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### Research Papers

J Biomech Eng. 2012;135(1):011001-011001-8. doi:10.1115/1.4023092.

Tendons function to transmit loads from muscle to move and stabilize joints and absorb impacts. Functionality of lacerated tendons is diminished, however clinical practice often considers surgical repair only after 50% or more of the tendon is lacerated, the “50% rule.” Few studies provide mechanical insight into the 50% rule. In this study cyclic and static stress relaxation tests were performed on porcine flexor tendons before and after a 0.5, 1.0, 2.0, or 2.75 mm deep transverse, midsubstance laceration. Elastic and viscoelastic properties, such as maximum stress, change in stress throughout each test, and stiffness, were measured and compared pre- and post-laceration. Nominal stress and stiffness parameters decreased, albeit disproportionately in magnitude, with increasing percent loss of cross-sectional area. Conversely, mean stress at the residual area (determined using remaining intact area at the laceration cross section) exhibited a marked increase in stress concentration beginning at 47.2% laceration using both specified load and constant strain analyses. The marked increase in stress concentration beginning near 50% laceration provides mechanical insight into the 50% rule. Additionally, a drastic decrease in viscoelastic stress parameters after only an 8.2% laceration suggests that time-dependent mechanisms protecting tissues during impact loadings are highly compromised regardless of laceration size.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;135(1):011002-011002-12. doi:10.1115/1.4023089.

Single ventricle heart defects are among the most serious congenital heart diseases, and are uniformly fatal if left untreated. Typically, a three-staged surgical course, consisting of the Norwood, Glenn, and Fontan surgeries is performed, after which the superior vena cava (SVC) and inferior vena cava (IVC) are directly connected to the pulmonary arteries (PA). In an attempt to improve hemodynamic performance and hepatic flow distribution (HFD) of Fontan patients, a novel Y-shaped graft has recently been proposed to replace the traditional tube-shaped extracardiac grafts. Previous studies have demonstrated that the Y-graft is a promising design with the potential to reduce energy loss and improve HFD. However these studies also found suboptimal Y-graft performance in some patient models. The goal of this work is to determine whether performance can be improved in these models through further design optimization. Geometric and hemodynamic factors that influence the HFD have not been sufficiently investigated in previous work, particularly for the Y-graft. In this work, we couple Lagrangian particle tracking to an optimal design framework to study the effects of boundary conditions and geometry on HFD. Specifically, we investigate the potential of using a Y-graft design with unequal branch diameters to improve hepatic distribution under a highly uneven RPA/LPA flow split. As expected, the resulting optimal Y-graft geometry largely depends on the pulmonary flow split for a particular patient. The unequal branch design is demonstrated to be unnecessary under most conditions, as it is possible to achieve the same or better performance with equal-sized branches. Two patient-specific examples show that optimization-derived Y-grafts effectively improve the HFD, compared to initial nonoptimized designs using equal branch diameters. An instance of constrained optimization shows that energy efficiency slightly increases with increasing branch size for the Y-graft, but that a smaller branch size is preferred when a proximal anastomosis is needed to achieve optimal HFD.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;135(1):011003-011003-9. doi:10.1115/1.4023132.

The development of an engineering transitional turbulence model and its subsequent evaluation and validation for some diseased cardiovascular flows have been suggestive of its likely utility in normal aortas. The existence of experimental data from human aortas, acquired in the early 1970s with catheter-mounted hot film velocimeters, provided the opportunity to compare the performance of the model on such flows. A generic human aorta, derived from magnetic resonance anatomical and velocity images of a young volunteer, was used as the basis for varying both Reynolds number (Re) and Womersley parameter (α) to match four experimental data points from human ascending aortas, comprising two with disturbed flow and two with apparently undisturbed flow. Trials were made with three different levels of inflow turbulence intensity (Tu) to find if a single level could represent the four different cases with 4000 < Re < 10,000 and 17 < α < 26. A necessary boundary condition includes the inflow “turbulence” level, and convincing results were obtained for all four cases with inflow Tu = 1.0%, providing additional confidence in the application of the transitional model in flows in larger arteries. The Reynolds-averaged Navier–Stokes (RANS)-based shear stress transport (SST) transitional model is capable of capturing the correct flow state in the human aorta when low inflow turbulence intensity (1.0%) is specified.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;135(1):011004-011004-9. doi:10.1115/1.4023090.

As the average age of the population has increased, the incidence of age-related bone fracture has also increased. While some of the increase of fracture incidence with age is related to loss of bone mass, a significant part of the risk is unexplained and may be caused by changes in intrinsic material properties of the hard tissue. This investigation focused on understanding how changes to the intrinsic damage properties affect bone fragility. We hypothesized that the intrinsic (μm) damage properties of bone tissue strongly and nonlinearly affect mechanical behavior at the apparent (whole tissue, cm) level. The importance of intrinsic properties on the apparent level behavior of trabecular bone tissue was investigated using voxel based finite element analysis. Trabecular bone cores from human T12 vertebrae were scanned using microcomputed tomography (μCT) and the images used to build nonlinear finite element models. Isotropic and initially homogenous material properties were used for all elements. The elastic modulus (Ei) of individual elements was reduced with a secant damage rule relating only principal tensile tissue strain to modulus damage. Apparent level resistance to fracture as a function of changes in the intrinsic damage properties was measured using the mechanical energy to failure per unit volume (apparent toughness modulus, Wa) and the apparent yield strength (σay, calculated using the 0.2% offset). Intrinsic damage properties had a profound nonlinear effect on the apparent tissue level mechanical response. Intrinsic level failure occurs prior to apparent yield strength (σay). Apparent yield strength (σay) and toughness vary strongly (1200% and 400%, respectively) with relatively small changes in the intrinsic damage behavior. The range of apparent maximum stresses predicted by the models was consistent with those measured experimentally for these trabecular bone cores from the experimental axial compressive loading (experimental: σmax = 3.0–4.3 MPa; modeling: σmax = 2–16 MPa). This finding differs significantly from previous studies based on nondamaging intrinsic material models. Further observations were that this intrinsic damage model reproduced important experimental apparent level behaviors including softening after peak load, microdamage accumulation before apparent yield (0.2% offset), unload softening, and sensitivity of the apparent level mechanical properties to variability of the intrinsic properties.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;135(1):011005-011005-9. doi:10.1115/1.4023133.

Arteriovenous fistulae are surgically created to provide adequate access for dialysis patients suffering from end-stage renal disease. It has long been hypothesized that the rapid blood vessel remodeling occurring after fistula creation is, in part, a process to restore the mechanical stresses to some preferred level, i.e., mechanical homeostasis. We present computational hemodynamic simulations in four patient-specific models of mature arteriovenous fistulae reconstructed from 3D ultrasound scans. Our results suggest that these mature fistulae have remodeled to return to ‘‘normal’’ shear stresses away from the anastomoses: about 1.0 Pa in the outflow veins and about 2.5 Pa in the inflow arteries. Large parts of the anastomoses were found to be under very high shear stresses $>15$ Pa, over most of the cardiac cycle. These results suggest that the remodeling process works toward restoring mechanical homeostasis in the fistulae, but that the process is limited or incomplete, even in mature fistulae, as evidenced by the elevated shear at or near the anastomoses. Based on the long term clinical viability of these dialysis accesses, we hypothesize that the elevated nonhomeostatic shear stresses in some portions of the vessels were not detrimental to fistula patency.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;135(1):011006-011006-9. doi:10.1115/1.4023091.

Little work has been done on the localization of microcracks in bone using acoustic emission. Microcrack localization is useful to study the fracture process in bone and to prevent fractures in patients. Locating microcracks that occur before fracture allows one to predict where fracture will occur if continued stress is applied to the bone. Two source location algorithms were developed to locate microcracks on rectangular bovine bone samples. The first algorithm uses a constant velocity approach which has some difficulty dealing with the anisotropic nature of bone. However, the second algorithm uses an iterative technique to estimate the correct velocity for the acoustic emission source location being located. In tests with simulated microcracks, the constant velocity algorithm achieves a median error of 1.78 mm (IQR 1.51 mm) and the variable velocity algorithm improves this to a median error of 0.70 mm (IQR 0.79 mm). An experiment in which the bone samples were loaded in a three point bend test until they fractured showed a good correlation between the computed location of detected microcracks and where the final fracture occurred. Microcracks can be located on bovine bone samples using acoustic emission with good accuracy and precision.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;135(1):011007-011007-11. doi:10.1115/1.4023151.

Both development and progression of knee osteoarthritis have been associated with the loading of the knee joint during walking. We are, therefore, interested in developing strategies for changing walking biomechanics to offload the knee joint without resorting to surgery. In this study, simulations of human walking were performed using a 2D bipedal forward dynamics model. A simulation generated by minimizing the metabolic cost of transport (CoT) resembled data measured from normal human walking. Three simulations targeted at minimizing the peak axial knee joint contact force instead of the CoT reduced the peak force by 12–25% and increased the CoT by 11–14%. The strategies used by the simulations were (1) reduction in gastrocnemius muscle force, (2) avoidance of knee flexion during stance, and (3) reduced stride length. Reduced gastrocnemius force resulted from a combination of changes in activation and changes in the gastrocnemius contractile component kinematics. The simulations that reduced the peak contact force avoided flexing the knee during stance when knee motion was unrestricted and adopted a shorter stride length when the simulated knee motion was penalized if it deviated from the measured human knee motion. A higher metabolic cost in an offloading gait would be detrimental for covering a long distance without fatigue but beneficial for exercise and weight loss. The predicted changes in the peak axial knee joint contact force from the simulations were consistent with estimates of the joint contact force in a human subject who emulated the predicted kinematics. The results demonstrate the potential of using muscle-actuated forward dynamics simulations to predict novel joint offloading interventions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;135(1):011008-011008-9. doi:10.1115/1.4023136.

A soft tissue's macroscopic behavior is largely determined by its microstructural components (often a collagen fiber network surrounded by a nonfibrillar matrix (NFM)). In the present study, a coupled fiber-matrix model was developed to fully quantify the internal stress field within such a tissue and to explore interactions between the collagen fiber network and nonfibrillar matrix (NFM). Voronoi tessellations (representing collagen networks) were embedded in a continuous three-dimensional NFM. Fibers were represented as one-dimensional nonlinear springs and the NFM, meshed via tetrahedra, was modeled as a compressible neo-Hookean solid. Multidimensional finite element modeling was employed in order to couple the two tissue components and uniaxial tension was applied to the composite representative volume element (RVE). In terms of the overall RVE response (average stress, fiber orientation, and Poisson's ratio), the coupled fiber-matrix model yielded results consistent with those obtained using a previously developed parallel model based upon superposition. The detailed stress field in the composite RVE demonstrated the high degree of inhomogeneity in NFM mechanics, which cannot be addressed by a parallel model. Distributions of maximum/minimum principal stresses in the NFM showed a transition from fiber-dominated to matrix-dominated behavior as the matrix shear modulus increased. The matrix-dominated behavior also included a shift in the fiber kinematics toward the affine limit. We conclude that if only gross averaged parameters are of interest, parallel-type models are suitable. If, however, one is concerned with phenomena, such as individual cell-fiber interactions or tissue failure that could be altered by local variations in the stress field, then the detailed model is necessary in spite of its higher computational cost.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2012;135(1):011009-011009-8. doi:10.1115/1.4023095.

Hydrostatic pressure-driven flows through soft tissues and gels cause deformations of the solid network to occur, due to drag from the flowing fluid. This phenomenon occurs in many contexts including physiological flows and infusions through soft tissues, in mechanically stimulated engineered tissues, and in direct permeation measurements of hydraulic permeability. Existing theoretical descriptions are satisfactory in particular cases, but none provide a description which is easy to generalize for the design and interpretation of permeation experiments involving a range of different boundary conditions and gel properties. Here a theoretical description of flow-induced permeation is developed using a relatively simple approximate constitutive law for strain-dependent permeability and an assumed constant elastic modulus, using dimensionless parameters which emerge naturally. Analytical solutions are obtained for relationships between fundamental variables, such as flow rate and pressure drop, which were not previously available. Guidelines are provided for assuring that direct measurements of hydraulic permeability are performed accurately, and suggestions emerge for alternative measurement protocols. Insights obtained may be applied to interpretation of flow-induced deformation and related phenomena in many contexts.

Commentary by Dr. Valentin Fuster