Research Papers

J Biomech Eng. 2013;135(3):031001-031001-7. doi:10.1115/1.4023369.

To properly simulate the behavior of biological structures through computer modeling, there exists a need to describe parameters that vary locally. These parameters can be obtained either from literature or from experimental data and they are often assigned to regions in the model as lumped values. Furthermore, parameter values may be obtained on a representative case and may not be available for each specific modeled organ. We describe a semiautomated technique to assign detailed maps of local tissue properties to a computational model of a biological structure. We applied the method to the left atrium of the heart. The orientation of myocytes in the tissue as obtained from histologic analysis was transferred to the 3D model of a porcine left atrium. Finite element method (FEM) dynamic simulations were performed by using an isotropic, neo-Hookean, constitutive model first, then adding an anisotropic, cardiomyocyte oriented, Fung-type component. Results showed higher stresses for the anisotropic material model corresponding to lower stretches in the cardiomyocyte directions. The same methodology can be applied to transfer any map of parameters onto a discretized finite element model.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(3):031002-031002-9. doi:10.1115/1.4007454.

Though remarkably robust, articular cartilage becomes susceptible to damage at high loading rates, particularly under shear. While several studies have measured the local static and steady-state shear properties of cartilage, it is the local viscoelastic properties that determine the tissue's ability to withstand physiological loading regimens. However, measuring local viscoelastic properties requires overcoming technical challenges that include resolving strain fields in both space and time and accurately calculating their phase offsets. This study combined recently developed high-speed confocal imaging techniques with three approaches for analyzing time- and location-dependent mechanical data to measure the depth-dependent dynamic modulus and phase angles of articular cartilage. For sinusoidal shear at frequencies f = 0.01 to 1 Hz with no strain offset, the dynamic shear modulus |G*| and phase angle δ reached their minimum and maximum values (respectively) approximately 100 μm below the articular surface, resulting in a profound focusing of energy dissipation in this narrow band of tissue that increased with frequency. This region, known as the transitional zone, was previously thought to simply connect surface and deeper tissue regions. Within 250 μm of the articular surface, |G*| increased from 0.32 ± 0.08 to 0.42 ± 0.08 MPa across the five frequencies tested, while δ decreased from 12 deg ± 1 deg to 9.1 deg ± 0.5 deg. Deeper into the tissue, |G*| increased from 1.5 ± 0.4 MPa to 2.1 ± 0.6 MPa and δ decreased from 13 deg ± 1 deg to 5.5 deg ± 0.2 deg. Viscoelastic properties were also strain-dependent, with localized energy dissipation suppressed at higher shear strain offsets. These results suggest a critical role for the transitional zone in dissipating energy, representing a possible shift in our understanding of cartilage mechanical function. Further, they give insight into how focal degeneration and mechanical trauma could lead to sustained damage in this tissue.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(3):031003-031003-11. doi:10.1115/1.4023135.

An accurate method to locate of the flexion-extension (F-E) axis and longitudinal rotation (LR) axis of the tibiofemoral joint is required to accurately characterize tibiofemoral kinematics. A method was recently developed to locate these axes using an instrumented spatial linkage (ISL) (2012, “On the Estimate of the Two Dominant Axes of the Knee Using an Instrumented Spatial Linkage,” J. Appl. Biomech., 28(2), pp. 200–209). However, a more comprehensive error analysis is needed to optimize the design and characterize the limitations of the device before using it experimentally. To better understand the errors in the use of an ISL in finding the F-E and LR axes, our objectives were to (1) develop a method to computationally determine the orientation and position errors in locating the F-E and LR axes due to transducer nonlinearity and hysteresis, ISL size and attachment position, and the pattern of applied tibiofemoral motion, (2) determine the optimal size and attachment position of an ISL to minimize these errors, (3) determine the best pattern of pattern of applied motion to minimize these errors, and (4) examine the sensitivity of the errors to range of flexion and internal-external (I-E) rotation. A mathematical model was created that consisted of a virtual “elbow-type” ISL that measured motion across a virtual tibiofemoral joint. Two orientation and two position errors were computed for each axis by simulating the axis-finding method for 200 iterations while adding transducer errors to the revolute joints of the virtual ISL. The ISL size and position that minimized these errors were determined from 1080 different combinations. The errors in locating the axes using the optimal ISL were calculated for each of three patterns of motion applied to the tibiofemoral joint, consisting of a sequential pattern of discrete tibiofemoral positions, a random pattern of discrete tibiofemoral positions, and a sequential pattern of continuous tibiofemoral positions. Finally, errors as a function of range of flexion and I-E rotation were determined using the optimal pattern of applied motion. An ISL that was attached to the anterior aspect of the knee with 300-mm link lengths had the lowest maximum error without colliding with the anatomy of the joint. A sequential pattern of discrete tibiofemoral positions limited the largest orientation or position error without displaying large bias error. Finally, the minimum range of applied motion that ensured all errors were below 1 deg or 1 mm was 30 deg flexion with ±15 deg I-E rotation. Thus a method for comprehensive analysis of error when using this axis-finding method has been established, and was used to determine the optimal ISL and range of applied motion; this method of analysis could be used to determine the errors for any ISL size and position, any applied motion, and potentially any anatomical joint.

Topics: Rotation , Errors , Linkages , Design
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(3):031004-031004-9. doi:10.1115/1.4023371.

The study of the mechanical properties of swine carotids has clinical relevance because it is important for the appropriate design of intravascular devices in the animal trial phases. The inelastic properties of porcine carotid tissue were investigated. Experimental uniaxial cyclic tests were performed along the longitudinal and circumferential directions of vessels. The work focused on the determination, comparison, and constitutive modeling of the softening properties and residual stretch set of the swine carotid artery over long stretches and stress levels in both proximal and distal regions. It was observed that the residual strain depends on the maximum stretch in the previous load cycle. The strain was higher for distal than for proximal samples and for circumferential than for longitudinal samples. In addition, a pseudoelastic model was used to reproduce the residual stretch and softening behavior of the carotid artery. The model presented a good approximation of the experimental data. The results demonstrate that the final results in animal trial studies could be affected by the location studied along the length of the porcine carotid.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(3):031005-031005-9. doi:10.1115/1.4023373.

In this paper, we assess the validity of two alternative tube-load models for describing the relationship between central aortic and peripheral arterial blood pressure (BP) waveforms in humans. In particular, a single-tube (1-TL) model and a serially connected two-tube (2-TL) model, both terminated with a Windkessel load, are considered as candidate representations of central aortic-peripheral arterial path. Using the central aortic, radial and femoral BP waveform data collected from eight human subjects undergoing coronary artery bypass graft with cardiopulmonary bypass procedure, the fidelity of the tube-load models was quantified and compared with each other. Both models could fit the central aortic-radial and central aortic-femoral BP waveform pairs effectively. Specifically, the models could estimate pulse travel time (PTT) accurately, and the model-derived frequency response was also close to the empirical transfer function estimate obtained directly from the central aortic and peripheral BP waveform data. However, 2-TL model was consistently superior to 1-TL model with statistical significance as far as the accuracy of the central aortic BP waveform was concerned. Indeed, the average waveform RMSE was 2.52 mmHg versus 3.24 mmHg for 2-TL and 1-TL models, respectively (p < 0.05); the r2 value between measured and estimated central aortic BP waveforms was 0.96 and 0.93 for 2-TL and 1-TL models, respectively (p < 0.05). We concluded that the tube-load models considered in this paper are valid representations that can accurately reproduce central aortic-radial/femoral BP waveform relationships in humans, although the 2-TL model is preferred if an accurate central aortic BP waveform is highly desired.

Technical Briefs

J Biomech Eng. 2013;135(3):034501-034501-5. doi:10.1115/1.4023134.

The underlying mechanisms for the viscoelastic behavior of tendon and ligament tissue are poorly understood. It has been suggested that both a flow-dependent and flow-independent mechanism may contribute at different structural levels. We hypothesized that the stress relaxation response of a single tendon fascicle is consistent with the flow-dependent mechanism described by the biphasic theory (Armstrong et al., 1984, “An Analysis of the Unconfined Compression of Articular Cartilage,” ASME J. Biomech. Eng., 106, pp. 165–173). To test this hypothesis, force, lateral strain, and Poisson's ratio were measured as a function of time during stress relaxation testing of six rat tail tendon fascicles from a Sprague Dawley rat. As predicted by biphasic theory, the lateral strain and Poisson's ratio were time dependent, a large estimated volume loss was seen at equilibrium and there was a linear correlation between the force and Poisson's ratio during stress relaxation. These results suggest that the fluid dependent mechanism described by biphasic theory may explain some or all of the apparent viscoelastic behavior of single tendon fascicles.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(3):034502-034502-5. doi:10.1115/1.4023370.

Cardiac imaging using magnetic resonance requires a gating signal in order to compensate for motion. Human patients are routinely scanned using an electrocardiogram (ECG) as a gating signal during imaging. However, we found that in sheep the ECG is not a reliable method for gating. We developed a software based method that allowed us to use the left ventricular pressure (LVP) as a reliable gating signal. By taking the time derivative of the LVP (dP/dt), we were able to start imaging at both end-diastole for systolic phase images, and end-systole for diastolic phase images. We also used MR tissue tagging to calculate 3D strain information during diastole. Using the LVP in combination with our digital circuit provided a reliable and time efficient method for ovine cardiac imaging. Unlike the ECG signal the left ventricular pressure was a clean signal and allowed for accurate, nondelay based triggering during systole and diastole.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(3):034503-034503-5. doi:10.1115/1.4023372.

The role of the recruitment-derecruitment of small structures in the lung (lung units) as the lung increases and decreases in volume has been debated. The objective of this study was to develop a model to estimate the change in the number and volume of open lung units as an excised lung is inflated-deflated between minimum and maximum lung volume. The model was formulated based on the observation that the compliance of the slowly changing quasi-static pressure-volume (P-V) curve of an excised rat lung can differ from the compliance of a faster changing small sinusoidal pressure volume perturbations superimposed on the curve. In those regions of the curve where differences in compliance occur, the lung tissue properties exhibit nonlinear characteristics, which cannot be linearized using “incremental” or “small signal” analysis. The model attributes the differences between the perturbation and quasi-static compliance to an additional nonlinear compliance term that results from the sequential opening and closing of lung units. Using this approach, it was possible to calculate the normalized average volume and the normalized number of open units as the lung is slowly inflated-deflated. Results indicate that the normalized average volume and the normalized number of open units are not linearly related to normalized lung volume, and at equal lung volumes the normalized number of open units is greater and the normalized average lung unit volume is smaller during lung deflation when compared to lung inflation. In summary, a model was developed to describe the recruitment-derecruitment process in excised lungs based on the differences between small signal perturbation compliance and quasi-static compliance. Values of normalized lung unit volume and the normalized number of open lung units were shown to be nonlinear functions of both transpulmonary pressure and normalized lung volume.

Topics: Lung , Pressure
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(3):034504-034504-5. doi:10.1115/1.4023137.

Since the flow of a magnetic fluid could easily be influenced by an external magnetic field, its hydrodynamic modeling promises to be useful for magnetically controllable delivery systems. It is desirable to understand the flow fields and characteristics before targeted magnetic particles arrive at their destination. In this study, we perform an analysis for the effects of particles and a magnetic field on biomedical magnetic fluid flow to study the targeted magnetic-particle delivery in a blood vessel. The fully developed solutions of velocity, flow rate, and flow drag are derived analytically and presented for blood with magnetite nanoparticles at body temperature. Results reveal that in the presence of magnetic nanoparticles, a minimum magnetic field gradient (yield gradient) is required to initiate the delivery. A magnetic driving force leads to the increase in velocity and has enhancing effects on flow rate and flow drag. Such a magnetic driving effect can be magnified by increasing the particle volume fraction.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(3):034505-034505-6. doi:10.1115/1.4023525.

Recently, continuous-flow ventricular assist devices (CF-VADs) have supplanted older, pulsatile-flow pumps, for treating patients with advanced heart failure. Despite the excellent results of the newer generation devices, the effects of long-term loss of pulsatility remain unknown. The aim of this study is to compare the ability of both axial and centrifugal continuous-flow pumps to intrinsically modify pulsatility when placed under physiologically diverse conditions. Four VADs, two axial- and two centrifugal-flow, were evaluated on a mock circulatory flow system. Each VAD was operated at a constant impeller speed over three hypothetical cardiac conditions: normo-tensive, hypertensive, and hypotensive. Pulsatility index (PI) was compared for each device under each condition. Centrifugal-flow devices had a higher PI than that of axial-flow pumps. Under normo-tension, flow PI was 0.98 ± 0.03 and 1.50 ± 0.02 for the axial and centrifugal groups, respectively (p < 0.01). Under hypertension, flow PI was 1.90 ± 0.16 and 4.21 ± 0.29 for the axial and centrifugal pumps, respectively (p = 0.01). Under hypotension, PI was 0.73 ± 0.02 and 0.78 ± 0.02 for the axial and centrifugal groups, respectively (p = 0.13). All tested CF-VADs were capable of maintaining some pulsatile-flow when connected in parallel with our mock ventricle. We conclude that centrifugal-flow devices outperform the axial pumps from the basis of PI under tested conditions.

Commentary by Dr. Valentin Fuster

Design Innovation Papers

J Biomech Eng. 2013;135(3):035001-035001-8. doi:10.1115/1.4023520.

The mechanism of noncontact anterior cruciate ligament (ACL) injury is not well understood. It is partly because previous studies have been unable to relate dynamic knee muscle forces during sports activities such as landing from a jump to the strain in the ACL. We present a combined in vivo/in vitro method to relate the muscle group forces to ACL strain during jump-landing using a newly developed dynamic knee simulator. A dynamic knee simulator system was designed and developed to study the sagittal plane biomechanics of the knee. The simulator is computer controlled and uses six powerful electromechanical actuators to move a cadaver knee in the sagittal plane and to apply dynamic muscle forces at the insertion sites of the quadriceps, hamstring, and gastrocnemius muscle groups and the net moment at the hip joint. In order to demonstrate the capability of the simulator to simulate dynamic sports activities on cadaver knees, motion capture of a live subject landing from a jump on a force plate was performed. The kinematics and ground reaction force data obtained from the motion capture were input into a computer based musculoskeletal lower extremity model. From the model, the force-time profile of each muscle group across the knee during the movement was extracted, along with the motion profiles of the hip and ankle joints. This data was then programmed into the dynamic knee simulator system. Jump-landing was simulated on a cadaver knee successfully. Resulting strain in the ACL was measured using a differential variable reluctance transducer (DVRT). Our results show that the simulator has the capability to accurately simulate the dynamic sagittal plane motion and the dynamic muscle forces during jump-landing. The simulator has high repeatability. The ACL strain values agreed with the values reported in the literature. This combined in vivo/in vitro approach using this dynamic knee simulator system can be effectively used to study the relationship between sagittal plane muscle forces and ACL strain during dynamic activities.

Commentary by Dr. Valentin Fuster

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