A computer model of myocardial disarray in simulating ECG features of hypertrophic cardiomyopathy

Hypertrophic cardiomyopathy (HCM) was simulated with a computer heart model having a realistic shape and rotating fiber orientation in order to elucidate possible mechanisms for abnormal ECG findings. The disarray of myocardial muscle in HCM was simulated by assigning random fiber direction and isotropic electrophysiologic properties to abnormal hypertrophic regions, in contrast to the anisotropic modeling for normal myocardium. With these models, main ECG features including abnormal Q wave and QS pattern were reproduced and were comparable with clinical findings. This study suggests that the change in anisotropy in the hypertrophic myocardium is likely to be the main factor responsible to the ECG features of HCM.     

Anisotropy, Fiber Curvature, and Bath Loading Effects on Activation in Thin and Thick Cardiac Tissue Preparations:

Anisotropy Effects in a 3D Bidomain. Introduction: A modeling study is presented to explore the effects of tissue conductivity, fiber orientation, and presence of an adjoining extracellular volume conductor on electrical conduction in cardiac muscle. Simulated results are compared with those of classical in vitro experiments on superfused thin layer preparations and on whole hearts. Methods and Results: The tissue is modeled as a three-dimensional bidomain block adjoining an isotropic bath. In the thin layer model, the fibers are assumed parallel. In the thick block model, fiber rotation, curvature, and tipping are incorporated. Results from the thin layer model explain experimental observations that the rate of rise of the entire action potential upstroke is faster and the magnitude of the extracellular potential is smaller across fibers than along fibers in a uniformly propagating front. The simulation identified that this behavior only arises in tissue with unequal anisotropy in the two spaces and adjoining an extracellular hath. Simulated conduction and potential distributions in the thick block model are shown to well approximate experimental maps. The potentials are sensitive to changes in the fiber orientations. A slight 5° tipping of intramural fibers out of the planes parallel to the epicardium and endocardium will lead to an asymmetry of the magnitudes of the positive regions. In addition, the introduction of fiber curvature leads to more realistic isochrone and extracellular potential distributions. The orientation of the central negative region of the extracellular potential is shown to be determined by the average of the fiber direction at the plane of pacing and the plane of recording. Conclusions: The simulations demonstrate the sensitivity of spread of activation and potential time courses and distributions to the underlying electrical properties in both thick and thin slabs. The bidomain model is shown to be a useful representation of cardiac tissue for interpreting experimental data of activation.     

Prediction of accessory pathway locations in Wolff-Parkinson-White syndrome with body surface potential Laplacian maps . A simulation study

An electrocardiographic computer simulation was conducted to study the feasibility of predicting accessory pathway locations in Wolff-Parkinson-White (WPW) syndrome with body surface potential Laplacian maps. Three-dimensional, realistically-shaped heart and torso models were used. Ten accessory pathways (APs) around the atrioventricular ring corresponding to Gallagher et al. were set in the heart model, and body surface Lapacian and potential maps of WPW syndrome with single or multiple APs were simulated and compared to each other. In simulations with a single AP in the anterior walls, the maximum-minimum pairs in Laplacian maps appeared to be similar to those in potential maps with respect to their locations and orientations, but the maximum-minimum pairs in Laplacian maps were sharper and more localized than in potential maps. In simulations with a posterior AP or multiple APs, the maximum-minimum pairs in the Laplacian maps showed features correlative to the AP locations, but no such features were found in potential maps. These results suggest the possibility of using Laplacian maps, as a non-invasive method for predicting accessory pathways locations in WPW syndrome.     

Three-Dimensional Muscular Architecture of the Human Tongue Determined In Vivo With Diffusion Tensor Magnetic Resonance Imaging

The myoarchitecture of the tongue is believed to consist of a complex network of interwoven fibers, which function together to produce a near limitless array of functional deformations. These deformations contribute mechanically to speech production and to oral cavity food handling during swallowing. We have previously imaged the 3D myoarchitecture of the mammalian tongue in excised tissue with diffusion tensor MRI, a technique which derives the 3D orientation of intramural fibers as a function of the extent to which a direction-specific MR signal attenuates under diffusion-encoding magnetic gradients. The resulting 3D diffusion tensor defines the relative orientations of the myofiber populations within a region of tissue. In this study, we have extended the use of this method to assess lingual myoarchitecture in normal human subjects in vivo. Subjects were imaged using a diffusion-sensitive stimulated-echo pulse sequence with single-shot echo-planar spatial encoding in the midsagittal plane. Differences in lingual fiber orientation were manifested by graduated changes in fiber direction throughout the tissue, without clear anatomical demarcations between regions of the tissue. The anterior tissue was composed generally of orthogonally oriented fibers surrounded by an axially oriented ring of tissue, whereas the posterior portion of the tissue was composed mostly of fibers projecting in the superior and posterior directions. The bulk of the tissue displayed a highly homogeneous, vertically oriented set of fibers, including the anteroinferior region of the tissue and extending nearly to the superior surface. Further analysis of the tissue in terms of diffusion anisotropy demonstrated that the tissue could be represented by varying degrees of anisotropy, with a tendency toward high anisotropy in the dorsal and anteroventral periphery and low anisotropy in the central region of the tissue. These findings demonstrate that the muscular anatomy of the tongue can be displayed as a continuous array of structural units, or tensors, representing fibers of varying orientations throughout the tissue.     

Computation of Heart Surface Potentials Using the Surface Source Model

Heart Surface Source Model. Introduction : The bidomain model of the heart leads to the result that the volume density of cardiac current source moment is proportional to the gradient of the macroscopic transmembrane action potential distribution. If the anisotropy ratios of the inner and outer domains (syncytia) of the myocardium are equal, then the volume distribution of cardiac sources can be replaced by an appropriate double layer on the heart surface. The double layer source distribution (heart surface source model) provides a basis for calculating heart surface potentials from cardiac sources.
Methods and Results : The heart surface model was used to calculate epicardial potentials for the normal heart as well as for a case of ischemia and of infarction. The model was also used to determine the effect of insulating the heart surface. Insulating the heart surface caused an almost fourfold increase in peak-to-peak amplitude of simulated electrograms, with little change in waveshape. Simulated electrograms showed good agreement with recorded electrograms reported in the literature.
Conclusion : The heart surface source model appears to provide a basis for relating heart surface potentials to the distribution of cellular action potential.     

Paced Activation Mapping Reveals Organization of Myocardial Fibers:

Pacing Reveals Fiber Orientation in 3D Bidomain. Introduction: A three-dimensional bidomain model of a block section of both the right and left ventricular walls that included rotational anisotropy and fiber curvature was used to investigate potential distributions generated during paced activation mapping. Unlike previous large-scale tissue models, the extracellular stimulus was included.
Methods and Results: The model was used to test the hypothesis that information about the underlying tissue structure (surface fiber angle gradients, amount of fiber rotation per unit depth, and anisotropy) can be extracted from surface potential distributions during stimulation. Results from distributions during stimulation were compared to those obtained using the distributions during activation. To better correlate results to possible experimental measurements, the analysis was performed using a 21 × 21 grid of "electrode" sites, each separated by 1 mm. Fiber orientation was estimated from the surface data by: (1) curve-fitting the elliptical shape of the epicardial potential distribution during stimulation: (2) identifying the location of the potential maxima leading the wavefront during early activation: and (3) for epicardial stimuli, curve-fitting the elliptical shape of the activation isochrones. Results show that surface potential distributions from the stimulus can be used to estimate fiber orientation: however, the accuracy of the reconstruction is highly dependent on the amount of fiber rotation per unit depth.
Conclusions: Extracellular potential data during and after stimulation is shown to reflect the organization of myocardial fibers and, as such, could be used to characterize the three-dimensional anisotropic electrical properties in situ.     

Breakthrough waves during ventricular fibrillation depend on the degree of rotational anisotropy and the boundary conditions: a simulation study

INTRODUCTION: The left ventricle (LV) and right ventricle (RV) are characterized by specific fiber orientation known as "rotational anisotropy." However, it remains unclear whether the LV and RV are different with regard to the effect of rotational anisotropy on the dynamics of scroll waves during ventricular fibrillation (VF). To resolve this issue, we used a computation-based model to study scroll wave behavior. METHODS AND RESULTS: We composed an environment of simulated three-dimensional ventricular wall slabs, with optional ratios of fiber rotation to wall thickness (0 degrees, 6 degrees, and 12 degrees/mm thickness; LV 10 mm, RV 5 mm), using Luo-Rudy phase I equations. When rotational anisotropy was not incorporated into the LV wall slab (theta endo to approximately theta epi = 0 degrees), most scroll waves rotated around the filaments perpendicular to the tissue surface, with only a few accompanying breakthrough waves. In a twisted LV model (theta endo to approximately theta epi = 60 degrees and 120 degrees), the scroll waves were demonstrated as multiple wavelets scattered spatiotemporally, frequently accompanied by breakthrough waves that were promoted by rotational anisotropy. In a twisted RV model (theta endo to approximately theta epi = 30 degrees and 60 degrees), single scroll waves and/or figure-of-eight reentrant waves appeared, with comparatively few breakthrough waves, regardless of the degree of fiber twist. CONCLUSION: The proportion of electrical effects of rotational anisotropy and tissue boundaries plays an important role in the genesis of breakthrough waves during VF, and the difference in wave propagating patterns and frequency spectrum of the ventricles may arise, in part, from the number of breakthrough waves promoted by rotational anisotropy.     

Useful Lessons from Body Surface Mapping

Useful Lessons from Body Surface Mapping. Body surface potential maps (BSMs) depict the time varying distribution of cardiac potentials on the entire surface of the torso. Hundreds of studies have shown that BSMs contain more diagnostic and prognostic information than can he elicited from the 12-lead ECG. Despite these advantages, body surface mapping has not become a routinely used clinical method. One reason is that visual examination and sophisticated analysis of BSMs do not permit inferring the sequence of excitation and repolarization in the heart with a sufficient degree of certainty and detail. These limitations can be partially overcome by implementing inverse procedures that reconstruct epicardial potentials, isochrones, and ECGs from body surface measurements. Furthermore, ongoing experimental work and simulation studies show that a great deal of information about intramural events can he elicited from measured or reconstructed epicardial potential distributions. Interpreting epicardial data in terms of deep activity requires extensive knowledge of the architecture of myocardial fibers, their anisotropic properties, and the role of rotational anisotropy in affecting propagation and the associated potential fields.     

Cardiomyocyte cultures with controlled macroscopic anisotropy: a model for functional electrophysiological studies of cardiac muscle

Structural and functional cardiac anisotropy varies with the development, location, and pathophysiology in the heart. The goal of this study was to design a cell culture model system in which the degree, change in fiber direction, and discontinuity of anisotropy can be controlled over centimeter-size length scales. Neonatal rat ventricular myocytes were cultured on fibronectin on 20-mm diameter circular cover slips. Structure-function relationships were assessed using immunostaining and optical mapping. Cell culture on microabraded cover slips yielded cell elongation and coalignment in the direction of abrasion, and uniform, macroscopically continuous, elliptical propagation with point stimulation. Coarser microabrasion (wider and deeper abrasion grooves) increased longitudinal (23.5 to 37.2 cm/s; r=0.66) and decreased transverse conduction velocity (18.1 to 9.2 cm/s; r=-0.84), which resulted in increased longitudinal-to-transverse velocity anisotropy ratios (1.3 to 3.7, n=61). A thin transition zone between adjacent uniformly anisotropic areas with 45 degrees or 90 degrees difference in fiber orientation acted as a secondary source during 2x threshold field stimulus. Cell culture on cover slips micropatterned with 12- or 25- micro m wide fibronectin lines and previously coated with decreasing concentrations of background fibronectin yielded transition from continuous to discontinuous anisotropic architecture with longitudinally oriented intercellular clefts, decreased transverse velocity (16.9 to 2.6 cm/s; r=-0.95), increased velocity anisotropy ratios (1.6 to 5.6, n=70), and decreased longitudinal velocity (36.4 to 14.6 cm/s; r=-0.85) for anisotropy ratios >3.5. Cultures of cardiac myocytes with controlled degree, uniformity and continuity of structural, and functional anisotropy may enable systematic 2-dimensional in vitro studies of macroscopic structure-related mechanisms of reentrant arrhythmias. The full text of this article is available at http://www.circresaha.org.     

Artificial Neural Networks for Predicting Plastic Anisotropy of Sheet Metals Based on Indentation Test

This paper mainly proposes two kinds of artificial neural network (ANN) models for predicting the plastic anisotropy properties of sheet metal using spherical indentation test, which minimizes measurement time, costs, and simplifies the process of obtaining the anisotropy properties than the conventional tensile test. The proposed ANN models for predicting anisotropic properties can replace the traditional complex dimensionless analysis. Moreover, this paper is not limited to the prediction of yield strength anisotropy but also further accurately predicts the Lankford coefficient in different orientations. We newly construct an FE spherical indentation model, which is suitable for sheet metal in consideration of actual compliance. To obtain a large dataset for training the ANN, the constructed FE model is utilized to simulate pure and alloyed engineering metals with one thousand elastoplastic parameter conditions. We suggest the specific variables of the residual indentation mark as input parameters, also with the indentation load–depth curve. The profile of the residual indentation, including the height and length in different orientations, are used to analyze the anisotropic properties of the material. Experimental validations have been conducted with three different sheet alloys, TRIP1180 steel, zinc alloy, and aluminum alloy 6063-T6, comparing the proposed ANN model and the uniaxial tensile test. In addition, machine vision was used to efficiently analyze the residual indentation marks and automatically measure the indentation profiles in different orientations. The proposed ANN model exhibits remarkable performance in the prediction of the flow curves and Lankford coefficient of different orientations.     

Spectroscopic Analysis of Rare-Earth Silicide Structures on the Si(111) Surface

Two-dimensional rare-earth silicide layers deposited on silicon substrates have been intensively investigated in the last decade, as they can be exploited both as Ohmic contacts or as photodetectors, depending on the substrate doping. In this study, we characterize rare-earth silicide layers on the Si(111) surface by a spectroscopic analysis. In detail, we combine Raman and reflectance anisotropy spectroscopy (RAS) with first-principles calculations in the framework of the density functional theory. RAS suggests a weakly isotropic surface, and Raman spectroscopy reveals the presence of surface localized phonons. Atomistic calculations allow to assign the detected Raman peaks to phonon modes localized at the silicide layer. The good agreement between the calculations and the measurements provides a strong argument for the employed structural model.     

Improving Numerical Modeling Accuracy for Fiber Orientation and Mechanical Properties of Injection Molded Glass Fiber Reinforced Thermoplastics

Local fiber alignment in fiber-reinforced thermoplastics is governed by complex flows during the molding process. As fiber-induced material anisotropy leads to non-homogeneous effective mechanical properties, accurate prediction of the final orientation state is critical for integrated structural simulations of these composites. In this work, a data-driven inverse modeling approach is proposed to improve the physics-based structural simulation of short glass fiber reinforced thermoplastics. The approach is divided into two steps: (1) optimization of the fiber orientation distribution (FOD) predicted by the Reduce Strain Closure (RSC) model, and (2) identification of the composite’s mechanical properties used in the Ramberg–Osgood (RO) multiscale structural model. In both steps, the identification of the model’s parameters was carried out using a Genetic Algorithm. Artificial Neural Networks were used as a machine learning-based surrogate model to approximate the simulation results locally and reduce the computational time. X-ray micro-computed tomography and tensile tests were used to acquire the FOD and mechanical data, respectively. The optimized parameters were then used to simulate a tensile test for a specimen injection molded in a dumbbell-shaped cavity selected as a case study for validation. The FOD prediction error was reduced by 51% using the RSC optimized coefficients if compared with the default coefficients of the RSC model. The proposed data-driven approach, which calculates both the RSC coefficients and the RO parameters by inverse modeling from experimental data, allowed improvement in the prediction accuracy by 43% for the elastic modulus and 59% for the tensile strength, compared with the non-optimized analysis.     

Image-based multiscale modeling predicts tissue-level and network-level fiber reorganization in stretched cell-compacted collagen gels

The mechanical environment plays an important role in cell signaling and tissue homeostasis. Unraveling connections between externally applied loads and the cellular response is often confounded by extracellular matrix (ECM) heterogeneity. Image-based multiscale models provide a foundation for examining the fine details of tissue behavior, but they require validation at multiple scales. In this study, we developed a multiscale model that captured the anisotropy and heterogeneity of a cell-compacted collagen gel subjected to an off-axis hold mechanical test and subsequently to biaxial extension. In both the model and experiments, the ECM reorganized in a nonaffine and heterogeneous manner that depended on multiscale interactions between the fiber networks. Simulations predicted that tensile and compressive fiber forces were produced to accommodate macroscopic displacements. Fiber forces in the simulation ranged from −11.3 to 437.7 nN, with a significant fraction of fibers under compression (12.1% during off-axis stretch). The heterogeneous network restructuring predicted by the model serves as an example of how multiscale modeling techniques provide a theoretical framework for understanding relationships between ECM structure and tissue-level mechanical properties and how microscopic fiber rearrangements could lead to mechanotransductive cell signaling.     

Study of Unipolar Electrogram Morphology in a Computer Model of Atrial Fibrillation

Introduction: Electrograms exhibit a wide variety of morphologies during atrial fibrillation (AF). The basis of these time courses, however, is not completely understood. In this study, data from computer models were studied to relate features of the signals to the underlying dynamics and tissue substrate.
Methods and Results: A computer model of entire human atria with a gross fiber architecture based on histology and membrane kinetics based on the Courtemanche et al. atrial model was developed to simulate paced activation and simulated AF. Unipolar electrograms were computed using a current source approximation at 256 sites in right atrium, to simulate a mapping array. The results show the following: (1) In a homogeneous and isotropic tissue, the presence of highly asymmetric electrograms is rare (<2%), although there is a marked variability in amplitude and symmetry. (2) The introduction of anisotropy increases this variability in symmetry and amplitude of the, electrograms especially for propagation across fibers. The percentage of highly asymmetric electrograms increases to 12% to 15% for anisotropy ratios greater than 3:1. (3) Multiphasic and fractionated electrograms are rarely seen in the model with uniform properties but are more common (15%–17%) in a model including regions with abrupt changes in conductivity. Beat-to-beat variations in the occurrence of multiphasic signals are possible with fixed anatomic heterogeneity, due to beat-to-beat variations in the direction of the wavefront relative to the heterogeneity.
Conclusion: Analysis of the amplitude and symmetry of unipolar atrial electrograms can provide information about the electrophysiologic substrate maintaining AF. (J Cardiovasc Electrophysiol, Vol. 14, pp. S172-S179, October 2003, Suppl.)     

Regional mechanics determine collagen fiber structure in healing myocardial infarcts

Following myocardial infarction, the mechanical properties of the healing infarct are an important determinant of heart function and the risk of progression to heart failure. In particular, mechanical anisotropy (having different mechanical properties in different directions) in the healing infarct can preserve pump function of the heart. Based on reports of different collagen structures and mechanical properties in various animal models, we hypothesized that differences in infarct size, shape, and/or location produce different patterns of mechanical stretch that guide evolving collagen fiber structure. We tested the effects of infarct shape and location using a combined experimental and computational approach. We studied mechanics and collagen fiber structure in cryoinfarcts in 53 Sprague-Dawley rats and found that regardless of shape or orientation, cryoinfarcts near the equator of the left ventricle stretched primarily in the circumferential direction and developed circumferentially aligned collagen, while infarcts at the apex stretched similarly in the circumferential and longitudinal directions and developed randomly oriented collagen. In a computational model of infarct healing, an effect of mechanical stretch on fibroblast and collagen alignment was required to reproduce the experimental results. We conclude that mechanical environment determines collagen fiber structure in healing myocardial infarcts. Our results suggest that emerging post-infarction therapies that alter regional mechanics will also alter infarct collagen structure, offering both potential risks and novel therapeutic opportunities.     

Magnetic resonance microimaging of intraaxonal water diffusion in live excised lamprey spinal cord

Anisotropy of water diffusion in axon tracts, as determined by diffusion-weighted MRI, has been assumed to reflect the restriction of water diffusion across axon membranes. Reduction in this anisotropy has been interpreted as degeneration of axons. These interpretations are based primarily on a priori reasoning that has had little empirical validation. We used the experimental advantages of the sea lamprey spinal cord, which contains several very large axons, to determine whether intraaxonal diffusion is isotropic and whether anisotropy is attributable to restriction of water mobility by axon surface membranes. Through the application of magnetic resonance microimaging, we were able to measure the purely intraaxonal diffusion characteristics of the giant reticulospinal axons (20-40 microm in diameter). The intraaxonal apparent diffusion coefficients of water parallel (longitudinal ADC, l-ADC) and perpendicular (transverse ADC, t-ADC) to the long axis were 0.98 +/- 0.06 (10(-3) mm2 sec) and 0.97 +/- 0.11 (10(-3) mm2 sec), respectively. In white matter regions that included multiple axons, l-ADCs were almost identical regardless of axon density in the sampled axon tract. By comparison, t-ADCs were reduced and varied inversely with the number of axons (and thus axolemmas) in a fixed cross-sectional area. Thus, diffusion was found to be isotropic when measured entirely within a single axon and anisotropic when measured in regions that included multiple axons. These findings support the hypothesis that the cell membrane is the primary source of diffusion anisotropy in fiber tracts of the central nervous system.     

Cardiac electrical activity-from heart to body surface and back again

We report here on our latest developments in the forward and inverse problems of electrocardiology. In the forward problem, a coupled cellular model of cardiac excitation-contraction is embedded within an anatomically realistic model of the cardiac ventricles, which is itself embedded within a torso model. This continuum modelling framework allows the effects of cellular-level activity on the surface electrocardiogram (ECG) to be carefully examined. Furthermore, the contributions of contraction and local ischemia on body surface recordings can also be elucidated. Such information can provide theoretical limits to the sensitivity and ultimately the detection capability of body surface ECG recordings. Despite being very useful, such detailed forward modelling is not directly applicable when seeking to use densely sampled ECG information to assess a patient in a clinical environment (the inverse problem). In such a situation patient specific models must be constructed and, due to the nature of the inverse problem, the level of detail that can be reliably reproduced is limited. Extensive simulation studies have shown that the accuracy with which the heart is localised within the torso is the primary limiting factor. To further identify the practical performance capabilities of the current inverse algorithms, high quality experimental data is urgently needed. We have been working towards such an objective with a number of groups, including our local hospital in Auckland. At that hospital, in patients undergoing catheter ablation surgery, up to 256 simultaneous body surface signals were recorded by using various catheter pacing protocols. The geometric information required to customize the heart and torso model was obtained using a combination of ultrasound and laser scanning technologies. Our initial results indicate that such geometric imaging modalities are sufficient to produce promising inversely-constructed activation profiles.     

Virtual Electrode Effects in Transvenous Defibrillation-Modulation by Structure and Interface: Evidence from Bidomain Simulations and Optical Mapping

Virtual Electrodes, Bidomain Model, and Defibrillation. Introduction : Our goal in this combined modeling and experimental study was to gain insight into the transmembrane potential changes in defibrillation conditions, namely, when shocks are delivered by an implantable cardioverter defibrillator (ICD). Two hypotheses concerning the presence and characteristics of virtual electrode effects (VEE) during an ICD shock were tested numerically and experimentally: (H1) anisotropy-dependent VEE are induced over a considerable portion of the "bulk" myocardium; and (H2) surface (epicardial and endocardial) VEE are generated under special tissue bath conditions and are not fully anisotropy determined.
Methods and Results : Optical mapping was performed on Langendorff-perfused rabbit hearts (n = 4) stained with di-4-ANEPPS. Monophasic shocks were applied during the plateau phase of an action potential through a 9-mm long distal electrode in the right or left ventricle and a 6-cm proximal electrode positioned 3 cm posteriorly to the heart. We modeled the experiment using an ellipsoidal bidomain heart with transmural fiber rotation, placed in a perfusing bath, and subjected to defibrillation shocks delivered by an electrode configuration as described. Our numerical simulations demonstrated VEE occupying a significant portion of the myocardium in the conditions of unequal anisotropy ratios for the intra- and extracellular domains. Statistically significant differences in epicardial polarization patterns were predicted numerically and confirmed experimentally when the interface conditions varied.
Conclusion : The present study concludes that VEE are present in transvenous defibrillation. They are shaped by the combined effect of cardiac tissue characteristics and interface conditions. Because of their size, VEE might contribute significantly to defibrillation outcome.     

Determination of the Forming Limit for a ZIRLO™ Sheet with High Anisotropy

In this study, the experimental two-dimensional forming limit diagram (FLD) data for a ZIRLO™ sheet, which is used in nuclear fuel rod support grids, were converted and presented as a triaxiality failure diagram (TFD). Most previous studies assumed ZIRLO™ to be isotropic when calculating the effective stress and strain. However, for highly anisotropic materials, the anisotropy should be considered for calculations of effective stress and strain; hence, in this study, they were calculated by introducing the normal anisotropy coefficient. To obtain this parameter of the ZIRLO™ specimens, tensile tests were performed on specimens with 0°, 45°, and 90° angles with respect to the rolling direction. It was observed that the average normal anisotropy coefficient measured during the tests was 4.94, which is very high. The von Mises isotropic and Hill 48 anisotropic yield criterion were applied to the FLD data that were experimentally determined using a limit dome height test and were converted into effective stress and effective strain. When the FLD is converted to TFD, the curve will increase in the top-right direction if the r-value is greater than 1, and this become more severe as the r-value increases. The TFD, which was converted considering the anisotropy, is almost the same to the TFD obtained using the digital image correlation method in the tensile tests of four specimens with different stress states. If anisotropy is not considered, then the formability is normally underestimated. However, a highly accurate TFD can be obtained with the method proposed in this study.     

Mechanisms of ST change in partial thickness ischemia

The origin of ST depression in ischemia remains poorly understood. The accepted source is of intracellular current flowing between the ischemic and non ischaemic muscle both in systole and diastole such that the AC recorded electrocardiogram shows ST elevation over the ischemic area. The difficulty comes with partial thickness ischemia where the body surface changes do not allow localisation of the ischemic region. In an animal model we have shown that the reason one cannot see the region on the body surface is that the epicardial distribution of ST segment is almost identical for partial thickness ischaemia in the left anterior descending coronary artery, (LAD) and circumflex coronary artery (Cx) territories. Dissection of the reasons for this finding has lead to 3 contributing factors. The first is the role of the right ventricular blood mass, the second the boundary between ischemia and normal and the third the presence of anisotropy and its contribution. In a block of myocardium with anisotropy included we have shown marked differences between the distributions depending on the anisotropy. We have also shown that the published values of conductivity for use in the bidomain model produce unacceptably disparate results.