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### Research Papers

J Biomech Eng. 2010;132(8):081001-081001-8. doi:10.1115/1.4001027.

A millimeter-for-millimeter relation between an increase in length of an anterior cruciate ligament graft construct and an increase in anterior laxity has been demonstrated in multiple in vitro studies. Based on this relation, a 3 mm increase in length of the graft construct following surgery could manifest as a 3 mm increase in anterior laxity in vivo, which is considered clinically unstable. Hence, the two primary objectives were to determine whether the millimeter-for-millimeter relation exists in vivo for slippage-resistant fixation of a soft-tissue graft and, if it does not exist, then to what extent the increase in stiffness caused by biologic healing of the graft to the bone tunnel offsets the potential increase in anterior laxity resulting from lengthening at the sites of fixation. Sixteen subjects were treated with a fresh-frozen, nonirradiated, nonchemically processed tibialis allograft. Tantalum markers were injected into the graft, fixation devices, and bones. On the day of surgery and at 1, 2, 3, and 4 months, Roentgen stereophotogrammetric analysis was used to compute anterior laxity at 150 N of anterior force and the total slippage from both sites of fixation. A simple linear regression was performed to determine whether the millimeter-for-millimeter relation existed and a springs-in-series model of the graft construct was used to determine the extent to which the increase in stiffness caused by biological healing of the graft to the bone tunnel offset the increase in anterior laxity resulting from lengthening at the sites of fixation. There was no correlation between lengthening at the sites of fixation and the increase in anterior laxity at 1 month ($R2=0.0$, $slope=0.2$). Also, the increase in stiffness of the graft construct caused by biologic healing of the graft to the bone tunnel offset 0.7 mm of the 1.5 mm potential increase in anterior laxity resulting from lengthening at the sites of fixation. This relatively large offset of nearly 50% occurred because lengthening at the sites of fixation was small.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(8):081002-081002-10. doi:10.1115/1.4001679.

In this paper, we develop structured tree outflow boundary conditions for modeling the airflow in patient specific human lungs. The utilized structured tree is used to represent the nonimageable vessels beyond the 3D domain. The coupling of the two different scales (1D and 3D) employs a Dirichlet–Neumann approach. The simulations are performed under a variety of conditions such as light breathing and constant flow ventilation (which is characterized by very rapid acceleration and deceleration). All results show that the peripheral vessels significantly impact the pressure, however, the flow is relatively unaffected, reinforcing the fact that the majority of the lung impedance is due to the lower generations rather than the peripheral vessels. Furthermore, simulations of a hypothetical diseased lung (restricted flow in the superior left lobe) under mechanical ventilation show that the mean pressure at the outlets of the 3D domain is about 28% higher. This hypothetical model illustrates potential causes of volutrauma in the human lung and furthermore demonstrates how different clinical scenarios can be studied without the need to assume the unknown flow distribution into the downstream region.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(8):081003-081003-10. doi:10.1115/1.4001680.

Functional electrical stimulation (FES) has the capacity to regenerate motion for individuals with spinal cord injuries. However, it is not straightforward to determine the stimulation parameters to generate a coordinated movement. Musculoskeletal models can provide a noninvasive simulation environment to estimate muscle force and activation timing sequences for a variety of tasks. Therefore, the purpose of this study was to develop a musculoskeletal model of the feline hindlimb for simulations to determine stimulation parameters for intrafascicular multielectrode stimulation (a method of FES). Additionally, we aimed to explore the differences in modeling neuromuscular compartments compared with representing these muscles as a single line of action. When comparing the modeled neuromuscular compartments of biceps femoris, sartorius, and semimembranosus to representations of these muscles as a single line of action, we observed that modeling the neuromuscular compartments of these three muscles generated different force and moment generating capacities when compared with single muscle representations. Differences as large as $4 N m$ ($∼400%$ in biceps femoris) were computed between the summed moments of the neuromuscular compartments and the single muscle representations. Therefore, modeling neuromuscular compartments may be necessary to represent physiologically reasonable force and moment generating capacities of the feline hindlimb.

Topics: Force , Modeling , Muscle , Knee , Motion
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(8):081004-081004-9. doi:10.1115/1.4001682.

Interest in developing durable mitral valve repair methods is growing, underscoring the need to better understand the native mitral valve mechanics. In this study, the authors investigate the dynamic deformation of the mitral valve strut chordae-to-anterior leaflet transition zone using a novel stretch mapping method and report the complex mechanics of this region for the first time. Eight structurally normal porcine mitral valves were studied in a pulsatile left heart simulator under physiological hemodynamic conditions −120 mm peak transvalvular pressure, 5 l/min cardiac output at 70 bpm. The chordal insertion region was marked with a structured array of 31 miniature markers, and their motions throughout the cardiac cycle were tracked using two high speed cameras. 3D marker coordinates were calculated using direct linear transformation, and a second order continuous surface was fit to the marker cloud at each time frame. Average areal stretch, principal stretch magnitudes and directions, and stretch rates were computed, and temporal changes in each parameter were mapped over the insertion region. Stretch distribution was heterogeneous over the entire strut chordae insertion region, with the highest magnitudes along the edges of the chordal insertion region and the least along the axis of the strut chordae. At early systole, radial stretch was predominant, but by mid systole, significant stretch was observed in both radial and circumferential directions. The compressive stretches measured during systole indicate a strong coupling between the two principal directions, explaining the small magnitude of the systolic areal stretch. This study for the first time provides the dynamic kinematics of the strut chordae insertion region in the functioning mitral valve. A heterogeneous stretch pattern was measured, with the mechanics of this region governed by the complex underlying collagen architecture. The insertion region seemed to be under stretch during both systole and diastole, indicating a transfer of forces from the leaflets to the chordae and vice versa throughout the cardiac cycle, and demonstrating its role in optimal valve function.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(8):081005-081005-7. doi:10.1115/1.4001739.

Characterization of high-intensity focused ultrasound (HIFU) systems using ex vivo tissues is an important part of the preclinical testing for new HIFU devices. In ex vivo characterization, the lesion volume produced by the absorption of HIFU energy is quantified as operational parameters are varied. This paper examines the three methods used for lesion-volume quantification: histology, magnetic resonance (MR) imaging, and numerical calculations. The methods were studied in the context of a clinically relevant problem for HIFU procedures—that of quantifying the change in the lesion volume with changing sonication time. The lesion volumes of sonicated samples of porcine liver were determined using the three methods, at focal intensities ranging from $800 W/cm2$ to $1700 W/cm2$ and sonication times between 20 s and 40 s. It was found that histology consistently yielded lower lesion volumes than the other two methods, and the calculated values were below magnetic resonance imaging (MRI) at high applied energies. Still, the three methods agreed with each other to within a $±10%$ difference for all of the experiments. Increasing the sonication time produced much larger changes in the lesion volume than increasing the acoustic intensity, for the same total energy expenditure, at lower energy (less than 1000 J) levels. At higher energy levels, (around 1500 J), increasing the sonication time and increasing the intensity produced roughly the same change in the lesion volume for the same total energy expenditure.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(8):081006-081006-6. doi:10.1115/1.4001257.

Elastography, which is the imaging of soft tissues on the basis of elastic modulus (or, more generally, stiffness) has become increasingly popular in the last decades and holds promise for application in many medical areas. Most of the attention has focused on inhomogeneous materials that are locally isotropic, the intent being to detect a (stiff) tumor within a (compliant) tissue. Many tissues of mechanical interest, however, are anisotropic, so a method capable of determining material anisotropy would be attractive. We present here an approach to determine the mechanical anisotropy of inhomogeneous, anisotropic tissues, by directly solving the finite element representation of the Cauchy stress balance in the tissue. The method divides the sample domain into subdomains assumed to have uniform properties and solves for the material constants in each subdomain. Two-dimensional simulated experiments on linear anisotropic inhomogeneous systems demonstrate the ability of the method, and simulated experiments on a nonlinear model demonstrate the ability of the method to capture anisotropy qualitatively even though only a linear model is used in the inverse problem. As with any inverse problem, ill-posedness is a serious concern, and multiple tests may need to be done on the same sample to determine the properties with confidence.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(8):081007-081007-8. doi:10.1115/1.4001681.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(8):081008-081008-10. doi:10.1115/1.4001358.

A finite element model was developed for numerical simulations of nanoindentation tests on cortical bone. The model allows for anisotropic elastic and post-yield behavior of the tissue. The material model for the post-yield behavior was obtained through a suitable linear transformation of the stress tensor components to define the properties of the real anisotropic material in terms of a fictitious isotropic solid. A tension-compression yield stress mismatch and a direction-dependent yield stress are allowed for. The constitutive parameters are determined on the basis of literature experimental data. Indentation experiments along the axial (the longitudinal direction of long bones) and transverse directions have been simulated with the purpose to calculate the indentation moduli and the tissue hardness in both the indentation directions. The results have shown that the transverse to axial mismatch of indentation moduli was correctly simulated regardless of the constitutive parameters used to describe the post-yield behavior. The axial to transverse hardness mismatch observed in experimental studies (see, for example, Rho [1999, “Elastic Properties of Microstructural Components of Human Bone Tissue as Measured by Nanoindentation,” J. Biomed. Mater. Res., 45, pp. 48–54] for results on human tibial cortical bone) can be correctly simulated through an anisotropic yield constitutive model. Furthermore, previous experimental results have shown that cortical bone tissue subject to nanoindentation does not exhibit piling-up. The numerical model presented in this paper shows that the probe tip-tissue friction and the post-yield deformation modes play a relevant role in this respect; in particular, a small dilatation angle, ruling the volumetric inelastic strain, is required to approach the experimental findings.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(8):081009-081009-6. doi:10.1115/1.4001883.

The fracture of bone due to indentation with a hard, sharp object is of significance in surgical procedures and certain trauma situations. In the study described below, the fracture of bovine bone under indentation was measured experimentally and predicted using the theory of critical distances (TCDs), a theory, which predicts failure due to cracking in the vicinity of stress concentrations. The estimated indentation fracture force was compared with the experimental results in three different cutting directions. Under indentation, the material experiences high levels of compression and shear, causing cracks to form and grow. The direction of crack growth was highly dependent on the bone’s microstructure: major cracks grew in the weakest possible structural direction. Using a single value of the critical distance $(L=320 μm)$, combined with a multiaxial failure criterion, it was possible to predict the experimental failure loads with less than 30% errors. Some differences are expected between the behavior of human bone and the bovine bone studied here, owing to its plexiform microstructure.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(8):081010-081010-6. doi:10.1115/1.4001678.

Evaluating total knee replacement kinematics and contact pressure distributions is an important element of preclinical assessment of implant designs. Although physical testing is essential in the evaluation process, validated computational models can augment these experiments and efficiently evaluate perturbations of the design or surgical variables. The objective of the present study was to perform an initial kinematic verification of a dynamic finite element model of the Kansas knee simulator by comparing predicted tibio- and patellofemoral kinematics with experimental measurements during force-controlled gait simulation. A current semiconstrained, cruciate-retaining, fixed-bearing implant mounted in aluminum fixtures was utilized. An explicit finite element model of the simulator was developed from measured physical properties of the machine, and loading conditions were created from the measured experimental feedback data. The explicit finite element model allows both rigid body and fully deformable solutions to be chosen based on the application of interest. Six degrees-of-freedom kinematics were compared for both tibio- and patellofemoral joints during gait loading, with an average root mean square (rms) translational error of 1.1 mm and rotational rms error of 1.3 deg. Model sensitivity to interface friction and damping present in the experimental joints was also evaluated and served as a secondary goal of this paper. Modifying the metal-polyethylene coefficient of friction from 0.1 to 0.01 varied the patellar flexion-extension and tibiofemoral anterior-posterior predictions by 7 deg and 2 mm, respectively, while other kinematic outputs were largely insensitive.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(8):081011-081011-7. doi:10.1115/1.4001159.

Insufficient lateralization of the femoral component coupled with exposed reamed cancellous bone has been speculated to predispose to femoral neck fracture. The current study examined the effect of mediolateral implant position and exposed cancellous bone on the strength of the resurfaced proximal femur. Composite femurs were prepared in three configurations: (1) partial, with the implant placed at the native femoral head offset of the femur, partially exposing reamed cancellous bone; (2) proud, with a medialized implant exposing a circumferential ring of cancellous bone; and (3) complete, with a lateralized implant covering all reamed cancellous bone. Specimens were loaded to failure in axial compression. A finite element model was used to further explore the effect of exposed cancellous bone, cement mantle thickness, and relative valgus orientation on the strain distributions in the resurfaced femur. The proud group (2063 N) was significantly weaker than both the partial (2974 N, $p=0.004$) and complete groups (5899 N, $p=0.001$) when tested to failure. The partial group was also significantly weaker than the complete group when tested to failure $(p=0.001)$. The finite element model demonstrated increasing levels of strain in the superior reamed cortical-cancellous bone interface with increasing degree of exposed cancellous bone. The condition of the femoral component medialized as the result of a thick cement mantle had the greatest detrimental impact on strain level in the superior reamed cancellous bone while a valgus oriented implant provided a protective effect. This study provides biomechanical evidence that exposed reamed cancellous bone significantly reduces the load-to-failure and increases maximum strains in the resurfaced proximal femur. The perceived benefit of reconstructing the femur to its native geometry may inherently weaken the proximal femur and increase femoral neck fracture risk if the femoral component is not sufficiently lateralized to cover all unsupported reamed cancellous bone. Relative valgus orientation of the implant may help to minimize the risk of neck fracture if reamed cancellous bone remains exposed following implant impaction.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(8):081012-081012-7. doi:10.1115/1.4000086.

In spinal vertebral burst fractures, the dynamic properties of the trabecular centrum, which is the central region of porous bone inside the vertebra, can play an important role in determining the failure mode. If the failure occurs in the posterior portion of the vertebral body, spinal canal occlusion can occur and ejected trabecular bone can impact the spinal cord resulting in serious injury. About 15% of all spinal cord injuries are caused by such burst fractures. Unfortunately, due to the uniqueness of burst fracture injuries, postinjury investigation cannot always accurately assess the degree of damage caused by these fractures. This research makes an effort to begin understanding the governing effects in this important bone fracture event. Measurements of the dynamic deformation response of bovine trabecular bone with the marrow intact and marrow removed using a modified split-Hopkinson pressure bar apparatus are reported and compared with quasistatic deformation response results. Because trabecular bone is more compliant and lower in strength than cortical bone, typical Hopkinson pressure bar experimental techniques used for high strain rate testing of harder materials cannot be applied. Instead, a quartz-crystal-embedded, split-Hopkinson pressure bar developed for testing compliant, low strength materials is used. Care is taken into account for the orthotropic properties in the bone by testing only along the principle material axes, determined through microcomputed tomography. In addition, shaping of the stress wave pulse is used to ensure a constant strain rate and homogeneous specimen deformation. Results indicate that the strength of trabecular bone increases by a factor of approximately 2–3 when the strain rate increases from $10−3 s−1$ to $500 s−1$ and that the bone fractures beyond a critical strain.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(8):081013-081013-10. doi:10.1115/1.4001891.

Endothelial cells are known to respond to hemodynamic forces. Their phenotype has been suggested to differ between atheroprone and atheroprotective regions of the vasculature, which are characterized by the local hemodynamic environment. Once an atherosclerotic plaque has formed in a vessel, the obstruction creates complex spatial gradients in wall shear stress. Endothelial cell response to wall shear stress may be linked to the stability of coronary plaques. Unfortunately, in vitro studies of the endothelial cell involvement in plaque stability have been limited by unrealistic and simplified geometries, which cannot reproduce accurately the hemodynamics created by a coronary stenosis. Hence, in an attempt to better replicate the spatial wall shear stress gradient patterns in an atherosclerotic region, a three dimensional asymmetric stenosis model was created. Human abdominal aortic endothelial cells were exposed to steady flow ($Re=50$, 100, and 200 and $τ=4.5 dyn/cm2$, $9 dyn/cm2$, and $18 dyn/cm2$) in idealized 50% asymmetric stenosis and straight/tubular in vitro models. Local morphological changes that occur due to magnitude, duration, and spatial gradients were quantified to identify differences in cell response. In the one dimensional flow regions, where flow is fully developed and uniform wall shear stress is observed, cells aligned in flow direction and had a spindlelike shape when compared with static controls. Morphological changes were progressive and a function of time and magnitude in these regions. Cells were more randomly oriented and had a more cobblestone shape in regions of spatial wall shear stress gradients. These regions were present, both proximal and distal, at the stenosis and on the wall opposite to the stenosis. The response of endothelial cells to spatial wall shear stress gradients both in regions of acceleration and deceleration and without flow recirculation has not been previously reported. This study shows the dependence of endothelial cell morphology on spatial wall shear stress gradients and demonstrates that care must be taken to account for altered phenotype due to geometric features. These results may help explain plaque stability, as cells in shoulder regions near an atherosclerotic plaque had a cobblestone morphology indicating that they may be more permeable to subendothelial transport and express prothrombotic factors, which would increase the risk of atherothrombosis.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J Biomech Eng. 2010;132(8):084501-084501-4. doi:10.1115/1.4001888.

A continuum model based on the contact mechanics theory was developed and used for evaluating virus indentation forces at the early stage of membrane invagination, as well as the work of the virus indentation forces and virus-cell contact pressures in a receptor-mediated endocytosis, depending on the virus size and virus/cell stiffnesses. The model indicated that early virus indentation forces are in the order of 1–10 pN and for a given extent of virus engulfment, they increase linearly with the elastic modulus of the host cell and also with the square of the virus radius. The work of invagination at the initial phase of virus endocytosis is in the order of tens of zeptojoules and peak virus-cell contact pressures at this stage are in the order of hundreds of Pascals to several kPa. For a given extent of virus engulfment, peak and average contact pressures increase linearly with the elastic modulus of the host cell but interestingly, they are negligibly affected by the virus size. The present model may be useful in the fields of cellular biomechanics, virology and nanodrug delivery to evaluate mechanical factors during the early phase of membrane invagination.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(8):084502-084502-4. doi:10.1115/1.4001893.

This study aimed at measuring the static coefficient of friction $(μ)$ between bone and skeletal muscle tissues in order to support finite element (FE) modeling in orthopaedic and rehabilitation research, where such contact conditions need to be defined. A custom-made friction meter (FM) that employs the load cell and motion-controlled loading arm of a materials testing machine was designed for this study. The FM was used to measure $μ$ between fresh ulna bones and extensor muscles surrounding the ulna, which were harvested from five young adult pigs. Mean bone-muscle $μ$ were between 0.36 and 0.29, decreased with the increase in loads applied on the bone $(p<0.05)$ and plateaued at a mean $∼0.3$ for loads exceeding 4 N. Hence, for FE modeling of bone-muscle contacts through which loads with magnitudes of kgs to 10s-of-kgs are transferred, assuming $μ$ of $∼0.3$ appears to be appropriate.

Commentary by Dr. Valentin Fuster