Research Papers

J Biomech Eng. 2011;133(3):031001-031001-12. doi:10.1115/1.4003259.

Simulations of blood flow in both healthy and diseased vascular models can be used to compute a range of hemodynamic parameters including velocities, time varying wall shear stress, pressure drops, and energy losses. The confidence in the data output from cardiovascular simulations depends directly on our level of certainty in simulation input parameters. In this work, we develop a general set of tools to evaluate the sensitivity of output parameters to input uncertainties in cardiovascular simulations. Uncertainties can arise from boundary conditions, geometrical parameters, or clinical data. These uncertainties result in a range of possible outputs which are quantified using probability density functions (PDFs). The objective is to systemically model the input uncertainties and quantify the confidence in the output of hemodynamic simulations. Input uncertainties are quantified and mapped to the stochastic space using the stochastic collocation technique. We develop an adaptive collocation algorithm for Gauss–Lobatto–Chebyshev grid points that significantly reduces computational cost. This analysis is performed on two idealized problems – an abdominal aortic aneurysm and a carotid artery bifurcation, and one patient specific problem – a Fontan procedure for congenital heart defects. In each case, relevant hemodynamic features are extracted and their uncertainty is quantified. Uncertainty quantification of the hemodynamic simulations is done using (a) stochastic space representations, (b) PDFs, and (c) the confidence intervals for a specified level of confidence in each problem.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(3):031002-031002-10. doi:10.1115/1.4003328.

Eye trauma results in 30,000 cases of blindness each year in the United States and is the second leading cause of monocular visual impairment. Eye injury is caused by a wide variety of projectile impacts and loading scenarios with common sources of trauma being motor vehicle crashes, military operations, and sporting impacts. For the current study, 79 experimental eye impact tests in literature were computationally modeled to analyze global and localized responses of the eye to a variety of blunt projectile impacts. Simulations were run with eight different projectiles (airsoft pellets, baseball, air gun pellets commonly known as BBs, blunt impactor, paintball, aluminum, foam, and plastic rods) to characterize effects of the projectile size, mass, geometry, material properties, and velocity on eye response. This study presents a matched comparison of experimental test results and computational model outputs including stress, energy, and pressure used to evaluate risk of eye injury. In general, the computational results agreed with the experimental results. A receiver operating characteristic curve analysis was used to establish the stress and pressure thresholds that best discriminated for globe rupture in the matched experimental tests. Globe rupture is predicted by the computational simulations when the corneoscleral stress exceeds 17.21 MPa or the vitreous pressure exceeds 1.01 MPa. Peak stresses were located at the apex of the cornea, the limbus, or the equator depending on the type of projectile impacting the eye. A multivariate correlation analysis revealed that area-normalized kinetic energy was the best single predictor of peak stress and pressure. Additional incorporation of a relative size parameter that relates the projectile area to the area of the eye reduced stress response variability and may be of importance in eye injury prediction. The modeling efforts shed light on the injury response of the eye when subjected to a variety of blunt projectile impacts and further validate the eye model’s ability to predict globe rupture. Results of this study are relevant to the design and regulation of safety systems and equipment to protect against eye injury.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(3):031003-031003-15. doi:10.1115/1.4003308.

A common problem in the analyses of upper limb unfettered reaching movements is the estimation of joint torques using inverse dynamics. The inaccuracy in the estimation of joint torques can be caused by the inaccuracy in the acquisition of kinematic variables, body segment parameters (BSPs), and approximation in the biomechanical models. The effect of uncertainty in the estimation of body segment parameters can be especially important in the analysis of movements with high acceleration. A sensitivity analysis was performed to assess the relevance of different sources of inaccuracy in inverse dynamics analysis of a planar arm movement. Eight regression models and one water immersion method for the estimation of BSPs were used to quantify the influence of inertial models on the calculation of joint torques during numerical analysis of unfettered forward arm reaching movements. Thirteen subjects performed 72 forward planar reaches between two targets located on the horizontal plane and aligned with the median plane. Using a planar, double link model for the arm with a floating shoulder, we calculated the normalized joint torque peak and a normalized root mean square (rms) of torque at the shoulder and elbow joints. Statistical analyses quantified the influence of different BSP models on the kinetic variable variance for given uncertainty on the estimation of joint kinematics and biomechanical modeling errors. Our analysis revealed that the choice of BSP estimation method had a particular influence on the normalized rms of joint torques. Moreover, the normalization of kinetic variables to BSPs for a comparison among subjects showed that the interaction between the BSP estimation method and the subject specific somatotype and movement kinematics was a significant source of variance in the kinetic variables. The normalized joint torque peak and the normalized root mean square of joint torque represented valuable parameters to compare the effect of BSP estimation methods on the variance in the population of kinetic variables calculated across a group of subjects with different body types. We found that the variance of the arm segment parameter estimation had more influence on the calculated joint torques than the variance of the kinematics variables. This is due to the low moments of inertia of the upper limb, especially when compared with the leg. Therefore, the results of the inverse dynamics of arm movements are influenced by the choice of BSP estimation method to a greater extent than the results of gait analysis.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(3):031004-031004-9. doi:10.1115/1.4003316.

Ureteral peristaltic mechanism facilitates urine transport from the kidney to the bladder. Numerical analysis of the peristaltic flow in the ureter aims to further our understanding of the reflux phenomenon and other ureteral abnormalities. Fluid-structure interaction (FSI) plays an important role in accuracy of this approach and the arbitrary Lagrangian–Eulerian (ALE) formulation is a strong method to analyze the coupled fluid-structure interaction between the compliant wall and the surrounding fluid. This formulation, however, was not used in previous studies of peristalsis in living organisms. In the present investigation, a numerical simulation is introduced and solved through ALE formulation to perform the ureteral flow and stress analysis. The incompressible Navier–Stokes equations are used as the governing equations for the fluid, and a linear elastic model is utilized for the compliant wall. The wall stimulation is modeled by nonlinear contact analysis using a rigid contact surface since an appropriate model for simulation of ureteral peristalsis needs to contain cell-to-cell wall stimulation. In contrast to previous studies, the wall displacements are not predetermined in the presented model of this finite-length compliant tube, neither the peristalsis needs to be periodic. Moreover, the temporal changes of ureteral wall intraluminal shear stress during peristalsis are included in our study. Iterative computing of two-way coupling is used to solve the governing equations. Two phases of nonperistaltic and peristaltic transport of urine in the ureter are discussed. Results are obtained following an analysis of the effects of the ureteral wall compliance, the pressure difference between the ureteral inlet and outlet, the maximum height of the contraction wave, the contraction wave velocity, and the number of contraction waves on the ureteral outlet flow. The results indicate that the proximal part of the ureter is prone to a higher shear stress during peristalsis compared with its middle and distal parts. It is also shown that the peristalsis is more efficient as the maximum height of the contraction wave increases. Finally, it is concluded that improper function of ureteropelvic junction results in the passage of part of urine back flow even in the case of slow start-up of the peristaltic contraction wave.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(3):031006-031006-7. doi:10.1115/1.4003323.
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(3):031007-031007-14. doi:10.1115/1.4003324.

Accurate modeling of arterial response to physiological or pathological loads may shed light on the processes leading to initiation and progression of a number of vascular diseases and may serve as a tool for prediction and diagnosis. In this study, a microstructure based hyperelastic constitutive model is developed for passive media of porcine coronary arteries. The most general model contains 12 independent parameters representing the three-dimensional inner fibrous structure of the media and includes the effects of residual stresses and osmotic swelling. Parameter estimation and model validation were based on mechanical data of porcine left anterior descending (LAD) media under radial inflation, axial extension, and twist tests. The results show that a reduced four parameter model is sufficient to reliably predict the passive mechanical properties. These parameters represent the stiffness and the helical orientation of each lamellae fiber and the stiffness of the interlamellar struts interconnecting these lamellae. Other structural features, such as orientational distribution of helical fibers and anisotropy of the interlamellar network, as well as possible transmural distribution of structural features, were found to have little effect on the global media mechanical response. It is shown that the model provides good predictions of the LAD media twist response based on parameters estimated from only biaxial tests of inflation and extension. In addition, good predictive capabilities are demonstrated for the model behavior at high axial stretch ratio based on data of law stretches.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(3):031008-031008-6. doi:10.1115/1.4003326.

Supraspinatus tendon tears are common and often propagate into larger tears that include the infraspinatus tendon, resulting in loss of function and increased pain. Previously, we showed that the supraspinatus and infraspinatus tendons mechanically interact through a range of rotation angles, potentially shielding the torn supraspinatus tendon from further injury while subjecting the infraspinatus tendon to increased risk of injury. Surgical repair of torn supraspinatus tendons is common, yet the effect of the repair on the infraspinatus tendon is unknown. Since we have established a relationship between strain in the supraspinatus and infraspinatus tendons the success of a supraspinatus tendon repair depends on its effect on the loading environment in the infraspinatus tendon. More specifically, the effect of transosseous supraspinatus tendon repair in comparison to one that utilizes suture anchors, as is commonly done with arthroscopic repairs, on this interaction through these joint positions will be evaluated. We hypothesize that at all joint positions evaluated, both repairs will restore the interaction between the two tendons. For both repairs, (1) increasing supraspinatus tendon load will increase infraspinatus tendon strain and (2) altering the rotation angle from internal to external will increase strain in the infraspinatus tendon. Strains were measured in the infraspinatus tendon insertion through a range of joint rotation angles and supraspinatus tendon loads, for the intact, transosseous, and suture anchor repaired supraspinatus tendons. Images corresponding to specific supraspinatus tendon loads were isolated for the infraspinatus tendon insertion for analysis. The effect of supraspinatus tendon repair on infraspinatus tendon strain differed with joint position. Altering the joint rotation did not change strain in the infraspinatus tendon for any supraspinatus tendon condition. Finally, increasing supraspinatus tendon load resulted in an increase in average maximum and decrease in average minimum principal strain in the infraspinatus tendon. There is a significant difference in infraspinatus tendon strain between the intact and arthroscopically (but not transosseous) repaired supraspinatus tendons that increases with greater loads. Results suggest that at low loads neither supraspinatus tendon repair technique subjects the infraspinatus tendon to potentially detrimental loads; however, at high loads, transosseous repairs may be more advantageous over arthroscopic repairs for the health of the infraspinatus tendon. Results emphasize the importance of limiting loading of the repaired supraspinatus tendon and that at low loads, both repair techniques restore the interaction to the intact supraspinatus tendon case.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(3):031009-031009-10. doi:10.1115/1.4003320.

Tracking or predicting physiological fatigue is important for developing more robust training protocols and better energy supplements and/or reducing muscle injuries. Current methodologies are usually impractical and/or invasive and may not be realizable outside of laboratory settings. It was recently demonstrated that smooth orthogonal decomposition (SOD) of phase space warping (PSW) features of motion kinematics can identify fatigue in individual muscle groups. We hypothesize that a nonlinear extension of SOD will identify more optimal fatigue coordinates and provide a lower-dimensional reconstruction of local fatigue dynamics than the linear SOD. Both linear and nonlinear SODs were applied to PSW features estimated from measured kinematics to reconstruct muscle fatigue dynamics in subjects performing a sawing motion. Ten healthy young right-handed subjects pushed a weighted handle back and forth until voluntary exhaustion. Three sets of joint kinematic angles were measured from the right upper extremity in addition to surface electromyography (EMG) recordings. The SOD coordinates of kinematic PSW features were compared against independently measured fatigue markers (i.e., mean and median EMG spectrum frequencies of individual muscle groups). This comparison was based on a least-squares linear fit of a fixed number of the dominant SOD coordinates to the appropriate local fatigue markers. Between subject variability showed that at most four to five nonlinear SOD coordinates were needed to reconstruct fatigue in local muscle groups, while on average 15 coordinates were needed for the linear SOD. Thus, the nonlinear coordinates provided a one-order-of-magnitude improvement over the linear ones.

Commentary by Dr. Valentin Fuster

Technical Briefs

J Biomech Eng. 2011;133(3):034501-034501-4. doi:10.1115/1.4003439.

High mechanical stress condition over the fibrous cap (FC) has been widely accepted as a contributor to plaque rupture. The relationships between the stress, lumen curvature, and FC thickness have not been explored in detail. In this study, we investigate lumen irregularity-dependent relationships between mechanical stress conditions, local FC thickness (LTFC), and lumen curvature (LClumen). Magnetic resonance imaging slices of carotid plaque from 100 patients with delineated atherosclerotic components were used. Two-dimensional structure-only finite element simulations were performed for the mechanical analysis, and maximum principal stress (stress-P1) at all integral nodes along the lumen was obtained. LTFC and LClumen were computed using the segmented contour. The lumen irregularity (L-δir) was defined as the difference between the largest and the smallest lumen curvature. The results indicated that the relationship between stress-P1, LTFC, and LClumen is largely dependent on L-δir. When L-δir1.31 (irregular lumen), stress-P1 strongly correlated with lumen curvature and had a weak/no correlation with local FC thickness, and in 73.4% of magnetic resonance (MR) slices, the critical stress (maximum of stress-P1 over the diseased region) was found at the site where the lumen curvature was large. When L-δir0.28 (relatively round lumen), stress-P1 showed a strong correlation with local FC thickness but weak/no correlation with lumen curvature, and in 71.7% of MR slices, the critical stress was located at the site of minimum FC thickness. Using lumen irregularity as a method of identifying vulnerable plaque sites by referring to the lumen shape is a novel and simple method, which can be used for mechanics-based plaque vulnerability assessment.

Commentary by Dr. Valentin Fuster

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