Luciano Teresi

An electromechanical model of cardiac tissue: Constitutive issues and electrophysiological effects

We present an electromechanical model of myocardium tissue coupling a modified FitzHugh-Nagumo type system, describing the electrical activity of the excitable media, with finite elasticity, endowed with the capability of describing muscle contractions. The high degree of deformability of the medium makes it mandatory to set the diffusion process in a moving domain, thereby producing a direct influence of the deformation on the electrical activity. Various mechano-electric effects concerning the propagation of cylindrical waves, the rotating spiral waves, and the spiral breakups are discussed.

Elastic Energies for Nematic Elastomers

We discuss several elastic energies for nematic elastomers and their small strain expansions both in the regime of large director rotations, and in the case that director changes are small. We propose two fully non-linear model anisotropic energies and compare the behavior they predict with the currently available experimental evidence.

Bite of the Cats: Relationships between Functional Integration and Mechanical Performance as Revealed by Mandible Geometry

Cat-like carnivorous mammals represent a relatively homogeneous group of species whose morphology appears constrained by exclusive adaptations for meat eating. We present the most comprehensive data set of extant and extinct cat-like species to test for evolutionary transformations in size, shape and mechanical performance, that is, von Mises stress and surface traction, of the mandible. Size and shape were both quantified by means of geometric morphometrics, whereas mechanical performance was assessed applying finite element models to 2D geometry of the mandible. Additionally, we present the first almost complete composite phylogeny of cat-like carnivorans for which well-preserved mandibles are known, including representatives of 35 extant and 59 extinct species of Felidae, Nimravidae, and Barbourofelidae. This phylogeny was used to test morphological differentiation, allometry, and covariation of mandible parts within and among clades. After taking phylogeny into account, we found that both allometry and mechanical variables exhibit a significant impact on mandible shape. We also tested whether mechanical performance was linked to morphological integration. Mechanical stress at the coronoid process is higher in sabertoothed cats than in any other clade. This is strongly related to the high degree of covariation within modules of sabertooths mandibles. We found significant correlation between integration at the clade level and per-clade averaged stress values, on both original data and by partialling out interclade allometry from shapes when calculating integration. This suggests a strong interaction between natural selection and the evolution of developmental and functional modules at the clade level.

A damage mechanics approach to stress softening and its application to rubber

Abstract We analyze stress softening phenomena within the framework of the ‘generalized standard material’ based on the notion of a ‘normal dissipative mechanism’. We prove that the monotonicity properties of the ‘yield function’ governing such mechanism lead to local and global uniqueness of the response. Applications to oscillators with a single degree of freedom, whose anharmonic spring exhibits stress softening, are also presented.

Torsion of the human left ventricle: Experimental analysis and computational modeling

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.

Testing Convergent and Parallel Adaptations in Talpids Humeral Mechanical Performance by means of Geometric Morphometrics and Finite Element Analysis

The shape and mechanical performance in Talpidae humeri were studied by means of Geometric Morphometrics and Finite Element Analysis, including both extinct and extant taxa. The aim of this study was to test whether the ability to dig, quantified by humerus mechanical performance, was characterized by convergent or parallel adaptations in different clades of complex tunnel digger within Talpidae, that is, Talpinae+Condylura (monophyletic) and some complex tunnel diggers not belonging to this clade. Our results suggest that the pattern underlying Talpidae humerus evolution is evolutionary parallelism. However, this insight changed to true convergence when we tested an alternative phylogeny based on molecular data, with Condylura moved to a more basal phylogenetic position. Shape and performance analyses, as well as specific comparative methods, provided strong evidence that the ability to dig complex tunnels reached a functional optimum in distantly related taxa. This was also confirmed by the lower phenotypic variance in complex tunnel digger taxa, compared to non‐complex tunnel diggers. Evolutionary rates of phenotypic change showed a smooth deceleration in correspondence with the most recent common ancestor of the Talpinae+Condylura clade. J. Morphol. 2012.

Modeling Helicoid to Spiral-Ribbon Transitions of Twist-Nematic Elastomers

Nematic Elastomers (NEs) possess very interesting properties stemming from the interaction between liquid crystal order and rubber elasticity. For such materials, thermally induced phase transition from the isotropic to the nematic phase may induce very large distortions, which in turn can affect the overall configuration of a macroscopic specimen. The behavior of NEs can be well modeled within the theory of finite elasticity with distortions; here, we test a theoretical model against fancy shapes formation; in particular, we deal with the many different shapes that a thin, slender bar, made of NE, may assume as a consequence of its chiral symmetry during solvent evaporation and subsequent heating. Our goal has been to replicate with numerical experiments the phenomena of shape formation in chiral NEs, and our results constitute a noteworthy assessment of the physical model underlying the numerical solutions.

4D-Analysis of Left Ventricular Heart Cycle Using Procrustes Motion Analysis

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.

Morphological integration and functional modularity in the crocodilian skull.

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.

On Variational Approaches to Plate Modes

The three basic functionals of potential energy, complementary energy and Hellinger–Prange–Reissner are usedto obtain a rational derivation of Reissner–Mindlinplate models, starting from the three-dimensional theory.We show that the models so obtained are instances of the same plate theory; nevertheless, due to the different constitutive relations governing their response, they mimic the three-dimensional behaviour in three different manners.