Browsing by Author "Rama, Ritesh Rao"

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    Local maximum entropy approximation-based modelling of the canine heart
    (2012) Rama, Ritesh Rao; Skatulla, Sebastian
    Local Maximum Entropy (LME) method is an approximation technique which has been known to have good approximation characteristics. This is due to its non-negative shape functions and the weak Kronecker delta property which allow the solutions to be continuous and smooth as compared to the Moving Least Square method (MLS) which is used in the Element Free Galerkin method (EFG). The method is based on a convex optimisation scheme where a non-linear equation is solved with the help of a Newton algorithm, implemented in an in-house code called SESKA. In this study, the aim is to compare LME and MLS and highlight the differences. Preliminary benchmark tests of LME are found to be very conclusive. The method is able to approximate deformation of a cantilever beam with higher accuracy as compared to MLS. Moreover, its rapid convergence rate, based on a Cook's membrane problem, demonstrated that it requires a relatively coarser mesh to reach the exact solution. With those encouraging results, LME is then applied to a larger non-linear cardiac mechanics problem. That is simulating a healthy and a myocardial infarcted canine left ventricle (LV) during one heart beat. The LV is idealised by a prolate spheroidal ellipsoid. It undergoes expansion during the diastolic phase, addressed by a non-linear passive stress model which incorporates the transversely isotropic properties of the material. The contraction, during the systolic phase, is simulated by Guccione's active stress model. The infarct region is considered to be non-contractile and twice as stiff as the healthy tissue. The material loss, especially during the necrotic phase, is incorporated by the use of a homogenisation approach. Firstly, the loss of the contraction ability of the infarct region counteracts the overall contraction behaviour by a bulging deformation where the occurrence of high stresses are noted. Secondly, with regards to the behaviour of LME, it is found to feature high convergence rate and a decrease in computation time with respect to MLS. However, it is also observed that LME is quite sensitive to the nodal spacing in particular for an unstructured nodal distribution where it produces results that are completely unreliable.
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    Proper orthogonal decomposition with interpolation-based real-time modelling of the heart
    (2017) Rama, Ritesh Rao; Skatulla, Sebastian; Reddy, Daya
    Several studies have been carried out recently with the aim of achieving cardiac modelling of the whole heart for a full heartbeat. However, within the context of the Galerkin method, those simulations require high computational demand, ranging from 16 - 200 CPUs, and long calculation time, lasting from 1 h - 50 h. To solve this problem, this research proposes to make use of a Reduced Order Method (ROM) called the Proper Orthogonal Decomposition with Interpolation method (PODI) to achieve real-time modelling with an adequate level of solution accuracy. The idea behind this method is to first construct a database of pre-computed full-scale solutions using the Element-free Galerkin method (EFG) and then project a selected subset of these solutions to a low dimensional space. Using the Moving Least Square method (MLS), an interpolation is carried out for the problem-at-hand, before the resulting coefficients are projected back to the original high dimensional solution space. The aim of this project is to tackle real-time modelling of a patient-specific heart for a full heartbeat in different stages, namely: modelling (i) the diastolic filling with variations of material properties, (ii) the isovolumetric contraction (IVC), ejection and isovolumetric relation (IVR) with arbitrary time evolutions, and (iii) variations in heart anatomy. For the diastolic filling, computations are carried out on a bi-ventricle model (BV) to investigate the performance and accuracy for varying the material parameters. The PODI calculations of the LV are completed within 14 s on a normal desktop machine with a relative L₂-error norm of 6x10⁻³. These calculations are about 2050 times faster than EFG, with each displacement step generated at a calculation frequency of 1074 Hz. An error sensitivity analysis is consequently carried out to find the most sensitive parameter and optimum dataset to be selected for the PODI calculation. In the second phase of the research, a so-called "time standardisation scheme" is adopted to model a full heartbeat cycle. This is due to the simulation of the IVC, ejection, and IVR phases being carried out using a displacement-driven calculation method which does not use uniform simulation steps across datasets. Generated results are accurate, with the PODI calculations being 2200 faster than EFG. The PODI method is, in the third phase of this work, extended to deal with arbitrary heart meshes by developing a method called "Degrees of freedom standardisation" (DOFS). DOFS consists of using a template mesh over which all dataset result fields are projected. Once the result fields are standardised, they are consequently used for the PODI calculation, before the PODI solution is projected back to the mesh of the problem-at-hand. The first template mesh to be considered is a cube mesh. However, it is found to produce results with high errors and non-physical behaviour. The second template mesh used is a heart template. In this case, a preprocessing step is required where a non-rigid transformation based on the coherent point drift method is used to transform all dataset hearts onto the heart template. The heart template approach generated a PODI solution of higher accuracy at a relatively low computational time. Following these encouraging results, a final investigation is carried out where the PODI method is coupled with a computationally expensive gradient-based optimisation method called the Levenberg- Marquardt (PODI-LVM) method. It is then compared against the full-scale simulation one where the EFG is used with the Levenberg-Marquardt method (EFG-LVM). In this case, the PODI-LVM simulations are 1025 times faster than the EFG-LVM, while its error is less than 1%. It is also observed that since the PODI database is built using EFG simulations, the PODI-LVM behaves similarly to the EFG-LVM one.