Validation of Numerical Simulations of Thoracic Aorta Hemodynamics: Comparison with In Vivo Measurements and Stochastic Sensitivity Analysis

Evaluation of enhanced external counterpulsation for diabetic foot based on a patient-specific 0D-1D cardiovascular system model

BACKGROUND AND OBJECTIVE

Diabetic foot (DF) complications often lead to severe vascular issues. This study investigated the effectiveness of enhanced external counterpulsation (EECP) and its derived innovative compression strategies in addressing poor perfusion in DF. Although developing non-invasive and efficient treatment methods for DF is critical, the hemodynamic alterations during EECP remain underexplored despite promising outcomes in microcirculation. This research sought to address this gap by developing a patient-specific 0D-1D model based on clinical ultrasound data to identify potentially superior compression strategies that could substantially enhance blood flow in patients with DF complications.

METHODS

Data were gathered from 10 patients with DF utilizing ultrasound for blood flow rate and computed tomography angiography (CTA) to identify lower limb conditions. Clinical measurements during standard EECP, with varying cuff pressures, facilitated the creation of a patient-specific 0D-1D model through a two-step parameter estimation process. The accuracy of this model was verified via comparison with the clinical measurements. Four compression strategies were proposed and rigorously evaluated using this model: EECP-Simp-I (removing hip cuffs), EECP-Simp-II (further removing the cuffs around the lower leg), EECP-Impr-I (removing all cuffs around the affected side), and EECP-Impr-II (building a loop circulation from the healthy side to the affected side).

RESULTS

The predicted results under the rest and standard EECP states were generally closely aligned with clinical measurements. The patient-specific 0D-1D model demonstrated that EECP-Simp-I and EECP-Impr-I contributed similar enhancement to perfusion in the dorsal artery (DA) and were comparable to standard EECP, while EECP-Simp-II had the least effect and EECP-Impr-II displayed the most significant enhancement. Pressure at the aortic root (AO) remained consistent across strategies.

CONCLUSIONS

EECP-Simp-I is recommended for patients with DF, emphasizing device simplification. However, EECP-Simp-II is discouraged as it significantly diminished blood perfusion in this study, except in cases of limb fragility. EECP-Impr-II showed superior enhancement of blood perfusion in DA to all other strategies but required a more complex EECP device. Despite increased AO pressure in all the proposed compression strategies, safety could be guaranteed as the pressue remained within a safe range.

A numerical study on the siphonic effect of enhanced external counterpulsation at lower extremities with a coupled 0D-1D closed-loop personalized hemodynamics model

Enhanced external counterpulsation (EECP) is a treatment and rehabilitation approach for ischemic diseases, including coronary artery disease. Its therapeutic benefits are primarily attributed to the improved blood circulation achieved through sequential mechanical compression of the lower extremities. However, despite the crucial role that hemodynamic effects in the lower extremity arteries play in determining the effectiveness of EECP treatment, most studies have focused on the diastole phase and ignored the systolic phase. In the present study, a novel siphon model (SM) was developed to investigate the interdependence of several hemodynamic parameters, including pulse wave velocity, femoral flow rate, the operation pressure of cuffs, and the mean blood flow changes in the femoral artery throughout EECP therapy. To verify the accuracy of the SM, we coupled the predicted afterload in the lower extremity arteries during deflation using SM with the 0D-1D patient-specific model. Finally, the simulation results were compared with clinical measurements obtained during EECP therapy to verify the applicability and accuracy of the SM, as well as the coupling method. The precision and reliability of the previously developed personalized approach were further affirmed in this study. The average waveform similarity coefficient between the simulation results and the clinical measurements during the rest state exceeded 90%. This work has the potential to enhance our understanding of the hemodynamic mechanisms involved in EECP treatment and provide valuable insights for clinical decision-making.

Impact of the Spatial Velocity Inlet Distribution on the Hemodynamics of the Thoracic Aorta

The impact of the distribution in space of the inlet velocity in the numerical simulations of the hemodynamics in the thoracic aorta is systematically investigated. A real healthy aorta geometry, for which in-vivo measurements are available, is considered. The distribution is modeled through a truncated cone shape, which is a suitable approximation of the real one downstream of a trileaflet aortic valve during the systolic part of the cardiac cycle. The ratio between the upper and the lower base of the truncated cone and the position of the center of the upper base are selected as uncertain parameters. A stochastic approach is chosen, based on the generalized Polynomial Chaos expansion, to obtain accurate response surfaces of the quantities of interest in the parameter space. The selected parameters influence the velocity distribution in the ascending aorta. Consequently, effects on the wall shear stress are observed, confirming the need to use patient-specific inlet conditions if interested in the hemodynamics of this region. The surface base ratio is globally the most important parameter. Conversely, the impact on the velocity and wall shear stress in the aortic arch and descending aorta is almost negligible.

Enabling supra-aortic vessels inclusion in statistical shape models of the aorta: a novel non-rigid registration method

Statistical Shape Models (SSMs) are well-established tools for assessing the variability of 3D geometry and for broadening a limited set of shapes. They are widely used in medical imaging due to their ability to model complex geometries and their high efficiency as generative models. The principal step behind these techniques is a registration phase, which, in the case of complex geometries, can be a critical issue due to the correspondence problem, as it necessitates the development of correspondence mapping between shapes. The thoracic aorta, with its high level of morphological complexity, poses a multi-scale deformation problem due to the presence of several branch vessels with varying diameters. Moreover, branch vessels exhibit significant variability in shape, making the correspondence optimization even more challenging. Consequently, existing studies have focused on developing SSMs based only on the main body of the aorta, excluding the supra-aortic vessels from the analysis. In this work, we present a novel non-rigid registration algorithm based on optimizing a differentiable distance function through a modified gradient descent approach. This strategy enables the inclusion of custom, domain-specific constraints in the objective function, which act as landmarks during the registration phase. The algorithm's registration performance was tested and compared to an alternative Statistical Shape modeling framework, and subsequently used for the development of a comprehensive SSM of the thoracic aorta, including the supra-aortic vessels. The developed SSM was further evaluated against the alternative framework in terms of generalisation, specificity, and compactness to assess its effectiveness.

Comparative study between 1-way and 2-way coupled fluid-structure interaction in numerical simulation of aortic arch aneurysms

Hemodynamic forces are related to pathological variations of the cardiovascular system, and numerical simulations for fluid-structure interaction have been systematically used to analyze the behavior of blood flow and the arterial wall in aortic aneurysms. This paper proposes a comparative analysis of 1-way and 2-way coupled fluid-structure interaction for aortic arch aneurysm. The coupling models of fluid-structure interaction were conducted using 3D geometry of the thoracic aorta from computed tomography. Hyperelastic anisotropic properties were estimated for the Holzapfel arterial wall model. The rheological behavior of the blood was modeled by the Carreau-Yasuda model. The results showed that the 1-way approach tends to underestimate von Mises stress, displacement, and strain over the entire cardiac cycle, compared to the 2-way approach. In contrast, the behavior of the variables of flow field, velocity, wall shear stress, and Reynolds number when coupled by the 1-way model was overestimated at the systolic moment and tends to be equal at the diastolic moment. The quantitative differences found, especially during the systole, suggest the use of 2-way coupling in numerical simulations of aortic arch aneurysms due to the hyperelastic nature of the arterial wall, which leads to a strong iteration between the fluid and the arterial wall.

Uncertainty Quantification in the In Vivo Image-Based Estimation of Local Elastic Properties of Vascular Walls

Introduction: Patient-specific computational models are a powerful tool for planning cardiovascular interventions. However, the in vivo patient-specific mechanical properties of vessels represent a major source of uncertainty. In this study, we investigated the effect of uncertainty in the elastic module (E) on a Fluid–Structure Interaction (FSI) model of a patient-specific aorta. Methods: The image-based χ-method was used to compute the initial E value of the vascular wall. The uncertainty quantification was carried out using the generalized Polynomial Chaos (gPC) expansion technique. The stochastic analysis was based on four deterministic simulations considering four quadrature points. A deviation of about ±20% on the estimation of the E value was assumed. Results: The influence of the uncertain E parameter was evaluated along the cardiac cycle on area and flow variations extracted from five cross-sections of the aortic FSI model. Results of stochastic analysis showed the impact of E in the ascending aorta while an insignificant effect was observed in the descending tract. Conclusions: This study demonstrated the importance of the image-based methodology for inferring E, highlighting the feasibility of retrieving useful additional data and enhancing the reliability of in silico models in clinical practice.

Patient-specific computational simulation of coronary artery bypass grafting

INTRODUCTION

Coronary artery bypass graft surgery (CABG) is an intervention in patients with extensive obstructive coronary artery disease diagnosed with invasive coronary angiography. Here we present and test a novel application of non-invasive computational assessment of coronary hemodynamics before and after bypass grafting.

METHODS AND RESULTS

We tested the computational CABG platform in n = 2 post-CABG patients. The computationally calculated fractional flow reserve showed high agreement with the angiography-based fractional flow reserve. Furthermore, we performed multiscale computational fluid dynamics simulations of pre- and post-CABG under simulated resting and hyperemic conditions in n = 2 patient-specific anatomies 3D reconstructed from coronary computed tomography angiography. We computationally created different degrees of stenosis in the left anterior descending artery, and we showed that increasing severity of native artery stenosis resulted in augmented flow through the graft and improvement of resting and hyperemic flow in the distal part of the grafted native artery.

CONCLUSIONS

We presented a comprehensive patient-specific computational platform that can simulate the hemodynamic conditions before and after CABG and faithfully reproduce the hemodynamic effects of bypass grafting on the native coronary artery flow. Further clinical studies are warranted to validate this preliminary data.

A personalized 0D-1D model of cardiovascular system for the hemodynamic simulation of enhanced external counterpulsation

BACKGROUND AND OBJECTIVE

Enhanced external counterpulsation (EECP) is a non-invasive treatment modality capable of treating a variety of ischemic diseases. Currently, no effective methods of predicting the patient-specific hemodynamic effects of EECP are available. In this study, a personalized 0D-1D model of the cardiovascular system was developed for hemodynamic simulation to simulate the changes in blood flow in the EECP state and develop the best treatment protocol for each individual.

METHODS

A 0D-1D closed-loop model of the cardiovascular system was developed for hemodynamic simulation, consisting of a 1D wave propagation model for arteries, a 0D model for veins and capillaries, and a one-fiber model for the heart. Additionally, a simulation model coupling EECP with a 1D model was established. Physiological data, including the blood flow in different arteries, were clinically collected from 22 volunteers at rest and in the EECP state. Sensitivity analysis and a simulated annealing algorithm were used to build personalized 0D-1D models using the clinical data in the rest state as optimization objectives. Then, the clinical data on EECP were used to verify the applicability and accuracy of the personalized models.

RESULTS

The simulation results and clinical data were found to be in agreement for all 22 subjects, with waveform similarity coefficients (r) exceeding 90% for most arteries at rest and 80% for most arteries during EECP.

CONCLUSIONS

The 0D-1D closed-loop model and the optimized method can facilitate personalized modeling of the cardiovascular system using the data in the rest state and effectively predict the hemodynamic changes in the EECP state, which is significant for the numerical simulation of personalized hemodynamics. The model can also potentially be used to make decisions regarding patient-specific treatment.

Cerebral hemodynamics during atrial fibrillation: Computational fluid dynamics analysis of lenticulostriate arteries using 7 T high-resolution magnetic resonance imaging

Atrial fibrillation (AF) is the most common cardiac arrhythmia, inducing irregular and faster heart beating. Aside from disabling symptoms-such as palpitations, chest discomfort, and reduced exercise capacity-there is growing evidence that AF increases the risk of dementia and cognitive decline, even in the absence of clinical strokes. Among the possible mechanisms, the alteration of deep cerebral hemodynamics during AF is one of the most fascinating and least investigated hypotheses. Lenticulostriate arteries (LSAs)-small perforating arteries perpendicularly departing from the anterior and middle cerebral arteries and supplying blood flow to basal ganglia-are especially involved in silent strokes and cerebral small vessel diseases, which are considered among the main vascular drivers of dementia. We propose for the first time a computational fluid dynamics analysis to investigate the AF effects on the LSAs hemodynamics by using 7 T high-resolution magnetic resonance imaging (MRI). We explored different heart rates (HRs)-from 50 to 130 bpm-in sinus rhythm and AF, exploiting MRI data from a healthy young male and internal carotid artery data from validated 0D cardiovascular-cerebral modeling as inflow condition. Our results reveal that AF induces a marked reduction of wall shear stress and flow velocity fields. This study suggests that AF at higher HR leads to a more hazardous hemodynamic scenario by increasing the atheromatosis and thrombogenesis risks in the LSAs region.

Hemodynamics in a three-dimensional printed aortic model: a comparison of four-dimensional phase-contrast magnetic resonance and image-based computational fluid dynamics

OBJECTIVE

This study aims to compare an electrocardiogram (ECG)-gated four-dimensional (4D) phase-contrast (PC) magnetic resonance imaging (MRI) technique and computational fluid dynamics (CFD) using variables controlled in a laboratory environment to minimize bias factors.

MATERIALS AND METHODS

Data from 4D PC-MRI were compared with computational fluid dynamics using steady and pulsatile flows at various inlet velocities. Anatomically realistic models for a normal aorta, a penetrating atherosclerotic ulcer, and an abdominal aortic aneurysm were constructed using a three-dimensional printer.

RESULTS

For the normal aorta model, the errors in the peak and the average velocities were within 5%. The peak velocities of the penetrating atherosclerotic ulcer and the abdominal aortic aneurysm models displayed a more extensive range of differences because of the high-speed and vortical fluid flows generated by the shape of the blood vessel. However, the average velocities revealed only relatively minor differences.

CONCLUSIONS

This study compared the characteristics of PC-MRI and CFD through a phantom study that only included controllable experimental parameters. Based on these results, 4D PC-MRI and CFD are powerful tools for analyzing blood flow patterns in vivo. However, there is room for future developments to improve velocity measurement accuracy.

Introduction of a Novel Image-Based and Non-Invasive Method for the Estimation of Local Elastic Properties of Great Vessels

Background: In the context of a growing demand for the use of in silico models to meet clinical requests, image-based methods play a crucial role. In this study, we present a parametric equation able to estimate the elasticity of vessel walls, non-invasively and indirectly, from information uniquely retrievable from imaging. Methods: A custom equation was iteratively refined and tuned from the simulations of a wide range of different vessel models, leading to the definition of an indirect method able to estimate the elastic modulus E of a vessel wall. To test the effectiveness of the predictive capability to infer the E value, two models with increasing complexity were used: a U-shaped vessel and a patient-specific aorta. Results: The original formulation was demonstrated to deviate from the ground truth, with a difference of 89.6%. However, the adoption of our proposed equation was found to significantly increase the reliability of the estimated E value for a vessel wall, with a mean percentage error of 9.3% with respect to the reference values. Conclusion: This study provides a strong basis for the definition of a method able to estimate local mechanical information of vessels from data easily retrievable from imaging, thus potentially increasing the reliability of in silico cardiovascular models.

The Hemodynamic Effect of Modified Blalock–Taussig Shunt Morphologies: A Computational Analysis Based on Reduced Order Modeling

The Modified Blalock Taussig Shunt (MBTS) is one of the most common palliative operations in case of cyanotic heart diseases. Thus far, the decision on the position, size, and geometry of the implant relies on clinicians’ experience. In this paper, a Medical Digital Twin pipeline based on reduced order modeling is presented for fast and interactive evaluation of the hemodynamic parameters of MBTS. An infant case affected by complete pulmonary atresia was selected for this study. A three-dimensional digital model of the infant’s MBTS morphology was generated. A wide spectrum of MBTS geometries was explored by introducing twelve Radial Basis Function mesh modifiers. The combination of these modifiers allowed for analysis of various MBTS shapes. The final results proved the potential of the proposed approach for the investigation of significant hemodynamic features such as velocity, pressure, and wall shear stress as a function of the shunt’s morphology in real-time. In particular, it was demonstrated that the modifications of the MBTS morphology had a profound effect on the hemodynamic indices. The adoption of reduced models turned out to be a promising path to follow for MBTS numerical evaluation, with the potential to support patient-specific preoperative planning.

Medical Image-Based Computational Fluid Dynamics and Fluid-Structure Interaction Analysis in Vascular Diseases

Hemodynamic factors, induced by pulsatile blood flow, play a crucial role in vascular health and diseases, such as the initiation and progression of atherosclerosis. Computational fluid dynamics, finite element analysis, and fluid-structure interaction simulations have been widely used to quantify detailed hemodynamic forces based on vascular images commonly obtained from computed tomography angiography, magnetic resonance imaging, ultrasound, and optical coherence tomography. In this review, we focus on methods for obtaining accurate hemodynamic factors that regulate the structure and function of vascular endothelial and smooth muscle cells. We describe the multiple steps and recent advances in a typical patient-specific simulation pipeline, including medical imaging, image processing, spatial discretization to generate computational mesh, setting up boundary conditions and solver parameters, visualization and extraction of hemodynamic factors, and statistical analysis. These steps have not been standardized and thus have unavoidable uncertainties that should be thoroughly evaluated. We also discuss the recent development of combining patient-specific models with machine-learning methods to obtain hemodynamic factors faster and cheaper than conventional methods. These critical advances widen the use of biomechanical simulation tools in the research and potential personalized care of vascular diseases.

On the Role and Effects of Uncertainties in Cardiovascular in silico Analyses

The assessment of cardiovascular hemodynamics with computational techniques is establishing its fundamental contribution within the world of modern clinics. Great research interest was focused on the aortic vessel. The study of aortic flow, pressure, and stresses is at the basis of the understanding of complex pathologies such as aneurysms. Nevertheless, the computational approaches are still affected by sources of errors and uncertainties. These phenomena occur at different levels of the computational analysis, and they also strongly depend on the type of approach adopted. With the current study, the effect of error sources was characterized for an aortic case. In particular, the geometry of a patient-specific aorta structure was segmented at different phases of a cardiac cycle to be adopted in a computational analysis. Different levels of surface smoothing were imposed to define their influence on the numerical results. After this, three different simulation methods were imposed on the same geometry: a rigid wall computational fluid dynamics (CFD), a moving-wall CFD based on radial basis functions (RBF) CFD, and a fluid-structure interaction (FSI) simulation. The differences of the implemented methods were defined in terms of wall shear stress (WSS) analysis. In particular, for all the cases reported, the systolic WSS and the time-averaged WSS (TAWSS) were defined.

Development of a computational fluid dynamic model to investigate the hemodynamic impact of REBOA

Background: Resuscitative endovascular balloon occlusion of the aorta (REBOA) is a lifesaving intervention for major truncal hemorrhage. Balloon-tipped arterial catheters are inserted via the femoral artery to create a temporary occlusion of the aorta, which minimizes the rate of internal bleeding until definitive surgery can be conducted. There is growing concern over the resultant hypoperfusion and potential damage to tissues and organs downstream of REBOA. To better understand the acute hemodynamic changes imposed by REBOA, we developed a three-dimensional computational fluid dynamic (CFD) model under normal, hemorrhage, and aortic occlusion conditions. The goal was to characterize the acute hemodynamic changes and identify regions within the aortic vascular tree susceptible to abnormal flow and shear stress. Methods: Hemodynamic data from established porcine hemorrhage models were used to build a CFD model. Swine underwent 20% controlled hemorrhage and were randomized to receive a full or partial aortic occlusion. Using CT scans, we generated a pig-specific aortic geometry and imposed physiologically relevant inlet flow and outlet pressure boundary conditions to match in vivo data. By assuming non-Newtonian fluid properties, pressure, velocity, and shear stresses were quantified over a cardiac cycle. Results: We observed a significant rise in blood pressure (∼147 mmHg) proximal to REBOA, which resulted in increased flow and shear stress within the ascending aorta. Specifically, we observed high levels of shear stress within the subclavian arteries (22.75 Pa). Alternatively, at the site of full REBOA, wall shear stress was low (0.04 ± 9.07E-4 Pa), but flow oscillations were high (oscillatory shear index of 0.31). Comparatively, partial REBOA elevated shear levels to 84.14 ± 19.50 Pa and reduced flow oscillations. Our numerical simulations were congruent within 5% of averaged porcine experimental data over a cardiac cycle. Conclusion: This CFD model is the first to our knowledge to quantify the acute hemodynamic changes imposed by REBOA. We identified areas of low shear stress near the site of occlusion and high shear stress in the subclavian arteries. Future studies are needed to determine the optimal design parameters of endovascular hemorrhage control devices that can minimize flow perturbations and areas of high shear.

Fully-Coupled FSI Computational Analyses in the Ascending Thoracic Aorta Using Patient-Specific Conditions and Anisotropic Material Properties

Computational hemodynamics has become increasingly important within the context of precision medicine, providing major insight in cardiovascular pathologies. However, finding appropriate compromise between speed and accuracy remains challenging in computational hemodynamics for an extensive use in decision making. For example, in the ascending thoracic aorta, interactions between the blood and the aortic wall must be taken into account for the sake of accuracy, but these fluid structure interactions (FSI) induce significant computational costs, especially when the tissue exhibits a hyperelastic and anisotropic response. The objective of the current study is to use the Small On Large (SOL) theory to linearize the anisotropic hyperelastic behavior in order to propose a reduced-order model for FSI simulations of the aorta. The SOL method is tested for fully-coupled FSI simulations in a patient-specific aortic geometry presenting an Ascending Thoracic Aortic Aneurysm (aTAA). The same model is also simulated with a fully-coupled FSI with non-linear material behavior, without SOL linearization. Eventually, the results and computational times with and without the SOL are compared. The SOL approach is demonstrated to provide a significant reduction of computational costs for FSI analysis in the aTAA, and the results in terms of stress state distribution are comparable. The method is implemented in ANSYS and will be further evaluated for clinical applications.

Investigations into the Potential of Using Open Source CFD to Analyze the Differences in Hemodynamic Parameters for Aortic Dissections (Healthy versus Stanford Type A and B)

BACKGROUND

The objective of this study was to develop a method to evaluate the effects of an aortic dissection on hemodynamic parameters by conducting a comparison with that of a healthy (nondissected) aorta. Open-source software will be implemented, no proprietary software/application will be used to ensure accessorily and repeatability, in all the data analysis and processing. Computed tomography (CT) images of aortic dissection are used for the model geometry segmentation. Boundary conditions from literature are implemented to computational fluid dynamics (CFD) to analyze the hemodynamic parameters.

METHODS

A numerical simulation model was created by obtaining accurate 3-dimensional geometries of aortae from CT images. In this study, CT images of 8 cases of aortic dissection (Stanford type-A and type-B) and 3 cases of healthy aortae are used for the actual aorta model geometry segmentation. These models were exported into an open-source CFD software, OpenFOAM, where a simplified pulsating flow was simulated by controlling the flow pressure. Ten cycles of the pulsatile flow (0.50 sec/cycle) conditions, totaling 5 sec, were calculated.

RESULTS

The pressure distribution, wall shear stress (WSS) and flow velocity streamlines within the aorta and the false lumen were calculated and visualized. It was found that the flow velocity and WSS had a high correlation in high WSS areas of the intermittent layer between the true and false lumen. Most of the Stanford type-A dissections in the study showed high WSS, over 38 Pa, at the systole phase. This indicates that the arterial walls in type-A dissections are more likely to be damaged with pulsatile flow.

CONCLUSIONS

Using CFD to estimate localized high WSS areas may help in deciding to treat a type-A or B dissection with a stent graft to prevent a potential rupture.

A novel MRI-based data fusion methodology for efficient, personalised, compliant simulations of aortic haemodynamics

We present a novel, cost-efficient methodology to simulate aortic haemodynamics in a patient-specific, compliant aorta using an MRI data fusion process. Based on a previously-developed Moving Boundary Method, this technique circumvents the high computational cost and numerous structural modelling assumptions required by traditional Fluid-Structure Interaction techniques. Without the need for Computed Tomography (CT) data, the MRI images required to construct the simulation can be obtained during a single imaging session. Black Blood MR Angiography and 2D Cine-MRI data were used to reconstruct the luminal geometry and calibrate wall movement specifically to each region of the aorta. 4D-Flow MRI and non-invasive pressure measurements informed patient-specific inlet and outlet boundary conditions. Luminal area closely matched 2D Cine-MRI measurements with a mean error of less than 4.6% across the cardiac cycle, while physiological pressure and flow distributions were simulated to within 3.3% of patient-specific targets. Moderate agreement with 4D-Flow MRI velocity data was observed. Despite lower peak velocity, an equivalent rigid-wall simulation predicted a mean Time-Averaged Wall Shear Stress (TAWSS) 13% higher than the compliant simulation. The agreement observed between compliant simulation results and MRI data is testament to the accuracy and efficiency of this MRI-based simulation technique.

An optimal control approach to determine resistance-type boundary conditions from in-vivo data for cardiovascular simulations

The choice of appropriate boundary conditions is a fundamental step in computational fluid dynamics (CFD) simulations of the cardiovascular system. Boundary conditions, in fact, highly affect the computed pressure and flow rates, and consequently haemodynamic indicators such as wall shear stress (WSS), which are of clinical interest. Devising automated procedures for the selection of boundary conditions is vital to achieve repeatable simulations. However, the most common techniques do not automatically assimilate patient-specific data, relying instead on expensive and time-consuming manual tuning procedures. In this work, we propose a technique for the automated estimation of outlet boundary conditions based on optimal control. The values of resistive boundary conditions are set as control variables and optimized to match available patient-specific data. Experimental results on four aortic arches demonstrate that the proposed framework can assimilate 4D-Flow MRI data more accurately than two other common techniques based on Murray's law and Ohm's law.

3D Printing in Modern Cardiology

BACKGROUND

3D printing represents an emerging technology in the field of cardiovascular medicine. 3D printing can help to perform a better analysis of complex anatomies to optimize intervention planning.

METHODS

A systematic review was performed to illustrate the 3D printing technology and to describe the workflow to obtain 3D printed models from patient-specific images. Examples from our laboratory of the benefit of 3D printing in planning interventions were also reported.

RESULTS

3D printing technique is reliable when applied to high-quality 3D image data (CTA, CMR, 3D echography), but it still needs the involvement of expert operators for image segmentation and mesh refinement. 3D printed models could be useful in interventional planning, although prospective studies with comprehensive and clinically meaningful endpoints are required to demonstrate the clinical utility.

CONCLUSION

3D printing can be used to improve anatomy understanding and surgical planning.

A distributed lumped parameter model of blood flow with fluid-structure interaction

A distributed lumped parameter (DLP) model of blood flow was recently developed that can be simulated in minutes while still incorporating complex sources of energy dissipation in blood vessels. The aim of this work was to extend the previous DLP modeling framework to include fluid-structure interactions (DLP-FSI). This was done by using a simple compliance term to calculate pressure that does not increase the simulation complexity of the original DLP models. Verification and validation studies found DLP-FSI simulations had good agreement compared to analytical solutions of the wave equations, experimental measurements of pulsatile flow in elastic tubes, and in vivo MRI measurements of thoracic aortic flow. This new development of DLP-FSI allows for significantly improved computational efficiency of FSI simulations compared to FSI approaches that solve the full 3D conservation of mass and momentum equations while also including the complex sources of energy dissipation occurring in cardiovascular flows that other simplified models neglect.

Toward an accurate estimation of wall shear stress from 4D flow magnetic resonance downstream of a severe stenosis

PURPOSE

First, to investigate the agreement between velocity, velocity gradient, and Reynolds stress obtained from four-dimensional flow magnetic resonance (4D flow MRI) measurements and direct numerical simulation (DNS). Second, to propose and optimize based on DNS, 2 alternative methods for the accurate estimation of wall shear stress (WSS) when the resolution of the flow measurements is limited. Thirdly, to validate the 2 methods based on 4D flow MRI data.

METHODS

In vitro 4D MRI has been conducted in a realistic rigid stenosed aorta model under a constant flow rate of 12 L/min. A DNS of transitional stenotic flow has been performed using the same geometry and boundary conditions.

RESULTS

Time-averaged velocity and Reynolds stresses are in good agreement between in vitro 4D MRI data and DNS (errors between 2% and 8% of the reference downsampled data). WSS estimation based on the 2 proposed methods applied to MRI data provide good agreement with DNS for slice-averaged values (maximum error is less than 15% of the mean reference WSS for the first method and 25% for the second method). The performance of both models is not strongly sensitive to spatial resolution up to 1.5 mm voxel size. While the performance of model 1 deteriorates appreciably at low signal-to-noise ratios, model 2 remains robust.

CONCLUSIONS

The 2 methods for WSS magnitude give an overall better agreement than the standard approach used in the literature based on direct calculation of the velocity gradient close to the wall (relative error of 84%).

Aortic aneurysms and dissections: Unmet needs from physicians and engineers perspectives

The treatment of aortic disease is complex, requiring cardiothoracic and vascular surgeons to make pre-, post- and intraoperative decisions directly influencing patient survival and well-being. Despite tremendous advancement in vascular surgery and endovascular techniques in the last two decades, along with the abundance of research in the field, many unmet needs and unanswered questions remain. Tight collaboration between engineers and physicians is a keystone in translating new tools, techniques, and devices into practice. Here, we have gathered our perspective, as physicians and engineers, in several pressing issues associated with the diagnosis and treatment of aortic aneurysms and dissection, referring to the current knowledge and practice, signifying unmet needs as well as future directions.

Computational Modeling of Blood Flow Hemodynamics for Biomechanical Investigation of Cardiac Development and Disease

The heart is the first functional organ in a developing embryo. Cardiac development continues throughout developmental stages while the heart goes through a serious of drastic morphological changes. Previous animal experiments as well as clinical observations showed that disturbed hemodynamics interfere with the development of the heart and leads to the formation of a variety of defects in heart valves, heart chambers, and blood vessels, suggesting that hemodynamics is a governing factor for cardiogenesis, and disturbed hemodynamics is an important source of congenital heart defects. Therefore, there is an interest to image and quantify the flowing blood through a developing heart. Flow measurement in embryonic fetal heart can be performed using advanced techniques such as magnetic resonance imaging (MRI) or echocardiography. Computational fluid dynamics (CFD) modeling is another approach especially useful when the other imaging modalities are not available and in-depth flow assessment is needed. The approach is based on numerically solving relevant physical equations to approximate the flow hemodynamics and tissue behavior. This approach is becoming widely adapted to simulate cardiac flows during the embryonic development. While there are few studies for human fetal cardiac flows, many groups used zebrafish and chicken embryos as useful models for elucidating normal and diseased cardiogenesis. In this paper, we explain the major steps to generate CFD models for simulating cardiac hemodynamics in vivo and summarize the latest findings on chicken and zebrafish embryos as well as human fetal hearts.

A novel formulation for the study of the ascending aortic fluid dynamics with in vivo data

Numerical simulations to evaluate thoracic aortic hemodynamics include a computational fluid dynamic (CFD) approach or fluid-structure interaction (FSI) approach. While CFD neglects the arterial deformation along the cardiac cycle by applying a rigid wall simplification, on the other side the FSI simulation requires a lot of assumptions for the material properties definition and high computational costs. The aim of this study is to investigate the feasibility of a new strategy, based on Radial Basis Functions (RBF) mesh morphing technique and transient simulations, able to introduce the patient-specific changes in aortic geometry during the cardiac cycle. Starting from medical images, aorta models at different phases of cardiac cycle were reconstructed and a transient shape deformation was obtained by proper activating incremental RBF solutions during the simulation process. The results, in terms of main hemodynamic parameters, were compared with two performed CFD simulations for the aortic model at minimum and maximum volume. Our implemented strategy copes the actual arterial variation during cardiac cycle with high accuracy, capturing the impact of geometrical variations on fluid dynamics, overcoming the complexity of a standard FSI approach.

Does the inflow velocity profile influence physiologically relevant flow patterns in computational hemodynamic models of left anterior descending coronary artery?

Patient-specific computational fluid dynamics is a powerful tool for investigating the hemodynamic risk in coronary arteries. Proper setting of flow boundary conditions in computational hemodynamic models of coronary arteries is one of the sources of uncertainty weakening the findings of in silico experiments, in consequence of the challenging task of obtaining in vivo 3D flow measurements within the clinical framework. Accordingly, in this study we evaluated the influence of assumptions on inflow velocity profile shape on coronary artery hemodynamics. To do that, (1) ten left anterior descending coronary artery (LAD) geometries were reconstructed from clinical angiography, and (2) eleven velocity profiles with realistic 3D features such as eccentricity and differently shaped (single- and double-vortex) secondary flows were generated analytically and imposed as inflow boundary conditions. Wall shear stress and helicity-based descriptors obtained prescribing the commonly used parabolic velocity profile were compared with those obtained with the other velocity profiles. Our findings indicated that the imposition of idealized velocity profiles as inflow boundary condition is acceptable as long the results of the proximal vessel segment are not considered, in LAD coronary arteries. As a pragmatic rule of thumb, a conservative estimation of the length of influence of the shape of the inflow velocity profile on LAD local hemodynamics can be given by the theoretical entrance length for cylindrical conduits in laminar flow conditions.

Recent Advances in Biomechanical Characterization of Thoracic Aortic Aneurysms

Thoracic aortic aneurysm (TAA) is a focal enlargement of the thoracic aorta, but the etiology of this disease is not fully understood. Previous work suggests that various genetic syndromes, congenital defects such as bicuspid aortic valve, hypertension, and age are associated with TAA formation. Though occurrence of TAAs is rare, they can be life-threatening when dissection or rupture occurs. Prevention of these adverse events often requires surgical intervention through full aortic root replacement or implantation of endovascular stent grafts. Currently, aneurysm diameters and expansion rates are used to determine if intervention is warranted. Unfortunately, this approach oversimplifies the complex aortopathy. Improving treatment of TAAs will likely require an increased understanding of the biological and biomechanical factors contributing to the disease. Past studies have substantially contributed to our knowledge of TAAs using various ex vivo, in vivo, and computational methods to biomechanically characterize the thoracic aorta. However, any singular approach typically focuses on only material properties of the aortic wall, intra-aneurysmal hemodynamics, or in vivo vessel dynamics, neglecting combinatorial factors that influence aneurysm development and progression. In this review, we briefly summarize the current understanding of TAA causes, treatment, and progression, before discussing recent advances in biomechanical studies of TAAs and possible future directions. We identify the need for comprehensive approaches that combine multiple characterization methods to study the mechanisms contributing to focal weakening and rupture. We hope this summary and analysis will inspire future studies leading to improved prediction of thoracic aneurysm progression and rupture, improving patient diagnoses and outcomes.

Statistical Shape Analysis of Ascending Thoracic Aortic Aneurysm: Correlation between Shape and Biomechanical Descriptors

An ascending thoracic aortic aneurysm (ATAA) is a heterogeneous disease showing different patterns of aortic dilatation and valve morphologies, each with distinct clinical course. This study aimed to explore the aortic morphology and the associations between shape and function in a population of ATAA, while further assessing novel risk models of aortic surgery not based on aortic size. Shape variability of n = 106 patients with ATAA and different valve morphologies (i.e., bicuspid versus tricuspid aortic valve) was estimated by statistical shape analysis (SSA) to compute a mean aortic shape and its deformation. Once the computational atlas was built, principal component analysis (PCA) allowed to reduce the complex ATAA anatomy to a few shape modes, which were correlated to shear stress and aortic strain, as determined by computational analysis. Findings demonstrated that shape modes are associated to specific morphological features of aneurysmal aorta as the vessel tortuosity and local bulging of the ATAA. A predictive model, built with principal shape modes of the ATAA wall, achieved better performance in stratifying surgically operated ATAAs versus monitored ATAAs, with respect to a baseline model using the maximum aortic diameter. Using current imaging resources, this study demonstrated the potential of SSA to investigate the association between shape and function in ATAAs, with the goal of developing a personalized approach for the treatment of the severity of aneurysmal aorta.

Correlation between LAA Morphological Features and Computational Fluid Dynamics Analysis for Non-Valvular Atrial Fibrillation Patients

The left atrial appendage (LAA) is a complex cardiovascular structure which can yield to thrombi formation in patients with non-valvular atrial fibrillation (AF). The study of LAA fluid dynamics together with morphological features should be investigated in order to evaluate the possible connection of geometrical and hemodynamics indices with the stroke risk. To reach this goal, we conducted a morphological analysis of four different LAA shapes considering their variation during the cardiac cycle and computational fluid dynamics (CFD) simulations in AF conditions were carried out. The analysis of main geometrical LAA parameters showed a huger ostium and a reduced motility for the cauliflower and cactus shapes, as well as a lower velocity values from the CFD analysis. Such findings are in line with literature and highlight the importance of coupling dynamics imaging data with CFD calculations for providing information not available at clinical level.

Hemodynamic effects of support modes of LVADs on the aortic valve

As the alternative treatment for heart failure, left ventricular assist devices (LVADs) have been widely applied to clinical practice. However, the effects of the support modes of LVADs on the biomechanical states of the aortic valve are still poorly understood. Hence, the present study investigates such effects and proposes a novel fluid-structure interaction (FSI) approach that combines the lattice Boltzmann method (LBM) and finite element (FE) method. Two support modes of LVADs, namely constant speed mode and constant flow mode, which have been widely applied to clinical practice, are also designed. Results demonstrate that the support modes of LVADs could significantly affect the biomechanical states of the aortic valve and the blood flow pattern of the ascending aorta. Compared with those in the constant flow mode, the leaflets in the constant speed mode could achieve better dynamic performance and lower stress during the systolic phase. The max radial displacement of the leaflets in the constant speed mode is at 8 mm, whereas that in the constant flow mode is at 0.8 mm. Furthermore, the outflow of LVADs directly impacts the aortic surfaces of the leaflets during the diastolic phase by increasing the level of wall shear stress of the leaflets. The leaflets in the constant speed mode receive less impact than those in the constant flow mode. The condition with such minimal impact is conducive to maintaining the normal structure of leaflets and benefits the reduction of the risk of valvular diseases. In sum, the support modes of LVADs exert a crucial effect on the biomechanical environment of the aortic valve. The constant speed mode is better than the constant flow mode in terms of providing a good hemodynamic environment for the aortic valve.

4D Flow MRI Estimation of Boundary Conditions for Patient Specific Cardiovascular Simulation

Accurate image based cardiovascular simulations require patient specific boundary conditions (BCs) for inlets, outlets and vessel wall mechanical properties. While inlet BCs are typically determined non-invasively, invasive pressure catheterization is often used to determine patient specific outlet BCs and vessel wall mechanical properties. A method using 4D Flow MRI to non-invasively determine both patient specific outlet BCs and vessel wall mechanical properties is presented and results for both in vitro validation with a latex tube and an in vivo pulmonary artery stenosis (PAS) stent intervention are presented. For in vitro validation, acceptable agreement is found between simulation using BCs from 4D Flow MRI and benchtop measurements. For the PAS virtual intervention, simulation correctly predicts flow distribution with 9% error compared to MRI. Using 4D Flow MRI to noninvasively determine patient specific BCs increases the ability to use image based simulations as pressure catheterization is not always performed.