Left Ventricular Trabeculations Decrease the Wall Shear Stress and Increase the Intra-Ventricular Pressure Drop in CFD Simulations

The aim of the present study is to characterize the hemodynamics of left ventricular (LV) geometries to examine the impact of trabeculae and papillary muscles (PMs) on blood flow using high performance computing (HPC). Five pairs of detailed and smoothed LV endocardium models were reconstructed from high-resolution magnetic resonance images (MRI) of ex-vivo human hearts. The detailed model of one LV pair is characterized only by the PMs and few big trabeculae, to represent state of art level of endocardial detail. The other four detailed models obtained include instead endocardial structures measuring ≥1 mm2 in cross-sectional area. The geometrical characterizations were done using computational fluid dynamics (CFD) simulations with rigid walls and both constant and transient flow inputs on the detailed and smoothed models for comparison. These simulations do not represent a clinical or physiological scenario, but a characterization of the interaction of endocardial structures with blood flow. Steady flow simulations were employed to quantify the pressure drop between the inlet and the outlet of the LVs and the wall shear stress (WSS). Coherent structures were analyzed using the Q-criterion for both constant and transient flow inputs. Our results show that trabeculae and PMs increase the intra-ventricular pressure drop, reduce the WSS and disrupt the dominant single vortex, usually present in the smoothed-endocardium models, generating secondary small vortices. Given that obtaining high resolution anatomical detail is challenging in-vivo, we propose that the effect of trabeculations can be incorporated into smoothed ventricular geometries by adding a porous layer along the LV endocardial wall. Results show that a porous layer of a thickness of 1.2·10−2 m with a porosity of 20 kg/m2 on the smoothed-endocardium ventricle models approximates the pressure drops, vorticities and WSS observed in the detailed models.This paper has been partially funded by CompBioMed project, under H2020-EU.1.4.1.3 European Union’s Horizon 2020 research and innovation programme, grant agreement n◦ 675451. FS is supported by a grant from Severo Ochoa (n◦ SEV-2015-0493-16-4), Spain. CB is supported by a grant from the Fundació LaMarató de TV3 (n◦ 20154031), Spain. TI and PI are supported by the Institute of Engineering in Medicine, USA, and the Lillehei Heart Institute, USA.Peer ReviewedPostprint (published version

Modelos newtonianos y no newtonianos asociados al flujo sanguíneo: revisión

The behavior and characteristics of blood in the circulatory system have generated various models that can be applied to the flow analysis blood, including Newtonian and non-Newtonian models. This review presents eleven models proposed from experimental parameters, which include studies of viscosity with different speeds of shear and density associated with fluid dynamics. Were characterized in accordance with methods, specific parameters, used experimental values. Comparing efficiency, certainty and precision of the models used.El comportamiento y características de la sangre en el sistema circulatorio han generado diversos modelos que pueden ser aplicados para el análisis del flujo sanguíneo, entre los que se incluyen modelos newtonianos y no newtonianos. En esta revisión se presentan once modelos propuestos a partir de parámetros experimentales que incluyen estudios de viscosidad con diferentes velocidades de cizallamiento y densidad asociada a la dinámica de fluidos. Se caracterizaron de acuerdo con métodos, parámetros específicos y valores experimentales utilizados; además, se comparó la eficacia, certeza y precisión de los modelos utilizados

Newtonian and non newtonian models associated with blood flow: review

El comportamiento y características de la sangre en el sistema circulatorio han generado diversos modelos que pueden ser aplicados para el análisis del flujo sanguíneo, que incluye modelos newtonianos y no newtonianos. En esta revisión se presentan ocho (8) modelos propuestos a partir de parámetros experimentales, que incluyen estudios de viscosidad con diferentes velocidades de cizallamiento, y densidad asociada a la dinámica de fluidos. Se caracterizaron de acuerdo con métodos, parámetros y valores experimentales. Al final se relacionan los elementos que debe tener cada modelo en función de sus variables como es la dependencia del hematocrito, la temperatura y la tasa de corte.The behavior and characteristics of the blood in the circulatory system have generated several models that can be applied to the blood flow analysis, which includes Newtonian and non-Newtonian models. In this review, proposed models of experimental parameters are presented, which include viscosity studies with different shear rates, and a density associated with fluid dynamics. They were characterized according to experimental methods, parameters and values. In the end, the elements that each model must have are related to its variables, such as the dependence on the hematocrit, the temperature and the cut rate

Sequential Coupling Shows Minor Effects of Fluid Dynamics on Myocardial Deformation in a Realistic Whole-Heart Model

Background: The human heart is a masterpiece of the highest complexity coordinating multi-physics aspects on a multi-scale range. Thus, modeling the cardiac function in silico to reproduce physiological characteristics and diseases remains challenging. Especially the complex simulation of the blood's hemodynamics and its interaction with the myocardial tissue requires a high accuracy of the underlying computational models and solvers. These demanding aspects make whole-heart fully-coupled simulations computationally highly expensive and call for simpler but still accurate models. While the mechanical deformation during the heart cycle drives the blood flow, less is known about the feedback of the blood flow onto the myocardial tissue. Methods and Results: To solve the fluid-structure interaction problem, we suggest a cycle-to-cycle coupling of the structural deformation and the fluid dynamics. In a first step, the displacement of the endocardial wall in the mechanical simulation serves as a unidirectional boundary condition for the fluid simulation. After a complete heart cycle of fluid simulation, a spatially resolved pressure factor (PF) is extracted and returned to the next iteration of the solid mechanical simulation, closing the loop of the iterative coupling procedure. All simulations were performed on an individualized whole heart geometry. The effect of the sequential coupling was assessed by global measures such as the change in deformation and—as an example of diagnostically relevant information—the particle residence time. The mechanical displacement was up to 2 mm after the first iteration. In the second iteration, the deviation was in the sub-millimeter range, implying that already one iteration of the proposed cycle-to-cycle coupling is sufficient to converge to a coupled limit cycle. Conclusion: Cycle-to-cycle coupling between cardiac mechanics and fluid dynamics can be a promising approach to account for fluid-structure interaction with low computational effort. In an individualized healthy whole-heart model, one iteration sufficed to obtain converged and physiologically plausible results

Effect of non-Newtonian fluid rheology on an arterial bypass graft: A numerical investigation guided by constructal design

In post-operative scenarios of arterial graft surgeries to bypass coronary artery stenosis, fluid dynamics plays a crucial role. Problems such as intimal hyperplasia have been related to fluid dynamics and wall shear stresses near the graft junction. This study focused on the question of the use of Newtonian and non-Newtonian models to represent blood in this type of problem in order to capture important flow features, as well as an analysis of the performance of geometry from the view of Constructive Theory. The objective of this study was to investigate the effects rheology on the steady-state flow and on the performance of a system consisting of an idealized version of a partially obstructed coronary artery and bypass graft. The Constructal Design Method was employed with two degrees of freedom: the ratio be- tween bypass and artery diameters and the junction angle at the bypass inlet. The flow problem was solved numerically using the Finite Volume Method with blood modeled employing the Carreau equation for viscosity. The Computational Fluid Dynamics model associated with the Sparse Grid method generated eighteen response surfaces, each representing a severe stenosis degree of 75% for specific combinations of rheological parameters, dimensionless viscosity ratio, Carreau number and flow index at two distinct Reynolds numbers of 150 and 250. There was a considerable dependence of the pressure drop on rhe- ological parameters. For the two Reynolds numbers studied, the Newtonian case presented the lowest value of the dimensionless pressure drop, suggesting that the choice of applying Newtonian blood may underestimate the value of pressure drop in the system by about 12.4% ( Re = 150) and 7.8% ( Re = 250). Even so, results demonstrated that non-Newtonian rheological parameters did not influence either the shape of the response surfaces or the optimum bypass geometry, which consisted of a diameter ratio of 1 and junction angle of 30 °. However, the viscosity ratio and the flow index had the greatest im- pact on pressure drop, recirculation zones and wall shear stress. Rheological parameters also affected the recirculation zones downstream of stenosis, where intimal hyperplasia is more prevalent. Newto- nian and most non-Newtonian results had similar wall shear stresses, except for the non-Newtonian case with high viscosity ratio. In the view of Constructal Design, the geometry of best performance was in- dependent of the rheological model. However, rheology played an important role on pressure drop and flow dynamics, allowing the prediction of recirculation zones that were not captured by a Newtonian model

Computational fluid dynamics of coronary arteries with implanted stents: effects of Newtonian and non‐Newtonian blood flows

This study introduces and compares computational fluid dynamics of Newtonian and non-Newtonian blood flows in coronary arteries, with and without considering stents. Three blood flow models, including Newtonian, Carreau, and non-Newtonian power-law models, were simulated to investigate their effect, and the solution algorithm includes drawing the geometry, creating the desired mesh, and then simulating Newtonian and non-Newtonian blood flow different models and comparing them with each other, is presented in the article. A Newtonian fluid model has been commonly used in the simulation of blood flow, whereas blood has non-Newtonian properties due to the nature of a solution containing suspended particles. The goal of this research is to investigate the differences between the models built with Newtonian and non-Newtonian fluid assumptions. In addition, a stent was designed and the effect of the stent on blood flow parameters was investigated for all three flow models, including Newtonian, Carreau, and non-Newtonian power-law models. Stents are medical devices that can be placed in arteries to open up blood flow in a blocked vessel. Stents can affect the wall shear stress. Knowing the slight deformation of the shear stress makes the importance of stent implantation and also helps to optimize the design of the intravascular stent, which can affect the occlusion of the vessels. The distribution of the velocity, pressure, and wall shear stress in all blood flow models with and without considering the effect of stents have been investigated and finally compared. Therefore, in general, the innovation of this article is to find the effect of implanted stents on blood flow parameters with different blood flow models, both Newtonian and non-Newtonian. A comparison of Newtonian and non-Newtonian flows showed that in the case of the Carreau non-Newtonian model, the wall shear stress was higher. In addition, in the results of the geometric model with a stent effect compared to the geometric model without a stent effect, it is evident that there was a higher velocity and wall shear stress

Computational investigation of left ventricular hemodynamics following bioprosthetic aortic and mitral valve replacement

The left ventricle of the heart is a fundamental structure in the human cardiac system that pumps oxygenated blood into the systemic circulation. Several valvular conditions can cause the aortic and mitral valves associated with the left ventricle to become severely diseased and require replacement. However, the clinical outcomes of such operations, specifically the postoperative ventricular hemodynamics of replacing both valves, are not well understood. This work uses computational fluid–structure interaction (FSI) to develop an improved understanding of this effect by modeling a left ventricle with the aortic and mitral valves replaced with bioprostheses. We use a hybrid Arbitrary Lagrangian–Eulerian/immersogeometric framework to accommodate the analysis of cardiac hemodynamics and heart valve structural mechanics in a moving fluid domain. The motion of the endocardium is obtained from a cardiac biomechanics simulation and provided as an input to the proposed numerical framework. The results from the simulations in this work indicate that the replacement of the native mitral valve with a tri-radially symmetric bioprosthesis dramatically changes the ventricular hemodynamics. Most significantly, the vortical motion in the left ventricle is found to reverse direction after mitral valve replacement. This study demonstrates that the proposed computational FSI framework is capable of simulating complex multiphysics problems and can provide an in-depth understanding of the cardiac mechanics.This is a manuscript of the article Published as Xu, Fei, Emily L. Johnson, Chenglong Wang, Arian Jafari, Cheng-Hau Yang, Michael S. Sacks, Adarsh Krishnamurthy, and Ming-Chen Hsu. "Computational investigation of left ventricular hemodynamics following bioprosthetic aortic and mitral valve replacement." Mechanics Research Communications 112 (2021): 103604. doi: https://doi.org/10.1016/j.mechrescom.2020.103604. Copyright 2021 The Authors. CC BY-NC-N

Patient-specific design of the right ventricle to pulmonary artery conduit via computational analysis

Cardiovascular prostheses are routinely used in surgical procedures to address congenital malformations, for example establishing a pathway from the right ventricle to the pulmonary arteries (RV-PA) in pulmonary atresia and truncus arteriosus. Currently available options are fixed size and have limited durability. Hence, multiple re-operations are required to match the patients’ growth and address structural deterioration of the conduit. Moreover, the pre-set shape of these implants increases the complexity of operation to accommodate patient specific anatomy. The goal of the research group is to address these limitations by 3D printing geometrically customised implants with growth capacity. In this study, patient-specific geometrical models of the heart were constructed by segmenting MRI data of patients using Mimics inPrint 2.0. Computational Fluid Dynamics (CFD) analysis was performed, using ANSYS CFX, to design customised geometries with better haemodynamic performance. CFD simulations showed that customisation of a replacement RV-PA conduit can improve its performance. For instance, mechanical energy dissipation and wall shear stress can be significantly reduced. Finite Element modelling also allowed prediction of the suitable thickness of a synthetic material to replicate the behaviour of pulmonary artery wall under arterial pressures. Hence, eliminating costly and time-consuming experiments based on trial-and-error. In conclusion, it is shown that patient-specific design is feasible, and these designs are likely to improve the flow dynamics of the RV-PA connection. Modelling also provides information for optimisation of biomaterial. In time, 3D printing a customised implant may simplify replacement procedures and potentially reduce the number of operations required over a life time, bringing substantial improvements in quality of life to the patient

Estudo numérico do escoamento sanguíneo como um fluido não-newtoniano nas artérias renais

Dissertação de mestrado integrado em Engenharia BiomédicaAs doenças cardiovasculares são um problema de saúde com elevada incidência na população mundial. Desta forma, a caracterização do fluxo sanguíneo é uma importante estratégia para estabelecer uma relação entre o comportamento hemodinâmico e a ocorrência de doenças cardiovasculares. As complexas propriedades do fluxo sanguíneo, tornam-se ainda mais evidentes quando associadas a doenças cardiovasculares. A aterosclerose é a doença cardiovascular mais comum nas artérias, esta caracteriza-se pela deposição de placas nas paredes internas das artérias, levando à redução da área de secção transversal, denominada por estenose. Esta redução, pode produzir um impacto significativo no fluxo sanguíneo. O objetivo do presente trabalho, é o estudo numérico das propriedades hemodinâmicas da aorta abdominal ao nível da bifurcação renal, através da implementação de diferentes condições de escoamento. Esta região é um local propicio ao desenvolvimento de aterosclerose, levando a uma diminuição da corrente sanguínea, e consequentemente a problemas, como a hipertensão. As simulações foram realizadas utilizando, ANSYS FLUENT®, um software que emprega o método dos volumes finitos. Esta ferramenta permite avaliar a distribuição dos perfis de velocidade e tensões de corte na parede durante o ciclo cardíaco para os diferentes casos estudados. Neste estudo, foram analisadas as diferenças existentes na hemodinâmica quando se considera o sangue como um fluido newtoniano, mas com um escoamento laminar e com um escoamento turbulento, utilizando-se os modelos: k-ɛ, o k-ω SST e o Reynolds Stress. Posteriormente, examinaram-se as principais diferenças existentes na hemodinâmica quando se considera o sangue como um fluido newtoniano e como um fluido não-newtoniano, utilizando-se o modelo de Carreau. Os resultados obtidos permitiram identificar a influência dos diferentes modelos de turbulência no escoamento sanguíneo, indicando que o modelo k-ω STT seria o mais adequado. Para o modelo newtoniano e não-newtoniano, as diferenças são apenas mais evidentes para velocidades mais baixas, no entanto o modelo não-newtoniano deve ser utilizado para estudos do escoamento sanguíneo.The cardiovascular diseases are a main health problem, with high incidence in the world population. Therefore, blood flow characterization is an important strategy to establish a relationship between the hemodynamic behavior and the appearing of cardiovascular pathologies. The complex properties of the blood flow, become even more evident when associated with vascular diseases. Atherosclerosis is the most common cardiovascular disease in arteries, leading to the reduction of the cross-sectional area, called stenosis. This reduction, is capable to induce a huge impact on the normal blood flow. The objective of the present work, is the study of hemodynamic properties on the abdominal aorta at the renal bifurcation region, through the implementation of different flow conditions. The renal arterial region is of high interest, once the development of atherosclerosis is recurrent, and may lead to renal problems, namely renal failure or to hypertension. The simulations were made using, ANSYS FLUENT ®, a software that uses the method of finite volumes. This tool allows to evaluate the distribution of the velocity and wall shear stress profiles, during a cardiac cycle for the diverse cases under study. In this investigation, were analyzed the existing differences on the hemodynamic, considering the blood as a Newtonian fluid, with a laminar flow and also with a turbulent flow, using the k-ɛ model, k-ω SST model and the Reynolds Stress model. Posteriorly, were examined the variances on the hemodynamic when considering now the blood flow as a Newtonian fluid and as a non-Newtonian fluid, using the Carreau model. The obtained results allowed to identify the influence of the different turbulence models on the blood flow, denoting that the k-ω SST model seems to be the more indicated. Between the Newtonian and the non-Newtonian flow models, the differences were more evident for lower velocities. On the other hand, the non-Newtonian model must be used for the study of the blood flow

The numerical analysis of non-Newtonian blood flow in human patient-specific left ventricle

Recently, various non-invasive tools such as the magnetic resonance image (MRI), ultrasound imaging (USI), computed tomography (CT), and the computational fluid dynamics (CFD) have been widely utilized to enhance our current understanding of the physiological parameters that affect the initiation and the progression of the cardiovascular diseases (CVDs) associated with heart failure (HF). In particular, the hemodynamics of left ventricle (LV) has attracted the attention of the researchers due to its significant role in the heart functionality. In this study, CFD owing its capability of predicting detailed flow field was adopted to model the blood flow in images-based patient-specific LV over cardiac cycle. In most published studies, the blood is modeled as Newtonian that is not entirely accurate as the blood viscosity varies with the shear rate in non-linear manner. In this paper, we studied the effect of Newtonian assumption on the degree of accuracy of intraventricular hemodynamics. In doing so, various non-Newtonian models and Newtonian model are used in the analysis of the intraventricular flow and the viscosity of the blood. Initially, we used the cardiac MRI images to reconstruct the time-resolved geometry of the patient-specific LV. After the unstructured mesh generation, the simulations were conducted in the CFD commercial solver FLUENT to analyze the intraventricular hemodynamic parameters. The findings indicate that the Newtonian assumption cannot adequately simulate the flow dynamic within the LV over the cardiac cycle, which can be attributed to the pulsatile and recirculation nature of the flow and the low blood shear rate