Mitral stenosis with posterior diastolic movement of posterior leaflet.

The echocardiographic diagnosis of mitral stenosis depends in part on the demonstration of abnormal posterior leaflet movement to distinguish it from other conditions that similarly affect anterior leaflet motion. In mitral stenosis the posterior leaflet has been shown to move anteriorly in diastole rather than in the normal posterior direction. A patient presented with clinical evidence of moderate mitral stenosis. The anterior leaflet echo was typical but the posterior leaflet showed posterior diastolic movement. At catheterization moderate mitral stenosis was confirmed. To our knowledge this is the first report of the echocardiographic demonstration of posterior diastolic movement of the posterior mitral leaflet in documented mitral stenosis.     

Material properties of the ovine mitral valve anterior leaflet in vivo from inverse finite element analysis

We measured leaflet displacements and used inverse finite-element analysis to define, for the first time, the material properties of mitral valve (MV) leaflets in vivo. Sixteen miniature radiopaque markers were sewn to the MV annulus, 16 to the anterior MV leaflet, and 1 on each papillary muscle tip in 17 sheep. Four-dimensional coordinates were obtained from biplane videofluoroscopic marker images (60 frames/s) during three complete cardiac cycles. A finite-element model of the anterior MV leaflet was developed using marker coordinates at the end of isovolumic relaxation (IVR; when the pressure difference across the valve is approximately 0), as the minimum stress reference state. Leaflet displacements were simulated during IVR using measured left ventricular and atrial pressures. The leaflet shear modulus (G(circ-rad)) and elastic moduli in both the commisure-commisure (E(circ)) and radial (E(rad)) directions were obtained using the method of feasible directions to minimize the difference between simulated and measured displacements. Group mean (+/-SD) values (17 animals, 3 heartbeats each, i.e., 51 cardiac cycles) were as follows: G(circ-rad) = 121 +/- 22 N/mm2, E(circ) = 43 +/- 18 N/mm2, and E(rad) = 11 +/- 3 N/mm2 (E(circ) > E(rad), P < 0.01). These values, much greater than those previously reported from in vitro studies, may result from activated neurally controlled contractile tissue within the leaflet that is inactive in excised tissues. This could have important implications, not only to our understanding of mitral valve physiology in the beating heart but for providing additional information to aid the development of more durable tissue-engineered bioprosthetic valves.     

Measuring and modeling patient-specific distributions of material properties in abdominal aortic aneurysm wall

Both the clinically established diameter criterion and novel approaches of computational finite element (FE) analyses for rupture risk stratification of abdominal aortic aneurysms (AAA) are based on assumptions of population-averaged, uniform material properties for the AAA wall. The presence of inter-patient and intra-patient variations in material properties is known, but has so far not been addressed sufficiently. In order to enable the preoperative estimation of patient-specific AAA wall properties in the future, we investigated the relationship between non-invasively assessable clinical parameters and experimentally measured AAA wall properties. We harvested n = 163 AAA wall specimens (n = 50 patients) during open surgery and recorded the exact excision sites. Specimens were tested for their thickness, elastic properties, and failure loads using uniaxial tensile tests. In addition, 43 non-invasively assessable patient-specific or specimen-specific parameters were obtained from recordings made during surgery and patient charts. Experimental results were correlated with the non-invasively assessable parameters and simple regression models were created to mathematically describe the relationships. Wall thickness was most significantly correlated with the metabolic activity at the excision site assessed by PET/CT (ρ = 0.499, P = 4 × 10^?7) and to thrombocyte counts from laboratory blood analyses (ρ = 0.445, P = 3 × 10^?9). Wall thickness was increased in patients suffering from diabetes mellitus, while it was significantly thinner in patients suffering from chronic kidney disease (CKD). Elastic AAA wall properties had significant correlations with the metabolic activity at the excision site (PET/CT), with existent calcifications, and with the diameter of the non-dilated aorta proximal to the AAA. Failure properties (wall strength and failure tension) had correlations with the patient’s medical history and with results from laboratory blood analyses. Interestingly, AAA wall failure tension was significantly reduced for patients with CKD and elevated blood levels of potassium and urea, respectively, both of which are associated with kidney disease. This study is a first step to a future preoperative estimation of AAA wall properties. Results can be conveyed to both the diameter criterion and FE analyses to refine rupture risk prediction. The fact that AAA wall from patients suffering from CKD featured reduced failure tension implies an increased AAA rupture risk for this patient group at comparably smaller AAA diameters.     

Consistent trilayer biomechanical modeling of aortic valve leaflet tissue

Aortic valve tissue exhibits highly nonlinear, anisotropic, and heterogeneous material behavior due to its complex microstructure. A thorough understanding of these characteristics permits us to develop numerical models that can shed insight on the function of the aortic valve in health and disease. Herein, we take a closer look at consistently capturing the observed physical response of aortic valve tissue in a continuum mechanics framework. Such a treatment is the first step in developing comprehensive multiscale and multiphysics models.We highlight two important aspects of aortic valve tissue behavior: the role of the collagen fiber microstructure and the native prestressing. We propose a model that captures these two features as well as the heterogeneous layer-scale topology of the tissue. We find the model can reproduce the experimentally observed multiscale mechanical behavior in a manner that provides intuition on the underlying mechanics.     

In vivo fatigue microcracks in human bone: material properties of the surrounding bone matrix

Human bones sustain fatigue damage in the form of in vivo microcracks as a result of the normal everyday loading activities. These microcracks appear to preferentially accumulate in certain regions of bone and most notably in interstitial bone matrix areas. These are remnants of old bone tissue left unremodelled, which show a higher than average mineral content and consequently the occurrence of microcracks has been attributed to the possible brittleness brought about by such hypermineralisation. There is a need, therefore, for information on the in situ bone matrix properties in the vicinity of such in vivo microcracks to elucidate the possible causes of their appearance. The present study examined the elastic, strain rate (viscous) and plastic properties of bone matrix in selectively targeted areas by nanoindentation and in both quasistatic and dynamic mode. The results showed that in vivo crack areas are not as stiff as some well-known extremely mineralised and brittle bone examples (bulla, rostrum); the strain rate effects of crack regions were identical to those of other regions of human bone and agreed well with values collected for human bone in the past at the macroscale; while the plasticity index of the crack regions was also not statistically different from most bone examples (including human at random, bovine, bulla and rostrum) except antler, which showed lower plasticity and thus a greater fraction of elastic recovery in indentation energy. It is difficult, therefore, to explain the susceptibility of these interstitial regions to crack in terms of the mineral content and its after-effects on elasticity, viscosity and plasticity alone, but one need to attribute the cracks to the cumulative loading history of these areas, or raise the suggestion that these areas of bone matrix are in some measure 'aged' or material/quality defective.     

A combined experimental and computational study on the material properties of shape memory polyurethane

A type of shape memory polyurethane with 60 wt% hard segments (SMPU60) was prepared. Its material properties were tested by dynamic mechanical analysis (DMA) and Instron, and simulated using fully atomistic molecular dynamics (MD). The glass transition temperature (T _g) of SMPU60 determined by DMA is 316 K, which is slightly lower than that estimated through MD simulations (T _g = 328 K) , showing the calculated T _g is in good agreement with experimental data. A complex hydrogen bonding network was revealed with the calculation of radial distribution functions (RDFs). The C═O⋯H bond is the predominant hydrogen-bonding interaction. With increasing temperature, both the hydrogen bonding and the moduli decreased, and the dissociation of intermolecular hydrogen bonding induced the decrease of the moduli.     

Identification of in vivo material and geometric parameters of a human aorta: toward patient-specific modeling of abdominal aortic aneurysm

Recent advances in computational modeling of vascular adaptations and the need for their extension to patient-specific modeling have introduced new challenges to the path toward abdominal aortic aneurysm modeling. First, the fundamental assumption in adaptation models, namely the existence of vascular homeostasis in normal vessels, is not easy to implement in a vessel model built from medical images. Second, subjecting the vessel wall model to the normal pressure often makes the configuration deviate from the original geometry obtained from medical images. To address those technical challenges, in this work, we propose a two-step optimization approach; first, we estimate constitutive parameters of a healthy human aorta intrinsic to the material by using biaxial test data and a weighted nonlinear least-squares parameter estimation method; second, we estimate the distributions of wall thickness and anisotropy using a 2-D parameterization of the vessel wall surface and a global approximation scheme integrated within an optimization routine. A direct search method is implemented to solve the optimization problem. The numerical optimization method results in a considerable improvement in both satisfying homeostatic condition and minimizing the deviation of geometry from the original shape based on in vivo images. Finally, the utility of the proposed technique for patient-specific modeling is demonstrated in a simulation of an abdominal aortic aneurysm enlargement.     

Mechanical properties of anterior malleolar ligament from experimental measurement and material modeling analysis

In this paper, mechanical properties of the anterior malleolar ligament (AML) of human middle ear were studied through the uniaxial tensile, stress relaxation and failure tests. The digital image correlation (DIC) method was used to assess the boundary effect in experiments and calculate the strain on specimens. The constitutive behavior of the AML was described by a transversely isotropic hyperelastic model which consists of a first-order Ogden model augmented by a I (4)-type reinforcing term. The material parameters of the model were estimated and the viscoelasticity of the AML was illustrated by hysteresis phenomena and stress relaxation function. The mechanical strength of the AML was obtained through the failure test and the mean ultimate stress and stretch ratio were measured as 1.05 MPa and 1.51, respectively. Finally, a linear Young's modulus-stress relationship of the AML was derived based on constitutive equation of the AML within a stress range of 0-0.5 MPa.     

Development of an in vivo method for determining material properties of passive myocardium

Calculation of mechanical stresses and strains in the left ventricular (LV) myocardium by the finite element (FE) method relies on adequate knowledge of the material properties of myocardial tissue. In this paper, we present a model-based estimation procedure to characterize the stress-strain relationship in passive LV myocardium. A 3D FE model of the LV myocardium was used, which included morphological fiber and sheet structure and a nonlinear orthotropic constitutive law with different stiffness in the fiber, sheet, and sheet-normal directions. The estimation method was based on measured wall strains. We analyzed the method's ability to estimate the material parameters by generating a set of synthetic strain data by simulating the LV inflation phase with known material parameters. In this way we were able to verify the correctness of the solution and to analyze the effects of measurement and model error on the solution accuracy and stability. A sensitivity analysis was performed to investigate the observability of the material parameters and to determine which parameters to estimate. The results showed a high degree of coupling between the parameters governing the stiffness in each direction. Thus, only one parameter in each of the three directions was estimated. For the tested magnitudes of added noise and introduced model errors, the resulting estimated stress-strain characteristics in the fiber and sheet directions converged with good accuracy to the known relationship. The sheet-normal stress-strain relationship had a higher degree of uncertainty as more noise was added and model error was introduced.     

Statistical shape modeling characterizes three-dimensional shape and alignment variability in the lumbar spine

The mechanics of the lumbar spine are heavily dependent on the underlying anatomy. Anatomical measures are used to assess the progression of pathologies related to low back pain and to screen patients for surgical treatment options. To describe anatomical norms and pathological differences for the population, statistical shape modeling, which uses full three-dimensional representations of bone morphology and relative alignment, can capture intersubject variability and enable comparative evaluations of subject to population. Accordingly, the objective of this study was to develop a comprehensive set of three-dimensional statistical models to characterize anatomical variability in the lumbar spine, by specifically describing the shape of individual vertebrae, and shape and alignment of the entire lumbar spine (L1-S1), with a focus on the L4-L5 and L5-S1 functional spinal units (FSU). Using CT scans for a cohort of 52 patients, lumbar spine geometries were registered to a template to establish correspondence and a principal component analysis identified the primary modes of variation. Scaling was the most prevalent mode of variation for all models. Subsequent modes of the statistical shape models of the individual bones characterized shape variation within the processes. Subsequent modes of variation for the FSU and entire spine models described alignment changes associated with disc height and lordosis. Quantification of anatomical variation in the spine with statistical models can inform implant design and sizing, assist clinicians in diagnosing pathologies, screen patients for treatment options, and support pre-operative planning.     

An inverse modeling approach for semilunar heart valve leaflet mechanics: exploitation of tissue structure

Determining the biomechanical behavior of heart valve leaflet tissues in a noninvasive manner remains an important clinical goal. While advances in 3D imaging modalities have made in vivo valve geometric data available, optimal methods to exploit such information in order to obtain functional information remain to be established. Herein we present and evaluate a novel leaflet shape-based framework to estimate the biomechanical behavior of heart valves from surface deformations by exploiting tissue structure. We determined accuracy levels using an “ideal” in vitro dataset, in which the leaflet geometry, strains, mechanical behavior, and fibrous structure were known to a high level of precision. By utilizing a simplified structural model for the leaflet mechanical behavior, we were able to limit the number of parameters to be determined per leaflet to only two. This approach allowed us to dramatically reduce the computational time and easily visualize the cost function to guide the minimization process. We determined that the image resolution and the number of available imaging frames were important components in the accuracy of our framework. Furthermore, our results suggest that it is possible to detect differences in fiber structure using our framework, thus allowing an opportunity to diagnose asymptomatic valve diseases and begin treatment at their early stages. Lastly, we observed good agreement of the final resulting stress–strain response when an averaged fiber architecture was used. This suggests that population-averaged fiber structural data may be sufficient for the application of the present framework to in vivo studies, although clearly much work remains to extend the present approach to in vivo problems.     

Conformon-driven biopolymer shape changes in cell modeling

Conceptual models of the atom preceded the mathematical model of the hydrogen atom in physics in the second decade of the 20th century. The computer modeling of the living cell in the 21st century may follow a similar course of development. A conceptual model of the cell called the Bhopalator was formulated in the mid-1980s, along with its twin theories known as the conformon theory of molecular machines and the cell language theory of biopolymer interactions [Ann. N.Y. Acad. Sci. 227 (1974) 211; BioSystems 44 (1997) 17; Ann. N.Y. Acad. Sci. 870 (1999a) 411; BioSystems 54 (2000) 107; Semiotica 138 (1-4) (2002a) 15; Fundamenta Informaticae 49 (2002b) 147]. The conformon theory accounts for the reversible actions of individual biopolymers coupled to irreversible chemical reactions, while the cell language theory provides a theoretical framework for understanding the complex networks of dynamic interactions among biopolymers in the cell. These two theories are reviewed and further elaborated for the benefit of both computational biologists and computer scientists who are interested in modeling the living cell and its functions. One of the critical components of the mechanisms of cell communication and cell computing has been postulated to be space- and time-organized teleonomic (i.e. goal-directed) shape changes of biopolymers that are driven by exergonic (free energy-releasing) chemical reactions. The generalized Franck-Condon principle is suggested to be essential in resolving the apparent paradox arising when one attempts to couple endergonic (free energy-requiring) biopolymer shape changes to the exergonic chemical reactions that are catalyzed by biopolymer shape changes themselves. Conformons, defined as sequence-specific mechanical strains of biopolymers first invoked three decades ago to account for energy coupling in mitochondria, have been identified as shape changers, the agents that cause shape changes in biopolymers. Given a set of space- and time-organized teleonomic shape changes of biopolymers driven by conformons, all of the functions of the cell can be accounted for in molecular terms-at least in principle. To convert a conceptual model of the cell into a computer model, it is necessary to represent the conceptual model in an algebraic language. To this end, we have begun to apply the process algebra of Milner [Communicating and Mobile Systems: The pi-calculus, Cambridge University Press, Cambridge, 1999] to develop what is here called the "shape algebra," capable of describing complex and mobile patterns of interactions among biomolecules leading to cell functions.     

In vivo dynamic strains of the ovine anterior mitral valve leaflet

Understanding the mechanics of the mitral valve is crucial in terms of designing and evaluating medical devices and techniques for mitral valve repair. In the current study we characterize the in vivo strains of the anterior mitral valve leaflet. On cardiopulmonary bypass, we sew miniature markers onto the leaflets of 57 sheep. During the cardiac cycle, the coordinates of these markers are recorded via biplane fluoroscopy. From the resulting four-dimensional data sets, we calculate areal, maximum principal, circumferential, and radial leaflet strains and display their profiles on the averaged leaflet geometry. Average peak areal strains are 13.8±6.3%, maximum principal strains are 13.0±4.7%, circumferential strains are 5.0±2.7%, and radial strains are 7.8±4.3%. Maximum principal strains are largest in the belly region, where they are aligned with the circumferential direction during diastole switching into the radial direction during systole. Circumferential strains are concentrated at the distal portion of the belly region close to the free edge of the leaflet, while radial strains are highest in the center of the leaflet, stretching from the posterior to the anterior commissure. In summary, leaflet strains display significant temporal, regional, and directional variations with largest values inside the belly region and toward the free edge. Characterizing strain distribution profiles might be of particular clinical significance when optimizing mitral valve repair techniques in terms of forces on suture lines and on medical devices.     

Joint modeling of cell and nuclear shape variation

Modeling cell shape variation is critical to our understanding of cell biology. Previous work has demonstrated the utility of nonrigid image registration methods for the construction of nonparametric nuclear shape models in which pairwise deformation distances are measured between all shapes and are embedded into a low-dimensional shape space. Using these methods, we explore the relationship between cell shape and nuclear shape. We find that these are frequently dependent on each other and use this as the motivation for the development of combined cell and nuclear shape space models, extending nonparametric cell representations to multiple-component three-dimensional cellular shapes and identifying modes of joint shape variation. We learn a first-order dynamics model to predict cell and nuclear shapes, given shapes at a previous time point. We use this to determine the effects of endogenous protein tags or drugs on the shape dynamics of cell lines and show that tagged C1QBP reduces the correlation between cell and nuclear shape. To reduce the computational cost of learning these models, we demonstrate the ability to reconstruct shape spaces using a fraction of computed pairwise distances. The open-source tools provide a powerful basis for future studies of the molecular basis of cell organization.     

Ablation of mitral annular and leaflet muscle: effects on annular and leaflet dynamics

Mitral annular (MA) and leaflet three-dimensional (3-D) dynamics were examined after circumferential phenol ablation of the MA and anterior mitral leaflet (AML) muscle. Radiopaque markers were sutured to the left ventricle, MA, and both mitral leaflets in 18 sheep. In 10 sheep, phenol was applied circumferentially to the atrial surface of the mitral annulus and the hinge region of the AML, whereas 8 sheep served as controls. Animals were studied with biplane video fluoroscopy for computation of 3-D mitral annular area (MAA) and leaflet shape. MAA contraction (MAACont) was determined from maximum to minimum value. Presystolic MAA (PS-MAACont) reduction was calculated as the percentage of total reduction occurring before end diastole. Phenol ablation decreased PS-MAACont (72 +/- 6 vs. 47 +/- 31%, P = 0.04) and delayed valve closure (31 +/- 11 vs. 57 +/- 25 ms, P = 0.017). In control, the AML had a compound sigmoid shape; after phenol, this shape was entirely concave to the atrium during valve closure. These data indicate that myocardial fibers on the atrial side of the valve influence the 3-D dynamic geometry and shape of the MA and AML.     

Simulation of long-term fatigue damage in bioprosthetic heart valves: effects of leaflet and stent elastic properties

One of the major failure modes of bioprosthetic heart valves (BHVs) is noncalcific structural deterioration due to fatigue of the tissue leaflets; yet, the mechanisms of fatigue are not well understood. BHV durability is primarily assessed based on visual inspection of the leaflets following accelerated wear testing. In this study, we developed a computational framework to simulate BHV leaflet fatigue, which is both efficient and quantitative, making it an attractive alternative to traditional accelerated wear testing. We utilize a phenomenological soft tissue fatigue damage model developed previously to describe the stress softening and permanent set of the glutaraldehyde-treated bovine pericardium leaflets in BHVs subjected to cyclic loading. A parametric study was conducted to determine the effects of altered leaflet and stent elastic properties on the fatigue of the leaflets. The simulation results show that heterogeneity of the leaflet elastic properties, poor leaflet coaptation, and little stent-tip deflection may accelerate leaflet fatigue, which agrees with clinical findings. Therefore, the developed framework may be an invaluable tool for evaluating leaflet durability in new tissue valve designs, including traditional BHVs as well as new transcatheter valves.     

Constitutive material modeling of cell: a micromechanics approach

The variations in mechanical properties of cells obtained from experimental and theoretical studies can be overcome only through the development of a sound mathematical framework correlating the derived mechanical property with the cellular structure. Such a formulation accounting for the inhomogeneity of the cytoplasm due to stress fibers and actin cortex is developed in this work. The proposed model is developed using the Mori-Tanaka method of homogenization by treating the cell as a fiber-reinforced composite medium satisfying the continuum hypothesis. The validation of the constitutive model using finite element analysis on atomic force microscopy (AFM) and magnetic twisting cytometry (MTC) has been carried out and is found to yield good correlation with reported experimental results. It is observed from the study that as the volume fraction of the stress fiber increases, the stiffness of the cell increases and it alters the force displacement behavior for the AFM and MTC experiments. Through this model, we have also been able to find the stress fiber as a likely cause of the differences in the derived mechanical property from the AFM and MTC experiments. The correlation of the mechanical behavior of the cell with the cell composition, as obtained through this study, is an important observation in cell mechanics.     

Superquadric modeling of cranial and cerebral shape and asymmetry

A new method for quantifying cranial and cerebral shape and asymmetry fits symmetric superquadric geometric models to three-dimensional coordinate measurements. Asymmetry is quantified as radial residuals of the surface data points from their best-fit superquadric models. Twenty human crania, 10 magnetic resonance imaging (MRI) exocranial surfaces, and 10 corresponding MRI cerebral surfaces as well as two infant head casts were digitized and modeled using superquadrics. Superquadric parameters have simple geometric interpretation, are very reproducible, and demonstrated statistically significant differences between crania of Amerindian ancestry and MRI exocranial surfaces of European ancestry used in this study. Superquadric models demonstrated strong congruence between MRI exocranial and cerebral surfaces. Typical asymmetry was 1-5 mm. Lastly, polar contour plots of radial residuals for head casts before and after orthotic cranioplasty demonstrated the efficacy of using superquadrics to quantify positional plagiocephaly and synostosis of infant crania.     

IVUS-based computational modeling and planar biaxial artery material properties for human coronary plaque vulnerability assessment

Image-based computational modeling has been introduced for vulnerable atherosclerotic plaques to identify critical mechanical conditions which may be used for better plaque assessment and rupture predictions. In vivo patient-specific coronary plaque models are lagging due to limitations on non-invasive image resolution, flow data, and vessel material properties. A framework is proposed to combine intravascular ultrasound (IVUS) imaging, biaxial mechanical testing and computational modeling with fluid-structure interactions and anisotropic material properties to acquire better and more complete plaque data and make more accurate plaque vulnerability assessment and predictions. Impact of pre-shrink-stretch process, vessel curvature and high blood pressure on stress, strain, flow velocity and flow maximum principal shear stress was investigated.     

Human annulus fibrosus material properties from biaxial testing and constitutive modeling are altered with degeneration

The annulus fibrosus (AF) of the intervertebral disk undergoes large and multidirectional stresses and strains. Uniaxial tensile tests are limited for measuring AF material properties, because freely contracting edges can prevent fiber stretch and are not representative of in situ boundary conditions. The objectives of this study were to measure human AF biaxial tensile mechanics and to apply and validate a constitutive model to determine material properties. Biaxial tensile tests were performed on samples oriented along the circumferential–axial and the radial–axial directions. Data were fit to a structurally motivated anisotropic hyperelastic model composed of isotropic extra-fibrillar matrix, nonlinear fibers, and fiber–matrix interactions (FMI) normal to the fibers. The validated model was used to simulate shear and uniaxial tensile behavior, to investigate AF structure–function, and to quantify the effect of degeneration. The biaxial stress–strain response was described well by the model (R ²?>?0.9). The model showed that the parameters for fiber nonlinearity and the normal FMI correlated with degeneration, resulting in an elongated toe-region and lower stiffness with degeneration. The model simulations in shear and uniaxial tension successfully matched previously published circumferential direction Young’s modulus, provided an explanation for the low values in previously published axial direction Young’s modulus, and was able to simulate shear mechanics. The normal FMI were important contributors to stress and changed with degeneration, therefore, their microstructural and compositional source should be investigated. Finally, the biaxial mechanical data and constitutive model can be incorporated into a disk finite element model to provide improved quantification of disk mechanics.