A Proof of Concept of a Non-Invasive Image-Based Material Characterization Method for Enhanced Patient-Specific Computational Modeling

Coupling synthetic and real-world data for a deep learning-based segmentation process of 4D flow MRI

BACKGROUND AND OBJECTIVE

Phase contrast magnetic resonance imaging (4D flow MRI) is an imaging technique able to provide blood velocity in vivo and morphological information. This capability has been used to study mainly the hemodynamics of large vessels, such as the thoracic aorta. However, the segmentation of 4D flow MRI data is a complex and time-consuming task. In recent years, neural networks have shown great accuracy in segmentation tasks if large datasets are provided. Unfortunately, in the context of 4D flow MRI, the availability of these data is limited due to its recent adoption in clinical settings. In this study, we propose a pipeline for generating synthetic thoracic aorta phase contrast magnetic resonance angiography (PCMRA) to expand the limited dataset of patient-specific PCMRA images, ultimately improving the accuracy of the neural network segmentation even with a small real dataset.

METHODS

The pipeline involves several steps. First, a statistical shape model is used to synthesize new artificial geometries to improve data numerosity and variability. Secondly, computational fluid dynamics simulations are employed to simulate the velocity fields and, finally, after a downsampling and a signal-to-noise and velocity limit adjustment in both frequency and spatial domains, volumes are obtained using the PCMRA formula. These synthesized volumes are used in combination with real-world data to train a 3D U-Net neural network. Different settings of real and synthetic data are tested.

RESULTS

Incorporating synthetic data into the training set significantly improved the segmentation performance compared to using only real data. The experiments with synthetic data achieved a DICE score (DS) value of 0.83 and a better target reconstruction with respect to the case with only real data (DS = 0.65).

CONCLUSION

The proposed pipeline demonstrated the ability to increase the dataset in terms of numerosity and variability and to improve the segmentation accuracy for the thoracic aorta using PCMRA.

Numerical investigation on circular and elliptical bulge tests for inverse soft tissue characterization

The acquisition of insights concerning the mechanobiology of aneurysmatic aortic tissues is an important field of investigation. The complete characterization of aneurysm mechanical behaviour can be carried out by biaxial experimental tests on ex vivo specimens. In literature, several works proposed bulge inflation tests as a valid method to analyse aneurysmatic tissue. Bulge test data processing requires the adoption of digital image correlation and inverse analysis approaches to estimate strain and stress distributions, respectively. In this context, however, the accuracy of inverse analysis method has not been evaluated yet. This aspect appears particularly interesting given the anisotropic behaviour of the soft tissue and the possibility to adopt different die geometries. The goal of this study is to provide an accuracy characterization of the inverse analysis applied to the bulge test technique using a numerical approach. In particular, different cases of bulge inflation were simulated in a finite element environment as a reference. To investigate the effect of tissue anisotropic degree and bulge die geometries (circular and elliptical), different input parameters were considered to obtain multiple test cases. The specimen deformed shapes, resulting from the reference finite element simulations, were then analysed through an inverse analysis approach to produce an estimation of stress distributions. The estimated stresses were, at last, compared with the values from the reference finite element simulations. The results demonstrated that the circular die geometry produces a satisfactory estimation accuracy only under certain conditions of material quasi-isotropy. On the other hand, the choice of an elliptical bulge die was proven to be more suitable for the analysis of anisotropic tissues.

Fabrication of deformable patient-specific AAA models by material casting techniques

Background

Abdominal Aortic Aneurysm (AAA) is a balloon-like dilatation that can be life-threatening if not treated. Fabricating patient-specific AAA models can be beneficial for in-vitro investigations of hemodynamics, as well as for pre-surgical planning and training, testing the effectiveness of different interventions, or developing new surgical procedures. The current direct additive manufacturing techniques cannot simultaneously ensure the flexibility and transparency of models required by some applications. Therefore, casting techniques are presented to overcome these limitations and make the manufactured models suitable for in-vitro hemodynamic investigations, such as particle image velocimetry (PIV) measurements or medical imaging.

Methods

Two complex patient-specific AAA geometries were considered, and the related 3D models were fabricated through material casting. In particular, two casting approaches, i.e. lost molds and lost core casting, were investigated and tested to manufacture the deformable AAA models. The manufactured models were acquired by magnetic resonance, computed tomography (CT), ultrasound imaging, and PIV. In particular, CT scans were segmented to generate a volumetric reconstruction for each manufactured model that was compared to a reference model to assess the accuracy of the manufacturing process.

Results

Both lost molds and lost core casting techniques were successful in the manufacturing of the models. The lost molds casting allowed a high-level surface finish in the final 3D model. In this first case, the average signed distance between the manufactured model and the reference was (- 0.2 ± 0.2 ) mm. However, this approach was more expensive and time-consuming. On the other hand, the lost core casting was more affordable and allowed the reuse of the external molds to fabricate multiple copies of the same AAA model. In this second case, the average signed distance between the manufactured model and the reference was (0.1 ± 0.6 ) mm. However, the final model's surface finish quality was poorer compared to the model obtained by lost molds casting as the sealing of the outer molds was not as firm as the other casting technique.

Conclusions

Both lost molds and lost core casting techniques can be used for manufacturing patient-specific deformable AAA models suitable for hemodynamic investigations, including medical imaging and PIV.

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.

An image-based approach for the estimation of arterial local stiffness in vivo

The analysis of mechanobiology of arterial tissues remains an important topic of research for cardiovascular pathologies evaluation. In the current state of the art, the gold standard to characterize the tissue mechanical behavior is represented by experimental tests, requiring the harvesting of ex-vivo specimens. In recent years though, image-based techniques for the in vivo estimation of arterial tissue stiffness were presented. The aim of this study is to define a new approach to provide local distribution of arterial stiffness, estimated as the linearized Young's Modulus, based on the knowledge of in vivo patient-specific imaging data. In particular, the strain and stress are estimated with sectional contour length ratios and a Laplace hypothesis/inverse engineering approach, respectively, and then used to calculate the Young's Modulus. After describing the method, this was validated by using a set of Finite Element simulations as input. In particular, idealized cylinder and elbow shapes plus a single patient-specific geometry were simulated. Different stiffness distributions were tested for the simulated patient-specific case. After the validation from Finite Element data, the method was then applied to patient-specific ECG-gated Computed Tomography data by also introducing a mesh morphing approach to map the aortic surface along the cardiac phases. The validation process revealed satisfactory results. In the simulated patient-specific case, root mean square percentage errors below 10% for the homogeneous distribution and below 20% for proximal/distal distribution of stiffness. The method was then successfully used on the three ECG-gated patient-specific cases. The resulting distributions of stiffness exhibited significant heterogeneity, nevertheless the resulting Young's moduli were always contained within the 1-3 MPa range, which is in line with literature.

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.

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.

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.

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.