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### Research Papers

J Biomech Eng. 2010;132(3):031001-031001-8. doi:10.1115/1.4000869.

Contact detection in cartilage contact mechanics is an important feature of any analytical or computational modeling investigation when the biphasic nature of cartilage and the corresponding tribology are taken into account. The fluid flow boundary conditions will change based on whether the surface is in contact or not, which will affect the interstitial fluid pressurization. This in turn will increase or decrease the load sustained by the fluid phase, with a direct effect on friction, wear, and lubrication. In laboratory experiments or clinical hemiarthroplasty, when a rigid indenter or metallic prosthesis is used to apply load to the cartilage, there will not be any fluid flow normal to the surface in the contact region due to the impermeable nature of the indenter/prosthesis. In the natural joint, on the other hand, where two cartilage surfaces interact, flow will depend on the pressure difference across the interface. Furthermore, in both these cases, the fluid would flow freely in non-contacting regions. However, it should be pointed out that the contact area is generally unknown in advance in both cases and can only be determined as part of the solution. In the present finite element study, a general and robust algorithm was proposed to decide nodes in contact on the cartilage surface and, accordingly, impose the fluid flow boundary conditions. The algorithm was first tested for a rigid indenter against cartilage model. The algorithm worked well for two-dimensional four-noded and eight-noded axisymmetric element models as well as three-dimensional models. It was then extended to include two cartilages in contact. The results were in excellent agreement with the previous studies reported in the literature.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(3):031002-031002-8. doi:10.1115/1.4000933.

Soft tissue injuries are poorly understood at the molecular level. Previous work using differential scanning calorimetry (DSC) has shown that tendon collagen becomes less thermally stable with rupture. However, most soft tissue injuries do not result in complete tissue rupture but in damaging fiber overextension. Covalent crosslinking, which increases with animal maturity and age, plays an important role in collagenous fiber mechanics. It is also a determinant of tissue strength and is hypothesized to inhibit the loss of thermal stability of collagen due to mechanical damage. Controlled overextension without rupture was investigated to determine if overextension was sufficient to reduce the thermal stability of collagen in the bovine tail tendon (BTT) model and to examine the effects of aging on the phenomenon. Baseline data from DSC and hydrothermal isometric tension (HIT) techniques were compared between two groups: steers aged 24–30 months (young group), and skeletally mature bulls and oxen aged greater than five years (old group). Covalent crosslinks were quantified by ion exchange chromatography. Overextension resulted in reduced collagen thermal stability in the BTT model. The Young specimens, showing detectably lower tissue thermomechanical competence, lost more thermal stability with overextension than did the old specimens. The effect on old specimens, while smaller, was detectable. Multiple overextension cycles increased the loss of stability in the young group. Compositional differences in covalent crosslinking corresponded with tissue thermomechanical competence and therefore inversely with the loss of thermal stability. HIT testing gave thermal denaturation temperatures similar to those measured with DSC. The thermal stability of collagen was reduced by overextension of the tendon—without tissue rupture—and this effect was amplified by increased cycles of overextension. Increased tissue thermomechanical competence with aging seemed to mitigate the loss of collagen stability due to mechanical overextension. Surprisingly, the higher tissue thermomechanical competence did not directly correlate with the concentration of endogenous enzymatically derived covalent crosslinking on a mole per mole of collagen basis. It did, however, correlate with the percentage of mature and thermally stable crosslinks. Compositional changes in fibrous collagens that occur with aging affect fibrous collagen mechanics and partially determine the nature of mechanical damage at the intermolecular level. As techniques develop and improve, this new information may lead to important future studies concerning improved detection, prediction, and modeling of mechanical damage at much finer levels of tissue hierarchy than currently possible.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(3):031003-031003-8. doi:10.1115/1.4000875.

In order to cryopreserve functional engineered tissues (ETs), the microstructure of the extracellular matrix (ECM) should be maintained, as well as the cellular viability since the functionality is closely related to the ECM microstructure. Since the post-thaw ECM microstructure is determined by the deformation of ETs during cryopreservation, freezing-induced deformation of ETs was measured with a newly developed quantum dot (QD)-mediated cell image deformetry system using dermal equivalents as a model tissue. The dermal equivalents were constructed by seeding QD-labeled fibroblasts in type I collagen matrices. After 24 h incubation, the ETs were directionally frozen by exposing them to a spatial temperature gradient (from $4°C$ to $−20°C$ over a distance of 6 mm). While being frozen, the ETs were consecutively imaged, and consecutive pairs of these images were two-dimensionally cross-correlated to determine the local deformation during freezing. The results showed that freezing induced the deformation of ET, and its magnitude varied with both time and location. The maximum local dilatation was $0.006 s−1$ and was always observed at the phase change interface. Due to this local expansion, the unfrozen region in front of the freezing interface experienced compression. This expansion-compression pattern was observed throughout the freezing process. In the unfrozen region, the deformation rate gradually decreased away from the freezing interface. After freezing/thawing, the ET experienced an approximately 28% decrease in thickness and 8% loss in weight. These results indicate that freezing-induced deformation caused the transport of interstitial fluid, and the interstitial fluid was extruded. In summary, the results suggest that complex cell-fluid-matrix interactions occur within ETs during freezing, and these interactions determine the post-thaw ECM microstructure and eventual post-thaw tissue functionality.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(3):031004-031004-5. doi:10.1115/1.4000935.

Measurement of the stress and strain applied to implants and bone tissue in the human body are important for fracture prediction and evaluations of implant adaptation. The strain of titanium (Ti) materials can be measuring by X-ray diffraction techniques. This study applied X-ray diffraction to the skin tissue-covered Ti. Characteristic X-rays of $Mo Kα$ were used and the X-rays diffracted from the Ti were detected through the covering skin tissue. The X-ray absorption by skin tissue is large under the diffracted X-rays detected in low angles because the length of penetration depends on the angle of inclination, equal to the Bragg angle. The effects of skin tissue to detect the diffracted X-rays were investigated in the experiments. And the strain measurements were conducted under bending loads applied to the Ti specimen. The effect of skin tissue was absorption of X-rays as well as the X-rays scattered from the physiological saline contained in the tissue. The X-rays scattered by the physiological saline creates a specific background pattern near the peaks from the (002) and (011) lattice planes of Ti in the X-ray diffraction profile. Diffracted X-rays from the Ti were detected after being transmitted through 1 mm thick skin tissue by $Mo Kα$. Individual peaks such as (010), (002), (011), and (110) were clearly established by using a parallel beam arrangement. The strains of (110) lattice planes were measured with or without the tissue cover were very similar. The strain of the (110) lattice planes of Ti could be measured by $Mo Kα$ when the Ti specimen was located under the skin tissue.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(3):031005-031005-9. doi:10.1115/1.4000871.

The convective transport of fluid within the human upper airways is investigated in a transparent model of the tracheobronchial tree. Oscillatory flow through the branching network with six generations was studied at varying Reynolds numbers between 400 and 2600 and Womersley numbers from 5.5 to 12.3 in the trachea representing clinical conditions during high frequency oscillatory ventilation. The flow partitioning within the model was visualized using advection of neutrally buoyant tracer particles, which were illuminated by short light pulses and recorded by a high speed camera. Integration of the particle locations for a large number of cycles provides the probability distribution of particles passing certain branches within the bifurcating network, and thus, the dispersion of particles in the airways. The results show the different characteristics of flow partitioning at varying Womersley and Reynolds numbers.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(3):031006-031006-8. doi:10.1115/1.4000967.

Elastic compression is the process of applying an elastic garment around the leg, supposedly for enhancing the venous flow. However, the response of internal tissues to the external pressure is still partially unknown. In order to improve the scientific knowledge about this topic, a slice of a human leg wearing an elastic garment is modeled by the finite-element method. The elastic properties of the tissues inside the leg are identified thanks to a dedicated approach based on image processing. After calibrating the model with magnetic resonance imaging scans of a volunteer, the pressure transmitted through the internal tissues of the leg is computed. Discrepancies of more than 35% are found from one location to another, showing that the same compression garment cannot be applied for treating deficiencies of the deep venous system or deficiencies of the large superficial veins. Moreover, it is shown that the internal morphology of the human leg plays an important role. Accordingly, the approach presented in this paper may provide useful information for adapting compression garments to the specificity of each patient.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(3):031007-031007-9. doi:10.1115/1.4001028.

Atherosclerotic plaque rupture leading to stroke is the major cause of long-term disability as well as the third most common cause of mortality. Image-based computational models have been introduced seeking critical mechanical indicators, which may be used for plaque vulnerability assessment. This study extends the previous 2D critical stress concept to 3D by using in vivo magnetic resonance image (MRI) data of human atherosclerotic carotid plaques and 3D fluid-structure interaction (FSI) models to: identify 3D critical plaque wall stress (CPWS) and critical flow shear stress (CFSS) and to investigate their associations with plaque rupture. In vivo MRI data of carotid plaques from 18 patients scheduled for endarterectomy were acquired using histologically validated multicontrast protocols. Of the 18 plaques, histology-confirmed that six had prior rupture (group 1) as evidenced by presence of ulceration. The remaining 12 plaques (group 2) contained no rupture. The 3D multicomponent FSI models were constructed for each plaque to obtain 3D plaque wall stress (PWS) and flow shear stress (FSS) distributions. Three-dimensional CPWS and CFSS, defined as maxima of PWS and FSS from all vulnerable sites, were determined for each plaque to investigate their association with plaque rupture. Slice-based critical PWS and FSS were also calculated for all slices for more detailed analysis and comparison. The mean 3D CPWS of group 1 was 263.44 kPa, which was 100% higher than that from group 2 (132.77, $p=0.03984$). Five of the six ruptured plaques had 3D CPWS sites, matching the histology-confirmed rupture sites with an 83% agreement. Although the mean 3D CFSS $(92.94 dyn/cm2)$ for group 1 was 76% higher than that for group 2 $(52.70 dyn/cm2)$, slice-based CFSS showed no significant difference between the two groups. Only two of the six ruptured plaques had 3D CFSS sites matching the histology-confirmed rupture sites with a 33% agreement. CFSS had a good correlation with plaque stenosis severity ($R2=0.40$ with an exponential function fitting 3D CFSS data). This in vivo MRI pilot study using plaques with and without rupture demonstrates that 3D critical plaque wall stress values are more closely associated with atherosclerotic plaque rupture then critical flow shear stresses. Critical wall stress values may become indicators of high risk sites of rupture. Future work with a larger population will establish a possible CPWS-based plaque vulnerability classification.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(3):031008-031008-7. doi:10.1115/1.4001035.

Tissue ablation finds an increasing use in modern medicine. Nonthermal irreversible electroporation (NTIRE) is a biophysical phenomenon and an emerging novel tissue ablation modality, in which electric fields are applied in a pulsed mode to produce nanoscale defects to the cell membrane phospholipid bilayer, in such a way that Joule heating is minimized and thermal damage to other molecules in the treated volume is reduced while the cells die. Here we present a two-dimensional transient finite element model to simulate the electric field and thermal damage to the arterial wall due to an endovascular NTIRE novel device. The electric field was used to calculate the Joule heating effect, and a transient solution of the temperature is presented using the Pennes bioheat equation. This is followed by a kinetic model of the thermal damage based on the Arrhenius formulation and calculation of the Henriques and Moritz thermal damage integral. The analysis shows that the endovascular application of 90, $100 μs$ pulses with a potential difference of 600 V can induce electric fields of 1000 V/cm and above across the entire arterial wall, which are sufficient for irreversible electroporation. The temperature in the arterial wall reached a maximum of $66.7°C$ with a pulse frequency of 4 Hz. Thermal damage integral showed that this protocol will thermally damage less than 2% of the molecules around the electrodes. In conclusion, endovascular NTIRE is possible. Our study sets the theoretical basis for further preclinical and clinical trials with endovascular NTIRE.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(3):031009-031009-13. doi:10.1115/1.4000872.

Numerical simulations are performed to investigate the flow within the end-to-side proximal anastomosis of a pulsatile pediatric ventricular assist device (PVAD) to an aorta. The anastomotic model is constructed from a patient-specific pediatric aorta. The three great vessels originating from the aortic arch— brachiocephalic (innominate), left common carotid, and left subclavian arteries—are included. An implicit large eddy simulation method based on a finite volume approach is used to study the resulting turbulent flow. A resistance boundary condition is applied at each branch outlet to study flow splitting. The PVAD anastomosis is found to alter the aortic flow dramatically. More flow is diverted into the great vessels with the PVAD support. Turbulence is found in the jet impingement area at peak systole for 100% bypass, and a maximum principal normal Reynolds stress of $7081 dyn/cm2$ is estimated based on ten flow cycles. This may be high enough to cause hemolysis and platelet activation. Regions prone to intimal hyperplasia are identified by combining the time-averaged wall shear stress and oscillatory shear index. These regions are found to vary, depending on the percentage of the flow bypass.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(3):031010-031010-11. doi:10.1115/1.4000934.

The effect of phase angle between pressure and flow waveforms on the flow characteristics in stenosed compliant vessels for coronary (phase angle (PA) of approximately $−225 deg$) and peripheral flows (PA of approximately $−45 deg$) is investigated using time resolved digital particle image velocimetry. Synthetic arteries with 50% and 75% stenosis at various physiological conditions with Reynolds numbers (Re) of 250, 350, and 450 and corresponding Womersley parameter $(α)$ of 2.7, 3.2, and 3.7 were studied; wall-shear stresses (WSSs), oscillatory shear index (OSI), and recirculation lengths were determined. Additionally, flow transitional characteristics were examined using power spectral density (PSD), wavenumber spectra, and turbulence statistics of the axial velocity component. It is observed that the coronary flow conditions exhibit lower wall-shear stresses and larger recirculation lengths compared with peripheral flows. Mean peak shear stresses can be as high as $150 dyn/cm2$ and $92 dyn/cm2$ for peripheral and coronary flows, respectively, with 50% stenosis at $Re=450$ and $α=3.7$. These values can be as high as $590 dyn/cm2$ and $490 dyn/cm2$, respectively, for the same conditions with 75% stenosis. The OSI is close to 0.5 near the reattachment point indicating fluctuating WSS over the entire cardiac cycle for both 50% and 75% stenosis. For 50% stenosis, the OSI fluctuated at various locations over the length of the vessel indicating several regions of recirculation in contrast to a distinct recirculation region observed for 75% stenosis. PSD plots across various cross-sections along the length of the vessel and wavenumber spectra along the centerline indicate that turbulence occurs only for 75% stenosis. For coronary flows, the streamwise locations where the flow transitions to turbulence and relaminarizes are approximately one diameter upstream compared with peripheral flows indicating that coronary flows are more susceptible to turbulence.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(3):031011-031011-13. doi:10.1115/1.4000938.

The pericellular matrix (PCM) is the narrow tissue region surrounding all chondrocytes in articular cartilage and, together, the chondrocyte(s) and surrounding PCM have been termed the chondron. Previous theoretical and experimental studies suggest that the structure and properties of the PCM significantly influence the biomechanical environment at the microscopic scale of the chondrocytes within cartilage. In the present study, an axisymmetric boundary element method (BEM) was developed for linear elastic domains with internal interfaces. The new BEM was employed in a multiscale continuum model to determine linear elastic properties of the PCM in situ, via inverse analysis of previously reported experimental data for the three-dimensional morphological changes of chondrons within a cartilage explant in equilibrium unconfined compression (Choi, , 2007, “Zonal Changes in the Three-Dimensional Morphology of the Chondron Under Compression: The Relationship Among Cellular, Pericellular, and Extracellular Deformation in Articular Cartilage  ,” J. Biomech., 40, pp. 2596–2603). The microscale geometry of the chondron (cell and PCM) within the cartilage extracellular matrix (ECM) was represented as a three-zone equilibrated biphasic region comprised of an ellipsoidal chondrocyte with encapsulating PCM that was embedded within a spherical ECM subjected to boundary conditions for unconfined compression at its outer boundary. Accuracy of the three-zone BEM model was evaluated and compared with analytical finite element solutions. The model was then integrated with a nonlinear optimization technique (Nelder–Mead) to determine PCM elastic properties within the cartilage explant by solving an inverse problem associated with the in situ experimental data for chondron deformation. Depending on the assumed material properties of the ECM and the choice of cost function in the optimization, estimates of the PCM Young's modulus ranged from $∼24 kPa$ to 59 kPa, consistent with previous measurements of PCM properties on extracted chondrons using micropipette aspiration. Taken together with previous experimental and theoretical studies of cell-matrix interactions in cartilage, these findings suggest an important role for the PCM in modulating the mechanical environment of the chondrocyte.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(3):031012-031012-9. doi:10.1115/1.4000954.

The Fontan operation is a palliative surgical procedure performed on children, born with congenital heart defects that have yielded only a single functioning ventricle. The total cavo-pulmonary connection (TCPC) is a common variant of the Fontan procedure, where the superior vena cava (SVC) and inferior vena cava (IVC) are routed directly into the pulmonary arteries (PA). Due to the limited pumping energy available, optimized hemodynamics, in turn, minimized power loss, inside the TCPC pathway is required for the best optimal surgical outcomes. To complement ongoing efforts to optimize the anatomical geometric design of the surgical Fontan templates, here, we focused on the characterization of power loss changes due to the temporal variations in between SVC and IVC flow waveforms. An experimentally validated pulsatile computational fluid dynamics solver is used to quantify the effect of phase-shift between SVC and IVC inflow waveforms and amplitudes on internal energy dissipation. The unsteady hemodynamics of two standard idealized TCPC geometries are presented, incorporating patient-specific real-time PC-MRI flow waveforms of “functional” Fontan patients. The effects of respiration and pulsatility on the internal energy dissipation of the TCPC pathway are analyzed. Optimization of phase-shift between caval flows is shown to lead to lower energy dissipation up to 30% in these idealized models. For physiological patient-specific caval waveforms, the power loss is reduced significantly (up to 11%) by the optimization of all three major harmonics at the same mean pathway flow (3 L/min). Thus, the hemodynamic efficiency of single ventricle circuits is influenced strongly by the caval flow waveform quality, which is regulated through respiratory dependent physiological pathways. The proposed patient-specific waveform optimization protocol may potentially inspire new therapeutic applications to aid postoperative hemodynamics and improve the well being of the Fontan patients.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J Biomech Eng. 2010;132(3):034501-034501-4. doi:10.1115/1.4000937.

The comparison, evaluation, and optimization of new techniques, models, or algorithms often require the use of realistic deformable test phantoms. The purpose of this paper is to present a multilayer deformable test specimen mimicking an atherosclerotic coronary artery, suitable for mechanical testing and intravascular imaging. Mock arteries were constructed in three phases using two molds: building a first layer of polyvinyl alcohol (PVA) cryogel, adding a lipid pool and building a second layer of PVA cryogel. To illustrate the deformation of the mock arteries, one has been placed in a custom-made bath, axially stretched then inflated while acquiring intravascular ultrasound (IVUS) images. The resulting specimen presents a progressing lumen narrowing of 25% in cross-sectional area at the peak and a lipid pool. The average inner gel layer is about 0.4 mm thick and the outer about 0.6 mm. The dimensions are of the same order as clinical observations, the first gel layer mimicking the intima-media and the second layer the adventitia. In the sequence of IVUS images, the different components of the mock artery are visible and differentiable. The variation in diameter of the segmented contours is presented for a specific specimen subjected to intraluminal pressure. This double-layer stenotic mock artery is approximately the size of a human coronary artery, has a lipid inclusion, can withstand relative large deformation, suitable for (intravascular) ultrasound imaging, and has customizable geometry and wall material parameters.

Commentary by Dr. Valentin Fuster