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Left ventricle and left atrium are and have been practically always analyzed separately in common clinically and non-clinically oriented cardiovascular investigations. Both classic and speckle tracking echocardiographic data contributed to the knowledge about deformational impairments occurring in systo-diastolic differences. Recently new trajectory based approaches allowed a greater awareness about the entire left ventricle or left atrium revolution and on their deficiencies that take place in presence of hypertrophic cardiomyopathy. However, surprisingly, the concomitant function of the two left heart chambers has not been analyzed for their geometrical/mechanical relationship. For the first time we study here, by acquiring left ventricle and left atrial geometries on the same heartbeat, the trajectory attributes of the entire left heart treated as a whole shape and the shape covariation of its two subunits. We contrasted healthy subjects with patients affected by hypertrophic cardiomyopathy. We found impaired left heart trajectory mainly in terms of orientation and size. More importantly, we found profound differences in the direction of morphological covariation of left ventricle and left atrium. These findings open to new perspectives in pathophysiological evaluation of different diseases by allowing the appreciation of concomitant functioning of both left heart whole geometry and of its two chambers.

The controversy between passive and active ventricular filling has been debated for decades and the question about the existence of an active diastole remains open. In this work, we advocate the model of active diastole by considering the heart as a suction pump and we add some more clues to support this point of view by the analysis of the pressure-volume (PV) loops of the left heart, comprising of the left ventricle (LV) and atrium (LA). Our working hypothesis is based on the dichotomy motor-brake: the cardiac muscle can act as a motor, when shortening against a load, or as a brake, when lengthening to a load. We discuss our hypothesis by means of a lumped model of the left heart, where both chambers are considered as hollow spherical shells. The notion of active stretch, introduced to describe the contractile behavior of the muscle fibers, plays a major role in our model. Then, the contraction of the muscle is related to the pressure and volume of the chamber through a nonlinear hyperelastic energy density function. Despite its simplicity, the model enlightens some important features of the LV-LA coupling and of the pumping function of the heart. Based on experimental PV data of the left heart of a normal human subject, it is shown that the contraction patterns of the LV and LA are synchronized with each other and have distinguishing features in each phase of the cardiac cycle. These results highlight the interplay between the two chambers and support the idea that the heart may act as a suction pump functioning in turn as a motor or a brake in order to meet specific demands in each phase of the cardiac cycle.

Statistical shape modeling is a powerful tool for visualizing and quantifying geometric and functional patterns of the heart. After myocardial infarction (MI), the left ventricle typically remodels in response to physiological challenges. Several methods have been proposed in the literature to describe statistical shape changes. Which method best characterizes the left ventricular remodeling after MI is an open research question. A better descriptor of remodeling is expected to provide a more accurate evaluation of disease status in MI patients. We therefore designed a challenge to test shape characterization in MI given a set of three-dimensional left ventricular surface points. The training set comprised 100 MI patients, and 100 asymptomatic volunteers (AV). The challenge was initiated in 2015 at the Statistical Atlases and Computational Models of the Heart workshop, in conjunction with the MICCAI conference. The training set with labels was provided to participants, who were asked to submit the likelihood of MI from a different (validation) set of 200 cases (100 AV and 100 MI). Sensitivity, specificity, accuracy, and area under the receiver operating characteristic curve were used as the outcome measures. The goals of this challenge were to 1) establish a common dataset for evaluating statistical shape modeling algorithms in MI, and 2) test whether statistical shape modeling provides additional information characterizing MI patients over standard clinical measures. Eleven groups with a wide variety of classification and feature extraction approaches participated in this challenge. All methods achieved excellent classification results with accuracy ranges from 0.83 to 0.98. The areas under the receiver operating characteristic curves were all above 0.90. Four methods showed significantly higher performance than standard clinical measures. The dataset and software for evaluation are available from the Cardiac Atlas Project website. 1 1 http://www.cardiacatlas.org .

A mechanics–based analysis of data from three–dimensional speckle tracking echocardiography is proposed, aimed at investigating deformations in myocardium and at assessing shape and function of distinct strain lines corresponding to the principal strain lines of the cardiac tissue. The analysis is based on the application of a protocol of measurement of the endocardial and epicardial principal strain lines, which was already tested on simulated left ventricles. In contrast with similar studies, it is established that endocardial principal strain lines cannot be identified with any structural fibers, not even along the systolic phase and is suggested that it is due to the capacity of the endocardial surface to contrast the dilation of the left ventricle. A mechanics-based analysis of data from three-dimensional speckle tracking echocardiography is proposed, aimed at investigating deformations in myocardium and at assessing shape and function of distinct strain lines corresponding to the principal strain lines of the cardiac tissue. The analysis is based on the application of a protocol of measurement of the endocardial and epicardial principal strain lines, which was already tested on simulated left ventricles. In contrast with similar studies, it is established that endocardial principal strain lines cannot be identified with any structural fibers, not even along the systolic phase and is suggested that it is due to the capacity of the endocardial surface to contrast the dilation of the left ventricle.

The heart is a specialized muscle acting as the body’s circulatory pump. The effectiveness of the pumping action is commonly assessed through different measurements; among the most important are th...

We aim at coupling the theory of swelling, describing the effects of solvent uptake in polymeric solids, with that of growing, describing the change of the relaxed state in a continuum body. Basing on the hypotheses underlying the two theories, and using some key principles of continuum mechanics, we develop a chemo-mechanical model which describes the combined effects of swelling and growing in solids.

We present and discuss a method to infer noninvasively information on the fibre architecture in real human left ventricle walls. The method post-processes the echocardiographic data acquired by three-dimensional speckle tracking echocardiography through a MatLab-based protocol, already presented, discussed and validated. Our results indicate the difference between the role of endocardial and epicardial principal strain lines, at the systolic peak, and set the bases for possible future investigations aimed to analyse the onset of specific cardiac diseases through noninvasive analysis of LV fibre architecture. Moreover, we set a rational statistical analysis to investigate the reliability of the proposed method.

The analysis of full Left Atrium (LA) deformation and whole LA deformational trajectory in time has been poorly investigated and, to the best of our knowledge, seldom discussed in patients with Hypertrophic Cardiomyopathy. Therefore, we considered 22 patients with Hypertrophic Cardiomyopathy (HCM) and 46 healthy subjects, investigated them by three–dimensional Speckle Tracking Echocardiography, and studied the derived landmark clouds via Geometric Morphometrics with Parallel Transport. Trajectory shape and trajectory size were different in Controls versus HCM and their classification powers had high AUC (Area Under the Receiving Operator Characteristic Curve) and accuracy. The two trajectories were much different at the transition between LA conduit and booster pump functions. Full shape and deformation analyses with trajectory analysis enabled a straightforward perception of pathophysiological consequences of HCM condition on LA functioning. It might be worthwhile to apply these techniques to look for novel pathophysiological approaches that may better define atrio–ventricular interaction.

Soft membranes are commonly employed in shape-morphing applications, where the material is programmed to achieve a target shape upon activation by an external trigger, and as coating layers that alter the surface characteristics of bulk materials, such as the properties of spreading and absorption of liquids. In particular, polymer gel membranes experience swelling or shrinking when their solvent content change, and the non-homogeneous swelling field may be exploited to control their shape. Here, we develop a theory of swelling material surfaces to model polymer gel membranes and demonstrate its features by numerically studying applications in the contexts of biomedicine, micro-motility, and coating technology. We also specialize the theory to thermo-responsive gels, which are made of polymers that change their affinity with a solvent when temperature varies.

We investigate the swelling dynamics driven by solvent absorption in a hydrogel sphere immersed in a solvent bath, through a computational model and a numerical study. We extensively describe the transient process from dry to wet and discuss the onset of surface instabilities through a measure of the lack of smoothness of the outer surface and a morphological pattern of that surface with respect to the two material paremeters driving the swelling dynamics.

We present recent investigations on the state of strain in human left ventricle based on the synergy between continuum mechanics and echocardiographic imaging. When data from three-dimensional Speckle Tracking Echocardiography are available, special strain directions can be detected on the epicardial and endocardial surfaces, which are well-known in continuum mechanics as principal strain lines (PSLs), further classified into primary and secondary strain lines. An appropriate investigation on PSLs can help to identify lines where strains are largest as primary and smallest as secondary. As PSLs change when cardiac diseases appear, the challenge is that the analysis may allow for the identification of new indicators of cardiac function.

We describe the anisotropic swelling within the Flory-Rehner thermodynamic model through an extension of the elastic component of the free-energy, which takes into account the oriented hampering of the swelling-induced deformations due to the presence of stiffer fibers. We also characterize the homogeneous free-swelling solutions of the corresponding anisotropic stress-diffusion problem, and discuss an asymptotic approximation of the key equations, which allows us to explicitly derive the anisotropic solution of the problem. We propose a proof-of-concept of our model, realizing thin bilayered gel sheets with layers having different anisotropic structures. In particular, for seedpod-like sheets, we observe and quantitatively measure the helicoid versus ribbon transition determined by the aspect ratio of the composite sheet.

The assessment of left ventricular shape changes during cardiac revolution may be a new step in clinical cardiology to ease early diagnosis and treatment. To quantify these changes, only point registration was adopted and neither Generalized Procrustes Analysis nor Principal Component Analysis were applied as we did previously to study a group of healthy subjects. Here, we extend to patients affected by hypertrophic cardiomyopathy the original approach and preliminarily include genotype positive/phenotype negative individuals to explore the potential that incumbent pathology might also be detected. Using 3D Speckle Tracking Echocardiography, we recorded left ventricular shape of 48 healthy subjects, 24 patients affected by hypertrophic cardiomyopathy and 3 genotype positive/phenotype negative individuals. We then applied Generalized Procrustes Analysis and Principal Component Analysis and inter-individual differences were cleaned by Parallel Transport performed on the tangent space, along the horizontal geodesic, between the per-subject consensuses and the grand mean. Endocardial and epicardial layers were evaluated separately, different from many ecocardiographic applications. Under a common Principal Component Analysis, we then evaluated left ventricle morphological changes (at both layers) explained by first Principal Component scores. Trajectories’ shape and orientation were investigated and contrasted. Logistic regression and Receiver Operating Characteristic curves were used to compare these morphometric indicators with traditional 3D Speckle Tracking Echocardiography global parameters. Geometric morphometrics indicators performed better than 3D Speckle Tracking Echocardiography global parameters in recognizing pathology both in systole and diastole. Genotype positive/phenotype negative individuals clustered with patients affected by hypertrophic cardiomyopathy during diastole, suggesting that incumbent pathology may indeed be foreseen by these methods. Left ventricle deformation in patients affected by hypertrophic cardiomyopathy compared to healthy subjects may be assessed by modern shape analysis better than by traditional 3D Speckle Tracking Echocardiography global parameters. Hypertrophic cardiomyopathy pathophysiology was unveiled in a new manner whereby also diastolic phase abnormalities are evident which is more difficult to investigate by traditional ecocardiographic techniques.

We explored the morphological organization of the skull within Crocodylidae, analyzing functional and phylogenetic interactions between its 2 constituent functional modules: the rostrum and the postrostrum. We used geometric morphometrics to identify localized shape changes, focusing on the differences between the major clades of the crown-group Crocodylia: Alligatoridae and Crocodylidae. We used published bite performance data to correlate rostral function with postrostral morphology. The skull modules appear more integrated within Alligatoridae than within Crocodyliade. Phylogenetic effects on shape variation are more evident in Alligatoridae than in Crocodylidae, where functional parameters concerning the rostral morphology are proportionally more important than phylogeny. Long-snouted species are characterized by low structural performance, which is significantly associated with a reduction of the pterygoid-quadrate cranial nipper, suggesting that the nipper is important for the ingestion of large food items in generalist species. This functional association is coupled with a significant evolutionary allometry at the clade level, while Alligatoridae and Crocodylidae show different degrees of evolutionary allometry for their entire shape and rostrum. The postrostrum is more conservative than the rostrum in terms of morphospace occupation, evolutionary allometry and phylogenetic signal. 2013 International Society of Zoological Sciences, Institute of Zoology/Chinese Academy of Sciences and Wiley Publishing Asia Pty Ltd.

In this paper we are presenting a method for achieving strain analysis of cardiac tissues from 3D ultrasound images. First of all, the left ventricle was segmented by an iterative snake algorithm which exploits the gradient vector flow field estimated from the 3D images. Once the ventricle was segmented, a set of points located on the external surface of the ventricle was selected. The movement of all these points along the entire cardiac cycle was calculated by using speckle tracking techniques based on the minimization of a Sum of Absolute Differences. The strain of all the segments connecting two of the considered points was computed, together with the rotation of the points along the long axis of the ventricle. The method was tested on images acquired from 10 patients: 3 with heart pathologies, 5 healthy subjects, and 2 patients with mild hypertrophy. The segmentation of the left ventricle with iterative methods demonstrated to be able to delineate the external surface of the ventricle in a consistent way. Preliminary results showed the feasibility of characterizing healthy subjects and patients with well-defined heart pathologies by using the outcomes achieved with the strain analysis.

The purpose of the research is to describe the swelling-induced large deformations in polymer gels: a theoretical model is developed, and then implemented and solved using the finite element method. The model is firstly assessed with two well-known bench- mark problems; moreover, the proposed approach is benchmarked against a recent experiment involving localized exposure of the gel boundary to a solvent, where large bending deformations appear during solvent absorption. In both cases, our results are quite satisfying.

The swelling–induced mechanical response of homogeneous anisotropic gels under free conditions and uniaxial loading is investigated. Semi–analytical and numerical analyses show that fibers hamper solvent uptake regardless of their orientation, causing the several changes in shape that occur. Finally, we verified that fibers do not significantly alter relaxation time, which determines the steady state under free–swelling conditions.

We present a simplified heart model with the aim of introducing a mechanical point of view in the interpretation of the pressure–volume loops. In particular, we propose a mechanical description of muscle contraction, and discuss its implications with reference to a specific pressure–volume loop representative of a normal human patient.

We set a twofold investigation: we assess left ventricular (LV) rotation and twist in the human heart through 3D-echocardiographic speckle tracking, and use representative experimental data as benchmark with respect to numerical results obtained by solving our mechanical model of the LV. We aim at new insight into the relationships between myocardial contraction patterns and the overall behavior at the scale of the whole organ. It is concluded that torsional rotation is sensitive to transmural gradients of contractility which is assumed linearly related to action potential duration (APD). Pressure-volume loops and other basic strain measures are not affected by these gradients. Therefore, realistic torsional behavior of human LV may indeed correspond to the electrophysiological and functional differences between endocardial and epicardial cells recently observed in non-failing hearts. Future investigations need now to integrate the mechanical model proposed here with minimal models of human ventricular APD to drive excitation-contraction coupling transmurally.

Implantation of drug eluting stents following percutaneous transluminal angioplasty has revealed a well established technique for treating occlusions caused by the atherosclerotic plaque. However, due to the risk of vascular re-occlusion, other alternative therapeutic strategies of drug delivery are currently being investigated. Polymeric endoluminal pave stenting is an emerging technology for preventing blood erosion and for optimizing drug release. The classical and novel methodologies are compared through a mathematical model able to predict the evolution of the drug concentration in a cross-section of the wall. Though limited to an idealized configuration, the present model is shown to catch most of the relevant aspects of the drug dynamics in a delivery system. Results of numerical simulations shows that a bi-layer gel paved stenting guarantees a uniform drug elution and a prolonged perfusion of the tissues, and remains a promising and effective technique in drug delivery.

Our work aims at modelling and simulating the growth processes that allow the cardiovascular system to adapt to the overall body development and to changing physiological (and pathological) conditions. Within the cardiovascular system, we pay particular attention to the heart and the aorta. A healthy aortic wall succeeds in keeping a homeostatic stress level in spite of long-standing alterations in pressure or flow by triggering growth and remodelling processes that change its stress-free shape and its structure. A normal heart grows in response to the gradually increasing haemodynamic loading exerted on myocardial fibres. Postnatal cardiac growth is a form of volume-overload hypertrophy, produced essentially by a progressive myocardial cell enlargement, with no cell proliferation involved. In our continuum model, growth is basically conceived of as the time evolution of the stress-free configuration of the tiny fragments into which the modelled tissue may be subdivided in imagination. It is governed by a novel balance law—the balance of accretive couples—independent of, but constitutively coupled with, the standard balance of forces.

The aim of this study is to investigate human left ventricular heart morphological changes in time among 17 healthy subjects. Preliminarily, 2 patients with volumetric overload due to aortic insufficiency were added to our analyses. We propose a special strategy to compare the shape, orientation and size of cardiac cycle's morphological trajectories in time. We used 3D data obtained by Speckle Tracking Echocardiography in order to detect semi-automated and homologous landmarks clouds as proxies of left ventricular heart morphology. An extended Geometric Morphometrics toolkit in order to distinguish between intra- and inter-individual shape variations was used. Shape of trajectories with inter-individual variation were compared under the assumption that trajectories attributes, estimated at electrophysiologically homologous times are expressions of left ventricular heart function. We found that shape analysis as commonly applied in Geometric Morphometrics studies fails in identifying a proper morpho-space to compare the shape of morphological trajectories in time. To overcome this problem, we performed a special type of Riemannian Parallel Transport, called "linear shift". Whereas the two patients with aortic insufficiency were not differentiated in the static shape analysis from the healthy subjects, they set apart significantly in the analyses of motion trajectory's shape and orientation. We found that in healthy subjects, the variations due to inter-individual morphological differences were not related to shape and orientation of morphological trajectories. Principal Component Analysis showed that volumetric contraction, torsion and twist are differently distributed on different axes. Moreover, global shape change appeared to be more correlated with endocardial shape change than with the epicardial one. Finally, the total shape variation occurring among different subjects was significantly larger than that observable across properly defined morphological trajectories.