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### EDITORIAL

J Biomech Eng. 2005;127(7):1045. doi:10.1115/1.2084668.
FREE TO VIEW

An important and increasingly popular feature at each of the Summer Bioengineering Conferences is the student paper competition. Students from undergraduate to graduate levels submit their work for selection for either poster or podium presentations at the meeting—at which time final judging occurs. At the 2005 meeting, the competition was the largest in the history of the Bioengineering Division. The overall competition was chaired by Amy Lerner with the help of Michele Grimm, chair of the Ph.D. competition (149 papers); James Iatridis and Matt Gounis, chairs of the M.S. competition (70 papers); and X. Sheldon Wang, chair of the B.S. competition (30 papers). 102 of the submitted papers were selected for on-site judging in poster sessions or, for the Ph.D. competition, in both poster and podium sessions. On behalf of the BED, I would like to thank Amy and Michelle and the many judges who contributed their time and expertise to this important endeavor. I would also like to acknowledge and give appreciation to The Whitaker Foundation for sponsoring the competition.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Bone/Orthopedics

J Biomech Eng. 2005;127(7):1046-1053. doi:10.1115/1.2073671.

Measuring the microscopic mechanical properties of bone tissue is important in support of understanding the etiology and pathogenesis of many bone diseases. Knowledge about these properties provides a context for estimating the local mechanical environment of bone related cells that coordinate the adaptation to loads experienced at the whole organ level. The objective of this study was to determine the effects of experimental testing parameters on nanoindentation measures of lamellar-level bone mechanical properties. Specifically, we examined the effect of specimen preparation condition, indentation depth, repetitive loading, time delay, and displacement rate. The nanoindentation experiments produced measures of lamellar elastic moduli for human cortical bone (average value of $17.7±4.0GPa$ for osteons and $19.3±4.7GPa$ for interstitial bone tissue). In addition, the hardness measurements produced results consistent with data in the literature (average $0.52±0.15GPa$ for osteons and $0.59±0.20GPa$ for interstitial bone tissue). Consistent modulus values can be obtained from a 500-nm-deep indent. The results also indicated that the moduli and hardnesses of the dry specimens are significantly greater (22.6% and 56.9%, respectively) than those of the wet and wet and embedded specimens. The latter two groups were not different. The moduli obtained at a $5‐nm∕s$ loading rate were significantly lower than the values at the 10- and $20‐nm∕s$ loading rates while the 10- and $20‐nm∕s$ rates were not significantly different. The hardness measurements showed similar rate-dependent results. The preliminary results indicated that interstitial bone tissue has significantly higher modulus and hardness than osteonal bone tissue. In addition, a significant correlation between hardness and elastic modulus was observed.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Cell

J Biomech Eng. 2005;127(7):1054-1061. doi:10.1115/1.2073407.

A sphere within a cylinder representing the islet encapsulated in a hollow fiber can model an implantable bioartificial pancreas. Based on a finite element model for insulin response to a glucose load in the presence of various oxygen supplies, the present study aimed at pointing out the major parameters influencing this secretion. The computational results treated with the Taguchi method clearly demonstrated that geometrical parameters (fiber length and islet density) should be precisely optimized for an enhanced insulin response. This requires the collection of more relevant experimental data concerning the islet oxygen consumption. Moreover, the relative errors on glucose consumption or insulin secretion by the islets do not seem to affect the whole optimization process, which should focus on the oxygen supply to islets.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(7):1062-1069. doi:10.1115/1.2073527.

In the classical “first approximation” theory of thin-shell structures, the constitutive relations for a generic shell element—i.e. the elastic relations between the bending moments and membrane stresses and the corresponding changes in curvature and strain, respectively—are written as if an element of the shell is flat, although in reality it is curved. In this theory it is believed that discrepancies on account of the use of “flat” constitutive relations will be negligible provided the ratio shell-radius∕thickness is of sufficiently large order. In the study of drawing of narrow, cylindrical “tethers” from liposomes it has been known for many years that it is necessary to use instead a constitutive law which explicitly describes a curved element in order to make sense of the mechanics; and indeed such tethers are generally of “thick-walled” proportions. In this paper we show that the proper constitutive relations for a curved element must also be used in the study, by means of shell equations, of the buckling of initially spherical thin-walled giant liposomes under exterior pressure: these involve the inclusion of what we call the “$Mκ$” terms, which are not present in the standard “first-approximation” theory. We obtain analytical expressions for both the bifurcation buckling pressure and the slope of the post-buckling path, in terms of the dimensions and elastic constants of the lipid bi-layer, and also the initial state of bending moment in the vesicle. We explain physically how the initial bending moment can affect the bifurcation pressure, whereas it cannot in “first-approximation” theory. We use these results to map the conditions under which the vesicle buckles into an oblate, as distinct from a prolate (“rugby-ball”) shape. Some of our results were obtained long ago by the use of energy methods; but our aim here has been to identify precisely what is lacking in “first-approximation” theory in relation to liposomes, and so to put the “shell equations” approach onto a firm footing in mechanics.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(7):1070-1080. doi:10.1115/1.2112907.

We present computational fluid dynamic (CFD) simulation of aggregation of two deformable cells in a shear flow. This work is motivated by an attempt to develop computational models of aggregation of red blood cells (RBCs). Aggregation of RBCs is a major determinant of blood viscosity in microcirculation under physiological and pathological conditions. Deformability of the RBCs plays a major role in determining their aggregability. Deformability depends on the viscosity of the cytoplasmic fluid and on the rigidity of the cell membrane, in a macroscopic sense. This paper presents a computational study of RBC aggregation that takes into account the rheology of the cells as well as cell-cell adhesion kinetics. The simulation technique considered here is two dimensional and based on the front tracking/immersed boundary method for multiple fluids. Results presented here are on the dynamic events of aggregate formation between two cells, and its subsequent motion, rolling, deformation, and breakage. We show that the rheological properties of the cells have significant effects on the dynamics of the aggregate. A stable aggregate is formed at higher cytoplasmic viscosity and membrane rigidity. We also show that the bonds formed between the cells change in a cyclic manner as the aggregate rolls in a shear flow. The cyclic behavior is related to the rolling orientation of the aggregate. The frequency and amplitude of oscillation in the number of bonds also depend on the rheological properties.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(7):1081-1086. doi:10.1115/1.2073673.

A differential scanning calorimeter technique was used to generate experimental data for volumetric shrinkage during cooling at $20°C∕min$ in adipose derived adult stem cells (ASCs) in the presence and absence of cryoprotective agents (CPAs). By fitting a model of water transport to the experimentally determined volumetric shrinkage data, the membrane permeability parameters of ASCs were obtained. For passage-4 (P4) ASCs, the reference hydraulic conductivity $Lpg$ and the value of the apparent activation energy $ELp$ were determined to be $1.2×10−13m3∕Ns$ and $177.8kJ∕mole$, respectively. We found that the addition of either glycerol or dimethylsulfoxide (DMSO) significantly decreased the value of the reference hydraulic conductivity $Lpg(cpa)$ and the value of the apparent activation energy $ELp(cpa)$ in P4 ASCs. The values of $Lpg(cpa)$ in the presence of glycerol and DMSO were determined as $0.39×10−13$ and $0.50×10−13m3∕Ns$, respectively, while the corresponding values of $ELp(cpa)$ were 51.0 and $61.5kJ∕mole$. Numerical simulations of water transport were then performed under a variety of cooling rates $(5–100°C∕min)$ using the experimentally determined membrane permeability parameters. And finally, the simulation results were analyzed to predict the optimal rates of freezing P4 adipose derived cells in the presence and absence of CPAs.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Fluids/Heat/Transport

J Biomech Eng. 2005;127(7):1087-1098. doi:10.1115/1.2073507.

We consider the effect of geometrical configuration on the steady flow field of representative geometries from an in vivo anatomical data set of end-to-side distal anastomoses constructed as part of a peripheral bypass graft. Using a geometrical classification technique, we select the anastomoses of three representative patients according to the angle between the graft and proximal host vessels (GPA) and the planarity of the anastomotic configuration. The geometries considered include two surgically tunneled grafts with shallow GPAs which are relatively planar but have different lumen characteristics, one case exhibiting a local restriction at the perianastomotic graft and proximal host whilst the other case has a relatively uniform cross section. The third case is nonplanar and characterized by a wide GPA resulting from the graft being constructed superficially from an in situ vein. In all three models the same peripheral resistance was imposed at the computational outflows of the distal and proximal host vessels and this condition, combined with the effect of the anastomotic geometry, has been observed to reasonably reproduce the in vivo flow split. By analyzing the flow fields we demonstrate how the local and global geometric characteristics influences the distribution of wall shear stress and the steady transport of fluid particles. Specifically, in vessels that have a global geometric characteristic we observe that the wall shear stress depends on large scale geometrical factors, e.g., the curvature and planarity of blood vessels. In contrast, the wall shear stress distribution and local mixing is significantly influenced by morphology and location of restrictions, particular when there is a shallow GPA. A combination of local and global effects are also possible as demonstrated in our third study of an anastomosis with a larger GPA. These relatively simple observations highlight the need to distinguish between local and global geometric influences for a given reconstruction. We further present the geometrical evolution of the anastomoses over a series of follow-up studies and observe how the lumen progresses towards the faster bulk flow of the velocity in the original geometry. This mechanism is consistent with the luminal changes in recirculation regions that experience low wall shear stress. In the shallow GPA anastomoses the proximal part of the native host vessel occludes or stenoses earlier than in the case with wide GPA. A potential contribution to this behavior is suggested by the stronger mixing that characterizes anastomoses with large GPA.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(7):1099-1109. doi:10.1115/1.2073607.

A two-dimensional axi-symmetric numerical model is constructed of the spinal cord, consisting of elastic cord tissue surrounded by aqueous cerebrospinal fluid, in turn surrounded by elastic dura. The geometric and elastic parameters are simplified but of realistic order, compared with existing measurements. A distal reflecting site models scar tissue formed by earlier trauma to the cord, which is commonly associated with syrinx formation. Transients equivalent to both arterial pulsation and percussive coughing are used to excite wave propagation. Propagation is investigated in this model and one with a central canal down the middle of the cord tissue, and in further idealized versions of it, including a model with no cord, one with a rigid cord, one with a rigid dura, and a double-length untapered variant of the rigid-dura model. Analytical predictions for axial and radial wave-speeds in these different situations are compared with, and used to explain, the numerical outcomes. We find that the anatomic circumstances of the spinal cerebrospinal fluid cavity probably do not allow for significant wave steepening phenomena. The results indicate that wave propagation in the real cord is set by the elastic properties of both the cord tissue and the confining dura mater, fat, and bone. The central canal does not influence the wave propagation significantly.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(7):1110-1120. doi:10.1115/1.2073687.

A simplified in vitro model of the spinal canal, based on in vivo magnetic resonance imaging, was used to examine the hydrodynamics of the human spinal cord and subarachnoid space with syringomyelia. In vivo magnetic resonance imaging (MRI) measurements of subarachnoid (SAS) geometry and cerebrospinal fluid velocity were acquired in a patient with syringomyelia and used to aid in the in vitro model design and experiment. The in vitro model contained a fluid-filled coaxial elastic tube to represent a syrinx. A computer controlled pulsatile pump was used to subject the in vitro model to a CSF flow waveform representative of that measured in vivo. Fluid velocity was measured at three axial locations within the in vitro model using the same MRI scanner as the patient study. Pressure and syrinx wall motion measurements were conducted external to the MR scanner using the same model and flow input. Transducers measured unsteady pressure both in the SAS and intra-syrinx at four axial locations in the model. A laser Doppler vibrometer recorded the syrinx wall motion at 18 axial locations and three polar positions. Results indicated that the peak-to-peak amplitude of the SAS flow waveform in vivo was approximately tenfold that of the syrinx and in phase $(SAS∼5.2±0.6ml∕s,syrinx∼0.5±0.3ml∕s)$. The in vitro flow waveform approximated the in vivo peak-to-peak magnitude $(SAS∼4.6±0.2ml∕s,syrinx∼0.4±0.3ml∕s)$. Peak-to-peak in vitro pressure variation in both the SAS and syrinx was approximately 6 mm Hg. Syrinx pressure waveform lead the SAS pressure waveform by approximately 40 ms. Syrinx pressure was found to be less than the SAS for $∼200ms$ during the 860-ms flow cycle. Unsteady pulse wave velocity in the syrinx was computed to be a maximum of $∼25m∕s$. LDV measurements indicated that spinal cord wall motion was nonaxisymmetric with a maximum displacement of $∼140μm$, which is below the resolution limit of MRI. Agreement between in vivo and in vitro MR measurements demonstrates that the hydrodynamics in the fluid filled coaxial elastic tube system are similar to those present in a single patient with syringomyelia. The presented in vitro study of spinal cord wall motion, and complex unsteady pressure and flow environment within the syrinx and SAS, provides insight into the complex biomechanical forces present in syringomyelia.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(7):1121-1126. doi:10.1115/1.2073674.

The transport of oxygen and lactate (i.e., lactic acid) in the human intervertebral disc was investigated accounting for the measured coupling between species via the $pH$ level in the tissue. Uncoupled cases were also analyzed to identify the extent of the effect of such coupling on the solute gradients across the disc. Moreover, nonlinear lactic production rate versus lactic concentration and oxygen consumption rate versus oxygen concentration were considered. The nonlinear coupled diffusion equations were solved using an in-house finite element program and an axisymmetric model of the disc with distinct nucleus and anulus regions. A pseudotransient approach with a backward integration scheme was employed to improve convergence. Coupled simulations influenced the oxygen concentration and lactic acid concentration throughout the disc, in particular the gradient of concentrations along the disc mid-height to the nucleus-anulus boundary where the solutes reached their most critical values; minimum for the oxygen tension and maximum for the lactate. Results suggest that for realistic estimates of nutrient and metabolite gradients across the disc, it could be important to take into account the coupling between the rates of synthesis and overall local metabolite∕nutrient concentration.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(7):1127-1140. doi:10.1115/1.2073669.

A computational methodology for accurately predicting flow and oxygen-transport characteristics and performance of an intravenous membrane oxygenator (IMO) device is developed, tested, and validated. This methodology uses extensive numerical simulations of three-dimensional computational models to determine flow-mixing characteristics and oxygen-transfer performance, and analytical models to indirectly validate numerical predictions with experimental data, using both blood and water as working fluids. Direct numerical simulations for IMO stationary and pulsating balloons predict flow field and oxygen transport performance in response to changes in the device length, number of fibers, and balloon pulsation frequency. Multifiber models are used to investigate interfiber interference and length effects for a stationary balloon whereas a single fiber model is used to analyze the effect of balloon pulsations on velocity and oxygen concentration fields and to evaluate oxygen transfer rates. An analytical lumped model is developed and validated by comparing its numerical predictions with experimental data. Numerical results demonstrate that oxygen transfer rates for a stationary balloon regime decrease with increasing number of fibers, independent of the fluid type. The oxygen transfer rate ratio obtained with blood and water is approximately two. Balloon pulsations show an effective and enhanced flow mixing, with time-dependent recirculating flows around the fibers regions which induce higher oxygen transfer rates. The mass transfer rates increase approximately 100% and 80%, with water and blood, respectively, compared with stationary balloon operation. Calculations with combinations of frequency, number of fibers, fiber length and diameter, and inlet volumetric flow rates, agree well with the reported experimental results, and provide a solid comparative base for analysis, predictions, and comparisons with numerical and experimental data.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(7):1141-1146. doi:10.1115/1.2112927.

Arteriovenous (AV) grafts and fistulas used for hemodialysis frequently develop intimal hyperplasia (IH) at the venous anastomosis of the graft, leading to flow-limiting stenosis, and ultimately to graft failure due to thrombosis. Although the high AV access blood flow has been implicated in the pathogenesis of graft stenosis, the potential role of needle turbulence during hemodialysis is relatively unexplored. High turbulent stresses from the needle jet that reach the venous anastomosis may contribute to endothelial denudation and vessel wall injury. This may trigger the molecular and cellular cascade involving platelet activation and IH, leading to eventual graft failure. In an in-vitro graft/needle model dye injection flow visualization was used for qualitative study of flow patterns, whereas laser Doppler velocimetry was used to compare the levels of turbulence at the venous anastomosis in the presence and absence of a venous needle jet. Considerably higher turbulence was observed downstream of the venous needle, in comparison to graft flow alone without the needle. While turbulent RMS remained around $0.1m∕s$ for the graft flow alone, turbulent RMS fluctuations downstream of the needle soared to $0.4–0.7m∕s$ at 2 cm from the tip of the needle and maintained values higher than $0.1m∕s$ up to 7–8 cm downstream. Turbulent intensities were 5–6 times greater in the presence of the needle, in comparison with graft flow alone. Since hemodialysis patients are exposed to needle turbulence for four hours three times a week, the role of post-venous needle turbulence may be important in the pathogenesis of AV graft complications. A better understanding of the role of needle turbulence in the mechanisms of AV graft failure may lead to improved design of AV grafts and venous needles associated with reduced turbulence, and to pharmacological interventions that attenuate IH and graft failure resulting from turbulence.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(7):1147-1157. doi:10.1115/1.2073628.

In the present paper, a closely coupled numerical and experimental investigation of pulsatile flow in a prototypical stenotic site is presented. Detailed laser Doppler velocimetry measurements upstream of the stenosis are used to guide the specification of velocity boundary conditions at the inflow plane in a series of direct numerical simulations (DNSs). Comparisons of the velocity statistics between the experiments and DNS in the post-stenotic area demonstrate the great importance of accurate inflow conditions, and the sensitivity of the post-stenotic flow to the disturbance environment upstream. In general, the results highlight a borderline turbulent flow that sequentially undergoes transition to turbulence and relaminarization. Before the peak mass flow rate, the strong confined jet that forms just downstream of the stenosis becomes unstable, forcing a role-up and subsequent breakdown of the shear layer. In addition, the large-scale structures originating from the shear layer are observed to perturb the near wall flow, creating packets of near wall hairpin vortices.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Soft Tissue

J Biomech Eng. 2005;127(7):1158-1167. doi:10.1115/1.2073467.

In vivo rodent tail models are becoming more widely used for exploring the role of mechanical loading on the initiation and progression of intervertebral disc degeneration. Historically, finite element models (FEMs) have been useful for predicting disc mechanics in humans. However, differences in geometry and tissue properties may limit the predictive utility of these models for rodent discs. Clearly, models that are specific for rodent tail discs and accurately simulate the disc’s transient mechanical behavior would serve as important tools for clarifying disc mechanics in these animal models. An FEM was developed based on the structure, geometry, and scale of the mouse tail disc. Importantly, two sources of time-dependent mechanical behavior were incorporated: viscoelasticity of the matrix, and fluid permeation. In addition, a novel strain-dependent swelling pressure was implemented through the introduction of a dilatational stress in nuclear elements. The model was then validated against data from quasi-static tension-compression and compressive creep experiments performed previously using mouse tail discs. Finally, sensitivity analyses were performed in which material parameters of each disc subregion were individually varied. During disc compression, matrix consolidation was observed to occur preferentially at the periphery of the nucleus pulposus. Sensitivity analyses revealed that disc mechanics was greatly influenced by changes in nucleus pulposus material properties, but rather insensitive to variations in any of the endplate properties. Moreover, three key features of the model—nuclear swelling pressure, lamellar collagen viscoelasticity, and interstitial fluid permeation—were found to be critical for accurate simulation of disc mechanics. In particular, collagen viscoelasticity dominated the transient behavior of the disc during the initial $2200s$ of creep loading, while fluid permeation governed disc deformation thereafter. The FEM developed in this study exhibited excellent agreement with transient creep behavior of intact mouse tail motion segments. Notably, the model was able to produce spatial variations in nucleus pulposus matrix consolidation that are consistent with previous observations in nuclear cell morphology made in mouse discs using confocal microscopy. Results of this study emphasize the need for including nucleus swelling pressure, collagen viscoelasticity, and fluid permeation when simulating transient changes in matrix and fluid stress/strain. Sensitivity analyses suggest that further characterization of nucleus pulposus material properties should be pursued, due to its significance in steady-state and transient disc mechanical response.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(7):1168-1175. doi:10.1115/1.2073587.

The effects of frequency or duration of cyclic stress on the mechanical properties of collagen fascicles were studied by means of in vitro tissue culture experiments. Collagen fascicles of approximately $300μm$ in diameter were obtained from rabbit patellar tendons. During culture, cyclic stress having the peak stress of approximately $2MPa$ was applied to the fascicles at $1Hz$ for $1hour∕day$ ($1Hz-1h$ group), at $1Hz$ for $4hours∕day$ ($1Hz-4h$ group), or at $4Hz$ for $1hour∕day$ ($4Hz-1h$ group). The frequency of $4Hz$ and the duration of $1hour∕day$ are considered to be similar to those of the in vivo stress applied to fascicles in the intact rabbit patellar tendon. After culture for 1 or $2weeks$, the mechanical properties of the fascicles were determined using a micro-tensile tester, and were compared to the properties of non-cultured, fresh fascicles (control group) and the fascicles cultured under no load condition (non-loaded group). The tangent modulus and tensile strength of fascicles in the $4Hz-1h$ group were similar to those in the control group; however, the fascicles of the $1Hz-1h$ and $1Hz-4h$ groups had significantly lower values than those of the control group. There was no significant difference in the tensile strength between the $1Hz-1h$ and non-loaded groups, although the strength in the $1Hz-4h$ group was significantly higher than that of the non-loaded group. It was concluded that the frequency and duration of cyclic stress significantly affect the mechanical properties of cultured collagen fascicles. If we apply cyclic stress having the frequency and duration which are experienced in vivo, the biomechanical properties are maintained at control, normal level. Lower frequencies or less cycles of applied force induce adverse effects.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(7):1176-1184. doi:10.1115/1.2073487.

In order to function in vivo, tissue engineered blood vessels (TEBVs) must encumber pulsatile blood flow and withstand hemodynamic pressures for long periods of time. To date TEBV mechanical assessment has typically relied on single time point burst and/or uniaxial tensile testing to gauge the strengths of the constructs. This study extends this analysis to include creep and stepwise stress relaxation viscoelastic testing methodologies. TEBV models exhibiting diverse mechanical behaviors as a result of different architectures ranging from reconstituted collagen gels to hybrid constructs reinforced with either untreated or glutaraldhyde-crosslinked collagen supports were evaluated after 8 and 23 days of in vitro culturing. Data were modeled using three and four-parameter linear viscoelastic mathematical representations and compared to porcine carotid arteries. While glutaraldhyde-treated hybrid TEBVs exhibited the largest overall strengths and toughness, uncrosslinked hybrid samples exhibited time-dependent behaviors most similar to native arteries. These findings emphasize the importance of viscoelastic characterization when evaluating the mechanical performance of TEBVs. Limits of testing methods and modeling systems are presented and discussed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(7):1185-1194. doi:10.1115/1.2073668.

Background: Atherosclerotic plaques may rupture without warning and cause acute cardiovascular syndromes such as heart attack and stroke. Methods to assess plaque vulnerability noninvasively and predict possible plaque rupture are urgently needed. Method: MRI-based three-dimensional unsteady models for human atherosclerotic plaques with multi-component plaque structure and fluid-structure interactions are introduced to perform mechanical analysis for human atherosclerotic plaques. Results: Stress variations on critical sites such as a thin cap in the plaque can be 300% higher than that at other normal sites. Large calcification block considerably changes stress/strain distributions. Stiffness variations of plaque components (50% reduction or 100% increase) may affect maximal stress values by 20–50 %. Plaque cap erosion causes almost no change on maximal stress level at the cap, but leads to 50% increase in maximal strain value. Conclusions: Effects caused by atherosclerotic plaque structure, cap thickness and erosion, material properties, and pulsating pressure conditions on stress/strain distributions in the plaque are quantified by extensive computational case studies and parameter evaluations. Computational mechanical analysis has good potential to improve accuracy of plaque vulnerability assessment.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(7):1195-1207. doi:10.1115/1.2073677.

The assessment of regional heart wall motion (local strain) can localize ischemic myocardial disease, evaluate myocardial viability, and identify impaired cardiac function due to hypertrophic or dilated cardiomyopathies. The objectives of this research were to develop and validate a technique known as hyperelastic warping for the measurement of local strains in the left ventricle from clinical cine-magnetic resonance imaging (MRI) image datasets. The technique uses differences in image intensities between template (reference) and target (loaded) image datasets to generate a body force that deforms a finite element (FE) representation of the template so that it registers with the target image. To validate the technique, MRI image datasets representing two deformation states of a left ventricle were created such that the deformation map between the states represented in the images was known. A beginning diastolic cine-MRI image dataset from a normal human subject was defined as the template. A second image dataset (target) was created by mapping the template image using the deformation results obtained from a forward FE model of diastolic filling. Fiber stretch and strain predictions from hyperelastic warping showed good agreement with those of the forward solution ($R2=0.67$ stretch, $R2=0.76$ circumferential strain, $R2=0.75$ radial strain, and $R2=0.70$ in-plane shear). The technique had low sensitivity to changes in material parameters ($ΔR2=−0.023$ fiber stretch, $ΔR2=−0.020$ circumferential strain, $ΔR2=−0.005$ radial strain, and $ΔR2=0.0125$ shear strain with little or no change in rms error), with the exception of changes in bulk modulus of the material. The use of an isotropic hyperelastic constitutive model in the warping analyses degraded the predictions of fiber stretch. Results were unaffected by simulated noise down to a signal-to-noise ratio (SNR) of 4.0 ($ΔR2=−0.032$ fiber stretch, $ΔR2=−0.023$ circumferential strain, $ΔR2=−0.04$ radial strain, and $ΔR2=0.0211$ shear strain with little or no increase in rms error). This study demonstrates that warping in conjunction with cine-MRI imaging can be used to determine local ventricular strains during diastole.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Other

J Biomech Eng. 2005;127(7):1208-1215. doi:10.1115/1.2073647.

Atomic force microscopy (AFM) has been widely used for measuring mechanical properties of biological specimens such as cells, DNA, and proteins. This is usually done by monitoring deformations in response to controlled applied forces, which have to be at ultralow levels due to the extreme softness of the specimens. Consequently, such experiments may be susceptible to thermal excitations, manifested as force and displacement fluctuations that could reduce the measurement accuracy. To take advantage of, rather than to be limited by, such fluctuations, we have characterized the thermomechanical responses of an arbitrarily shaped AFM cantilever with the tip coupled to an elastic spring. Our analysis shows that the cantilever and the specimen behave as springs in parallel. This provides a method for determining the elasticity of the specimen by measuring the change in the tip fluctuations in the presence and absence of coupling. For rectangular and V-shaped cantilevers, we have derived a relationship between the mean-square deflection and the mean-square inclination and an approximate expression for the specimen spring constant in terms of contributions to the mean-square inclination from the first few vibration modes.

Commentary by Dr. Valentin Fuster

### TECHNICAL BRIEF

J Biomech Eng. 2005;127(7):1216-1221. doi:10.1115/1.2073676.