Development and characterization of the arterial windkessel and its role during left ventricular assist device assistance

Modeling of the cardiovascular system is challenging, but it has the potential to further advance our understanding of normal and pathological conditions. Morphology and function are closely related. The arterial system provides steady blood flow to each organ and damps out wave fluctuations as a consequence of intermittent ventricular ejection. These actions can be approached separately in terms of mathematical relationships between pressure and flow. Lumped parameter models are helpful for the study of the interactions between the heart and the arterial system. The arterial windkessel model still plays a significant role despite its limitations. This review aims to discuss the model and its modifications and derive the fundamental equations by applying electric circuits theory. In addition, its role during left ventricular assist device assistance is explored and discussed in relation to rotary blood pumps

A non-conforming monolithic finite element method for problems of coupled mechanics

In this study, a Lagrange multiplier technique is developed to solve problems of coupled mechanics and is applied to the case of a Newtonian fluid coupled to a quasi-static hyperelastic solid. Based on theoretical developments in [57], an additional Lagrange multiplier is used to weakly impose displacement/velocity continuity as well as equal, but opposite, force. Through this approach, both mesh conformity and kinematic variable interpolation may be selected independently within each mechanical body, allowing for the selection of grid size and interpolation most appropriate for the underlying physics. In addition, the transfer of mechanical energy in the coupled system is proven to be conserved. The fidelity of the technique for coupled fluid-solid mechanics is demonstrated through a series of numerical experiments which examine the construction of the Lagrange multiplier space, stability of the scheme, and show optimal convergence rates. The benefits of non-conformity in multi-physics problems is also highlighted. Finally, the method is applied to a simplified elliptical model of the cardiac left ventricle. © 2010 Elsevier Inc

Electromechanical large scale computational models of the ventricular myocardium

Els models computacionals del cor són una eina important que pot donar als investigadors biomèdics una font addicional d’informació per entendre el funcionament del miocardi. Els models numèrics poden ajudar a interpretar dades experimentals i proporcionar informació complementària sobre mecanismes cardíacs que no poden ser determinats amb precisió mitjançant dispositius clínics clàssics. En aquesta tesi, s’apliquen tècniques de computació a gran escala per construir una eina computacional capaç d’executar-se en paral•lel en milers de processadors, permetent simulacions d’alta fidelitat en malles fines. Per simular el bombeig del cor, s’utilitza un esquema d’acoblament explícit entre les equacions electrofisiològiques en tres dimensions i la formulació en mecànica de sòlids. Per trobar la solució numèrica, s’utilitza el mètode d’elements finits. A més, s’implementen tècniques en assimilació de dades per a l’estimació efectiva dels paràmetres electrofisiològics i mecànics rellevants que apareixen a les equacions, la qual cosa ´es un pas crucial cap a un model cardíac sensible a cada pacient. El codi computacional s’aplica per simular problemes físics reals. S’estudia la propagació electromecànica en una geometria de conill, on es prova la sensibilitat del model a les variacions d’entrada. En particular, l’eina de càlcul s’utilitza per avaluar la influència del camp de fibres cardíaques en la contracció del teixit. Per desenvolupar una simulació cardíaca útil per a fins clínics, el model requereix la integració i combinació de la mecànica computacional i les tècniques de processament d’imatge més recents. El model resultant pot ser la base d’estudis teòrics sobre mecanismes de patologies, oferint als investigadors i cardiòlegs pistes addicionals per comprendre el funcionament del cor. Pot ajudar a la planificació de cirurgia i modelització, com és la predicció dels efectes de compostos farmacològics en el ritme cardíac o l’estudi de l’efecte de medicaments. Aquest projecte només és possible en un equip multidisciplinar, on grups especialitzats uneixen les seves forces en les respectives disciplines: cardiòlegs, investigadors imatge, bioenginyers i científics de la computació. El present model computacional del cor és un pas més cap a la creació d’un laboratori cardíac virtual.A cardiac computational model is a relevant tool that can give biomedical researchers an additional source of information to understand how the heart works. Numerical models can help to interpret experimental data and provide information about cardiac mechanisms that can not be determined accurately by classical clinical devices. In this thesis, High Performance Computing (HPC) techniques are used to build a cardiac computational tool, which is capable of running in parallel in thousands of processors, bioengineers and computational scientists. The present cardiac computational model is one further step towards the creation of a virtual lab, allowing high fidelity simulations on fine meshes. To simulate the pumping heart, an explicit coupling scheme between the three-dimensional electrophysiological equations and the solid mechanics formulation is used, solving the governing equations with finite element methods. Also, data assimilation techniques are implemented for the effective estimation of some relevant electrophysiological parameters, which is a crucial step towards the patient-sensitive cardiac model. The data assimilation techniques are assessed on synthetic data generated by the model. Finally, the computational code is applied to simulate real physical problems. The electromechanical propagation in a rabbit geometry is studied to test the sensitivity of the framework to input variations. Particularly, the computational tool is used to evaluate the influence of the fiber field in the contraction of the tissue. To develop a cardiac simulation useful for clinical purposes, the integrative model requires combining computational mechanics and image processing techniques via data assimilation methods. Coupled with the most advanced image processing analysis, the framework can be the base of theoretical studies into the mechanisms of cardiac pathologies. It can help surgery planning and cardiac modeling, such as the prediction of the impact of pharmacological compounds on the heart’s rhythm or to improve the knowledge of drug study, giving medical researchers additional hints to understand the heart. This realization is only possible in a multidisciplinary team, where specialized groups join forces in their respective disciplines: cardiologists, image researchers, bioengineers and computational scientists. The present cardiac computational model is one further step towards the creation of a virtual la