0

### TECHNICAL PAPERS: Bone/Orthopedics

J Biomech Eng. 2005;128(3):281-289. doi:10.1115/1.2187044.

Background. The Florida manatee (Trichechus manatus latirostris) is listed as endangered by the U.S. Department of the Interior. Manatee ribs have different microstructure from the compact bone of other mammals. Biomechanical properties of the manatee ribs need to be better understood. Fracture toughness $(KC)$ has been shown to be a good index to assess the mechanical performance of bone. Quantitative fractography can be used in concert with fracture mechanics equations to identify fracture initiating defects∕cracks and to calculate the fracture toughness of bone materials. Method of approach. Fractography is a standard technique for analyzing fracture behavior of brittle and quasi-brittle materials. Manatee ribs are highly mineralized and fracture in a manner similar to quasi-brittle materials. Therefore, quantitative fractography was applied to determine the fracture toughness of manatee ribs. Results. Average fracture toughness values of small flexure specimens from six different sizes of manatees ranged from $1.3to2.6MPa(m)1∕2$. Scanning electron microscope (SEM) images show most of the fracture origins were at openings for blood vessels and interlayer spaces. Conclusions. Quantitative fractography and fracture mechanics can be combined to estimate the fracture toughness of the material in manatee rib bone. Fracture toughness of subadult and calf manatees appears to increase as the size of the manatee increases. Average fracture toughness of the manatee rib bone materials is less than the transverse fracture toughness of human and bovine tibia and femur.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;128(3):290-299. doi:10.1115/1.2187045.

The stiffness of the external fixation highly influences the fracture healing pattern. In this work we study this aspect by means of a finite element model of a simple transverse mid-diaphyseal fracture of an ovine metatarsus fixed with a bilateral external fixator. In order to simulate the regenerative process, a previously developed mechanobiological model of bone fracture healing was implemented in three dimensions. This model is able to simulate tissue differentiation, bone regeneration, and callus growth. A physiological load of $500N$ was applied and three different stiffnesses of the external fixator were simulated (2300, 1725, and $1150N∕mm$). The interfragmentary strain and load sharing mechanism between bone and the external fixator were compared to those recorded in previous experimental works. The effects of the stiffness on the callus shape and tissue distributions in the fracture site were also analyzed. We predicted that a lower stiffness of the fixator delays fracture healing and causes a larger callus, in correspondence to well-documented clinical observations.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;128(3):300-308. doi:10.1115/1.2187037.

Background. The vibrational characteristics of any object are directly dependent on the physical properties of that object. Therefore, changing the physical properties of an object will cause the object to adopt changed natural frequencies. A fracture in a bone results in the loss of mechanical stability of the bone. This change in mechanical properties of a bone should result in a change of the resonant frequencies of that bone. A vibrational method for bone evaluation has been introduced. Method of approach. This method uses the radiation force of focused amplitude-modulated ultrasound to exert a vibrating force directly, and remotely, on a bone. The vibration frequency is varied in the range of interest to induce resonances in the bone. The resulting bone motion is recorded and the resonance frequencies are determined. Experiments are conducted on excised rat femurs and resonance frequencies of intact, fractured, and bonded (simulating healed) bones are measured. Results. The experiments demonstrate that changes in the resonance frequency are indicative of bone fracture and healing, i.e., the fractured bone exhibits a lower resonance frequency than the intact bone, and the resonance frequency of the bonded bone approaches that of the intact bone. Conclusion. It is concluded that the proposed radiation force method may be used as a remote and noninvasive tool for monitoring bone fracture and healing process, and the use of focused ultrasound enables one to selectively evaluate individual bones.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;128(3):309-316. doi:10.1115/1.2187039.

A two-level micromechanical model of cortical bone based on a generalized self-consistent method was developed to take into consideration the transversely isotropic elasticity of many microstructural features in cortical bone, including Haversian canals, resorption cavities, and osteonal and interstitial lamellae. In the first level, a single osteon was modeled as a two-phase composite such that Haversian canals were represented by elongated pores while the surrounding osteonal lamellae were considered as matrix. In the second level, osteons and resorption cavities were modeled as multiple inclusions while interstitial lamellae were regarded as matrix. The predictions of cortical bone elasticity from this two-level micromechanical model were mostly in agreement with experimental data for the dependence of transversely isotropic elasticity of human femoral cortical bone on porosity. However, variation in cortical bone elastic constants was greater in experimental data than in model predictions. This could be attributed to variations in the elastic properties of microstructural features in cortical bone. The present micromechanical model of cortical bone will be useful in understanding the contribution of cortical bone porosity to femoral neck fractures.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Cell

J Biomech Eng. 2005;128(3):317-328. doi:10.1115/1.2187047.

To investigate the structural mechanisms by which elevation of the intraendothelial cAMP levels abolishes or attenuates the transient increase in microvascular permeability by vascular endothelial growth factor (VEGF), we examined cAMP effect on VEGF-induced hyperpermeability to small solute sodium fluorescein (Stokes $radius=0.45nm$) $Psodiumfluorescein$, intermediate-sized solute $α$-lactalbumin (Stokes $radius=2.01nm$) $Pα-lactalbumin$, and large solute albumin (BSA, Stokes $radius=3.5nm$) $PBSA$ on individually perfused microvessels of frog mesenteries. After $20min$ pretreatment of $2mM$ cAMP analog, 8-bromo-cAMP, the initial increase by $1nM$ VEGF was completely abolished in $Psodiumfluorescein$ (from a peak increase of $2.6±0.37$ times control with VEGF alone to $0.96±0.07$ times control with VEGF and cAMP), in $Pα-lactalbumin$ (from a peak increase of $2.7±0.33$ times control with VEGF alone to $0.76±0.07$ times control with VEGF and cAMP), and in $PBSA$ (from a peak increase of $6.5±1.0$ times control with VEGF alone to $0.97±0.08$ times control with VEGF and cAMP). Based on these measured data, the prediction from our mathematical models suggested that the increase in the number of tight junction strands in the cleft between endothelial cells forming the microvessel wall is one of the mechanisms for the abolishment of VEGF-induced hyperpermeability by cAMP.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(3):329-334. doi:10.1115/1.1824120.

Hemodynamics plays an important role in cardiovascular physiology and pathology. Pulsatile flow (Q), pressure (P), and diameter (D) waveforms exert wall shear stress (WSS), normal stress, and circumferential strain (CS) on blood vessels. Most in vitro studies to date have focused on either WSS or CS but not their interaction. Recently, we have shown that concomitant WSS and CS affect EC biochemical response modulated by the temporal phase angle between WSS and CS (stress phase angle, SPA). Large negative SPA has been shown to occur in regions of the circulation where atherosclerosis and intimal hyperplasia are prevalent. Here, we report that nitric oxide (NO) biochemical secretion was significantly decreased in response to a large negative SPA of −180 deg with respect to an SPA of 0° in bovine aortic endothelial cells (BAEC) at 5 h. A new hemodynamic simulator for the study of the physiologic SPA was used to provide the hemodynamic conditions of pro-atherogenic (SPA=−180 deg) and normopathic (SPA=0 deg) states. The role of complex hemodynamics in vascular remodeling, homeostasis, and pathogenesis can be advanced by further assessment of the hypothesis that a large negative SPA is pro-atherogenic.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(3):335-346. doi:10.1115/1.2187051.

Trehalose is believed to offer desiccation protection to mammalian cells by forming stable glassy matrices. The goal of the current study was to explore the desiccation kinetics of thin films of trehalose-water solution under forced and natural convective conditions and to investigate the thermophysical state of mammalian cells at the bottom of the thin film. We developed a finite difference model based on the mass and energy conservation equations coupled to the water transport model from the cells. The boundary conditions were obtained from correlations or experimental measurements and the Gordon-Taylor equation was used to predict the glass transition temperature at every location. Results indicated that there are three distinct regimes for drying for both forced and natural convection, characterized by the slope of the moisture content plot as a function of time. Our results also indicate that the surface of the solution reached the glassy state in less than $10min$ for the Reynolds (forced) numbers explored and $∼30min$ for some Rayleigh (natural convective) numbers; however, significant water was trapped at this instant. Larger drying force hastened quicker glass formation but trapped more water. The numerical model was capable of predicting the drying kinetics for the dilute region accurately, but deviated while predicting the other regimes. Based on these experimental validations of the model, the osmotic response of different cells located at the bottom of the solution with orders of magnitude difference in their membrane permeability $(Lp)$ was predicted. The results suggested that extracellular glass formed around cells at the bottom of a trehalose-water solution by the propagation of glass into the solution; however it takes more than an order of magnitude time ($∼7minto>100min$ for forced convective drying) to remove sufficient water to form glass around cells from the time when the first surface glass is formed. This is attributed to low diffusivity of water through the glass. In addition, the water transport from the glassy matrix could be either diffusion or $Lp$ limited. For diffusion-limited transport, lowering the film thickness at the beginning of drying by half almost lowers the drying time by an order of magnitude. In summary, the optimal design of convective desiccation protocols requires accounting for the size of the cell, their membrane permeability $(Lp)$ and the starting thickness of the solution.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Fluids/Heat/Transport

J Biomech Eng. 2005;128(3):347-359. doi:10.1115/1.2194067.

A major consequence of stent implantation is restenosis that occurs due to neointimal formation. This patho-physiologic process of tissue growth may not be completely eliminated. Recent evidence suggests that there are several factors such as geometry and size of vessel, and stent design that alter hemodynamic parameters, including local wall shear stress distributions, all of which influence the restenosis process. The present three-dimensional analysis of developing pulsatile flow in a deployed coronary stent quantifies hemodynamic parameters and illustrates the changes in local wall shear stress distributions and their impact on restenosis. The present model evaluates the effect of entrance flow, where the stent is placed at the entrance region of a branched coronary artery. Stent geometry showed a complex three-dimensional variation of wall shear stress distributions within the stented region. Higher order of magnitude of wall shear stress of $530dyn∕cm2$ is observed on the surface of cross-link intersections at the entrance of the stent. A low positive wall shear stress of $10dyn∕cm2$ and a negative wall shear stress of $−10dyn∕cm2$ are seen at the immediate upstream and downstream regions of strut intersections, respectively. Modified oscillatory shear index is calculated which showed persistent recirculation at the downstream region of each strut intersection. The portions of the vessel where there is low and negative wall shear stress may represent locations of thrombus formation and platelet accumulation. The present results indicate that the immediate downstream regions of strut intersections are areas highly susceptible to restenosis, whereas a high shear stress at the strut intersection may cause platelet activation and free emboli formation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;128(3):360-370. doi:10.1115/1.2187034.

Background: Vena Cava filters are used to prevent pulmonary embolism in patients with deep vein thrombosis who are unresponsive to anticoagulation therapy. Various filter designs exist in the market with different characteristics distinguishing them. An understanding of the characteristics of these filters is desirable in order to develop better designs. Methods: A computational fluid dynamical study of the flow over an unoccluded stainless steel Greenfield Vena Cava filter (Boston Scientific, Watertown, MA) to determine its properties has been performed. Simulation of flow over a filter placed axisymmetrically in a rounded inferior vena cava has been performed at a Reynolds numbers of 1000 and the consequences of the flow (by studying parameters like shear stress and stagnation zones) have been discussed. Furthermore, a new finite element based numerical method has been developed that allows the study of capturing properties of Inferior Vena Cava filters. The key idea is the introduction of a thin-wire-model (TWM) that enables a drastic reduction in the computational cost while still maintaining control on the physics of the problem. This numerical technique has been applied to evaluate the embolus capture characteristic of a Greenfield filter. Results: The flow around the unoccluded filter is found to be steady and laminar at the conditions studied. A recirculation/stagnation zone develops immediately downstream of the filter head. This zone is significantly larger when the central hole is occluded. The shear stress and stagnation zone properties for such a flow over a Greenfield filter are compared with existing literature (in vitro studies). A graph showing the regions wherein clots escape or get captured has been determined by a means of numerical simulations. The data has further been analyzed to determine the probability of clot capture as function of the clot size. Conclusions: The stagnation zone formed behind the head of the Greenfield filter is found to be smaller in size when compared to that of the same filter with the central hole occluded. A map of the shear stress distribution shows a small region having the potential for thrombogenesis. The non-Newtonian properties of blood are not seen to cause much variation in the flow field when compared to the Newtonian model. However variation in the cava size leads to a significant change in the shear stresses. This study also establishes a novel method wherein computational means are used to determine the efficacy of clot capturing of filters. These techniques can further be used to compare the different characteristics among filters.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2006;128(3):371-379. doi:10.1115/1.2187035.

Background: Computational fluid dynamics tools are useful for their ability to model patient specific data relevant to the genesis and progression of atherosclerosis, but unavailable to measurement tools. The sensitivity of the physiologically relevant parameters of wall shear stress (WSS) and the oscillatory shear index (OSI) to secondary flow in the inlet velocity profiles was investigated in three realistic models of the carotid bifurcation. Method of Approach: Secondary flow profiles were generated using sufficiently long entrance lengths, to which curvature and helical pitch were added. The differences observed were contextualized with respect to effect of the uncertainty of the models’ geometry on the same parameters. Results: The effects of secondary velocities in the inlet profile on WSS and OSI break down within a few diameters of the inlet. Overall, the effect of secondary inlet flow on these models was on average more than 3.5 times smaller than the effect of geometric variability, with 13% and 48% WSS variability induced by inlet secondary flow and geometric differences, respectively. Conclusions: The degree of variation is demonstrated to be within the range of the other computational assumptions, and we conclude that given a sufficient entrance length of realistic geometry, simplification to fully developed axial (i.e., Womersley) flow may be made without penalty. Thus, given a choice between measuring three components of inlet velocity or a greater geometric extent, we recommend effort be given to more accurate and detailed geometric reconstructions, as being of primary influence on physiologically significant indicators.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;128(3):380-390. doi:10.1115/1.2187042.

Flow visualization with smoke particles illuminated by a laser sheet was used to obtain a qualitative description of the air flow structures through a dynamically similar $7.5×$ symmetric static scale model of the human larynx (divergence angle of $10deg$, minimal diameter of $0.04cm$ real life). The acoustic level downstream of the vocal folds was measured by using a condenser microphone. False vocal folds (FVFs) were included. In general, the glottal flow was laminar and bistable. The glottal jet curvature increased with flow rate and decreased with the presence of the FVFs. The glottal exit flow for the lowest flow rate showed a curved jet which remained laminar for all geometries. For the higher flow rates, the jet flow patterns exiting the glottis showed a laminar jet core, transitioning to vortical structures, and leading spatially to turbulent dissipation. This structure was shortened and tightened with an increase in flow rate. The narrow FVF gap lengthened the flow structure and reduced jet curvature via acceleration of the flow. These results suggest that laryngeal flow resistance and the complex jet flow structure exiting the glottis are highly affected by flow rate and the presence of the false vocal folds. Acoustic consequences are discussed in terms of the quadrupole- and dipole-type sound sources due to ordered flow structures.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Joint/Whole Body

J Biomech Eng. 2005;128(3):391-398. doi:10.1115/1.2193543.

Nondriving intersegmental knee moment components (i.e., varus/valgus and internal/external axial moments) are thought to be primarily responsible for the etiology of overuse knee injuries such as patellofermoral pain syndrome in cycling because of their relationship to muscular imbalances. However the relationship between these moments and muscle activity has not been studied. Thus the four primary objectives of this study were to test whether manipulating the inversion/eversion foot angle alters the varus/valgus knee moment (Objective 1) and axial knee moment (Objective 2) and to determine whether activation patterns of the vastus medialis oblique (VMO), vastus lateralis (VL), and tensor fascia latae (TFL) were affected by changes in the varus/valgus (Objective 3) and axial knee moments (Objective 4). To fulfill these objectives, pedal loads and lower limb kinematic data were collected from 15 subjects who pedaled with five randomly assigned inversion/eversion angles: 10 deg and 5 deg everted and inverted and $0deg$ (neutral). A previously described mathematical model was used to compute the nondriving intersegmental knee moments throughout the crank cycle. The excitations of the VMO, VL, and TFL muscles were measured with surface electromyography and the muscle activations were computed. On average, the 10-deg everted position decreased the peak varus moment by 55% and decreased the peak internal axial moment by 53% during the power stroke (crank cycle region where the knee moment is extensor). A correlation analysis revealed that the VMO/VL activation ratio increased significantly and the TFL activation decreased significantly as the varus moment decreased. For both the VMO/VL activation ratio and the TFL activation, a path analysis indicated that the varus/valgus moment was highly correlated to the axial moment but that the correlation between muscle activation and the varus moment was due primarily to the varus/valgus knee moment rather than the axial knee moment. The conclusion from these results is that everting the foot may be beneficial towards either preventing or ameliorating patellofemoral pain syndrome in cycling.

Topics: Muscle , Knee , Stress
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;128(3):399-408. doi:10.1115/1.2191077.

This study investigated the role of the material properties assumed for articular cartilage, meniscus and meniscal attachments on the fit of a finite element model (FEM) to experimental data for meniscal motion and deformation due to an anterior tibial loading of $45N$ in the anterior cruciate ligament-deficient knee. Taguchi style L18 orthogonal arrays were used to identify the most significant factors for further examination. A central composite design was then employed to develop a mathematical model for predicting the fit of the FEM to the experimental data as a function of the material properties and to identify the material property selections that optimize the fit. The cartilage was modeled as isotropic elastic material, the meniscus was modeled as transversely isotropic elastic material, and meniscal horn and the peripheral attachments were modeled as noncompressive and nonlinear in tension spring elements. The ability of the FEM to reproduce the experimentally measured meniscal motion and deformation was most strongly dependent on the initial strain of the meniscal horn attachments $(ε1H)$, the linear modulus of the meniscal peripheral attachments $(EP)$ and the ratio of meniscal moduli in the circumferential and transverse directions $(Eθ∕ER)$. Our study also successfully identified values for these critical material properties ($ε1H=−5%$, $EP=5.6MPa$, $Eθ∕ER=20$) to minimize the error in the FEM analysis of experimental results. This study illustrates the most important material properties for future experimental studies, and suggests that modeling work of meniscus, while retaining transverse isotropy, should also focus on the potential influence of nonlinear properties and inhomogeneity.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Soft Tissue

J Biomech Eng. 2005;128(3):409-418. doi:10.1115/1.2187033.

The esophagus, like other soft tissues, exhibits nonlinear and anisotropic mechanical properties. As a composite structure, the properties of the outer muscle and inner mucosal layer are different. It is expected that the complex mechanical properties will induce nonhomogeneous stress distributions in the wall and nonuniform tissue remodeling. Both are important factors which influence the function of mechanosensitive receptor located in various layers of the wall. Hence, the characterization of the mechanical properties is essential to understand the neuromuscular motion of the esophagus. In this study, the uniaxial tensile tests were conducted along two mutually orthogonal directions of porcine esophageal tissue to identify the directional (circumferential and axial), regional (abdominal, thoracic, and cervical), and layer (muscle and mucosa) variations of the mechanical properties. A structure-based constitutive model, which took the architectures of the tissue’s microstructures into account, was applied to describe the mechanical behavior of the esophagus. Results showed that the constitutive model successfully described the mechanical behavior and provided robust estimates of the material parameters. In conclusion, the model was demonstrated to be a good descriptor of the mechanical properties of the esophagus and it was able to facilitate the directional, layer, and regional comparisons of the mechanical properties in terms of the associated material parameters.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;128(3):419-427. doi:10.1115/1.2187036.

This paper presents a nonlinearly elastic anisotropic microplane formulation in 3D for computational constitutive modeling of arterial soft tissue in the passive regime. The constitutive modeling of arterial (and other biological) soft tissue is crucial for accurate finite element calculations, which in turn are essential for design of implants, surgical procedures, bioartificial tissue, as well as determination of effect of progressive diseases on tissues and implants. The model presented is defined at a lower scale (mesoscale) than the conventional macroscale and it incorporates the effect of all the (collagen) fibers which are anisotropic structural components distributed in all directions within the tissue material in addition to that of isotropic bulk tissue. It is shown that the proposed model not only reproduces Holzapfel’s recent model but also improves on it by accounting for the actual three-dimensional distribution of fiber orientation in the arterial wall, which endows the model with advanced capabilities in simulation of remodeling of soft tissue. The formulation is flexible so that its parameters could be adjusted to represent the arterial wall either as a single material or a material composed of several layers in finite element analyses of arteries. Explicit algorithms for both the material subroutine and the explicit integration with dynamic relaxation of equations of motion using finite element method are given. To circumvent the slow convergence of the standard dynamic relaxation and small time steps dictated by the stability of the explicit integrator, an adaptive dynamic relaxation technique that ensures stability and fastest possible convergence rates is developed. Incompressibility is enforced using penalty method with an updated penalty parameter. The model is used to simulate experimental data from the literature demonstrating that the model response is in excellent agreement with the data. An experimental procedure to determine the distribution of fiber directions in 3D for biological soft tissue is suggested in accordance with the microplane concept. It is also argued that this microplane formulation could be modified or extended to model many other phenomena of interest in biomechanics.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;128(3):428-436. doi:10.1115/1.2187040.

Traditionally, the complex mechanical behavior of planar soft biological tissues is characterized by (multi)axial tensile testing. While uniaxial tests do not provide sufficient information for a full characterization of the material anisotropy, biaxial tensile tests are difficult to perform and tethering effects limit the analyses to a small central portion of the test sample. In both cases, determination of local mechanical properties is not trivial. Local mechanical characterization may be performed by indentation testing. Conventional indentation tests, however, often assume linear elastic and isotropic material properties, and therefore these tests are of limited use in characterizing the nonlinear, anisotropic material behavior typical for planar soft biological tissues. In this study, a spherical indentation experiment assuming large deformations is proposed. A finite element model of the aortic valve leaflet demonstrates that combining force and deformation gradient data, one single indentation test provides sufficient information to characterize the local material behavior. Parameter estimation is used to fit the computational model to simulated experimental data. The aortic valve leaflet is chosen as a typical example. However, the proposed method is expected to apply for the mechanical characterization of planar soft biological materials in general.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;128(3):437-442. doi:10.1115/1.2187038.

Although single-loop tibialis tendon allografts have increased in popularity owing to their many advantages over patellar tendon and double-loop hamstring tendon autografts, some percentage of the patient population do not have clinically stable knees following anterior cruciate ligament reconstruction with single-loop tibialis tendon allografts. Therefore, it would be advantageous to determine the causes of increased anterior laxity which ultimately must be traced to lengthening of the graft construct. One objective of this study was to demonstrate the feasibility of using Roentgen stereophotogrammetric analysis (RSA) to determine the causes of lengthening of a single-loop graft construct subjected to cyclic loading. A second objective was to determine which cause(s) contributes most to an increase in length of this graft construct. Radio-opaque markers were inserted into ten grafts to measure the lengthening at the sites of the tibial and femoral fixations and between the sites of fixation. Each graft was passed through a tibial tunnel in a calf tibia, looped around a rigid cross-pin, and fixed to the tibia with a Washerloc fixation device. The grafts were cyclically loaded for $225,000$ cycles from $20to170N$. Prior to and at intervals during the cyclic loading, simultaneous radiographs were taken. RSA was used to determine the three-dimensional coordinates of the markers from which the lengthening at the sites of fixation and between the sites of fixation was computed at each interval. The sites of the femoral and tibial fixations were the largest contributors to the increase in length of the graft construct, with maximum average values of 0.68 and $0.55$ mm, respectively, after $225,000$ cycles. The graft substance between the sites of fixation contributed least to lengthening of the graft, with a maximum average value of $0.31$ mm. Ninety percent of the maximum average values occurred before $100,000$ cycles of loading for the largest contributors. RSA proved to be a useful method for measuring lengthening due to all three causes. Lengthening of the graft construct at the sites of both fixations is sufficiently large that the combined contributions may manifest as a clinically important increase in anterior laxity.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;128(3):443-448. doi:10.1115/1.2187041.

This study examined the stress response of bovine periodontal ligament (PDL) under sinusoidal straining. The principle of the test consisted in subjecting transverse tooth, PDL and bone sections of known geometries to controlled oscillatory force application. The samples were secured to the actuator by support plates fabricated using a laser sintering technique to fit their contours to the tooth and the alveolar bone. The actuator was attached to the root slices located in the specimen’s center. Hence the machine was able to push or pull the root relative to its surrounding alveolar bone. After determining an optimal distraction amplitude, the samples were cyclically loaded first in ramps and then in sinusoidal oscillations at frequencies ranging from $0.2to5Hz$. In the present study the following observations were made: (1) Imaging and the laser sintering technique can be used successfully to fabricate custom-made support plates for cross-sectional root-PDL-bone sections using a laser sintering technique, (2) the load-response curves were symmetric in the apical and the coronal directions, (3) both the stress response versus phase angle and the stress response versus. strain curves tended to “straighten” with increasing frequency, and (4) the phase lag between applied strain and resulting stress was small and did not differ in the intrusive and the extrusive directions. As no mechanical or time-dependent anisotropy was demonstrable in the intrusive and extrusive directions, such results may considerably simplify the development of constitutive laws for the PDL.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;128(3):449-457. doi:10.1115/1.2187046.

This paper presents a constitutive model for predicting the nonlinear viscoelastic behavior of soft biological tissues and in particular of ligaments. The constitutive law is a generalization of the well-known quasi-linear viscoelastic theory (QLV) in which the elastic response of the tissue and the time-dependent properties are independently modeled and combined into a convolution time integral. The elastic behavior, based on the definition of anisotropic strain energy function, is extended to the time-dependent regime by means of a suitably developed time discretization scheme. The time-dependent constitutive law is based on the postulate that a constituent-based relaxation behavior may be defined through two different stress relaxation functions: one for the isotropic matrix and one for the reinforcing (collagen) fibers. The constitutive parameters of the viscoelastic model have been estimated by curve fitting the stress relaxation experiments conducted on medial collateral ligaments (MCLs) taken from the literature, whereas the predictive capability of the model was assessed by simulating experimental tests different from those used for the parameter estimation. In particular, creep tests at different maximum stresses have been successfully simulated. The proposed nonlinear viscoelastic model is able to predict the time-dependent response of ligaments described in experimental works (Bonifasi-Lista, 2005, J. Orthopaed. Res., 23, pp. 67–76;Hingorani, 2004, Ann. Biomed. Eng., 32, pp. 306–312;Provenzano, 2001, Ann. Biomed. Eng., 29, pp. 908–214;Weiss, 2002, J. Biomech., 35, pp. 943–950). In particular, the nonlinear viscoelastic response which implies different relaxation rates for different applied strains, as well as different creep rates for different applied stresses and direction-dependent relaxation behavior, can be described.

Commentary by Dr. Valentin Fuster

### TECHNICAL BRIEFS

J Biomech Eng. 2005;128(3):458-461. doi:10.1115/1.2187049.

The objective of this research is to design and optimize a mini/micro-channel based surface-accumulator of E. coli bacteria to be detected by acoustic wave biosensors. A computational approach has been carried out using the state of the art software, CFD -ACE with water as bacteria bearing fluid. E. coli bacteria have been modeled as random discrete particles tracked by solving the Lagrangian equations. The design challenges are to achieve low shear force (pico-N), high concentration at accumulation, and high enough Reynolds number to avoid bacteria swimming. A range of low Reynolds number (Re) has been considered along with the effects of particle boundary interactions, gravity, Saffman lift, etc. More than two orders of magnitude higher concentration at the accumulation than the inlet concentration, and lower shear force of less than pico-N have been achieved in the optimized designs.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;128(3):462-466. doi:10.1115/1.2187048.

The Circle of Willis (CoW) is a ringlike structure of blood vessels found at the base of the brain. Its main function is to distribute oxygen-rich arterial blood to the cerebral mass. In a previous study, a one-dimensional (1D) model of the CoW was created to simulate a series of possible clinical scenarios such as occlusions in afferent arteries, absent or stringlike circulus vessels, or arterial infarctions (Moorhead, 2004, Comput. Methods Biomech. Biomed. Eng., 7(3), pp. 121–130). The model captured cerebral haemodynamic autoregulation by using a proportional-integral-derivative (PID) controller to modify efferent artery resistances. Although some good results and correlations were achieved, the model was too simple to capture all the transient dynamics of autoregulation. Hence a more physiologically accurate model has been created that additionally includes the oxygen dynamics that drive the autoregulatory response. Results very closely match accepted physiological response and limited clinical data. In addition, a set of boundary conditions and geometry is presented for which the autoregulated system cannot provide sufficient perfusion, representing a condition with increased risk of stroke and highlighting the importance of modeling the haemodynamics of the CoW. The system model created is computationally simple so it can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;128(3):467-470. doi:10.1115/1.2187050.