of a number of stroke patients for the purpose of improving both their performance at reaching tasks and their level of voluntary control over their impaired arm. Its purpose in this context is threefold: Firstly, changes occurring in the levels of stiffness and spasticity in each subject’s arm can be monitored by comparing frictional components of models identified at different times during treatment. Secondly, the model is used to calculate the moments applied during tracking tasks that are due to a patient’s voluntary effort, and it therefore constitutes a useful tool with which to analyze their performance. Thirdly, the model is used to derive the advanced controllers that govern the level of stimulation applied to subjects over the course of the treatment. Details are provided to show how the model is applied in each case, and sample results are shown.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(3):031012-031012-12. doi:10.1115/1.2947358.

Vacuum-assisted closure® (VAC® ) therapy, also referred to as vacuum-assisted closure® negative pressure wound therapy (VAC® NPWT), delivered to various dermal wounds is believed to influence the formation of granulation tissue via the mechanism of microdeformational signals. In recent years, numerous experimental investigations have been initiated to study the cause-effect relationships between the mechanical signals and the transduction pathways that result in improved granulation response. To accurately quantify the tissue microdeformations during therapy, a new three-dimensional finite element model has been developed and is described in this paper. This model is used to study the effect of dressing type and subatmospheric pressure level on the variations in the microdeformational strain fields in a model dermal wound bed. Three-dimensional geometric models representing typical control volumes of NPWT dressings were generated using micro-CT scanning of VAC® GranuFoam® , a reticulated open-cell polyurethane foam (ROCF), and a gauze dressing (constructed from USP Class VII gauze). Using a nonlinear hyperfoam constitutive model for the wound bed, simulated tissue microdeformations were generated using the foam and gauze dressing models at equivalent negative pressures. The model results showed that foam produces significantly greater strain than gauze in the tissue model at all pressures and in all metrics ($p<0.0001$ for all but $εvol$ at $−50mmHg$ and $−100mmHg$ where $p<0.05$). Specifically, it was demonstrated in this current work that the ROCF dressing produces higher levels of tissue microdeformation than gauze at all levels of subatmospheric pressure. This observation is consistent across all of the strain invariants assessed, i.e., $εvol$, $εdist$, the minimum and maximum principal strains, and the maximum shear strain. The distribution of the microdeformations and strain appears as a repeating mosaic beneath the foam dressing, whereas the gauze dressings appear to produce an irregular distribution of strains in the wound surface. Strain predictions from the developed computational model results agree well with those predicted from prior two-dimensional experimental and computational studies of foam-based NPWT (Saxena, V., , 2004, “Vacuum-assisted closure: Microdeformations of Wounds and Cell Proliferation  ,” Plast. Reconstr. Surg., 114(5), pp. 1086–1096). In conjunction with experimental in vitro and in vivo studies, the developed model can now be extended into more detailed investigations into the mechanobiological underpinnings of VAC® NPWT and can help to further develop and optimize this treatment modality for the treatment of challenging patient wounds.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J Biomech Eng. 2008;131(3):034501-034501-5. doi:10.1115/1.3005153.

In order to protect sensitive residual limb soft tissues, lower limb prostheses need to control torsional loads during gait. To assist with the design of a torsional prosthesis, this paper used simple mechanical elements to model the behavior of the human ankle in the transverse plane during straight walking. Motion capture data were collected from ten able-bodied subjects walking straight ahead at self-selected walking speeds. Gait cycle data were separated into four distinct states, and passive torsional springs and dampers were chosen to model the behavior in each state. Since prosthetic design is facilitated by simplicity, it was desirable to investigate if elastic behavior could account for the physiological ankle moment and include viscous behavior only if necessary to account for the inadequacies of the spring model. In all four states, a springlike behavior was able to account for most of the physiological ankle moments, rendering the use of a damper unnecessary. In State 1, a quadratic torsional spring was chosen to model the behavior, while linear torsional springs were chosen for States 2–4. A prosthetic system that actively changes stiffness could be able to replicate the physiological behavior of the human ankle in the transverse plane. The results of this study will contribute to the mechanical design and control of a biomimetic torsional prosthesis for lower limb amputees.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2008;131(3):034502-034502-5. doi:10.1115/1.3005345.

Individuals who cannot functionally reposition themselves often need dynamic seating interventions that change body posture from automatic chair adjustments. Pelvis alignment directly affects sitting posture, and systems that adjust and monitor pelvis angle simultaneously might be applicable to control body posture in sitting. The present study explores whether it is feasible to monitor pelvis angle from seat support forces. Pelvis angle estimation was based on equivalent “two-force member” loading for which pelvis orientation equals the orientation of the equivalent contact force. Theoretical evaluation was done to derive important conditions for practical application. An instrumented wheelchair was developed for experimental validation in healthy subjects. Seat support forces were measured, and mechanical analysis was done to derive the equivalent contact force from which we estimated the pelvis angle. Model analysis showed a significant influence of pelvis mass, hip force, and lumbar torque on the relation between the actual pelvis angle and the predicted pelvis angle. Proper force compensation and minimal lumbar torque seemed important for accurate pelvis angle estimations. Experimental evaluation showed no body postures that involved a clear relation between the pelvis angle and the orientation of the equivalent contact force. Findings suggest that pelvis angle could not be estimated in healthy individuals under the described experimental seating conditions. Validation experiments with impaired individuals must be performed under different seating conditions to provide a better understanding whether the principle is of interest for clinical application.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2008;131(3):034503-034503-4. doi:10.1115/1.3005165.

Tekscan pressure sensors are used in biomechanics research to measure joint contact loads. While the overall accuracy of these sensors has been reported previously, the effects of different calibration algorithms on sensor accuracy have not been compared. The objectives of this validation study were to determine the most appropriate calibration method supplied in the Tekscan program software and to compare its accuracy to the accuracy obtained with two user-defined calibration protocols. We evaluated the calibration accuracies for test loads within the low range, high range, and full range of the sensor. Our experimental setup used materials representing those found in standard prosthetic joints, i.e., metal against plastic. The Tekscan power calibration was the most accurate of the algorithms provided with the system software, with an overall rms error of 2.7% of the tested sensor range, whereas the linear calibrations resulted in an overall rms error of up to 24% of the tested range. The user-defined ten-point cubic calibration was almost five times more accurate, on average, than the power calibration over the full range, with an overall rms error of 0.6% of the tested range. The user-defined three-point quadratic calibration was almost twice as accurate as the Tekscan power calibration, but was sensitive to the calibration loads used. We recommend that investigators design their own calibration curves not only to improve accuracy but also to understand the range(s) of highest error and to choose the optimal points within the expected sensing range for calibration. Since output and sensor nonlinearity depend on the experimental protocol (sensor type, interface shape and materials, sensor range in use, loading method, etc.), sensor behavior should be investigated for each different application.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(3):034504-034504-7. doi:10.1115/1.2907750.

Gait analysis using optical tracking equipment has been demonstrated to be a clinically useful tool for measuring three-dimensional kinematics and kinetics of the human body. However, in current practice, the foot is treated as a single rigid segment that articulates with the lower leg, meaning the motions of the joints of the foot cannot be measured. A multisegment kinematic model of the foot was developed for use in a gait analysis laboratory. The foot was divided into hindfoot, talus, midfoot, and medial and lateral forefoot segments. Six functional joints were defined: Ankle and subtalar joints, frontal and transverse plane motions of the hindfoot relative to midfoot, supination-pronation twist of the forefoot relative to midfoot, and medial longitudinal arch height-to-length ratio. Twelve asymptomatic subjects were tested during barefoot walking with a six-camera optical stereometric system and passive markers organized in triads. Repeatability of reported motions was tested using coefficients of multiple correlation. Ankle and subtalar joint motions and twisting of the forefoot were most repeatable. Hindfoot motions were least repeatable both within subjects and between subjects. Hindfoot and forefoot pronations in the frontal place were found to coincide with dropping of the medial longitudinal arch between early to midstance, followed by supination and rising of the arch in late stance and swing phase. This multisegment foot model overcomes a major shortcoming in current gait analysis practice—the inability to measure motion within the foot. Such measurements are crucial if gait analysis is to remain relevant in orthopaedic and rehabilitative treatment of the foot and ankle.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(3):034505-034505-6. doi:10.1115/1.2965375.

Because instrumented spatial linkages (ISLs) have been commonly used in measuring joint rotations and must be calibrated before using the device in confidence, a calibration device design and associated method for quantifying calibration device error would be useful. The objectives of the work reported by this paper were to (1) design an ISL calibration device and demonstrate the design for a specific application, (2) describe a new method for calibrating the device that minimizes measurement error, and (3) quantify measurement error of the device using the new method. Relative translations and orientations of the device were calculated via a series of transformation matrices containing inherent fixed and variable parameters. These translations and orientations were verified with a coordinate measurement machine, which served as a gold standard. Inherent fixed parameters of the device were optimized to minimize measurement error. After parameter optimization, accuracy was determined. The root mean squared error (RMSE) was 0.175 deg for orientation and 0.587 mm for position. All RMSE values were less than 0.8% of their respective full-scale ranges. These errors are comparable to published measurement errors of ISLs for positions and lower by at least a factor of 2 for orientations. These errors are in spite of the many steps taken in design and manufacturing to achieve high accuracy. Because it is challenging to achieve the accuracy required for a custom calibration device to serve as a viable gold standard, it is important to verify that a calibration device provides sufficient precision to calibrate an ISL.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(3):034506-034506-3. doi:10.1115/1.3049528.

The rupture of a cerebral aneurysm can result in a hemorrhagic stroke. A flow diverter, which is a porous tubular mesh, can be placed across the neck of a cerebral aneurysm to induce the cessation of flow and initiate the formation of an intra-aneurysmal thrombus. By finding a correlation between particle image velocimetry (PIV) and digital subtraction angiography, a better assessment of how well an aneurysm is excluded from the parent artery can be made in the clinical setting. A model of a rabbit elastase-induced aneurysm was connected to a mock circulation loop. The model was then placed under angiography. Recorded angiograms were analyzed so that a contrast concentration-time curve based on the average grayscale intensity inside the aneurysm could be determined. That curve was then fitted to a mathematical model that quantifies the influence of convection and diffusion on contrast transport. Optimized parameters were correlated with the intraneurysmal mean kinetic energy measured by PIV in the same aneurysm model. A strong correlation was observed between the convection and diffusion time constants and the mean kinetic energy inside the aneurysm. Analyzing the flow of angiographic contrast into and out of the aneurysm after implantation of a flow diverter allows for prediction of the efficacy of the device in excluding the aneurysm. Correlating hydrodynamic measures obtained by angiography to those obtained by detailed techniques such as PIV increases confidence in such predictions.

Commentary by Dr. Valentin Fuster

### Design Innovation

J Biomech Eng. 2008;131(3):035001-035001-6. doi:10.1115/1.3002759.

We have developed a new technology for producing three-dimensional (3D) biological structures composed of living cells and hydrogel in vitro, via the direct and accurate printing of cells with an inkjet printing system. Various hydrogel structures were constructed with our custom-made inkjet printer, which we termed 3D bioprinter. In the present study, we used an alginate hydrogel that was obtained through the reaction of a sodium alginate solution with a calcium chloride solution. For the construction of the gel structure, sodium alginate solution was ejected from the inkjet nozzle (SEA-Jet™, Seiko Epson Corp., Suwa, Japan) and was mixed with a substrate composed of a calcium chloride solution. In our 3D bioprinter, the nozzle head can be moved in three dimensions. Owing to the development of the 3D bioprinter, an innovative fabrication method that enables the gentle and precise fixation of 3D gel structures was established using living cells as a material. To date, several 3D structures that include living cells have been fabricated, including lines, planes, laminated structures, and tubes, and now, experiments to construct various hydrogel structures are being carried out in our laboratory.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(3):035002-035002-7. doi:10.1115/1.3005335.

A conceptual design has been generated for a prosthetic ankle-foot mechanism that can automatically adapt to the slope of the walking surface. To help prove this concept, a prototype ankle-foot mechanism was designed, developed, and tested on three subjects with unilateral transtibial amputations walking on level and ramped surfaces. The mechanism is capable of automatically adapting to the walking surface by switching impedance modes at key points of the gait cycle. The mechanism simulates the behavior of the physiologic foot and ankle complex by having a low impedance in the early stance phase and then switching to a higher impedance once foot-flat is reached. The “set-point” at which these changes in impedance occur gets reset on every step in order to reach the proper alignment for the walking surface. The mechanism utilizes the user’s bodyweight to help switch impedance modes and does not require any active control. It was hypothesized that the ankle-foot mechanism would cause the equilibrium point of the ankle moment versus the ankle dorsiflexion angle curves to shift to accommodate the walking surface. For two of the three subjects tested, this behavior was confirmed, supporting the contention that the design provides automatic adaptation for different walking slopes. Further work is needed to develop the prototype into a commercial product, but the mechanism was sufficient for illustrating proof-of-concept.

Commentary by Dr. Valentin Fuster

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