On some numerical aspects of an active strain model in cardiac mechanics

We are interested in the development, implementation and testing of an orthotropic model for cardiac contraction based on an active strain decomposition. Our model addresses the coupling of a transversely isotropic mechanical description at the cell level, with an orthotropic constitutive law for incompressible tissue at the macroscopic level. The main differences with the active stress model are addressed in detail, and a finite element discretization using Taylor-Hood and MINI elements is proposed and illustrated with numerical examples.

Orthotropic active strain models for the numerical simulation of cardiac biomechanics

An active strain formulation for orthotropic constitutive laws arising in cardiac mechanics modeling is introduced and studied. The passive mechanical properties of the tissue are described by the Holzapfel-Ogden relation. In the active strain formulation, the Euler-Lagrange equations for minimizing the total energy are written in terms of active and passive deformation factors, where the active part is assumed to depend, at the cell level, on the electrodynamics and on the specific orientation of the cardiac cells. The well-posedness of the linear system derived from a generic Newton iteration of the original problem is analyzed and different mechanical activation functions are considered. In addition, the active strain formulation is compared with the classical active stress formulation from both numerical and modeling perspectives. Taylor-Hood and MINI finite elements are employed to discretize the mechanical problem. The results of several numerical experiments show that the proposed formulation is mathematically consistent and is able to represent the main key features of the phenomenon, while allowing savings in computational costs.

Active strain and activation models in cardiac electromechanics

We present a model for mechanical activation of the cardiac tissue depending on the evolution of the transmembrane electrical potential and certain gating/ionic variables that are available in most of electrophysiological descriptions of the cardiac membrane. The basic idea consists in adding to the chosen ionic model one ordinary differential equation for the kinetics of the mechanical activation function. A relevant example illustrates the desired properties of the proposed model, such as delayed muscle contraction and correct magnitude of the muscle fibers' shortening.

An active strain electromechanical model for cardiac tissue

We propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of electrical potential and large deformations of the cardiac tissue. The underlying mathematical model is based on the active strain assumption, in which it is assumed that a multiplicative decomposition of the deformation tensor into a passive and active part holds, the latter carrying the information of the electrical potential propagation and anisotropy of the cardiac tissue into the equations of either incompressible or compressible nonlinear elasticity, governing the mechanical response of the biological material. In addition, by changing from an Eulerian to a Lagrangian configuration, the bidomain or monodomain equations modeling the evolution of the electrical propagation exhibit a nonlinear diffusion term. Piecewise quadratic finite elements are employed to approximate the displacements field, whereas for pressure, electrical potentials and ionic variables are approximated by piecewise linear elements. Various numerical tests performed with a parallel finite element code illustrate that the proposed model can capture some important features of the electromechanical coupling, and show that our numerical scheme is efficient and accurate.

Parameters and algorithms to evaluate cardiac mechanics by conductance catheter

This work is structured as follows: In Section 1 we discuss the clinical problem of heart failure. In particular, we present the phenomenon known as ventricular mechanical dyssynchrony: its impact on cardiac function, the therapy for its treatment and the methods for its quantification. Specifically, we describe the conductance catheter and its use for the measurement of dyssynchrony. At the end of the Section 1, we propose a new set of indexes to quantify the dyssynchrony that are studied and validated thereafter. In Section 2 we describe the studies carried out in this work: we report the experimental protocols, we present and discuss the results obtained. Finally, we report the overall conclusions drawn from this work and we try to envisage future works and possible clinical applications of our results. Ancillary studies that were carried out during this work mainly to investigate several aspects of cardiac resynchronization therapy (CRT) are mentioned in Appendix. -------- Ventricular mechanical dyssynchrony plays a regulating role already in normal physiology but is especially important in pathological conditions, such as hypertrophy, ischemia, infarction, or heart failure (Chapter 1,2.). Several prospective randomized controlled trials supported the clinical efficacy and safety of cardiac resynchronization therapy (CRT) in patients with moderate or severe heart failure and ventricular dyssynchrony. CRT resynchronizes ventricular contraction by simultaneous pacing of both left and right ventricle (biventricular pacing) (Chapter 1.). Currently, the conductance catheter method has been used extensively to assess global systolic and diastolic ventricular function and, more recently, the ability of this instrument to pick-up multiple segmental volume signals has been used to quantify mechanical ventricular dyssynchrony. Specifically, novel indexes based on volume signals acquired with the conductance catheter were introduced to quantify dyssynchrony (Chapter 3,4.). Present work was aimed to describe the characteristics of the conductancevolume signals, to investigate the performance of the indexes of ventricular dyssynchrony described in literature and to introduce and validate improved dyssynchrony indexes. Morevoer, using the conductance catheter method and the new indexes, the clinical problem of the ventricular pacing site optimization was addressed and the measurement protocol to adopt for hemodynamic tests on cardiac pacing was investigated. In accordance to the aims of the work, in addition to the classical time-domain parameters, a new set of indexes has been extracted, based on coherent averaging procedure and on spectral and cross-spectral analysis (Chapter 4.). Our analyses were carried out on patients with indications for electrophysiologic study or device implantation (Chapter 5.). For the first time, besides patients with heart failure, indexes of mechanical dyssynchrony based on conductance catheter were extracted and studied in a population of patients with preserved ventricular function, providing information on the normal range of such a kind of values. By performing a frequency domain analysis and by applying an optimized coherent averaging procedure (Chapter 6.a.), we were able to describe some characteristics of the conductance-volume signals (Chapter 6.b.). We unmasked the presence of considerable beat-to-beat variations in dyssynchrony that seemed more frequent in patients with ventricular dysfunction and to play a role in discriminating patients. These non-recurrent mechanical ventricular non-uniformities are probably the expression of the substantial beat-to-beat hemodynamic variations, often associated with heart failure and due to cardiopulmonary interaction and conduction disturbances. We investigated how the coherent averaging procedure may affect or refine the conductance based indexes; in addition, we proposed and tested a new set of indexes which quantify the non-periodic components of the volume signals. Using the new set of indexes we studied the acute effects of the CRT and the right ventricular pacing, in patients with heart failure and patients with preserved ventricular function. In the overall population we observed a correlation between the hemodynamic changes induced by the pacing and the indexes of dyssynchrony, and this may have practical implications for hemodynamic-guided device implantation. The optimal ventricular pacing site for patients with conventional indications for pacing remains controversial. The majority of them do not meet current clinical indications for CRT pacing. Thus, we carried out an analysis to compare the impact of several ventricular pacing sites on global and regional ventricular function and dyssynchrony (Chapter 6.c.). We observed that right ventricular pacing worsens cardiac function in patients with and without ventricular dysfunction unless the pacing site is optimized. CRT preserves left ventricular function in patients with normal ejection fraction and improves function in patients with poor ejection fraction despite no clinical indication for CRT. Moreover, the analysis of the results obtained using new indexes of regional dyssynchrony, suggests that pacing site may influence overall global ventricular function depending on its relative effects on regional function and synchrony. Another clinical problem that has been investigated in this work is the optimal right ventricular lead location for CRT (Chapter 6.d.). Similarly to the previous analysis, using novel parameters describing local synchrony and efficiency, we tested the hypothesis and we demonstrated that biventricular pacing with alternative right ventricular pacing sites produces acute improvement of ventricular systolic function and improves mechanical synchrony when compared to standard right ventricular pacing. Although no specific right ventricular location was shown to be superior during CRT, the right ventricular pacing site that produced the optimal acute hemodynamic response varied between patients. Acute hemodynamic effects of cardiac pacing are conventionally evaluated after stabilization episodes. The applied duration of stabilization periods in most cardiac pacing studies varied considerably. With an ad hoc protocol (Chapter 6.e.) and indexes of mechanical dyssynchrony derived by conductance catheter we demonstrated that the usage of stabilization periods during evaluation of cardiac pacing may mask early changes in systolic and diastolic intra-ventricular dyssynchrony. In fact, at the onset of ventricular pacing, the main dyssynchrony and ventricular performance changes occur within a 10s time span, initiated by the changes in ventricular mechanical dyssynchrony induced by aberrant conduction and followed by a partial or even complete recovery. It was already demonstrated in normal animals that ventricular mechanical dyssynchrony may act as a physiologic modulator of cardiac performance together with heart rate, contractile state, preload and afterload. The present observation, which shows the compensatory mechanism of mechanical dyssynchrony, suggests that ventricular dyssynchrony may be regarded as an intrinsic cardiac property, with baseline dyssynchrony at increased level in heart failure patients. To make available an independent system for cardiac output estimation, in order to confirm the results obtained with conductance volume method, we developed and validated a novel technique to apply the Modelflow method (a method that derives an aortic flow waveform from arterial pressure by simulation of a non-linear three-element aortic input impedance model, Wesseling et al. 1993) to the left ventricular pressure signal, instead of the arterial pressure used in the classical approach (Chapter 7.). The results confirmed that in patients without valve abnormalities, undergoing conductance catheter evaluations, the continuous monitoring of cardiac output using the intra-ventricular pressure signal is reliable. Thus, cardiac output can be monitored quantitatively and continuously with a simple and low-cost method. During this work, additional studies were carried out to investigate several areas of uncertainty of CRT. The results of these studies are briefly presented in Appendix: the long-term survival in patients treated with CRT in clinical practice, the effects of CRT in patients with mild symptoms of heart failure and in very old patients, the limited thoracotomy as a second choice alternative to transvenous implant for CRT delivery, the evolution and prognostic significance of diastolic filling pattern in CRT, the selection of candidates to CRT with echocardiographic criteria and the prediction of response to the therapy.

Tectonic geomorphology and active strain of the Northern Apennines mountain front

The Northern Apennines (NA) chain is the expression of the active plate margin between Europe and Adria. Given the low convergence rates and the moderate seismic activity, ambiguities still occur in defining a seismotectonic framework and many different scenarios have been proposed for the mountain front evolution. Differently from older models that indicate the mountain front as an active thrust at the surface, a recently proposed scenario describes the latter as the frontal limb of a long-wavelength fold (> 150 km) formed by a thrust fault tipped around 17 km at depth, and considered as the active subduction boundary. East of Bologna, this frontal limb is remarkably very straight and its surface is riddled with small, but pervasive high- angle normal faults. However, west of Bologna, some recesses are visible along strike of the mountain front: these perturbations seem due to the presence of shorter wavelength (15 to 25 km along strike) structures showing both NE and NW-vergence. The Pleistocene activity of these structures was already suggested, but not quantitative reconstructions are available in literature. This research investigates the tectonic geomorphology of the NA mountain front with the specific aim to quantify active deformations and infer possible deep causes of both short- and long-wavelength structures. This study documents the presence of a network of active extensional faults, in the foothills south and east of Bologna. For these structures, the strain rate has been measured to find a constant throw-to-length relationship and the slip rates have been compared with measured rates of erosion. Fluvial geomorphology and quantitative analysis of the topography document in detail the active tectonics of two growing domal structures (Castelvetro - Vignola foothills and the Ghiardo plateau) embedded in the mountain front west of Bologna. Here, tilting and river incision rates (interpreted as that long-term uplift rates) have been measured respectively at the mountain front and in the Enza and Panaro valleys, using a well defined stratigraphy of Pleistocene to Holocene river terraces and alluvial fan deposits as growth strata, and seismic reflection profiles relationships. The geometry and uplift rates of the anticlines constrain a simple trishear fault propagation folding model that inverts for blind thrust ramp depth, dip, and slip. Topographic swath profiles and the steepness index of river longitudinal profiles that traverse the anti- clines are consistent with stratigraphy, structures, aquifer geometry, and seismic reflection profiles. Available focal mechanisms of earthquakes with magnitude between Mw 4.1 to 5.4, obtained from a dataset of the instrumental seismicity for the last 30 years, evidence a clear vertical separation at around 15 km between shallow extensional and deeper compressional hypocenters along the mountain front and adjacent foothills. In summary, the studied anticlines appear to grow at rates slower than the growing rate of the longer- wavelength structure that defines the mountain front of the NA. The domal structures show evidences of NW-verging deformation and reactivations of older (late Neogene) thrusts. The reconstructed river incision rates together with rates coming from several other rivers along a 250 km wide stretch of the NA mountain front and recently available in the literature, all indicate a general increase from Middle to Late Pleistocene. This suggests focusing of deformation along a deep structure, as confirmed by the deep compressional seismicity. The maximum rate is however not constant along the mountain front, but varies from 0.2 mm/yr in the west to more than 2.2 mm/yr in the eastern sector, suggesting a similar (eastward-increasing) trend of the apenninic subduction.

Finite element studies of the mechanical behaviour of the diaphragm in normal and pathological cases

The diaphragm is a muscular membrane separating the abdominal and thoracic cavities, and its motion is directly linked to respiration. In this study, using data from a 59-year-old female cadaver obtained from the Visible Human Project, the diaphragm is reconstructed and, from the corresponding solid object, a shell finite element mesh is generated and used in several analyses performed with the ABAQUS 6.7 software. These analyses consider the direction of the muscle fibres and the incompressibility of the tissue. The constitutive model for the isotropic strain energy as well as the passive and active strain energy stored in the fibres is adapted from Humphrey's model for cardiac muscles. Furthermore, numerical results for the diaphragmatic floor under pressure and active contraction in normal and pathological cases are presented.

Multi-slice three-dimensional myocardial strain tensor quantification using zHARP.

In this article we propose a novel method for calculating cardiac 3-D strain. The method requires the acquisition of myocardial short-axis (SA) slices only and produces the 3-D strain tensor at every point within every pair of slices. Three-dimensional displacement is calculated from SA slices using zHARP which is then used for calculating the local displacement gradient and thus the local strain tensor. There are three main advantages of this method. First, the 3-D strain tensor is calculated for every pixel without interpolation; this is unprecedented in cardiac MR imaging. Second, this method is fast, in part because there is no need to acquire long-axis (LA) slices. Third, the method is accurate because the 3-D displacement components are acquired simultaneously and therefore reduces motion artifacts without the need for registration. This article presents the theory of computing 3-D strain from two slices using zHARP, the imaging protocol, and both phantom and in-vivo validation.

Evaluación de la mecánica ventricular izquierda mediante speckle tracking en pacientes sanos en la Clínica Shaio

Introducción: La ecocardiografía es actualmente la técnica de imagen diagnóstica más utilizada para la evaluación de la anatomía y la función cardiovascular. En la actualidad se está utilizando la ecocardiografía por speckle tracking la cual permite una evaluación mas objetiva y confiable de la función ventricular, sin embargo se requieren valores de referencia que hagan que los valores obtenidos sean válidos y útiles para determinar en forma mas oportuna conductas previas al deterioro de su función. Objetivo general: Determinar los valores de referencia para mecánica ventricular izquierda mediante ecocardiografía bidimensional por speckle tracking con equipo Toshiba Artida con transductor multifrecuencia de 3 megahertzios en pacientes sin patología cardiaca conocida en la Fundación Clínica Shaio en el año 2014. Metodología: Análisis de una cohorte prospectiva de todos los pacientes que ingresaron a la Fundación Clínica Shaio para evaluación ecocardiográfica sin patología cardiaca conocida entre los meses Agosto y Diciembre del 2014. Resultados: Se presenta este estudio de la evaluación de la mecánica ventricular izquierda en adultos sanos, los resultados son similares a los obtenidos en estudios de referencia, sin embargo se consideran de gran importancia ya que de acuerdo a la guía actual de evaluación de la mecánica ventricular por strain rate es importante que cada equipo se encuentre estandarizado con el fin de tener resultados válidos de acuerdo a las diferentes patologías en las que se puede aplicar y a nuestra población.

Three-dimensional magnetic resonance myocardial motion tracking from a single image plane.

Three-dimensional imaging for the quantification of myocardial motion is a key step in the evaluation of cardiac disease. A tagged magnetic resonance imaging method that automatically tracks myocardial displacement in three dimensions is presented. Unlike other techniques, this method tracks both in-plane and through-plane motion from a single image plane without affecting the duration of image acquisition. A small z-encoding gradient is subsequently added to the refocusing lobe of the slice-selection gradient pulse in a slice following CSPAMM acquisition. An opposite polarity z-encoding gradient is added to the orthogonal tag direction. The additional z-gradients encode the instantaneous through plane position of the slice. The vertical and horizontal tags are used to resolve in-plane motion, while the added z-gradients is used to resolve through-plane motion. Postprocessing automatically decodes the acquired data and tracks the three-dimensional displacement of every material point within the image plane for each cine frame. Experiments include both a phantom and in vivo human validation. These studies demonstrate that the simultaneous extraction of both in-plane and through-plane displacements and pathlines from tagged images is achievable. This capability should open up new avenues for the automatic quantification of cardiac motion and strain for scientific and clinical purposes.

Geotechnical and structural behavior of the railroad track in large-scale apparatus

This paper analyses the static and dynamic behavior of the railroad track model in laboratory. Measurements of stresses and strains on a large-scale railroad track apparatus were studied. The model includes: compacted soil, representing the final layers of platform, ballast layer, and ties (steel, wooden, and pre-stressed concrete). The soil and soil ballast interface were instrumented with pneumatic stress gauge. Settlement measurement device were positioned at the same levels as the load cells. Loads were applied by hydraulic actuators, statically and dynamically. After the prescribed number of load cycles, in pre-determined intervals, stresses and strains were measured. Observations indicate that stress and strain distributions, transmitted by wooden or steel ties, behave similarly. A more favorable behavior was observed with pre-stressed concrete mono block ties. Non-linear response was observed after a threshold numbers of cycles were surpassed, showing that the strain modulus increases with the numbers of cycles. © 2009 IOS Press.

[Preoperative preparation of patients with cardiovascular disease for noncardiac surgery]

Preoperative preparation of patients with cardiovascular disease is best initiated by the general practitioner. Updated Guidelines on Perioperative Cardiovascular Evaluation and Care for Noncardiac Surgery have been published by the American Heart Association und American College of Cardiology (2007). Individual cardiac evaluation must take into account active cardiac conditions, functional capacity, additional clinical risk factors and surgical risk. Stable, asymptomatic patients with normal functional capacity can proceed to elective anesthesia and surgery without further cardiac evaluation. Active cardiac conditions require evaluation and treatment by a cardiology service prior to elective surgery. In stable patients with poor (<4 metabolic equivalents, MET) or unknown functional capacity and clinical risk factors, who are scheduled for intermediate- or high-risk surgery, further cardiac evaluation and preparation is to be considered. Established indicated beta blocker and statin medication is to be continued; timely institution of beta blocker medication (target heart rate, <65 bpm) may be required depending on the risk of surgery, the presence of coronary heart disease, and the number of clinical risk factors present. Following percutaneous coronary intervention, specific waiting periods are required prior to elective surgery. In patients on antiplatelet therapy, the risk of stopping it should be weighed against the benefit of reduction in bleeding complications from the planned surgery.

Intraspecific facilitation by allelochemical mediated grazing protection within a toxigenic dinoflagellate population, link to supplementary material

Dinoflagellates are a major cause of harmful algal blooms, with consequences for coastal marine ecosystem functioning and services. Alexandrium tamarense is one of the most abundant and widespread toxigenic species in the temperate northern and southern hemisphere, and produces paralytic shellfish poisoning toxins as well as lytic allelochemical substances. These bioactive compounds may support the success of A. tamarense and its ability to form blooms. Here we investigate the impact of grazing on monoclonal and mixed set-ups of highly (Alex2) and moderately (Alex4) allelochemically active A. tamarense strains and on a non-allelochemically active conspecific (Alex5) by the heterotrophic dinoflagellate Polykrikos kofoidii. While Alex4 and particularly Alex5 were strongly grazed by P. kofoidii when offered alone, both strains grew well in the mixed assemblages (Alex4+Alex5 and Alex2+Alex5). Hence, the allelochemical active strains facilitated growth of the non-active strain by protecting the population as a whole against grazing. Based on our results, we argue that facilitation among clonal lineages within a species may partly explain the high genotypic and phenotypic diversity of Alexandrium populations. Populations of Alexandrium may comprise multiple cooperative traits that act in concert with intraspecific facilitation, and hence promote the success of this notorious harmful algal bloom species.

Improved systolic ventricular function with normal myocardial mechanics in compensated cardiac hypertrophy

There is still controversy about the relation between changes in myocardial contractile function and global left ventricular (LV) performance during stable concentric hypertrophy. To clarify this, we analyzed LV function in vivo and myocardial mechanics in vitro in rats with pressure overload-induced cardiac hypertrophy. Male Wistar rats (70 g) Underwent ascending aortic stenosis for 8 weeks (group AAS, n = 9). LV performance wits assessed by transthoracic echocardiography Under anesthesia. Myocardial function Was studied in isolated papillary muscle preparations during isometric contraction. The data were compared with age- and sex-matched sham-operated rats (group C, 11 = 9). LV weight-to-body weight ratio (C: 2.13 +/- 0.14 mg/g; AAS: 3.24 +/- 0.44) LV relative wall thickness (C: 0.18 +/- 0.02; AAS: 0.33 +/- 0.09), and LV fractional shortening (C: 54 +/- 5%; AAS: 70 +/- 8%) were increased in group AAS (P<0.05). Echocardio-graphic analysis also indicated a significant association (r = 0.74 P<0.001) between the percent fractional shortening index and LV relative wall thickness. The performance of AAS isolated In muscle revealed that active tension (C: 6.6 +/- 1.7 g/mm(2); AAS: 6.5 +/- 1.5 g/mm(2)) and maximum rate of tension development (C: 69 +/- 21 g/mm(2)/s AAS: 69 +/- 18 g/mm(2)/s) were not significantly different Front group C (P>0.05). In conclusion, compensated pressure-overload myocardial hypertrophy is associated with preserved myocardial function and increased ventricular performance. The improved LV function might be due to the ventricular remodeling, characterized by an increased relative wall thickness.

Improved systolic ventricular function with normal myocardial mechanics in compensated cardiac hypertrophy

There still controversy about the relation between changes in myocardial contractile function and global left ventricular (LV) performance during stable concentric hypertrophy. To clarify this, we analyzed LV function in vivo and myocardial mechanics in vitro in rats with pressure overload-induced cardiac hypertrophy. Male Wistar rats (70 g) underwent ascending aorta stenosis for 8 weeks (group AAS, n=9). LV performance was assessed by transthoracic echocardiography under light anesthesia. Myocardial function was studied in isolated papillary muscle preparation during isometric contraction. The data were compared with age- and sex-matched sham-operated rats (group C, n=9). LV weight-to-body weight ratio (C: 2.0 ± 0.5 mg/g; AAS: 3.3 ± 0.7 mg/g), LV relative wall thickness (C: 0.19 ± 0.02; AAS; 0.34 ± 0.10), and LV fractional shortening (C: 54 ± 5%; AAS: 70 ± 8%) were increased in the group AAS (p<0.05). Echocardiographic analysis also indicated a significant association (r=0.74; p<0.001) between percent fractional shortening and LV relative wall thickness. The performance of AAS isolated muscle revealed that active tension (C: 6.6 ± 1.7 g/mm 2; AAS: 6.5 ± 1.5 g/mm 2) and maximum rate of tension development (C: 69 ± 21 g/mm 2/s; AAS: 69 ± 18 g/mm 2) were not significantly different from group C (p>0.05). In conclusion: 1) Compensated pressure-overload myocardial hypertrophy is associated with preserved myocardial function and increased ventricular performance; 2) The improved LV function might be due to the ventricular remodeling characterized by an increased relative wall thickness. Copyright © 2002 By PJD Publications Limited.