0

IN THIS ISSUE

### Research Papers

J Biomech Eng. 2011;133(11):111001-111001-7. doi:10.1115/1.4005378.

A study of biphasic soft tissues contact is fundamental to understanding the biomechanical behavior of human diarthrodial joints. To date, biphasic-biphasic contact has been developed for idealized geometries and not been accessible for more general geometries. In this paper a finite element formulation is developed for contact of biphasic tissues. The augmented Lagrangian method is used to enforce the continuity of contact traction and fluid pressure across the contact interface, and the resulting method is implemented in the commercial software COMSOL Multiphysics. The accuracy of the implementation is verified using 2D axisymmetric problems, including indentation with a flat-ended indenter, indentation with spherical-ended indenter, and contact of glenohumeral cartilage layers. The biphasic finite element contact formulation and its implementation are shown to be robust and able to handle physiologically relevant problems.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(11):111002-111002-9. doi:10.1115/1.4005172.

This study investigates the effect of the pilot hole size, implant depth, synthetic bone density, and screw size on the pullout strength of the self-tapping screw using analytical, finite element, and experimental methodologies. Stress distribution and failure propagation mode around the implant thread zone are also investigated. Based on the finite element analysis (FEA) results, an analytical model for the pullout strength of the self-tapping screw is constructed in terms of the (synthetic) bone mechanical properties, screw size, and the implant depth. The pullout performance of self-tapping screws is discussed. Results from the analytical and finite element models are experimentally validated.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(11):111003-111003-8. doi:10.1115/1.4005350.

Topics: Bone
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(11):111004-111004-8. doi:10.1115/1.4005416.

A new experimental setup has been implemented to precisely measure the deformations of an entire model abdominal aortic aneurysm (AAA). This setup addresses a gap between the computational and experimental models of AAA that have aimed at improving the limited understanding of aneurysm development and rupture. The experimental validation of the deformations from computational approaches has been limited by a lack of consideration of the large and varied deformations that AAAs undergo in response to physiologic flow and pressure. To address the issue of experimentally validating these calculated deformations, a stereoscopic imaging system utilizing two cameras was constructed to measure model aneurysm displacement in response to pressurization. The three model shapes, consisting of a healthy aorta, an AAA with bifurcation, and an AAA without bifurcation, were also evaluated with computational solid mechanical modeling using finite elements to assess the impact of differences between material properties and for comparison against the experimental inflations. The device demonstrated adequate accuracy (surface points were located to within 0.07 mm) for capturing local variation while allowing the full length of the aneurysm sac to be observed at once. The experimental model AAA demonstrated realistic aneurysm behavior by having cyclic strains consistent with reported clinical observations between pressures 80 and 120 mm Hg. These strains are 1–2%, and the local spatial variations in experimental strain were less than predicted by the computational models. The three different models demonstrated that the asymmetric bifurcation creates displacement differences but not cyclic strain differences within the aneurysm sac. The technique and device captured regional variations of strain that are unobservable with diameter measures alone. It also allowed the calculation of local strain and removed rigid body motion effects on the strain calculation. The results of the computations show that an asymmetric aortic bifurcation created displacement differences but not cyclic strain differences within the aneurysm sac.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(11):111005-111005-11. doi:10.1115/1.4005380.

Low Reynolds number airflow in the pulmonary acinus and aerosol particle kinetics therein are significantly conditioned by the nature of the tidal motion of alveolar duct geometry. At least two components of the ductal structure are known to exhibit stress-strain hysteresis: smooth muscle within the alveolar entrance rings, and surfactant at the air-tissue interface. We hypothesize that the geometric hysteresis of the alveolar duct is largely determined by the interaction of the amount of smooth muscle and connective tissue in ductal rings, septal tissue properties, and surface tension-surface area characteristics of surfactant. To test this hypothesis, we have extended the well-known structural model of the alveolar duct by Wilson and Bachofen (1982, “A Model for Mechanical Structure of the Alveolar Duct,” J. Appl. Physiol. 52 (4), pp. 1064–1070) by adding realistic elastic and hysteretic properties of (1) the alveolar entrance ring, (2) septal tissue, and (3) surfactant. With realistic values for tissue and surface properties, we conclude that: (1) there is a significant, and underappreciated, amount of geometric hysteresis in alveolar ductal architecture; and (2) the contribution of smooth muscle and surfactant to geometric hysteresis are of opposite senses, tending toward cancellation. Quantitatively, the geometric hysteresis found experimentally by Miki (1993, “Geometric Hysteresis in Pulmonary Surface-to-Volume Ratio during Tidal Breathing,” J. Appl. Physiol. 75 (4), pp. 1630–1636) is consistent with little or no smooth muscle tone in anesthetized rabbits in control conditions, and with substantial smooth muscle activation following methacholine challenge. The observed local hysteretic boundary motion of the acinar duct would result in irreversible acinar flow fields, which might be important mechanistic contributors to aerosol mixing and deposition deep in the lung.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(11):111006-111006-16. doi:10.1115/1.4005377.

While many congenital heart defects can be treated without significant long term sequelae, some achieve successful palliation as their definitive endpoints. The single-ventricle defect is one such defect and leaves the child with only one operational ventricle, requiring the systemic and the pulmonary circulations to be placed in series through several operations performed during early childhood. Numerical simulations may be used to investigate these hemodynamic conditions and their relation to post-operative sequelae; however, they rely heavily on boundary condition prescription. In this study, we investigate the impact of hemodynamic input data uncertainties on simulation results. Imaged-based patient-specific models of the multi-branched pulmonary arteries and superior vena cava were built for five cavopulmonary connection (i.e. Glenn) patients. Magnetic resonance imaging and catheterization data were acquired for each patient prior to their Fontan surgery. Inflow and outflow boundary conditions were constructed to match available clinical data and resulted in the development of a framework to incorporate these types of clinical data into patient-specific simulations. Three-dimensional computational fluid dynamics simulations were run and hemodynamic indicators were computed. Power loss was low (and efficiency very high) and a linear correlation was found between power loss and cardiac index among the five patients. Other indicators such as low wall shear stress were considered to better characterize these patients. Flow was complex and oscillatory near the anastomosis, and laminar in the smaller branches. While common trends were seen among patients, results showed differences among patients, especially in the 3D maps, strengthening the importance of patient-specific simulations. A sensitivity analysis was performed to investigate the impact of input data (clinical and modeling) to construct boundary conditions on several indicators. Overall, the sensitivity of the output indicators to the input data was small but non-negligible. The sensitivity of commonly used hemodynamic indicators to compare patients is discussed in this context. Power efficiency was much more sensitive to pressure variation than power loss. To increase the precision of such indicators, mean flow split between right and left lungs needs to be measured with more accuracy with higher priority than refining the model of how the flow is distributed on average among the smaller branches. Although $±10%$ flow split imprecision seemed reasonable in terms of patient comparison, this study suggests that the common practice of imposing a right pulmonary artery/left pulmonary artery flow split of $55%/45%$ when performing patient specific simulations should be avoided. This study constitutes a first step towards understanding the hemodynamic differences between pre- and post Fontan surgery, predicting these differences, and evaluating surgical outcomes based on preoperative data.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(11):111007-111007-11. doi:10.1115/1.4005427.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(11):111008-111008-10. doi:10.1115/1.4005434.

Patch angioplasty is the most common technique used for the performance of carotid endarterectomy. A large number of patching materials are available for use while new materials are being continuously developed. Surprisingly little is known about the mechanical properties of these materials and how these properties compare with those of the carotid artery wall. Mismatch of the mechanical properties can produce mechanical and hemodynamic effects that may compromise the long-term patency of the endarterectomized arterial segment. The aim of this paper was to systematically evaluate and compare the biaxial mechanical behavior of the most commonly used patching materials. We compared PTFE (n = 1), Dacron (n = 2), bovine pericardium (n = 10), autogenous greater saphenous vein (n = 10), and autogenous external jugular vein (n = 9) with the wall of the common carotid artery (n = 18). All patching materials were found to be significantly stiffer than the carotid wall in both the longitudinal and circumferential directions. Synthetic patches demonstrated the most mismatch in stiffness values and vein patches the least mismatch in stiffness values compared to those of the native carotid artery. All biological materials, including the carotid artery, demonstrated substantial nonlinearity, anisotropy, and variability; however, the behavior of biological and biologically-derived patches was both qualitatively and quantitatively different from the behavior of the carotid wall. The majority of carotid arteries tested were stiffer in the circumferential direction, while the opposite anisotropy was observed for all types of vein patches and bovine pericardium. The rates of increase in the nonlinear stiffness over the physiological stress range were also different for the carotid and patching materials. Several carotid wall samples exhibited reverse anisotropy compared to the average behavior of the carotid tissue. A similar characteristic was observed for two of 19 vein patches. The obtained results quantify, for the first time, significant mechanical dissimilarity of the currently available patching materials and the carotid artery. The results can be used as guidance for designing more efficient patches with mechanical properties resembling those of the carotid wall. The presented systematic comparative mechanical analysis of the existing patching materials provides valuable information for patch selection in the daily practice of carotid surgery and can be used in future clinical studies comparing the efficacy of different patches in the performance of carotid endarterectomy.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(11):111009-111009-10. doi:10.1115/1.4005301.

Pulmonary obstruction occurs in many common forms of congenital heart disease. In this study, pulmonary artery (PA) banding is used as a model for pulmonary stenosis. Significant remodeling of the vascular bed occurs as a result of a prolonged narrowing of the PAs, and here we quantify the biophysical and molecular changes proximal and distal to the obstruction. Main and branch PAs are harvested from banded and sham rabbits and their mechanical properties are assessed using a biaxial tensile tester. Measurements defined as initial and stiff slopes are taken, assuming a linear region at the start and end of the J-shaped stress-strain curves, along with a transitional knee point. Collagen, elastin assays, Movat’s pentachrome staining, and Doppler protocols are used to quantify biochemical, structural, and physiological differences. The banded main PAs have significantly greater initial slopes while banded branch PAs have lower initial slopes; however, this change in mechanical behavior cannot be explained by the assay results as the elastin content in both main and branch PAs is not significantly different. The stiff slopes of the banded main PAs are higher, which is attributed to the significantly greater amounts of insoluble collagen. Shifting of the knee points reveals a decreased toe region in the main PAs but an opposite trend in the branch PAs. The histology results show a loss of integrity of the media, increase in ground substance, and dispersion of collagen in the banded tissue samples. This indicates other structural changes could have led to the mechanical differences in banded and normal tissue.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J Biomech Eng. 2011;133(11):114501-114501-5. doi:10.1115/1.4005428.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(11):114502-114502-6. doi:10.1115/1.4005400.

To understand the role seating plays in the support of posture and spinal articulation, it is necessary to study the interface between a human and the seat. However, a method to quantify lumbar curvature in commercially available unmodified seats does not currently exist. This work sought to determine if the lumbar curvature for normal ranges of seated posture could be documented by using body landmarks located on the anterior portion of the body. The development of such a methodology will allow researchers to evaluate spinal articulation of a seated subject while in standard, commercially available seats and chairs. Anterior measurements of boney landmarks were used to quantify the relative positions of the ribcage and pelvis while simultaneous posterior measurements were made of lumbar curvature. The relationship between the anterior and the posterior measures was compared. The predictive capacity of this approach was evaluated by determining linear and second-order regressions for each of the four postures across all subjects and conducting a leave-one-out cross validation. The relationships between the anterior and posterior measures were approximated by linear and second-order polynomial regressions (r2  = 0.829, 0.935 respectively) across all postures. The quantitative analysis showed that openness had a significant relationship with lumbar curvature, and a first-order regression was superior to a second-order regression. Average standard errors in the prediction were 5.9° for the maximum kyphotic posture, 9.9° for the comfortable posture, 12.8° for the straight and tall, and 22.2° for the maximum lordotic posture. These results show predictions of lumbar curvature are possible in seated postures by using a motion capture system and anterior measures. This method of lumbar curvature prediction shows potential for use in the assessment of seated spinal curvatures and the corresponding design of seating to accommodate those curvatures; however, additional inputs will be necessary to better predict the postures as lordosis is increased.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(11):114503-114503-6. doi:10.1115/1.4005409.

Estimating the position of the bones from optical motion capture data is a challenge associated with human movement analysis. Bone pose estimation techniques such as the Point Cluster Technique (PCT) and simulations of movement through software packages such as OpenSim are used to minimize soft tissue artifact and estimate skeletal position; however, using different methods for analysis may produce differing kinematic results which could lead to differences in clinical interpretation such as a misclassification of normal or pathological gait. This study evaluated the differences present in knee joint kinematics as a result of calculating joint angles using various techniques. We calculated knee joint kinematics from experimental gait data using the standard PCT, the least squares approach in OpenSim applied to experimental marker data, and the least squares approach in OpenSim applied to the results of the PCT algorithm. Maximum and resultant RMS differences in knee angles were calculated between all techniques. We observed differences in flexion/extension, varus/valgus, and internal/external rotation angles between all approaches. The largest differences were between the PCT results and all results calculated using OpenSim. The RMS differences averaged nearly 5° for flexion/extension angles with maximum differences exceeding 15°. Average RMS differences were relatively small (< 1.08°) between results calculated within OpenSim, suggesting that the choice of marker weighting is not critical to the results of the least squares inverse kinematics calculations. The largest difference between techniques appeared to be a constant offset between the PCT and all OpenSim results, which may be due to differences in the definition of anatomical reference frames, scaling of musculoskeletal models, and/or placement of virtual markers within OpenSim. Different methods for data analysis can produce largely different kinematic results, which could lead to the misclassification of normal or pathological gait. Improved techniques to allow non-uniform scaling of generic models to more accurately reflect subject-specific bone geometries and anatomical reference frames may reduce differences between bone pose estimation techniques and allow for comparison across gait analysis platforms.

Commentary by Dr. Valentin Fuster