Inverse finite element characterization of the human myometrium derived from uniaxial compression experiments

The low strain-rate behavior of the human myometrium under compression was determined. To this end, uniaxial, unconstrained compression experiments were conducted on a total of 25 samples from three excised human uteri at strain rates between 0.001s-1 and 0.008s-1. A three-dimensional finite element model of each sample was created and used together with an optimization algorithm to find material parameters in an inverse estimation process. Friction and shape irregularities of samples were incorporated in the models. The uterine specimens in compression were modeled as viscoelastic, non-linear, nearly incompressible and isotropic continua. Simulations of uniaxial, frictionless compressions of an idealized cuboid were used to compare the resulting material parameters among each other. The intra- and inter-subject variability in stiffness of specimens was found to be large and to cover such a wide range that the effect of anisotropy which is of minor influence under compressive deformations in the first place could be neglected. Material parameters for a viscoelastic model based on a decoupled, reduced quadratic strain-energy function were presented for the uterine samples representing a median stiffnes

The architecture of the left ventricular myocytes relative to left ventricular systolic function

Objective: Mural thickening, combined with longitudinal and circumferential shortening, and apical along with basal twisting are critical components of the left ventricular systolic deformation that contribute to ventricular ejection. It is axiomatic that the spatial alignment of the actively contracting aggregates of myocytes must play a major role in the resulting ventricular deformation. The need to conserve functional global myocytic architecture, therefore, is an important aspect of the surgical manoeuvres affecting ventricular mass and geometry. To investigate the influence of the global alignment of the myocytes on ventricular contraction, we used a mathematical model simulating the large deformations produced by systolic contraction of the left ventricle of a human heart. Methods: The alignment and meshing of the myocytes within their supporting fibrous matrix cause mechanical anisotropy, which was included in the mathematical model in the form of a unit vector field, constructed from the measured trajectories of aggregated myocytes in an autopsied human heart. The relationship between ventricular structure and ventricular dynamics was assessed by analysing the influence of systematic deviations of the orientation of the myocytes from their original alignment, in longitudinal as well as radial directions, on the distribution of stress and strain within the myocardium, as well as on the ejection fraction. In addition, simplified idealised geometries were used to investigate the influence of the overall geometrical modifications. Results: Left ventricular function proved to be robust with respect to small-to-moderate rotational variations in myocytic alignment, up to 14°, a finding which we attribute to an equalising effect of the non-uniform anisotropic pattern found in a real heart involving substantial local irregularities in the architecture of the aggregated myocytes. Severe deterioration of function occurred only when deviations in alignment exceeded 30°. Conclusions: Our findings substantiate the concept of the myocardial walls representing a continuous three-dimensional meshwork, with the absence of any intermediate structures such as discrete bands or tracts extending over the ventricles, which could be destroyed surgically, thereby adversely affecting systolic function. With appropriate indications, they also support the validity of the surgical procedures performed to reduce ventricular radius and therefore to reduce mural stres

Ventricular myocardial architecture as visualised in postmortem swine hearts using magnetic resonance diffusion tensor imaging

Objective: The three-dimensional arrangement of the ventricular myocardial architecture remains controversial, in part because histological assessment is difficult to achieve, while anatomic dissections are, of necessity, destructive. In this study, we describe how the use of magnetic resonance diffusion tensor imaging has permitted us to reconstruct with precision the architecture of the ventricular myocardial fibres in the post-mortem swine heart. Methods and Results: We obtained diffusion-weighted spin-echo measurements of autopsied porcine hearts using a whole body MR system. We calculated the diffusion tensor and the corresponding eigenvectors on a voxel-by-voxel basis. This permitted us to colour code the fibres, and reconstruct them by connecting voxels in direction of the largest eigenvector. Such reconstructions show that, in the middle layer of the left ventricle, most of the fibres have a circular orientation, albit that a far from negligible component runs in a transverse direction. With increasing distance from the epicardium, the orientation of the fibres shows a continuous change in angulation with respect to an axis normal to the epicardium. Conclusion: Our data presented here supports the concept that the ventricular mass is arranged as a complex three-dimensional mesh of tangential and intruding fibres. The data offers no support for the concept of a ‘unique myocardial band'. The method has the potential to detecting deviations from this basic normal architecture, being capable of reconstructing the ventricular mass so as to assess the spatial coordinates of any single fibre strand. The technique, therefore, has major potential clinical applications in the setting of the failing or malformed heart, potentially being able to identify either systematic or regional disarray of the myocardial fibre

Tracing glacier wastage in the Northern Tien Shan (Kyrgyzstan/Central Asia) over the last 40years

The status and dynamics of glaciers are crucial for agriculture in semiarid parts of Central Asia, since river flow is characterized by major runoff in spring and summer, supplied by glacier- and snowmelt. Ideally, this coincides with the critical period of water demand for irrigation. The present study shows a clear trend in glacier retreat between 1963 and 2000 in the Sokoluk watershed, a catchment of the Northern Tien Shan mountain range in Kyrgyzstan. The overall area loss of 28% observed for the period 1963-2000, and a clear acceleration of wastage since the 1980s, correlate with the results of previous studies in other regions of the Tien Shan as well as the Alps. In particular, glaciers smaller than 0.5km2 have exhibited this phenomenon most starkly. While they registered a medium decrease of only 9.1% for 1963-1986, they lost 41.5% of their surface area between 1986 and 2000. Furthermore, a general increase in the minimum glacier elevation of 78m has been observed over the last three decades. This corresponds to about one-third of the entire retreat of the minimum glacier elevation in the Northern Tien Shan since the Little Ice Age maximu

Pressure-dependent hydrometra dimensions in hysteroscopy

Aim: To investigate the relation between intrauterine pressures and volumes for virtual-reality-based surgical training in hysteroscopy. Material and methods: Ten fresh extirpated uteri were insufflated by commercial hysteroscopy pump and imaged by computer tomography (CT) under intrauterine air pressure in distension-collapse cycles between 0, 20 (150mmHg), and 0kPa, performing a CT scan at every step at about 2.7kPa (20mmHg). Results: An initial threshold pressure to distend the cavity was avoided by introducing the insufflation tube up to the fundus. The filling and release phases of seven uteri that were completely distended showed the typical characteristics of a hysteresis curve which is expected from a viscoelastic, nonlinear, anisotropic soft tissue organ like the uterus. In three cases tightening the extirpated uterus especially at the lateral resection lines caused significant problems that inhibited registration of a complete distension-collapse cycle. Interpolated volumes for complete distended cavities and extrapolated for incomplete data sets, derived from the digitally reconstructed three-dimensional (3D) geometries, ranged from 0.6 to 11.4mL at 20kPa. These values highly correlate with the uterine volume (not insufflated) considering different biometric data of the uteri and patient data. Linear (R 2=0.66) and quadratic least-squares fits (R 2=0.74) were used to derive the formulas y=0.069x and y=0.00037x 2+0.036x, where x is the uterine volume in mL (not insufflated) and y is the cavity volume in mL at 20kPa intrauterine pressure. Conclusions: Our experimental hysteroscopical setup enabled us to reconstruct the changes in volumes of insufflated uteri under highly realistic conditions in 3D. The relation between intrauterine pressure and cavity volume in distension-collapse cycles describes a typical hysteresis curv

Representations of the discrete inhomogeneous Lorentz group and Dirac wave equation on the lattice

We propose the fundamental and two dimensional representation of the Lorentz groups on a (3+1)-dimensional hypercubic lattice, from which representations of higher dimensions can be constructed. For the unitary representation of the discrete translation group we use the kernel of the Fourier transform. From the Dirac representation of the Lorentz group (including reflections) we derive in a natural way the wave equation on the lattice for spin 1/2 particles. Finally the induced representation of the discrete inhomogeneous Lorentz group is constructed by standard methods and its connection with the continuous case is discussed.Comment: LaTeX, 20 pages, 1 eps figure, uses iopconf.sty (late submission

An analysis of the spatial arrangement of the myocardial aggregates making up the wall of the left ventricle

Objective: We used the technique of peeling of myocardial aggregates, usually described as ‘fibres', to determine the spatial arrangement of the myocytes in the left ventricular wall of a healthy autopsied human heart. Methods: We digitised the left ventricular outer and inner boundaries, as well as the pathways in space, of almost 3000 aggregates harvested from the left ventricular myocardium. During the process of gradual peeling, we sought to identify the myocardial aggregates as uniformly as possible. Despite this, interpolation was necessary to complete the pattern so as to construct a unit vector field that represented the preferred direction of the myocardial aggregates throughout the entirety of the walls of the left ventricle of this individual human heart. Results: Apart from the overall systematic arrangement of the aggregates necessary to achieve physiologic ventricular contraction, we documented substantial local heterogeneities in the orientation of the myocardial aggregates. In particular, a significant proportion of aggregates was found to intrude obliquely with respect to the ventricular boundaries, with markedly heterogeneous distribution. Moreover, the distribution of the helical angle of the aggregates relative to the ventricular base varied notably throughout the left ventricular free walls and the septum. Within the generally quite uniform and continuous structure of the ventricular mass, we were, however, unable to identify any organised tracts or functional subunits such as a ‘helical ventricular band', nor did we find radial fibrous lamellas coursing across the ventricular wall. Conclusion: We suggest that the impact of local anatomical inhomogeneities, associated with gradients in regional contractile function on global ventricular dynamics, has been systematically underestimated in the past. Our analysis confirms furthermore the continuous nature of the myocardium associated with an overall gross organisation of the fibre direction field; however, there is no evidence of substructures compartmentalising the ventricle

The myocardium and its fibrous matrix working in concert as a spatially netted mesh: a critical review of the purported tertiary structure of the ventricular mass

With the increasing interest now paid to volume reduction surgery, in which the cardiac surgeon is required to resect the ventricular myocardium to an extent unenvisaged in the previous century, it is imperative that we develop as precise knowledge as is possible of the basic structure of the ventricular myocardial mass and its functional correlates. This is the most important in the light of the adoption by some cardiac surgeons of an unvalidated model which hypothesises that the entire myocardial mass can be unravelled to produce one continuous band. It is our opinion that this model, and the phylogenetic and functional correlates derived from it, is incompatible with current concepts of cardiac structure and cardiodynamics. Furthermore, the proponents of the continuous myocardial band have made no effort to demonstrate perceived deficiencies with current concepts, nor have they performed any histological studies to validate their model. Clinical results using modifications of radius reduction surgery based on the concept of the continuous myocardial band show that the procedure essentially becomes ineffective. As we show in this review, if we understand the situation correctly, it was the erstwhile intention of the promoters of the continuous band to elucidate the basic mechanism of diastolic ventricular dilation. Their attempts, however, are doomed to failure, as is any attempt to conceptualise the myocardial mass on the basis of a tertiary structure, because of the underlying three-dimensional netting of the myocardial aggregates and the supporting fibrous tissue to form the myocardial syncytium. Thus, the ventricular myocardium is arranged in the form of a modified blood vessel rather than a skeletal muscle. If an analogy is required with skeletal muscle, then the ventricular myocardium possesses the freedom of motion, and the ability for shaping and conformational self-controlling that is better seen in the tongue. It is part of this ability that contributes to the rapid end-systolic ventricular dilation. Histologic investigations reveal that the fibrous content of the three-dimensional mesh is relatively inhomogeneous through the ventricular walls, particularly when the myocardium is diseased. The regional capacity to control systolic mural thickening, therefore, varies throughout the walls of the ventricular components. The existence of the spatially netted structure of the ventricular mass, therefore, must invalidate any attempt to conceptualise the ventricular myocardium as a tertiary arrangement of individual myocardial bands or tract