Sector 9 colorful wave5/23/2023 ![]() Three-Dimensional Architecture of the Left Ventricular Myocardium. Ex Vivo 3D Diffusion Tensor Imaging and Quantification of Cardiac Laminar Structure. New developments in a strongly coupled cardiac electromechanical model. Three-dimensional analysis of regional cardiac function: A model of rabbit ventricular anatomy. Models of cardiac electromechanics based on individual hearts imaging data: Image-based electromechanical models of the heart. Approaches to modeling crossbridges and calcium-dependent activation in cardiac muscle. Sarcomere mechanics in uniform and non-uniform cardiac muscle: A link between pump function and arrhythmias. A quantitative analysis of cardiac myocyte relaxation: A simulation study. Mathematical modeling of mechanically modulated rhythm disturbances in homogeneous and heterogeneous myocardium with attenuated activity of Na + – K + pump. Simulation of the Undiseased Human Cardiac Ventricular Action Potential: Model Formulation and Experimental Validation. A novel computational model of the human ventricular action potential and Ca transient. Alternans and spiral breakup in a human ventricular tissue model. Modelling the mechanical properties of cardiac muscle. Integrative systems models of cardiac excitation-contraction coupling. A computer study of the left ventricular performance based on fiber structure, sarcomere dynamics, and transmural electrical propagation velocity. Electromechanical models of the ventricles. The fictitious node is located above the LV base. The required derivatives can be found numerically. This will allow researchers to construct fiber direction fields based on the shape of patients’ hearts without DT-MRI data. We hope that our parameters can be averaged or fitted on the species level or at least for the norm and pathologies of particular species. Moreover, the numbers of those parameters for different hearts vary, so the coefficients cannot be averaged to obtain recommended species-level parameter sets. Furthermore, the parameters in have unclear geometrical or physical meaning, unlike ours. Yet, that method usually requires about 10 parameters for each algebraic and 10–40 for trigonometric polynomials, whereas our technique uses only three parameters. The reported root-mean-square error was about 2.3 °–10°. A certain advantage of that approach is its flexibility. In that work, fiber direction field in mice was approximated in spheroidal coordinates by a product of two algebraic and one trigonometric polynomials. Fiber directions can also be fitted through widely-used fitting functions with many more parameters, as was done in. Our model fits the shape of the LV and has only three parameters ( γ 0, γ 1, ϕ max) to adapt fiber directions. We compute the potential in this node not by a finite difference method, but by interpolation, using the node’s closest “in-mesh” neighbors. If for a node ( i, j, k ), at least one of Q v a r d i r cannot be found, this node is marked “out-of-mesh”. The values of Q have to be found once, at the initialization stage. The index of the ϕ-neighbor in direction d i r is k + d i r The index of the ψ-neighbor in direction d i r is j + d i r The meaning of Q v a r d i r is that the index of the γ-neighbor of the node in direction d i r is i + d i r In the case of the non-symmetric LV model, we have to introduce six arrays instead of one, Q v a r d i r, where v a r ∈. Its ϕ-neighbors have indices k ± Q, where Q is an array of natural numbers, and the differences are found so that the Cartesian distances between nodes are within some given limits. In the case of the symmetric LV model, we propose that its γ- and ψ-neighbors have indices i ± 1, j ± 1. Let us consider a mesh node with indices i, j, k of special coordinates γ, ψ, ϕ. We used s = 5, and the results of the 3D comparison are shown in Table 1 and Table 2. Full averaging was impossible because an increase in the smoothing parameter above s ≈ 5 led to an oversmoothing without an essential noise reduction. The noise in the data diminishes with the growth of s. If s = 0, the algorithm makes no changes in the input data. The averaging is controlled by the smoothing parameter s ≥ 0. To identify these parts of errors, we partly averaged the true fiber angle ( α ) and helix angle ( α 1 ) data using the Smoothn function in MATLAB, so we obtained data without outliers. Even if a blue curve is in the middle of a point cloud, such errors accrue. The second part is caused by errors of measurement and by the dispersion of data. This error can be seen in Figure 7, Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12, where the blue curves are out of the red point clouds. One of them is the modeling error caused by inaccuracies in the model. The degree of error in the angles consists of two parts.
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