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IN THIS ISSUE

### Research Papers

J Biomech Eng. 2011;133(6):061001-061001-11. doi:10.1115/1.4004180.

Patient-specific high order finite-element (FE) models of human femurs based on quantitative computer tomography (QCT) with inhomogeneous orthotropic and isotropic material properties are addressed. The point-wise orthotropic properties are determined by a micromechanics (MM) based approach in conjunction with experimental observations at the osteon level, and two methods for determining the material trajectories are proposed (along organs outer surface, or along principal strains). QCT scans on four fresh-frozen human femurs were performed and high-order FE models were generated with either inhomogeneous MM-based orthotropic or empirically determined isotropic properties. In vitro experiments were conducted on the femurs by applying a simple stance position load on their head, recording strains on femurs’ surface and head’s displacements. After verifying the FE linear elastic analyses that mimic the experimental setting for numerical accuracy, we compared the FE results to the experimental observations to identify the influence of material properties on models’ predictions. The strains and displacements computed by FE models having MM-based inhomogeneous orthotropic properties match the FE-results having empirically based isotropic properties well, and both are in close agreement with the experimental results. When only the strains in the femoral neck are being compared a more pronounced difference is noticed between the isotropic and orthotropic FE result. These results lay the foundation for applying more realistic inhomogeneous orthotropic material properties in FEA of femurs.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(6):061002-061002-11. doi:10.1115/1.4004231.

To measure spatial variations in mechanical properties of biological materials, prior studies have typically performed mechanical tests on excised specimens of tissue. Less invasive measurements, however, are preferable in many applications, such as patient-specific modeling, disease diagnosis, and tracking of age- or damage-related degradation of mechanical properties. Elasticity imaging (elastography) is a nondestructive imaging method in which the distribution of elastic properties throughout a specimen can be reconstructed from measured strain or displacement fields. To date, most work in elasticity imaging has concerned incompressible, isotropic materials. This study presents an extension of elasticity imaging to three-dimensional, compressible, transversely isotropic materials. The formulation and solution of an inverse problem for an anisotropic tissue subjected to a combination of quasi-static loads is described, and an optimization and regularization strategy that indirectly obtains the solution to the inverse problem is presented. Several applications of transversely isotropic elasticity imaging to cancellous bone from the human vertebra are then considered. The feasibility of using isotropic elasticity imaging to obtain meaningful reconstructions of the distribution of material properties for vertebral cancellous bone from experiment is established. However, using simulation, it is shown that an isotropic reconstruction is not appropriate for anisotropic materials. It is further shown that the transversely isotropic method identifies a solution that predicts the measured displacements, reveals regions of low stiffness, and recovers all five elastic parameters with approximately 10% error. The recovery of a given elastic parameter is found to require the presence of its corresponding strain (e.g., a deformation that generates $ɛ12$ is necessary to reconstruct C1212 ), and the application of regularization is shown to improve accuracy. Finally, the effects of noise on reconstruction quality is demonstrated and a signal-to-noise ratio (SNR) of $40dB$ is identified as a reasonable threshold for obtaining accurate reconstructions from experimental data. This study demonstrates that given an appropriate set of displacement fields, level of regularization, and signal strength, the transversely isotropic method can recover the relative magnitudes of all five elastic parameters without an independent measurement of stress. The quality of the reconstructions improves with increasing contrast, magnitude of deformation, and asymmetry in the distributions of material properties, indicating that elasticity imaging of cancellous bone could be a useful tool in laboratory studies to monitor the progression of damage and disease in this tissue.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(6):061004-061004-8. doi:10.1115/1.4004251.

Emphysema is a progressive lung disease that involves permanent destruction of the alveolar walls. Fluid mechanics in the pulmonary region and how they are altered with the presence of emphysema are not well understood. Much of our understanding of the flow fields occurring in the healthy pulmonary region is based on idealized geometries, and little attention has been paid to emphysemic geometries. The goal of this research was to utilize actual replica lung geometries to gain a better understanding of the mechanisms that govern fluid motion and particle transport in the most distal regions of the lung and to compare the differences that exist between healthy and emphysematous lungs. Excised human healthy and emphysemic lungs were cast, scanned, graphically reconstructed, and used to fabricate clear, hollow, compliant models. Three dimensional flow fields were obtained experimentally using stereoscopic particle image velocimetry techniques for healthy and emphysematic breathing conditions. Measured alveolar velocities ranged over two orders of magnitude from the duct entrance to the wall in both models. Recirculating flow was not found in either the healthy or the emphysematic model, while the average flow rate was three times larger in emphysema as compared to healthy. Diffusion dominated particle flow, which is characteristic in the pulmonary region of the healthy lung, was not seen for emphysema, except for very small particle sizes. Flow speeds dissipated quickly in the healthy lung (60% reduction in 0.25 mm) but not in the emphysematic lung (only 8% reduction 0.25 mm). Alveolar ventilation per unit volume was 30% smaller in emphysema compared to healthy. Destruction of the alveolar walls in emphysema leads to significant differences in flow fields between the healthy and emphysemic lung. Models based on replica geometry provide a useful means to quantify these differences and could ultimately improve our understanding of disease progression.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(6):061005-061005-9. doi:10.1115/1.4004230.

Models of post-traumatic osteoarthritis where early degenerative changes can be monitored are valuable for assessing potential therapeutic strategies. Current methods for evaluating cartilage mechanical properties may not capture the low-grade cartilage changes expected at these earlier time points following injury. In this study, an explant model of cartilage injury was used to determine whether streaming potential measurements by manual indentation could detect cartilage changes immediately following mechanical impact and to compare their sensitivity to biomechanical tests. Impacts were delivered ex vivo, at one of three stress levels, to specific positions on isolated adult equine trochlea. Cartilage properties were assessed by streaming potential measurements, made pre- and post-impact using a commercially available arthroscopic device, and by stress relaxation tests in unconfined compression geometry of isolated cartilage disks, providing the streaming potential integral (SPI), fibril modulus (Ef), matrix modulus (Em), and permeability (k). Histological sections were stained with Safranin-O and adjacent unstained sections examined in polarized light microscopy. Impacts were low, 17.3 ± 2.7 MPa (n = 15), medium, 27.8 ± 8.5 MPa (n = 13), or high, 48.7 ± 12.1 MPa (n = 16), and delivered using a custom-built spring-loaded device with a rise time of approximately 1 ms. SPI was significantly reduced after medium (p = 0.006) and high (p<0.001) impacts. Ef, representing collagen network stiffness, was significantly reduced in high impact samples only (p < 0.001 lateral trochlea, p = 0.042 medial trochlea), where permeability also increased (p = 0.003 lateral trochlea, p = 0.007 medial trochlea). Significant (p < 0.05, n = 68) moderate to strong correlations between SPI and Ef (r = 0.857), Em (r = 0.493), log(k) (r = −0.484), and cartilage thickness (r = −0.804) were detected. Effect sizes were higher for SPI than Ef, Em, and k, indicating greater sensitivity of electromechanical measurements to impact injury compared to purely biomechanical parameters. Histological changes due to impact were limited to the presence of superficial zone damage which increased with impact stress. Non-destructive streaming potential measurements were more sensitive to impact-related articular cartilage changes than biomechanical assessment of isolated samples using stress relaxation tests in unconfined compression geometry. Correlations between electromechanical and biomechanical methods further support the relationship between non-destructive electromechanical measurements and intrinsic cartilage properties.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(6):061006-061006-6. doi:10.1115/1.4004288.

The risk of myocardial penetration due to active-fixation screw-in type pacing leads has been reported to increase as the helix electrodes become smaller. In order to understand the contributing factors for lead penetration, we conducted finite element analyses of acute myocardial micro-damage induced by a pacemaker lead screw-in helix electrode. We compared the propensity for myocardial micro-damage of seven lead designs including a baseline model, three modified designs with various helix wire cross-sectional diameters, and three modified designs with different helix diameters. The comparisons show that electrodes with a smaller helix wire diameter cause more severe micro-damage to the myocardium in the early stage. The damage severity, represented by the volume of failed elements, is roughly the same in the middle stage, whereas in the later stage the larger helix wire diameter generally causes more severe damage. The onset of myocardial damage is not significantly affected by the helix diameter. As the helix diameter increases, however, the extent of myocardial damage increases accordingly. The present findings identified several of the major risk factors for myocardial damage whose consideration for lead use and design might improve acute and chronic lead performance.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(6):061007-061007-15. doi:10.1115/1.4004232.

Aortic valve (AV) calcification is a highly prevalent disease with serious impact on mortality and morbidity. The exact cause and mechanism of the progression of AV calcification is unknown, although mechanical forces have been known to play a role. It is thus important to characterize the mechanical environment of the AV. In the current study, we establish a methodology of measuring shear stresses experienced by the aortic surface of the AV leaflets using an in vitro valve model and adapting the laser Doppler velocimetry (LDV) technique. The valve model was constructed from a fresh porcine aortic valve, which was trimmed and sutured onto a plastic stented ring, and inserted into an idealized three-lobed sinus acrylic chamber. Valve leaflet location was measured by obtaining the location of highest back-scattered LDV laser light intensity. The technique of performing LDV measurements near to biological surfaces as well as the leaflet locating technique was first validated in two phantom flow systems: (1) steady flow within a straight tube with AV leaflet adhered to the wall, and (2) steady flow within the actual valve model. Dynamic shear stresses were then obtained by applying the techniques on the valve model in a physiologic pulsatile flow loop. Results show that aortic surface shear stresses are low during early systole (<5dyn/cm2 ) but elevated to its peak during mid to late systole at about 18–20 dyn/cm2 . Low magnitude shear stress (<5dyn/cm2 ) was observed during early diastole and dissipated to zero over the diastolic duration. Systolic shear stress was observed to elevate only with the formation of sinus vortex flow. The presented technique can also be used on other in vitro valve models such as congenitally geometrically malformed valves, or to investigate effects of hemodynamics on valve shear stress. Shear stress data can be used for further experiments investigating effects of fluid shear stress on valve biology, for conditioning tissue engineered AV, and to validate numerical simulations.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(6):061008-061008-12. doi:10.1115/1.4004249.

Accurate modeling of arterial elasticity is imperative for predicting pulsatile blood flow and transport to the periphery, and for evaluating the mechanical microenvironment of the vessel wall. The goal of the present study is to compare a recently developed structural model of porcine left anterior descending artery media to two commonly used typical representatives of phenomenological and structure-motivated invariant-based models, in terms of the number of model parameters, model descriptive and predictive powers, and requisite different test protocols for reliable parameter estimation. The three models were compared against 3D data of radial inflation, axial extension, and twist tests. Also checked are the models predictive capabilities to response data not used for estimation, including both tests outside the range of estimation database, as well as protocols of a different nature. The results show that the descriptive estimation error (model fit to estimation database), measured by the sum of squared residuals (SSE) between full 3D data and model predictions, was about twice as low for the structural (4.58%) model compared to the other two (9.71 and 8.99% for the phenomenological and structure-motivated models, respectively). Similar SSE ratios were obtained for the predictive capabilities. Prediction SSE at high stretch based on estimation of two low stretches yielded an SSE value of 2.81% for the structural model, and 10.54% and 7.87% for the phenomenological and structure-motivated models, respectively. For the prediction of twist from inflation-extension data, SSE values for the torsional stiffness was 1.76% for the structural model and 39.62 and 2.77% for the phenomenological and structure-motivated models. The required number of model parameters for the structural model is four, whereas the phenomenological model requires six to nine and the structure-motivated has four parameters. These results suggest that modeling based on the tissue structural features improves model reliability in describing given data and in predicting the tissue general response.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(6):061009-061009-7. doi:10.1115/1.4004287.

Current finite element modeling techniques utilize geometrically inaccurate cartilage distribution representations in the lumbar spine. We hypothesize that this shortcoming severely limits the predictive fidelity of these simulations. Specifically, it is unclear how these anatomically inaccurate cartilage representations alter range of motion and facet contact predictions. In the current study, cadaveric vertebrae were serially sectioned, and images were taken of each slice in order to identify the osteochondral interface and the articulating surface. A series of custom-written algorithms were utilized in order to quantify each facet joint’s three-dimensional cartilage distribution using a previously developed methodology. These vertebrae-dependent thickness cartilage distributions were implemented on an L1 through L5 lumbar spine finite element model. Moments were applied in three principal planes of motion, and range of motion and facet contact predictions from the variable thickness and constant thickness distribution models were determined. Initial facet gap thickness dimensions were also parameterized. The data indicate that the mean and maximum cartilage thickness increased inferiorly from L1 to L5, with an overall mean thickness value of 0.57 mm. Cartilage distribution and initial facet joint gap thickness had little influence on the lumbar range of motion in any direction, whereas the mean contact pressure, total contact force, and total contact area predictions were altered considerably. The data indicate that range of motion predictions alone are insufficient to establish model validation intended to predict mechanical contact parameters. These data also emphasize the need for the careful consideration of the initial facet joint gap thickness with respect to the spinal condition being studied.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;133(6):067001-067001-1. doi:10.1115/1.4004286.

The above referenced paper is retracted from the ASME Journal of Biomechanical Engineering.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J Biomech Eng. 2011;133(6):064501-064501-5. doi:10.1115/1.4004248.

This study reports the results of 38 infraorbital maxilla impacts performed on male cadavers. Impacts were performed using an unpadded, cylindrical impactor (3.2 kg) at velocities between 1 and 5 m/s. The peak force and acoustic emission data were used to develop a statistical relationship of fracture risk as a function of impact force. Acoustic emission sensors were used to provide a noncensored measure of the maxilla tolerance and were essential due to the increase in impactor force after fracture onset. Parametric and nonparametric techniques were used to estimate the risk of fracture tolerance. The nonparametric technique produced an estimated 50% risk of fracture between 970 and 1223 N. The results obtained from the parametric and nonparametric techniques were in good agreement. Peak force values achieved in this study were similar to those of previous work and were unaffected by impactor velocity. The results of this study suggest that an impact to the infraorbital maxilla is a load-limited event due to compromise of structural integrity.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(6):064502-064502-5. doi:10.1115/1.4004164.

Although microdamage is known to accumulate in trabecular bone with overloading and aging, the tissue-level stresses and strains associated with local bone failure are not well known. Local correlation of microdamage with microstructural stresses and strains requires methods to accurately register histological sections with micro-computed tomography (micro-CT) based finite element models. In addition, the resolution of correlation (i.e., grid size) selected for analysis may affect the observed results. Therefore, an automated, repeatable, and accurate image registration algorithm was developed to determine the range of local stresses and strains associated with microdamage initiation. Using a two-dimensional rigid registration algorithm, bone structures from histology and micro-CT imaging were aligned. Once aligned, microdamaged regions were spatially correlated with local stresses and strains obtained from micro-CT based finite element analysis. Using this more sophisticated registration technique, we were able to analyze the effects of varying spatial grid resolution on local stresses and strains initiating microdamage. The results indicated that grid refinement to the individual pixel level (pixel-by-pixel method) more precisely defined the range of microdamage initiation compared to manually selected individual damaged and undamaged trabeculae. Using the pixel-by-pixel method, we confirmed that trabecular bone from younger cows sustained higher local strains prior to microdamage initiation compared to older bone.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(6):064503-064503-5. doi:10.1115/1.4004189.

It has been hypothesized that mechanical risk factors may be used to predict future atherosclerotic plaque rupture. Truly predictive methods for plaque rupture and methods to identify the best predictor(s) from all the candidates are lacking in the literature. A novel combination of computational and statistical models based on serial magnetic resonance imaging (MRI) was introduced to quantify sensitivity and specificity of mechanical predictors to identify the best candidate for plaque rupture site prediction. Serial in vivo MRI data of carotid plaque from one patient was acquired with follow-up scan showing ulceration. 3D computational fluid-structure interaction (FSI) models using both baseline and follow-up data were constructed and plaque wall stress (PWS) and strain (PWSn) and flow maximum shear stress (FSS) were extracted from all 600 matched nodal points (100 points per matched slice, baseline matching follow-up) on the lumen surface for analysis. Each of the 600 points was marked “ulcer” or “nonulcer” using follow-up scan. Predictive statistical models for each of the seven combinations of PWS, PWSn, and FSS were trained using the follow-up data and applied to the baseline data to assess their sensitivity and specificity using the 600 data points for ulcer predictions. Sensitivity of prediction is defined as the proportion of the true positive outcomes that are predicted to be positive. Specificity of prediction is defined as the proportion of the true negative outcomes that are correctly predicted to be negative. Using probability 0.3 as a threshold to infer ulcer occurrence at the prediction stage, the combination of PWS and PWSn provided the best predictive accuracy with (sensitivity, specificity) = (0.97, 0.958). Sensitivity and specificity given by PWS, PWSn, and FSS individually were (0.788, 0.968), (0.515, 0.968), and (0.758, 0.928), respectively. The proposed computational-statistical process provides a novel method and a framework to assess the sensitivity and specificity of various risk indicators and offers the potential to identify the optimized predictor for plaque rupture using serial MRI with follow-up scan showing ulceration as the gold standard for method validation. While serial MRI data with actual rupture are hard to acquire, this single-case study suggests that combination of multiple predictors may provide potential improvement to existing plaque assessment schemes. With large-scale patient studies, this predictive modeling process may provide more solid ground for rupture predictor selection strategies and methods for image-based plaque vulnerability assessment.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(6):064504-064504-5. doi:10.1115/1.4004314.

There is a direct correlation between ligament function and the articulating surface of the normal knee, and changes to any of these structures can affect the other. This is also true for knee replacements, where the articulating surface is greatly changed compared to the natural knee. This study investigated the morphometry of healthy knees and proposes a method to predict original normal knee profiles. A variety of mathematical techniques are compared in terms of the accuracy with which they can represent the original knee joint geometry. Additionally, a method of predicting the irregular femoral condyle geometry for an individual knee is described by making use of the mathematical techniques presented, and the accuracy of this method is also investigated. The mathematical approach using B-splines provides flexibility and can accurately describe the complex geometry of the femoral condyles in both the sagittal and transverse planes. It was further found that the condyles are highly asymmetrical; therefore simpler methods cannot portray the condyles sufficiently and are especially inaccurate in representing the lateral condyle. The study proposes a method for predicting the geometry of the femoral condyles with good accuracy. The B-spline model showed best results.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(6):064505-064505-3. doi:10.1115/1.4004289.

There is an increasing need to understand the mechanical properties of human orbital fat and its encapsulating connective tissue (OFCT), but such knowledge is not available in the current literature. The purpose of the present study is to examine the mechanical properties of the OFCT. From 5 pairs of 76- to 92-year-old Caucasian human eyes and 33 5- to 7-month-old porcine eyes, 5 human and 11 porcine OFCT samples were dissected at the posterior pole or adjacent to the pole in the vertical, horizontal, and radial directions. Sample dimensions were fixed or measured. Tensile tests were performed on the samples in body-temperature saline. The stress-strain relationship was first approximately linear and then became nonlinear. The linear, the neo-Hookean, and the Mooney–Rivlin constants are reported in Tables 1 and 2. No statistical difference was found among their properties in the different directions in either the human or the porcine samples. Statistical differences were found between the human and the porcine material constants in the horizontal and radial directions. Among our material models, only the Mooney–Rivlin model was able to capture the mechanical properties of the OFCT in large deformation properly. The Mooney–Rivlin model was especially adaptive to the human data. This is the first time the mechanical properties of the human and porcine OFCT have been examined in the literature. We believe our data will provide valuable information to others regarding designing implant biomaterials in orbital treatments and developing computer models to study orbital biomechanics.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(6):064506-064506-4. doi:10.1115/1.4004205.

Commentary by Dr. Valentin Fuster