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Research Papers

J Biomech Eng. 2011;133(7):071001-071001-8. doi:10.1115/1.4004190.

Inaccuracies in the estimation of material properties and errors in the assignment of these properties into finite element models limit the reliability, accuracy, and precision of quantitative computed tomography (QCT)-based finite element analyses of the vertebra. In this work, a new mesh-independent, material mapping procedure was developed to improve the quality of predictions of vertebral mechanical behavior from QCT-based finite element models. In this procedure, an intermediate step, called the material block model, was introduced to determine the distribution of material properties based on bone mineral density, and these properties were then mapped onto the finite element mesh. A sensitivity study was first conducted on a calibration phantom to understand the influence of the size of the material blocks on the computed bone mineral density. It was observed that varying the material block size produced only marginal changes in the predictions of mineral density. Finite element (FE) analyses were then conducted on a square column-shaped region of the vertebra and also on the entire vertebra in order to study the effect of material block size on the FE-derived outcomes. The predicted values of stiffness for the column and the vertebra decreased with decreasing block size. When these results were compared to those of a mesh convergence analysis, it was found that the influence of element size on vertebral stiffness was less than that of the material block size. This mapping procedure allows the material properties in a finite element study to be determined based on the block size required for an accurate representation of the material field, while the size of the finite elements can be selected independently and based on the required numerical accuracy of the finite element solution. The mesh-independent, material mapping procedure developed in this study could be particularly helpful in improving the accuracy of finite element analyses of vertebroplasty and spine metastases, as these analyses typically require mesh refinement at the interfaces between distinct materials. Moreover, the mapping procedure is not specific to the vertebra and could thus be applied to many other anatomic sites.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(7):071002-071002-8. doi:10.1115/1.4003870.

Mechanical loading protocols in tissue engineering (TE) aim to improve the deposition of a properly organized collagen fiber network. In addition to collagen remodeling, these conditioning protocols can result in tissue compaction. Tissue compaction is beneficial to tissue collagen alignment, yet it may lead to a loss of functionality of the TE construct due to changes in geometry after culture. Here, a mathematical model is presented to relate the changes in collagen architecture to the local compaction within a TE small blood vessel, assuming that under static conditions, compaction is the main factor responsible for collagen fiber organization. An existing structurally based model is extended to incorporate volumetric tissue compaction. Subsequently, the model is applied to describe the collagen architecture of TE constructs under either strain based or stress based stimulus functions. Our computations indicate that stress based simulations result in a helical collagen fiber distribution along the vessel wall. The helix pitch angle increases from a circumferential direction in the inner wall, over about 45 deg in the middle vessel layer, to a longitudinal direction in the outer wall. These results are consistent with experimental data from TE small diameter blood vessels. In addition, our results suggest a stress dependent remodeling of the collagen, suggesting that cell traction is responsible for collagen orientation. These findings may be of value to design improved mechanical conditioning protocols to optimize the collagen architecture in engineered tissues.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(7):071003-071003-12. doi:10.1115/1.4004315.

In this work we analyzed the response of a stenotic trachea after a stent implantation. An endotracheal stent is the common treatment for tracheal diseases such as stenosis, chronic cough, or dispnoea episodes. Medical treatment and surgical techniques are still challenging due to the difficulties in overcoming potential complications after prosthesis implantation. A finite element model of a diseased and stented trachea was developed starting from a patient specific computerized tomography (CT) scan. The tracheal wall was modeled as a fiber reinforced hyperelastic material in which we modeled the anisotropy due to the orientation of the collagen fibers. Deformations of the tracheal cartilage rings and of the muscular membrane, as well as the maximum principal stresses, are analyzed using a fluid solid interaction (FSI) approach. For this reason, as boundary conditions, impedance-based pressure waveforms were computed modeling the nonreconstructed vessels as a binary fractal network. The results showed that the presence of the stent prevents tracheal muscle deflections and indicated a local recirculatory flow on the stent top surface which may play a role in the process of mucous accumulation. The present work gives new insight into clinical procedures, predicting their mechanical consequences. This tool could be used in the future as preoperative planning software to help the thoracic surgeons in deciding the optimal prosthesis type as well as its size and positioning.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(7):071004-071004-9. doi:10.1115/1.4004409.

The facet joint contributes to the normal biomechanical function of the spine by transmitting loads and limiting motions via articular contact. However, little is known about the contact pressure response for this joint. Such information can provide a quantitative measure of the facet joint’s local environment. The objective of this study was to measure facet pressure during physiologic bending in the cervical spine, using a joint capsule-sparing technique. Flexion and extension bending moments were applied to six human cadaveric cervical spines. Global motions (C2-T1) were defined using infra-red cameras to track markers on each vertebra. Contact pressure in the C5-C6 facet was also measured using a tip-mounted pressure transducer inserted into the joint space through a hole in the postero-inferior region of the C5 lateral mass. Facet contact pressure increased by 67.6 ± 26.9 kPa under a 2.4 Nm extension moment and decreased by 10.3 ± 9.7 kPa under a 2.7 Nm flexion moment. The mean rotation of the overall cervical specimen motion segments was 9.6 ± 0.8° and was 1.6 ± 0.7° for the C5-C6 joint, respectively, for extension. The change in pressure during extension was linearly related to both the change in moment (51.4 ± 42.6 kPa/Nm) and the change in C5-C6 angle (18.0 ± 108.9 kPa/deg). Contact pressure in the inferior region of the cervical facet joint increases during extension as the articular surfaces come in contact, and decreases in flexion as the joint opens, similar to reports in the lumbar spine despite the difference in facet orientation in those spinal regions. Joint contact pressure is linearly related to both sagittal moment and spinal rotation. Cartilage degeneration and the presence of meniscoids may account for the variation in the pressure profiles measured during physiologic sagittal bending. This study shows that cervical facet contact pressure can be directly measured with minimal disruption to the joint and is the first to provide local pressure values for the cervical joint in a cadaveric model.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(7):071005-071005-9. doi:10.1115/1.4004410.

Cerebral aneurysms constitute a major medical challenge as treatment options are limited and often associated with high risks. Statistically, up to 3% of patients with a brain aneurysm may suffer from bleeding for each year of life. Eight percent of all strokes are caused by ruptured aneurysms. In order to prevent this rupture, endovascular stenting using so called flow diverters is increasingly being regarded as an alternative to the established coil occlusion method in minimally invasive treatment. Covering the neck of an aneurysm with a flow diverter has the potential to alter the hemodynamics in such a way as to induce thrombosis within the aneurysm sac, stopping its further growth, preventing its rupture and possibly leading to complete resorption. In the present study the influence of different flow diverters is quantified considering idealized patient configurations, with a spherical sidewall aneurysm placed on either a straight or a curved parent vessel. All important hemodynamic parameters (exchange flow rate, velocity, and wall shear stress) are determined in a quantitative and accurate manner using computational fluid dynamics when varying the key geometrical properties of the aneurysm. All simulations are carried out using an incompressible, Newtonian fluid with steady conditions. As a whole, 72 different cases have been considered in this systematic study. In this manner, it becomes possible to compare the efficiency of different stents and flow diverters as a function of wire density and thickness. The results show that the intra-aneurysmal flow velocity, wall shear stress, mean velocity, and vortex topology can be considerably modified thanks to insertion of a suitable implant. Intra-aneurysmal residence time is found to increase rapidly with decreasing stent porosity. Of the three different implants considered in this study, the one with the highest wire density shows the highest increase of intra-aneurysmal residence time for both the straight and the curved parent vessels. The best hemodynamic modifications are always obtained for a small aneurysm diameter.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(7):071006-071006-5. doi:10.1115/1.4004411.

The lack of standardization in experimental protocols for unconfined compression tests of intervertebral discs (IVD) tissues is a major issue in the quantification of their mechanical properties. Our hypothesis is that the experimental protocols influence the mechanical properties of both annulus fibrosus and nucleus pulposus. IVD extracted from bovine tails were tested in unconfined compression stress-relaxation experiments according to six different protocols, where for each protocol, the initial swelling of the samples and the applied preload were different. The Young’s modulus was calculated from a viscoelastic model, and the permeability from a linear biphasic poroviscoelastic model. Important differences were observed in the prediction of the mechanical properties of the IVD according to the initial experimental conditions, in agreement with our hypothesis. The protocol including an initial swelling, a 5% strain preload, and a 5% strain ramp is the most relevant protocol to test the annulus fibrosus in unconfined compression, and provides a permeability of 5.0 ± 4.2e−14 m4 /N·s and a Young’s modulus of 7.6 ± 4.7 kPa. The protocol with semi confined swelling and a 5% strain ramp is the most relevant protocol for the nucleus pulposus and provides a permeability of 10.7 ± 3.1 e−14 m4 /N·s and a Young’s modulus of 6.0 ± 2.5 kPa.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(7):071007-071007-6. doi:10.1115/1.4004415.

Determining arterial mechanical properties is important for understanding the work done by the heart and how it changes with cardiovascular disease. Ex vivo tests are necessary to apply various loads to the artery and obtain data to model and predict the behavior under any load. Most ex vivo tests are performed within 24 h of dissection, so the tissue is still “alive.” For large elastic arteries; however, the passive mechanical behavior is attributed mostly to the very stable proteins, elastin, and collagen. If the testing equipment fails, is in use, or is located at another facility, it would be useful to store the vessels and postpone the tests until the equipment is available. The goal of this study is to determine the effects of storage time on the mechanical behavior of the common carotid artery from adult mice. Each artery was tested after storage for 1–28 days in physiologic saline at 4°C. There were no significant effects of storage time on the arterial diameter or force at each pressure, but there were significant effects on the stretch ratio and stress at each pressure. The significant effects on the stretch ratio and stress were due to decreases in the unloaded dimensions with storage time, when measured from cut arterial rings. When the unloaded dimensions were measured instead from histology sections, there were no significant changes with storage time. We conclude that histology sections yield a more consistent measurement of the unloaded dimensions and that there are no significant changes in the mechanical behavior of mouse carotid artery with storage up to 28 days.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(7):071008-071008-7. doi:10.1115/1.4004413.

The incidence of anterior cruciate ligament (ACL) injury remains high, and there is a need for simple, cost effective methods to identify athletes at a higher risk for ACL injury. Wearable measurement systems offer potential methods to assess the risk of ACL injury during jumping tasks. The objective of this study was to assess the capacity of a wearable inertial-based system to evaluate ACL injury risk during jumping tasks. The system accuracy for measuring temporal events (initial contact, toe-off), jump height, and sagittal plane angles (knee, trunk) was assessed by comparing results obtained with the wearable system to simultaneous measurements obtained with a marker-based optoelectronic reference system. Thirty-eight healthy participants (20 male and 18 female) performed drop jumps with bilateral and unilateral support landing. The mean differences between the temporal events obtained with both systems were below 5 ms, and the precisions were below 24 ms. The mean jump heights measured with both systems differed by less than 1 mm, and the associations (Pearson correlation coefficients) were above 0.9. For the discrete angle parameters, there was an average association of 0.91 and precision of 3.5° for the knee flexion angle and an association of 0.77 and precision of 5.5° for the trunk lean. The results based on the receiver-operating characteristic (ROC) also demonstrated that the proposed wearable system could identify movements at higher risk for ACL injury. The area under the ROC plots was between 0.89 and 0.99 for the knee flexion angle and between 0.83 and 0.95 for the trunk lean. The wearable system demonstrated good concurrent validity with marker-based measurements and good discriminative performance in terms of the known risk factors for ACL injury. This study suggests that a wearable system could be a simple cost-effective tool for conducting risk screening or for providing focused feedback.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(7):071009-071009-7. doi:10.1115/1.4004494.

Stress relaxation tests using a custom designed microindentation device were performed on ten anatomic regions of fresh porcine brain (postmortem time <3 h). Using linear viscoelastic theory, a Prony series representation was used to describe the shear relaxation modulus for each anatomic region tested. Prony series parameters fit to load data from indentations performed to ∼10% strain differed significantly by anatomic region. The gray and white matter of the cerebellum along with corpus callosum and brainstem were the softest regions measured. The cortex and hippocampal CA1/CA3 were found to be the stiffest. To examine the large strain behavior of the tissue, multistep indentations were performed in the corona radiata to strains of 10%, 20%, and 30%. Reduced relaxation functions were not significantly different for each step, suggesting that quasi-linear viscoelastic theory may be appropriate for representing the nonlinear behavior of this anatomic region of porcine brain tissue. These data, for the first time, describe the dynamic and short time scale behavior of multiple anatomic regions of the porcine brain which will be useful for understanding porcine brain injury biomechanics at a finer spatial resolution than previously possible.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(7):071010-071010-31. doi:10.1115/1.4004493.

The facet joint is a crucial anatomic region of the spine owing to its biomechanical role in facilitating articulation of the vertebrae of the spinal column. It is a diarthrodial joint with opposing articular cartilage surfaces that provide a low friction environment and a ligamentous capsule that encloses the joint space. Together with the disc, the bilateral facet joints transfer loads and guide and constrain motions in the spine due to their geometry and mechanical function. Although a great deal of research has focused on defining the biomechanics of the spine and the form and function of the disc, the facet joint has only recently become the focus of experimental, computational and clinical studies. This mechanical behavior ensures the normal health and function of the spine during physiologic loading but can also lead to its dysfunction when the tissues of the facet joint are altered either by injury, degeneration or as a result of surgical modification of the spine. The anatomical, biomechanical and physiological characteristics of the facet joints in the cervical and lumbar spines have become the focus of increased attention recently with the advent of surgical procedures of the spine, such as disc repair and replacement, which may impact facet responses. Accordingly, this review summarizes the relevant anatomy and biomechanics of the facet joint and the individual tissues that comprise it. In order to better understand the physiological implications of tissue loading in all conditions, a review of mechanotransduction pathways in the cartilage, ligament and bone is also presented ranging from the tissue-level scale to cellular modifications. With this context, experimental studies are summarized as they relate to the most common modifications that alter the biomechanics and health of the spine—injury and degeneration. In addition, many computational and finite element models have been developed that enable more-detailed and specific investigations of the facet joint and its tissues than are provided by experimental approaches and also that expand their utility for the field of biomechanics. These are also reviewed to provide a more complete summary of the current knowledge of facet joint mechanics. Overall, the goal of this review is to present a comprehensive review of the breadth and depth of knowledge regarding the mechanical and adaptive responses of the facet joint and its tissues across a variety of relevant size scales.

Commentary by Dr. Valentin Fuster

Technical Briefs

J Biomech Eng. 2011;133(7):074501-074501-8. doi:10.1115/1.4004408.

A significant amount of evidence linking wall shear stress to neointimal hyperplasia has been reported in the literature. As a result, numerical and experimental models have been created to study the influence of stent design on wall shear stress. Traditionally, blood has been assumed to behave as a Newtonian fluid, but recently that assumption has been challenged. The use of a linear model; however, can reduce computational cost, and allow the use of Newtonian fluids (e.g., glycerine and water) instead of a blood analog fluid in an experimental setup. Therefore, it is of interest whether a linear model can be used to accurately predict the wall shear stress caused by a non-Newtonian fluid such as blood within a stented arterial segment. The present work compares the resulting wall shear stress obtained using two linear and one nonlinear model under the same flow waveform. All numerical models are fully three-dimensional, transient, and incorporate a realistic stent geometry. It is shown that traditional linear models (based on blood’s lowest viscosity limit, 3.5 Pa s) underestimate the wall shear stress within a stented arterial segment, which can lead to an overestimation of the risk of restenosis. The second linear model, which uses a characteristic viscosity (based on an average strain rate, 4.7 Pa s), results in higher wall shear stress levels, but which are still substantially below those of the nonlinear model. It is therefore shown that nonlinear models result in more accurate predictions of wall shear stress within a stented arterial segment.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(7):074502-074502-7. doi:10.1115/1.4004412.

Developing appropriate mathematical models for biological soft tissues such as ligaments, tendons, and menisci is challenging. Stress-strain behavior of these tissues is known to be continuous and characterized by an exponential toe region followed by a linear elastic region. The conventional curve-fitting technique applies a linear curve to the elastic region followed by a separate exponential curve to the toe region. However, this technique does not enforce continuity at the transition between the two regions leading to inaccuracies in the material model. In this work, a Continuous Method is developed to fit both the exponential and linear regions simultaneously, which ensures continuity between regions. Using both methods, three cases were evaluated: idealized data generated mathematically, noisy idealized data produced by adding random noise to the idealized data, and measured data obtained experimentally. In all three cases, the Continuous Method performed superiorly to the conventional technique, producing smaller errors between the model and data and also eliminating discontinuities at the transition between regions. Improved material models may lead to better predictions of nonlinear biological tissues’ behavior resulting in improved the accuracy for a large array of models and computational analyses used to predict clinical outcomes.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(7):074503-074503-6. doi:10.1115/1.4004414.

With the resurgence of composite materials in orthopaedic applications, a rigorous assessment of stress is needed to predict any failure of bone-implant systems. For current biomechanics research, strain gage measurements are employed to experimentally validate finite element models, which then characterize stress in the bone and implant. Our preliminary study experimentally validates a relatively new nondestructive testing technique for orthopaedic implants. Lock-in infrared (IR) thermography validated with strain gage measurements was used to investigate the stress and strain patterns in a novel composite hip implant made of carbon fiber reinforced polyamide 12 (CF/PA12). The hip implant was instrumented with strain gages and mechanically tested using average axial cyclic forces of 840 N, 1500 N, and 2100 N with the implant at an adduction angle of 15 deg to simulate the single-legged stance phase of walking gait. Three-dimensional surface stress maps were also obtained using an IR thermography camera. Results showed almost perfect agreement of IR thermography versus strain gage data with a Pearson correlation of R2  = 0.96 and a slope = 1.01 for the line of best fit. IR thermography detected hip implant peak stresses on the inferior-medial side just distal to the neck region of 31.14 MPa (at 840 N), 72.16 MPa (at 1500 N), and 119.86 MPa (at 2100 N). There was strong correlation between IR thermography-measured stresses and force application level at key locations on the implant along the medial (R2  = 0.99) and lateral (R2  = 0.83 to 0.99) surface, as well as at the peak stress point (R2  = 0.81 to 0.97). This is the first study to experimentally validate and demonstrate the use of lock-in IR thermography to obtain three-dimensional stress fields of an orthopaedic device manufactured from a composite material.

Commentary by Dr. Valentin Fuster

Design Innovation

J Biomech Eng. 2011;133(7):075001-075001-8. doi:10.1115/1.4004495.

Murine models of disease are a powerful tool for researchers to gain insight into disease formation, progression, and therapies. The biomechanical indicators of diseased tissue provide a unique insight into some of these murine models, since the biomechanical properties in scenarios such as aneurysm and Marfan syndrome can dictate tissue failure and mortality. Understanding the properties of the tissue on the macroscopic scale has been shown to be important, as one can then understand the tissue’s ability to withstand the high stresses seen in the cardiac pulsatile cycle. Alterations in the biomechanical response can foreshadow prospective mechanical failure of the tissue. These alterations are often seen on the microstructural level, and obtaining detailed information on such changes can offer a better understanding of the phenomena seen on the macroscopic level. Unfortunately, mouse models present problems due to the size and delicate features in the mechanical testing of such tissues. In addition, some smaller arteries in large-animal studies (e.g., coronary and cerebral arteries) can present the same issues, and are sometimes unsuitable for planar biaxial testing. The purpose of this paper is to present a robust method for the investigation of the mechanical properties of small arteries and the classification of the microstructural orientation and degree of fiber alignment. This occurs through the cost-efficient modification of a planar biaxial tester that works in conjunction with a two-photon nonlinear microscope. This system provides a means to further investigate how microstructure and mechanical properties are modified in diseased transgenic animals where the tissue is in small tube form. Several other hard-to-test tubular specimens such as cerebral aneurysm arteries and atherosclerotic coronary arteries can also be tested using the described modular device.

Commentary by Dr. Valentin Fuster

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