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Aims Modern imaging techniques provide evermore-detailed anatomical and physiological information for use in computational fluid dynamics to predict the behaviour of physiological phenomena. Computer modelling can help plan suitable interventions. Our group used magnetic resonance imaging and computational fluid dynamics to study the haemodynamic variables in the ascending aorta in patients with bicuspid aortic valve before and after isolated tissue aortic valve replacement. Computer modelling requires turning a physiological model into a mathematical one, solvable by equations that undergo multiple iterations in four dimensions. Creating these models involves several steps with manual inputs, making the process prone to errors and limiting its inter- and intra-operator reproducibility. Despite these challenges, we created computational models for each patient to study ascending aorta blood flow before and after surgery. Methods and results Magnetic resonance imaging provided the anatomical and velocity data required for the blood flow simulation. Patient-specific in- and outflow boundary conditions were used for the computational fluid dynamics analysis. Haemodynamic variables pertaining to blood flow pattern and derived from the magnetic resonance imaging data were calculated. However, we encountered problems in our multi-step methodology, most notably processing the flow data. This meant that other variables requiring computation with computational fluid dynamics could not be calculated. Conclusion Creating a model for computational fluid dynamics analysis is as complex as the physiology under scrutiny. We discuss some of the difficulties associated with creating such models, along with suggestions for improvements in order to yield reliable and beneficial results.

Objective: We propose a novel method to obtainmap patient-specific blood velocity profiles (obtained from imaging data such as 2D flow MRI or 3D colour Doppler ultrasound) and map them to geometric vascular models suitable to perform CFD simulations of haemodynamics. We describe the implementation and utilisation of the method within an open-source computational hemodynamics simulation software (CRIMSON). Methods: tThe proposed method establishes point-wise correspondences between the contour of a fixed geometric model and time-varying contours containing the velocity image data, from which a continuous, smooth and cyclic deformation field is calculated. Our methodology is validated using synthetic data, and demonstrated using two different in-vivo aortic velocity datasets: a healthy subject with normal tricuspid valve and a patient with bicuspid aortic valve. Results: We compare the performance of our method with results obtained with the state-of-the-art Schwarz-Christoffel method, in terms of preservation of velocities and execution time. Our method is as accurate as the Schwarz-Christoffel method, while being over 8 times faster. The proposed method can preserve either the flow rate or the velocity field through the surface, and can cope with inconsistencies in motion and contour shape. Conclusions: Our results show that the method is as accurate as the Schwarz-Christoffel method in terms of maintaining the velocity distributions, while being more computationally efficient.Our mapping method can accurately preserve either the flow rate or the velocity field through the surface, and can cope with inconsistencies in motion and contour shape. Significance: The proposed method and its integration into the CRIMSON software enable a streamlined approach towards incorporating more patient-specific data in blood flow simulations.

In this work, we describe the CRIMSON (CardiovasculaR Integrated Modelling and SimulatiON) software environment. CRIMSON provides a powerful, customizable and user-friendly system for performing three-dimensional and reduced-order computational haemodynamics studies via a pipeline which involves: 1) segmenting vascular structures from medical images; 2) constructing analytic arterial and venous geometric models; 3) performing finite element mesh generation; 4) designing, and 5) applying boundary conditions; 6) running incompressible Navier-Stokes simulations of blood flow with fluid-structure interaction capabilities; and 7) post-processing and visualizing the results, including velocity, pressure and wall shear stress fields. A key aim of CRIMSON is to create a software environment that makes powerful computational haemodynamics tools accessible to a wide audience, including clinicians and students, both within our research laboratories and throughout the community. The overall philosophy is to leverage best-in-class open source standards for medical image processing, parallel flow computation, geometric solid modelling, data assimilation, and mesh generation. It is actively used by researchers in Europe, North and South America, Asia, and Australia. It has been applied to numerous clinical problems; we illustrate applications of CRIMSON to real-world problems using examples ranging from pre-operative surgical planning to medical device design optimization., Author summary We provide the first full presentation in the literature of CRIMSON, the Cardiovascular Integrated Modelling and Simulation Package. CRIMSON consists of a graphical user interface desktop computer program for creating geometric models of blood vessels from medical imaging scans, specifying parameters such as the stiffness of the artery walls, the resistance of connected vessels which are not visible on the scans, and determining the appropriate parameters for all aspects of the model. CRIMSON additionally consists of the Flowsolver, a high-performance computing package which simulates the flow of blood through the models created in the graphical user interface. Whilst several packages which can simulate blood flow exist, most target general fluid simulations, and this lack of specialisation means that blood flow simulation is harder to perform, and can require ad hoc (and potentially scientifically-limiting) workflow decisions. CRIMSON’s specialisation deals with these problems, as well as presenting a number of unique features which are unavailable elsewhere.

Objectives Aortic arch repair remains a major surgical challenge. Multiple manufacturers are developing branched endografts for Zone 0 endovascular repair, extending the armamentarium for minimally invasive treatment of aortic arch pathologies. We hypothesize that the design of the Zone 0 endograft has a significant impact on the postoperative haemodynamic performance, particularly in the cervical arteries. The goal of our study was to compare the postoperative haemodynamic performance of different Zone 0 endograft designs. Methods Patient-specific, clinically validated, computational fluid dynamics simulations were performed in a 71-year-old woman with a 6.5-cm saccular aortic arch aneurysm. Additionally, 4 endovascular repair scenarios using different endograft designs were created. Haemodynamic performance was evaluated by calculation of postoperative changes in blood flow and platelet activation potential (PLAP) in the cervical arteries. Results Preoperative cervical blood flow and mean PLAP were 1080 ml/min and 151.75, respectively. Cervical blood flow decreased and PLAP increased following endovascular repair in all scenarios. Endografts with 2 antegrade inner branches performed better compared to single-branch endografts. Scenario 3 performed the worst with a decrease in the total cervical blood flow of 4.8%, a decrease in the left hemisphere flow of 6.7% and an increase in the mean PLAP of 74.3%. Conclusions Endograft design has a significant impact on haemodynamic performance following Zone 0 endovascular repair, potentially affecting cerebral blood flow during follow-up. Our results demonstrate the use of computational modelling for virtual testing of therapeutic interventions and underline the need to monitor the long-term outcomes in this cohort of patients.

The goal of this work is to train a neural network which approximates solutions to the Navier-Stokes equations across a region of parameter space, in which the parameters define physical properties such as domain shape and boundary conditions. The contributions of this work are threefold: 1) To demonstrate that neural networks can be efficient aggregators of whole families of parameteric solutions to physical problems, trained using data created with traditional, trusted numerical methods such as finite elements. Advantages include extremely fast evaluation of pressure and velocity at any point in physical and parameter space (asymptotically, ~3 $\mu s$ / query), and data compression (the network requires 99\% less storage space compared to its own training data). 2) To demonstrate that the neural networks can accurately interpolate between finite element solutions in parameter space, allowing them to be instantly queried for pressure and velocity field solutions to problems for which traditional simulations have never been performed. 3) To introduce an active learning algorithm, so that during training, a finite element solver can automatically be queried to obtain additional training data in locations where the neural network's predictions are in most need of improvement, thus autonomously acquiring and efficiently distributing training data throughout parameter space. In addition to the obvious utility of Item 2, above, we demonstrate an application of the network in rapid parameter sweeping, very precisely predicting the degree of narrowing in a tube which would result in a 50\% increase in end-to-end pressure difference at a given flow rate. This capability could have applications in both medical diagnosis of arterial disease, and in computer-aided design., Comment: 16 pages, 9 figures; added missing details from author affiliations

This paper presents a new mathematical model of the dynamic control of coronary resistance. It shows a remarkable ability to predict coronary flow in an exercising patient, which would otherwise be impossible, and provides new insight into the purpose and action of the coronary flow control systems. It is applicable as part of a controlled boundary condition at the coronary outlets of a three-dimensional Navier-Stokes simulation of hemodynamics., This work presents a mathematical model of the metabolic feedback and adrenergic feedforward control of coronary blood flow that occur during variations in the cardiac workload. It is based on the physiological observations that coronary blood flow closely follows myocardial oxygen demand, that myocardial oxygen debts are repaid, and that control oscillations occur when the system is perturbed and so are phenomenological in nature. Using clinical data, we demonstrate that the model can provide patient-specific estimates of coronary blood flow changes between rest and exercise, requiring only the patient's heart rate and peak aortic pressure as input. The model can be used in zero-dimensional lumped parameter network studies or as a boundary condition for three-dimensional multidomain Navier-Stokes blood flow simulations. For the first time, this model provides feedback control of the coronary vascular resistance, which can be used to enhance the physiological accuracy of any hemodynamic simulation, which includes both a heart model and coronary arteries. This has particular relevance to patient-specific simulation for which heart rate and aortic pressure recordings are available. In addition to providing a simulation tool, under our assumptions, the derivation of our model shows that β-feedforward control of the coronary microvascular resistance is a mathematical necessity and that the metabolic feedback control must be dependent on two error signals: the historical myocardial oxygen debt, and the instantaneous myocardial oxygen deficit.

Numerical simulations of cardiovascular mass transport pose significant challenges due to the wide range of P\'eclet numbers and backflow at Neumann boundaries. In this paper we present and discuss several numerical tools to address these challenges in the context of a stabilized finite element computational framework. To overcome numerical instabilities when backflow occurs at Neumann boundaries, we propose an approach based on the prescription of the total flux. In addition, we introduce a "consistent flux" outflow boundary condition and demonstrate its superior performance over the traditional zero diffusive flux boundary condition. Lastly, we discuss discontinuity capturing (DC) stabilization techniques to address the well-known oscillatory behavior of the solution near the concentration front in advection-dominated flows.We present numerical examples in both idealized and patient-specific geometries to demonstrate the efficacy of the proposed procedures. The three contributions dis-cussed in this paper enable to successfully address commonly found challenges when simulating mass transport processes in cardiovascular flows.

Objective:Suprarenal abdominal aortic coarctation (SAAC) alters flow and pressure patterns to the kidneys and is often associated with severe angiotensin-mediated hypertension refractory to drug therapy. SAAC is most often treated by a thoracoabdominal bypass (TAB) or patch aortoplasty (PA). It is currently unclear what effect these interventions have on renal flow and pressure waveforms. This study, using retrospective data from a patient with SAAC subjected to a TAB, undertook computational modeling to analyze aortorenal blood flow preoperatively as well as postoperatively after a variety of TAB and PA interventions. Methods:Patient-specific anatomic models were constructed from preoperative computed tomography angiograms of a 9-year-old child with an isolated SAAC. Fluid-structure interaction (FSI) simulations of hemodynamics were performed to analyze preoperative renal flow and pressure waveforms. A parametric study was then performed to examine the hemodynamic impact of different bypass diameters and patch oversizing. Results:Preoperative FSI results documented diastole-dominated renal perfusion with considerable high-frequency disturbances in blood flow and pressure. The postoperative TAB right and left kidney volumes increased by 58% and 79%, respectively, reflecting the increased renal artery blood flows calculated by the FSI analysis. Postoperative increases in systolic flow accompanied decreases in high-frequency disturbances, aortic pressure, and collateral flow after all surgical interventions. In general, lesser degrees of high-frequency disturbances followed PA interventions. High-frequency disturbances were eliminated with the 0% PA in contrast to the 30% and 50% PA oversizing and TAB interventions, in which these flow disturbances remained. Conclusions:Both TAB and PA dramatically improved renal artery flow and pressure waveforms, although disturbed renal waveforms remained in many of the surgical scenarios. Importantly, only the 0% PA oversizing scenario eliminated all high-frequency disturbances, resulting in nearly normal aortorenal blood flow. The study also establishes the relevance of patient-specific computational modeling in planning interventions for the midaortic syndrome. Clinical Relevance:We performed computational fluid dynamics modeling to assess aortorenal blood flow in a child with a suprarenal abdominal aortic coarctation and to test the performance of different surgical interventions. We discovered high-frequency disturbances in the renal arteries that could potentially trigger excessive renin release. Thoracoabdominal bypass and patch aortoplasty with oversizing did not remove these disturbances completely. This could explain why the hypertension cure rates of surgical repair of suprarenal abdominal aortic coarctation are suboptimal. In addition, this study establishes the relevance of computational fluid dynamics modeling as a valuable tool to analyze complex hemodynamics and to test the performance of different surgical interventions.

OBJECTIVES Current endografts for thoracic endovascular aortic repair (TEVAR) are much stiffer than the aorta and have been shown to induce acute stiffening. In this study, we aimed to estimate the impact of TEVAR on left ventricular (LV) stroke work (SW) and mass using a non-invasive image-based workflow. METHODS The University of Michigan database was searched for patients treated with TEVAR for descending aortic pathologies (2013–2016). Patients with available pre-TEVAR and post-TEVAR computed tomography angiography and echocardiography data were selected. LV SW was estimated via patient-specific fluid–structure interaction analyses. LV remodelling was quantified through morphological measurements using echocardiography and electrocardiographic-gated computed tomography angiography data. RESULTS Eight subjects were included in this study, the mean age of the patients was 68 (73, 25) years, and 6 patients were women. All patients were prescribed antihypertensive drugs following TEVAR. The fluid–structure interaction simulations computed a 26% increase in LV SW post-TEVAR [0.94 (0.89, 0.34) J to 1.18 (1.11, 0.65) J, P = 0.012]. Morphological measurements revealed an increase in the LV mass index post-TEVAR of +26% in echocardiography [72 (73, 17) g/m2 to 91 (87, 26) g/m2, P = 0.017] and +15% in computed tomography angiography [52 (46, 29) g/m2 to 60 (57, 22) g/m2, P = 0.043]. The post- to pre-TEVAR LV mass index ratio was positively correlated with the post- to pre-TEVAR ratios of SW and the mean blood pressure (ρ = 0.690, P = 0.058 and ρ = 0.786, P = 0.021, respectively). CONCLUSIONS TEVAR was associated with increased LV SW and mass during follow-up. Medical device manufacturers should develop more compliant devices to reduce the stiffness mismatch with the aorta. Additionally, intensive antihypertensive management is needed to control blood pressure post-TEVAR.

We present a computationally efficient method of simulating cardiac electrical propagation using an adaptive high-order finite element method to automatically concentrate computational effort where it is most needed in space on each time-step. We drive the adaptivity using a residual-based error indicator, and demonstrate using norms of the error that the indicator allows us to control it successfully. Our results using two-dimensional domains of varying complexity demonstrate that significant improvements in efficiency are possible over the standard linear FEM in our single-thread studies, and our preliminary three-dimensional results suggest that improvements are also possible in 3D. We do not work in parallel or investigate the challenges for adaptivity such as dynamic load-balancing which are associated with parallelisation. However, based upon recent work demonstrating that in some circumstances and with moderate processor counts parallel h-adaptive methods are efficient, and upon the claim that p-adaptivity will outperform h-adaptivity, we argue that p-adaptivity should be investigated for efficiency in parallel for simulation on moderate numbers of processors.

Computational fluid dynamics (CFD) provides a noninvasive method to functionally assess aortic hemodynamics. The thoracic aorta has an anatomically complex inlet comprising of the aortic valve and root, which is highly prone to different morphologies and pathologies. We investigated the effect of using patient-specific (PS) inflow velocity profiles compared to idealized profiles based on the patient's flow waveform. A healthy 31 yo with a normally functioning tricuspid aortic valve (subject A), and a 52 yo with a bicuspid aortic valve (BAV), aortic valvular stenosis, and dilated ascending aorta (subject B) were studied. Subjects underwent MR angiography to image and reconstruct three-dimensional (3D) geometric models of the thoracic aorta. Flow-magnetic resonance imaging (MRI) was acquired above the aortic valve and used to extract the patient-specific velocity profiles. Subject B's eccentric asymmetrical inflow profile led to highly complex velocity patterns, which were not replicated by the idealized velocity profiles. Despite having identical flow rates, the idealized inflow profiles displayed significantly different peak and radial velocities. Subject A's results showed some similarity between PS and parabolic inflow profiles; however, other parameters such as Flowasymmetry were significantly different. Idealized inflow velocity profiles significantly alter velocity patterns and produce inaccurate hemodynamic assessments in the thoracic aorta. The complex structure of the aortic valve and its predisposition to pathological change means the inflow into the thoracic aorta can be highly variable. CFD analysis of the thoracic aorta needs to utilize fully PS inflow boundary conditions in order to produce truly meaningful results.

We present the possible utility of computational fluid dynamics in the assessment of thrombus formation and virtual surgical planning illustrated in a patient with aortic thrombus in a kinked ascending aortic graft following thoracic endovascular aortic repair.A patient-specific three-dimensional model was built from computed tomography. Additionally, we modeled 3 virtual aortic interventions to assess their effect on thrombosis potential: (1) open surgical repair, (2) conformable endografting, and (3) single-branched endografting. Flow waveforms were extracted from echocardiography and used for the simulations. We used the computational index termed platelet activation potential (PLAP) representing accumulated shear rates of fluid particles within a fluid domain to assess thrombosis potential.The baseline model revealed high PLAP in the entire arch (119.8 ± 42.5), with significantly larger PLAP at the thrombus location (125.4 ± 41.2, p0.001). Surgical repair showed a 37% PLAP reduction at the thrombus location (78.6 ± 25.3, p0.001) and a 24% reduction in the arch (91.6 ± 28.9, p0.001). Single-branched endografting reduced PLAP in the thrombus region by 20% (99.7 ± 24.6, p0.001) and by 14% in the arch (103.8 ± 26.1, p0.001), whereas a more conformable endograft did not have a profound effect, resulting in a modest 4% PLAP increase (130.6 ± 43.7, p0.001) in the thrombus region relative to the baseline case.Regions of high PLAP were associated with aortic thrombus. Aortic repair resolved pathologic flow patterns, reducing PLAP. Branched endografting also relieved complex flow patterns reducing PLAP. Computational fluid dynamics may assist in the prediction of aortic thrombus formation in hemodynamically complex cases and help guide repair strategies.

We create a multiphysics cardiovascular model by integrating the electrical and active tension generation properties of the cardiac myocyte into a lumped parameter network model of the left ventricle, which is then applied to create a boundary condition for three-dimensional haemodynamics simulation. The process demonstrates the power and flexibility of the CRIMSON Boundary Condition Toolbox and Control Systems Framework, our accessible tools for designing, implementing and testing novel physiological controlled boundary conditions for fluid flow.

We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.