Towards patient-specific modelling as a pre-operative planning strategy and follow up assessment for the treatment of advanced heart failure with rotary blood pumps

Background: Ventricular Assist Devices (VADs) insertion is an established treatment for patients with end-stage heart failure waiting for a heart transplant or in need for long-term circulatory support (destination therapy). Rotary blood pumps (RBP) are the most popular devices in view of their size and performance. Pre-operative planning strategy for the insertion of a left ventricular assist device (LVAD) requires a timely discussion at a Multi-Disciplinary Team Meeting (MDT). Clinical-decision making is based according to the needs of the patient and must be processed without delays. Nevertheless, thrombus formation remains a feared complication which affects outcome. VADs operate in a flow regime which is difficult to simulate: the transitional region at the boundary of laminar and turbulent flow (low Reynolds number). Different methods have been used but the best approach remains debatable. Computational Fluid Dynamics (CFD) is an attractive and invaluable tool for the study of the interactions between VADs and the cardiovascular system. The aim of this thesis is three-fold: a) to investigate the use of pressure-volume analysis in a clinical setting through the review of six heart failure patients previously discussed at a MDT meeting with a view to predict or guide further management; b) to review the theory behind modelling approaches to VADs and their interactions with the cardiovascular system for better understanding of their clinical use. Then, an overview of computational fluid dynamics (CFD) is considered as a prelude to its application to the analysis of VADs performance. Additionally, the development of a simplified model of centrifugal pump will be used in initial simulations as preliminary analysis; c) to examine an example of a proof-of-concept pilot patient-specific model of an axial flow pump (HeartMate II) as pre-operative planning strategy in a patient-specific model with a view to identify potential critical areas that may affect pump function and outcome in a clinical setting. Material and Methods: 3D reconstruction from CT-scan images of patients who underwent the insertion of rotary blood pumps, namely HeartWare HVAD and HeartMate II. Ansys Fluent has been used for CFD analysis based on the fundamental governing equations of motion. Blood has been modelled as incompressible, Newtonian fluid with density = 1060 and viscosity = 0.0035 kg/m-s. The laminar and SST models have been used for comparison purposes. The rotational motion of the impeller has been implemented using the moving reference frame (MRF) approach. The sliding mesh method has also been used to account for unsteady interaction between stationary and moving part. The no-slip condition has been applied to all walls, which were assumed to be rigid. Boundary conditions consisting of velocity inlet and pressure outlet of the pump based on different settings and constant rotational speed for the impeller. Pressure-velocity coupling has been based on the coupled scheme. Spatial discretisation consisted of the “least square cell based” gradient for velocity and “PRESTO” or second order for pressure. Second order upwind has been set for the momentum, turbulent kinetic energy and specific dissipation rate. First order implicit has been set for transient formulation. The pseudo transient algorithm (steady state), the high order relaxation term and the warped-face gradient correction have been used to add an unsteady term to the solution equations with the aim to improve stability and enhance convergence. Specific settings have been considered for comparison purposes. Results: Pressure-volume simulation analysis in six advanced heart failure patients showed that an integrated model of the cardiovascular system based on lumped-parameter representation, modified time-varying elastance and pressure-volume analysis of ventricular function seems a feasible and suitable approach yielding a sufficiently accurate quantitative analysis in real time, therefore applicable within the time-constraints of a clinical setting. Lumped-parameter models consist of simultaneous ordinary differential equations complemented by an algebraic balance equation and are suitable for examination of global distribution of pressure, flow and volume over a range of physiological conditions with inclusion of the interaction between modelled components. Higher level lumped-parameter modelling is needed to address the interaction between the circulation and other systems based on a compromise between complexity and ability to set the required parameters to personalise an integrated lumped-parameter model for a patient-specific approach. CARDIOSIM© fulfils these requirements and does address the systems interaction with its modular approach and assembly of models with varying degree of complexity although 0-D and 1-D coupling may be required for the evaluation of long-term VAD support. The challenge remains the ability to predict outcome over a longer period of time. The preliminary CFD simulations with the HeartWare HVAD centrifugal pump demonstrated that it is possible to obtain an accurate analysis in a timely manner to complement the clinical review process. The simulations with the pilot patient-specific model of the HeartMate II axial flow pump revealed that a complex 3D reconstruction is feasible in a timely manner and can be used to generate sufficiently accurate results to be used in the context of a MDT meeting for the purposes of clinical decision-making. Overall, these three studies demonstrate that the time frame of the simulations was within hours which may fit the time constraints of the clinical environment in the context of a MDT meeting. More specifically, it was shown that the laminar model may be used for an initial evaluation of the flow development within the pump. Nonetheless, the k- model offers higher accuracy if the timeline of the clinical setting allows for a longer simulation. Conclusion: This thesis aimed at the understanding of the use of computational modelling as a pre-operative planning strategy and follow up assessment for the treatment of advanced heart failure with rotary blood pumps. The novelty lays in the use of both pressure-volume simulation analysis and 3D flow dynamics studies in VADs with a view to treatment optimisation and outcome prediction within the time constraints of a clinical setting in the context of a MDT meeting. The clinical significance and the contribution to the field is a more targeted approach for different groups of patients and a more quantitative evaluation in the clinical decision process based on a pro-active co-operation between clinicians and scientists reducing the potential for “guess work”. The results of this thesis are a proof-of-concept as a prelude to a potential future implementation of patient-specific modelling within a clinical setting on a daily basis demonstrating a clear clinical significance and contribution to the field. The proposed approach does not consider modelling and simulation as a substitute for clinical experience but an additional tool to guide therapeutic intervention and complement the clinical decision process in which the clinician remains the ultimate decision-maker. Such an approach may well add a different dimension to the problem of heart failure with potential for high return in terms of patient’s outcome and long-term surveillance. The same principles would be applicable to other cardiovascular problems in line with the current concept of “Team Approach” such as the Heart Team, the Structural Heart Team or the Aortic Team. The present work has taken this concept closer to clinical delivery and has highlighted its potential but further work remains to be done in refining the technique.Background: Ventricular Assist Devices (VADs) insertion is an established treatment for patients with end-stage heart failure waiting for a heart transplant or in need for long-term circulatory support (destination therapy). Rotary blood pumps (RBP) are the most popular devices in view of their size and performance. Pre-operative planning strategy for the insertion of a left ventricular assist device (LVAD) requires a timely discussion at a Multi-Disciplinary Team Meeting (MDT). Clinical-decision making is based according to the needs of the patient and must be processed without delays. Nevertheless, thrombus formation remains a feared complication which affects outcome. VADs operate in a flow regime which is difficult to simulate: the transitional region at the boundary of laminar and turbulent flow (low Reynolds number). Different methods have been used but the best approach remains debatable. Computational Fluid Dynamics (CFD) is an attractive and invaluable tool for the study of the interactions between VADs and the cardiovascular system. The aim of this thesis is three-fold: a) to investigate the use of pressure-volume analysis in a clinical setting through the review of six heart failure patients previously discussed at a MDT meeting with a view to predict or guide further management; b) to review the theory behind modelling approaches to VADs and their interactions with the cardiovascular system for better understanding of their clinical use. Then, an overview of computational fluid dynamics (CFD) is considered as a prelude to its application to the analysis of VADs performance. Additionally, the development of a simplified model of centrifugal pump will be used in initial simulations as preliminary analysis; c) to examine an example of a proof-of-concept pilot patient-specific model of an axial flow pump (HeartMate II) as pre-operative planning strategy in a patient-specific model with a view to identify potential critical areas that may affect pump function and outcome in a clinical setting. Material and Methods: 3D reconstruction from CT-scan images of patients who underwent the insertion of rotary blood pumps, namely HeartWare HVAD and HeartMate II. Ansys Fluent has been used for CFD analysis based on the fundamental governing equations of motion. Blood has been modelled as incompressible, Newtonian fluid with density = 1060 and viscosity = 0.0035 kg/m-s. The laminar and SST models have been used for comparison purposes. The rotational motion of the impeller has been implemented using the moving reference frame (MRF) approach. The sliding mesh method has also been used to account for unsteady interaction between stationary and moving part. The no-slip condition has been applied to all walls, which were assumed to be rigid. Boundary conditions consisting of velocity inlet and pressure outlet of the pump based on different settings and constant rotational speed for the impeller. Pressure-velocity coupling has been based on the coupled scheme. Spatial discretisation consisted of the “least square cell based” gradient for velocity and “PRESTO” or second order for pressure. Second order upwind has been set for the momentum, turbulent kinetic energy and specific dissipation rate. First order implicit has been set for transient formulation. The pseudo transient algorithm (steady state), the high order relaxation term and the warped-face gradient correction have been used to add an unsteady term to the solution equations with the aim to improve stability and enhance convergence. Specific settings have been considered for comparison purposes. Results: Pressure-volume simulation analysis in six advanced heart failure patients showed that an integrated model of the cardiovascular system based on lumped-parameter representation, modified time-varying elastance and pressure-volume analysis of ventricular function seems a feasible and suitable approach yielding a sufficiently accurate quantitative analysis in real time, therefore applicable within the time-constraints of a clinical setting. Lumped-parameter models consist of simultaneous ordinary differential equations complemented by an algebraic balance equation and are suitable for examination of global distribution of pressure, flow and volume over a range of physiological conditions with inclusion of the interaction between modelled components. Higher level lumped-parameter modelling is needed to address the interaction between the circulation and other systems based on a compromise between complexity and ability to set the required parameters to personalise an integrated lumped-parameter model for a patient-specific approach. CARDIOSIM© fulfils these requirements and does address the systems interaction with its modular approach and assembly of models with varying degree of complexity although 0-D and 1-D coupling may be required for the evaluation of long-term VAD support. The challenge remains the ability to predict outcome over a longer period of time. The preliminary CFD simulations with the HeartWare HVAD centrifugal pump demonstrated that it is possible to obtain an accurate analysis in a timely manner to complement the clinical review process. The simulations with the pilot patient-specific model of the HeartMate II axial flow pump revealed that a complex 3D reconstruction is feasible in a timely manner and can be used to generate sufficiently accurate results to be used in the context of a MDT meeting for the purposes of clinical decision-making. Overall, these three studies demonstrate that the time frame of the simulations was within hours which may fit the time constraints of the clinical environment in the context of a MDT meeting. More specifically, it was shown that the laminar model may be used for an initial evaluation of the flow development within the pump. Nonetheless, the k- model offers higher accuracy if the timeline of the clinical setting allows for a longer simulation. Conclusion: This thesis aimed at the understanding of the use of computational modelling as a pre-operative planning strategy and follow up assessment for the treatment of advanced heart failure with rotary blood pumps. The novelty lays in the use of both pressure-volume simulation analysis and 3D flow dynamics studies in VADs with a view to treatment optimisation and outcome prediction within the time constraints of a clinical setting in the context of a MDT meeting. The clinical significance and the contribution to the field is a more targeted approach for different groups of patients and a more quantitative evaluation in the clinical decision process based on a pro-active co-operation between clinicians and scientists reducing the potential for “guess work”. The results of this thesis are a proof-of-concept as a prelude to a potential future implementation of patient-specific modelling within a clinical setting on a daily basis demonstrating a clear clinical significance and contribution to the field. The proposed approach does not consider modelling and simulation as a substitute for clinical experience but an additional tool to guide therapeutic intervention and complement the clinical decision process in which the clinician remains the ultimate decision-maker. Such an approach may well add a different dimension to the problem of heart failure with potential for high return in terms of patient’s outcome and long-term surveillance. The same principles would be applicable to other cardiovascular problems in line with the current concept of “Team Approach” such as the Heart Team, the Structural Heart Team or the Aortic Team. The present work has taken this concept closer to clinical delivery and has highlighted its potential but further work remains to be done in refining the technique

Integrating Biomechanics, Hemodynamics, and Vascular Adaptation to Relate Mechanisms of Vascular Adaptation to Arterial Pulsatile Pressure in Health and Disease

The inherent complexity of the mammalian systemic arterial system has presented numerous challenges to relating basic vascular biology to clinically-relevant derangements of blood pressures and flows. The field of biomechanics has identified how local changes in pulsatile blood pressures and flows lead to changes in local endothelial shear stress and circumferential wall stress. The field of mechanobiology has identified how local changes in wall circumferential stress and endothelial shear stress lead to changes in arterial radii, wall thicknesses and stiffnesses. The field of pulsatile hemodynamics has identified how changes in local radii, wall thicknesses and stiffnesses lead to changes in the complex distributions of pressures and flows throughout an arterial network. These three fields have primarily been studied in isolation, and yet the properties of a single vessel emerge from the interaction of these three processes. The effect of adaptation of one artery on hemodynamics, stress, and structure of all other vessels in the network makes the arterial system a complex adaptive system that is difficult to study experimentally. This dissertation addresses this unmet need by integrating hemodynamics, vessel mechanics, and vascular adaptation by developing a novel framework with mathematical models at different scales. Allowing arteries simultaneously to adapt to mechanical stresses in a computational model of the human systemic arterial system, the present work illustrated that simple arterial adaptation to wall circumferential and endothelial shear stresses are sufficient to explain nine salient features of the cardiovascular system when traversing away from the aortic root towards the peripheral arteries: decrease in lumen radii, wall thicknesses, vessel compliances, shear stresses, wall stresses and pulsatile flows, and increase in wall stiffnesses, pulse wave velocities, and pulsatile pressures. In addition, it revealed that pulse pressure homeostasis emerges to mechanical perturbations such as reduced ejection fraction, increased peripheral resistance and aortic coarctation. Finally, it illustrated how changes in sensitivity of arterial adaptation to pulsatile wall stress can lead to manifestations of disease states such as increased pulse wave velocity and isolated systolic hypertension. The governing principles leading to the emergence of complex, adaptive behavior in the systemic arterial system have thus been identified

Partitioned Solution of Geometrical Multiscale Problems for the Cardiovascular System:Models, Algorithms, and Applications

The aim of this work is the development of a geometrical multiscale framework for the simulation of the human cardiovascular system under either physiological or pathological conditions. More precisely, we devise numerical algorithms for the partitioned solution of geometrical multiscale problems made of different heterogeneous compartments that are implicitly coupled with each others. The driving motivation is the awareness that cardiovascular dynamics are governed by the global interplay between the compartments in the network. Thus, numerical simulations of stand-alone local components of the circulatory system cannot always predict effectively the physiological or pathological states of the patients, since they do not account for the interaction with the missing elements in the network. As a matter of fact, the geometrical multiscale method provides an automatic way to determine the boundary (more precisely, the interface) data for the specific problem of interest in absence of clinical measures and it also offers a platform where to study the interaction between local changes (due, for instance, to pathologies or surgical interventions) and the global systemic dynamics. To set up the framework an abstract setting is devised; the local specific mathematical equations (partial differential equations, differential algebraic equations, etc.) and the numerical approximation (finite elements, finite differences, etc.) of the heterogeneous compartments are hidden behind generic operators. Consequently, the resulting global interface problem is formulated and solved in a completely transparent way. The coupling between models of different dimensional scale (three-dimensional, one-dimensional, etc.) and type (Navier-Stokes, fluid-structure interaction, etc.) is addressed writing the interface equations in terms of scalar quantities, i.e., area, flow rate, and mean (total) normal stress. In the resulting flexible framework the heterogeneous models are treated as black boxes, each one equipped with a specific number of compatible interfaces such that (i) the arrangement of the compartments in the network can be easily manipulated, thus allowing a high level of customization in the design and optimization of the global geometrical multiscale model, (ii) the parallelization of the solution of the different compartments is straightforward, leading to the opportunity to make use of the latest high-performance computing facilities, and (iii) new models can be easily added and connected to the existing ones. The methodology and the algorithms devised throughout the work are tested over several applications, ranging from simple benchmark examples to more complex cardiovascular networks. In addition, two real clinical problems are addressed: the simulation of a patient-specific left ventricle affected by myocardial infarction and the study of the optimal position for the anastomosis of a left ventricle assist device cannula

In-Vitro and In-Silico Investigations of Alternative Surgical Techniques for Single Ventricular Disease

Single ventricle (SV) anomalies account for one-fourth of all cases of congenital Heart disease. The conventional second and third stage i.e. Comprehensive stage II and Fontan procedure of the existing three-staged surgical approach serving as a palliative treatment for this anomaly, entails multiple complications and achieves a survival rate of 50%. Hence, to reduce the morbidity and mortality rate associated with the second and third stages of the existing palliative procedure, the novel alternative techniques called “Hybrid Comprehensive Stage II” (HCSII), and a “Self-powered Fontan circulation” have been proposed. The goal of this research is to conduct in-vitro investigations to validate computational and clinical findings on these proposed novel surgical techniques. The research involves the development of a benchtop study of HCSII and self-powered Fontan circulation

Use of Machine Learning for Automated Convergence of Numerical Iterative Schemes

Convergence of a numerical solution scheme occurs when a sequence of increasingly refined iterative solutions approaches a value consistent with the modeled phenomenon. Approximations using iterative schemes need to satisfy convergence criteria, such as reaching a specific error tolerance or number of iterations. The schemes often bypass the criteria or prematurely converge because of oscillations that may be inherent to the solution. Using a Support Vector Machines (SVM) machine learning approach, an algorithm is designed to use the source data to train a model to predict convergence in the solution process and stop unnecessary iterations. The discretization of the Navier Stokes (NS) equations for a transient local hemodynamics case requires determining a pressure correction term from a Poisson-like equation at every time-step. The pressure correction solution must fully converge to avoid introducing a mass imbalance. Considering time, frequency, and time-frequency domain features of its residual’s behavior, the algorithm trains an SVM model to predict the convergence of the Poisson equation iterative solver so that the time-marching process can move forward efficiently and effectively. The fluid flow model integrates peripheral circulation using a lumped-parameter model (LPM) to capture the field pressures and flows across various circulatory compartments. Machine learning opens the doors to an intelligent approach for iterative solutions by replacing prescribed criteria with an algorithm that uses the data set itself to predict convergence

A Systems Approach to Cardiovascular Health and Disease with a Focus on Aortic Wave Dynamics

Cardiovascular diseases (CVDs) have reached an epidemic proportion in the US and worldwide with serious consequences in terms of human suffering and economic impact. More than one third of American adults are suffering from CVDs. The total direct and indirect costs of CVDs are more than $500 billion per year. Therefore, there is an urgent need to develop noninvasive diagnostics methods, to design minimally invasive assist devices, and to develop economical and easy-to-use monitoring systems for cardiovascular diseases. In order to achieve these goals, it is necessary to gain a better understanding of the subsystems that constitute the cardiovascular system. The aorta is one of these subsystems whose role in cardiovascular functioning has been underestimated. Traditionally, the aorta and its branches have been viewed as resistive conduits connected to an active pump (left ventricle of the heart). However, this perception fails to explain many observed physiological results. My goal in this thesis is to demonstrate the subtle but important role of the aorta as a system, with focus on the wave dynamics in the aorta. The operation of a healthy heart is based on an optimized balance between its pumping characteristics and the hemodynamics of the aorta and vascular branches. The delicate balance between the aorta and heart can be impaired due to aging, smoking, or disease. The heart generates pulsatile flow that produces pressure and flow waves as it enters into the compliant aorta. These aortic waves propagate and reflect from reflection sites (bifurcations and tapering). They can act constructively and assist the blood circulation. However, they may act destructively, promoting diseases or initiating sudden cardiac death. These waves also carry information about the diseases of the heart, vascular disease, and coupling of heart and aorta. In order to elucidate the role of the aorta as a dynamic system, the interplay between the dominant wave dynamic parameters is investigated in this study. These parameters are heart rate, aortic compliance (wave speed), and locations of reflection sites. Both computational and experimental approaches have been used in this research. In some cases, the results are further explained using theoretical models. The main findings of this study are as follows: (i) developing a physiologically realistic outflow boundary condition for blood flow modeling in a compliant vasculature; (ii) demonstrating that pulse pressure as a single index cannot predict the true level of pulsatile workload on the left ventricle; (iii) proving that there is an optimum heart rate in which the pulsatile workload of the heart is minimized and that the optimum heart rate shifts to a higher value as aortic rigidity increases; (iv) introducing a simple bio-inspired device for correction and optimization of aortic wave reflection that reduces the workload on the heart; (v) deriving a non-dimensional number that can predict the optimum wave dynamic state in a mammalian cardiovascular system; (vi) demonstrating that waves can create a pumping effect in the aorta; (vii) introducing a system parameter and a new medical index, Intrinsic Frequency, that can be used for noninvasive diagnosis of heart and vascular diseases; and (viii) proposing a new medical hypothesis for sudden cardiac death in young athletes.</p