Numerical simulation of wave propagation through interfaces using the extended finite element method for magnetic resonance elastography.

Magnetic resonance elastography (MRE) is an elasticity imaging technique for quantitatively assessing the stiffness of human tissues. In MRE, finite element method (FEM) is widely used for modeling wave propagation and stiffness reconstruction. However, in front of inclusions with complex interfaces, FEM can become burdensome in terms of the model partition and computationally expensive. In this work, we implement a formulation of FEM, known as the eXtended finite element method (XFEM), which is a method used for modeling discontinuity like crack and heterogeneity. Using a level-set method, it makes the interface independent of the mesh, thus relieving the meshing efforts. We investigate this method in two studies: wave propagation across an oblique linear interface and stiffness reconstruction of a random-shape inclusion. In the first study, numerical results by XFEM and FEM models revealing the wave conversion rules at linear interface are presented and successfully compared to the theoretical predictions. The second study, investigated in a pseudo-practical application, demonstrates further the applicability of XFEM in MRE and the convenience, accuracy, and speed of XFEM with respect to FEM. XFEM can be regarded as a promising alternative to FEM for inclusion modeling in MRE.

Aortic roadmapping during EVAR: a combined FEM-EM tracking feasibility study.

PURPOSE: Currently, the intra-operative visualization of vessels during endovascular aneurysm repair (EVAR) relies on contrast-based imaging modalities. Moreover, traditional image fusion techniques lack a continuous and automatic update of the vessel configuration, which changes due to the insertion of stiff guidewires. The purpose of this work is to develop and evaluate a novel approach to improve image fusion, that takes into account the deformations, combining electromagnetic (EM) tracking technology and finite element modeling (FEM). METHODS: To assess whether EM tracking can improve the prediction of the numerical simulations, a patient-specific model of abdominal aorta was segmented and manufactured. A database of simulations with different insertion angles was created. Then, an ad hoc sensorized tool with three embedded EM sensors was designed, enabling tracking of the sensors' positions during the insertion phase. Finally, the corresponding cone beam computed tomography (CBCT) images were acquired and processed to obtain the ground truth aortic deformations of the manufactured model. RESULTS: Among the simulations in the database, the one minimizing the in silico versus in vitro discrepancy in terms of sensors' positions gave the most accurate aortic displacement results. CONCLUSIONS: The proposed approach suggests that the EM tracking technology could be used not only to follow the tool, but also to minimize the error in the predicted aortic roadmap, thus paving the way for a safer EVAR navigation.

Calibration of the Mechanical Boundary Conditions for a Patient-Specific Thoracic Aorta Model Including the Heart Motion Effect.

OBJECTIVE: We propose a procedure for calibrating 4 parameters governing the mechanical boundary conditions (BCs) of a thoracic aorta (TA) model derived from one patient with ascending aortic aneurysm. The BCs reproduce the visco-elastic structural support provided by the soft tissue and the spine and allow for the inclusion of the heart motion effect. METHODS: We first segment the TA from magnetic resonance imaging (MRI) angiography and derive the heart motion by tracking the aortic annulus from cine-MRI. A rigid-wall fluid-dynamic simulation is performed to derive the time-varying wall pressure field. We build the finite element model considering patient-specific material properties and imposing the derived pressure field and the motion at the annulus boundary. The calibration, which involves the zero-pressure state computation, is based on purely structural simulations. After obtaining the vessel boundaries from the cine-MRI sequences, an iterative procedure is performed to minimize the distance between them and the corresponding boundaries derived from the deformed structural model. A strongly-coupled fluid-structure interaction (FSI) analysis is finally performed with the tuned parameters and compared to the purely structural simulation. RESULTS AND CONCLUSION: The calibration with structural simulations allows to reduce maximum and mean distances between image-derived and simulation-derived boundaries from 8.64 mm to 6.37 mm and from 2.24 mm to 1.83 mm, respectively. The maximum root mean square error between the deformed structural and FSI surface meshes is 0.19 mm. This procedure may prove crucial for increasing the model fidelity in replicating the real aortic root kinematics.

Real-time simulation of the transplanted tooth using model order reduction.

The biomechanics of transplanted teeth remain poorly understood due to a lack of models. In this context, finite element (FE) analysis has been used to evaluate the influence of occlusal morphology and root form on the biomechanical behavior of the transplanted tooth, but the construction of a FE model is extremely time-consuming. Model order reduction (MOR) techniques have been used in the medical field to reduce computing time, and the present study aimed to develop a reduced model of a transplanted tooth using the higher-order proper generalized decomposition method. The FE model of a previous study was used to learn von Mises root stress, and axial and lateral forces were used to simulate different occlusions between 75 and 175N. The error of the reduced model varied between 0.1% and 5.9% according to the subdomain, and was the highest for the highest lateral forces. The time for the FE simulation varied between 2.3 and 7.2 h. In comparison, the reduced model was built in 17s and interpolation of new results took approximately 2.10-2s. The use of MOR reduced the time for delivering the root stresses by a mean 5.9 h. The biomechanical behavior of a transplanted tooth simulated by FE models was accurately captured with a significant decrease of computing time. Future studies could include using jaw tracking devices for clinical use and the development of more realistic real-time simulations of tooth autotransplantation surgery.

Comparison of ultrasound elastography, magnetic resonance elastography and finite element model to quantify nonlinear shear modulus.

Objective. The aim of this study is to validate the estimation of the nonlinear shear modulus (A) from the acoustoelasticity theory with two experimental methods, ultrasound (US) elastography and magnetic resonance elastography (MRE), and a finite element method.Approach. Experiments were performed on agar (2%)-gelatin (8%) phantom considered as homogeneous, elastic and isotropic. Two specific setups were built to ensure a uniaxial stress step by step on the phantom, one for US and a nonmagnetic version for MRE. The stress was controlled identically in both imaging techniques, with a water tank placed on the top of the phantom and filled with increasing masses of water during the experiment. In US, the supersonic shear wave elastography was implemented on an ultrafast US device, driving a 6 MHz linear array to measure shear wave speed. In MRE, a gradient-echo sequence was used in which the three spatial directions of a 40 Hz continuous wave displacement generated with an external driver were encoded successively. Numerically, a finite element method was developed to simulate the propagation of the shear wave in a uniaxially stressed soft medium.Main results. Similar shear moduli were estimated at zero stress using experimental methods,µ0US= 12.3 ± 0.3 kPa andµ0MRE= 11.5 ± 0.7 kPa. Numerical simulations were set with a shear modulus of 12 kPa and the resulting nonlinear shear modulus was found to be -58.1 ± 0.7 kPa. A very good agreement between the finite element model and the experimental models (AUS= -58.9 ± 9.9 kPa andAMRE= -52.8 ± 6.5 kPa) was obtained.Significance. These results show the validity of such nonlinear shear modulus measurement quantification in shear wave elastography. This work paves the way to develop nonlinear elastography technique to get a new biomarker for medical diagnosis.

Patient-specific finite element simulation of peripheral artery percutaneous transluminal angioplasty to evaluate the procedure outcome without stent implantation.

The purpose of this work is to present a patient-specific (PS) modeling approach for simulating percutaneous transluminal angioplasty (PTA) endovascular treatment and assessing the balloon sizing influence on short-term outcomes in peripheral arteries, i.e. without stent implantation. Two 3D PS stenosed femoral artery models, one with a dominant calcified atherosclerosis while the other with a lipidic plaque, were generated from pre-operative computed tomography angiography images. Elastoplastic constitutive laws were implemented within the plaque and artery models. Implicit finite element method (FEM) was used to simulate the balloon inflation and deflation for different sizings. Besides vessel strains, results were mainly evaluated in terms of the elastic recoil ratio (ERR) and lumen gain ratio (LGR) attained immediately after PTA. Higher LGR values were shown within the stenosed region of the lipidic patient. Simulated results also showed a direct and quantified correlation between balloon sizing and LGR and ERR for both patients after PTA, with a more significant influence on the lumen gain. The max principal strain values in the outer arterial wall increased at higher balloon sizes during inflation as well, with higher rates of increase when the plaque was calcified. Results show that our model could serve in finding a compromise for each stenosis type: maximizing the achieved lumen gain after PTA, but at the same time without damaging the arterial tissue. The proposed methodology can serve as a step toward a clinical decision support system to improve angioplasty balloon sizing selection prior to the surgery.

Assessment of shape-based features ability to predict the ascending aortic aneurysm growth.

The current guidelines for the ascending aortic aneurysm (AsAA) treatment recommend surgery mainly according to the maximum diameter assessment. This criterion has already proven to be often inefficient in identifying patients at high risk of aneurysm growth and rupture. In this study, we propose a method to compute a set of local shape features that, in addition to the maximum diameter D, are intended to improve the classification performances for the ascending aortic aneurysm growth risk assessment. Apart from D, these are the ratio DCR between D and the length of the ascending aorta centerline, the ratio EILR between the length of the external and the internal lines and the tortuosity T. 50 patients with two 3D acquisitions at least 6 months apart were segmented and the growth rate (GR) with the shape features related to the first exam computed. The correlation between them has been investigated. After, the dataset was divided into two classes according to the growth rate value. We used six different classifiers with input data exclusively from the first exam to predict the class to which each patient belonged. A first classification was performed using only D and a second with all the shape features together. The performances have been evaluated by computing accuracy, sensitivity, specificity, area under the receiver operating characteristic curve (AUROC) and positive (negative) likelihood ratio LHR+ (LHR-). A positive correlation was observed between growth rate and DCR (r = 0.511, p = 1.3e-4) and between GR and EILR (r = 0.472, p = 2.7e-4). Overall, the classifiers based on the four metrics outperformed the same ones based only on D. Among the diameter-based classifiers, k-nearest neighbours (KNN) reported the best accuracy (86%), sensitivity (55.6%), AUROC (0.74), LHR+ (7.62) and LHR- (0.48). Concerning the classifiers based on the four shape features, we obtained the best accuracy (94%), sensitivity (66.7%), specificity (100%), AUROC (0.94), LHR+ (+∞) and LHR- (0.33) with support vector machine (SVM). This demonstrates how automatic shape features detection combined with risk classification criteria could be crucial in planning the follow-up of patients with ascending aortic aneurysm and in predicting the possible dangerous progression of the disease.

Computer-aided shape features extraction and regression models for predicting the ascending aortic aneurysm growth rate.

OBJECTIVE: ascending aortic aneurysm growth prediction is still challenging in clinics. In this study, we evaluate and compare the ability of local and global shape features to predict the ascending aortic aneurysm growth. MATERIAL AND METHODS: 70 patients with aneurysm, for which two 3D acquisitions were available, are included. Following segmentation, three local shape features are computed: (1) the ratio between maximum diameter and length of the ascending aorta centerline, (2) the ratio between the length of external and internal lines on the ascending aorta and (3) the tortuosity of the ascending tract. By exploiting longitudinal data, the aneurysm growth rate is derived. Using radial basis function mesh morphing, iso-topological surface meshes are created. Statistical shape analysis is performed through unsupervised principal component analysis (PCA) and supervised partial least squares (PLS). Two types of global shape features are identified: three PCA-derived and three PLS-based shape modes. Three regression models are set for growth prediction: two based on gaussian support vector machine using local and PCA-derived global shape features; the third is a PLS linear regression model based on the related global shape features. The prediction results are assessed and the aortic shapes most prone to growth are identified. RESULTS: the prediction root mean square error from leave-one-out cross-validation is: 0.112 mm/month, 0.083 mm/month and 0.066 mm/month for local, PCA-based and PLS-derived shape features, respectively. Aneurysms close to the root with a large initial diameter report faster growth. CONCLUSION: global shape features might provide an important contribution for predicting the aneurysm growth.

Simulation of multi-curve active catheterization for endovascular navigation to complex targets.

The recent development of endovascular therapies has been accompanied by increasingly accurate navigation simulations to assist surgeons in decision making processes or to produce training tools. However, they have been focused mostly on targets within the aortic vasculature. In order to reach complex targets such as cerebral arteries by endovascular navigation, an active guidewire made of a Shape Memory Alloy (SMA) was recently proposed. The active part becomes deformed by the Joule effect and this deformation induces a bending of the guidewire. This setup is particularly suited for facilitating the access to Supra-Aortic Trunks (SATs) and, in our case, especially the left carotid artery. A complete characterization of the endovascular active navigation was conducted. In this framework, a test bench was developed to obtain an order of magnitude of the velocities applied on the guidewire as well as on the passive catheter going along with it in endovascular navigation. A numerical model was developed and validated in the case of navigation in a complex phantom aorta. We succeeded in representing crucial phenomena observed experimentally: snapping, active curvatures, interactions between the tools. In the last part of this study, it was demonstrated that adapting the guidewire design made it possible to hook the left carotid on three complex aortas.

Influence of balloon design, plaque material composition, and balloon sizing on acute post angioplasty outcomes: An implicit finite element analysis.

In this work we propose a generic modeling approach for simulating percutaneous transluminal angioplasty (PTA) endovascular treatment, and evaluating the influence of balloon design, plaque composition, and balloon sizing on acute post-procedural outcomes right after PTA, without stent implantation. Clinically-used PTA balloons were classified into two categories according to their compliance characteristics, and were modeled correspondingly. Self-defined elastoplastic constitutive laws were implemented within the plaque and artery models, after calibration based on experimental and clinical data. Finite element method (FEM) implicit solver was used to simulate balloon inflation and deflation. Besides balloon profile at max inflation, results are mainly assessed in terms of the elastic recoil ratio (ERR) and lumen gain ratio (LGR) obtained immediately after PTA. No variations in ERR nor LGR values were detected when the balloon design changed, despite the differences observed in their profile at max inflation. Moreover, LGR and ERR inversely varied with the augmentation of calcification level within the plaque (-11% vs. +4% respectively, from fully lipidic to fully calcified plaque). Furthermore, results showed a direct correlation between balloon sizing and LGR and ERR, with noticeably higher rates of change for LGR (+18% and +2% for LGR and ERR respectively for a calcified plaque and a balloon pressure increasing from 10 to 14 atm). However a larger LGR comes with a higher risk of arterial rupture. This proposed methodology opens the way for evaluation of angioplasty balloon selections towards clinical procedure optimization.

Optical elastography: tracking surface waves with digital image correlation.

Elastography consists in evaluating the propagation speed of waves into a tissue to estimate its stiffness. Usually this method is based on Ultrasounds, magnetic resonance imaging or optical coherent tomography. This paper proposes a simple optic method using ultrafast cameras. Based on digital image correlation (DIC), the tracking of elastic surface wave from white light intensity pattern, allows estimating the propagation speed as an indicator of the tissue local stiffness. Two configurations are presented: (1) 2D imaging of a flat phantom surface with a single camera and (2) 3D imaging of a curved phantom surface with two cameras. As a feasibility study of the first configuration, surface wave speed was measured on isotropic and anisotropic phantoms. Comparisons with ultrasound methods fully validate this approach. Although more sophisticated, the second configuration account for propagation distortions caused by locally curved topology. Triangulation techniques used to retrieve local topology are named stereo-correlation in the field of biomechanics. Stereo-elastography is thus proposed to determine tissue local elasticity from any soft tissue surface wave.

Finite element simulation of the insertion of guidewires during an EVAR procedure: example of a complex patient case, a first step toward patient-specific parameterized models.

Deformations of the vascular structure due to the insertion of tools during endovascular treatment of aneurysms of the abdominal aorta, unless properly anticipated during the preoperative planning phase, may be the source of intraoperative or postoperative complications. We propose here an explicit finite element simulation method which enables one to predict such deformations. This method is based on a mechanical model of the vascular structure which takes into account the nonlinear behavior of the arterial wall, the prestressing effect induced by the blood pressure and the mechanical support of the surrounding organs and structures. An analysis of the model sensitivity to the parameters used to represent this environment is done. This allows determining the parameters that have the largest influence on the quality of the prediction and also provides realistic values for each of them as no experimental data are available in the literature. Moreover, for the first time, the results are compared with 3D intraoperative data. This is done for a patient-specific case with a complex anatomy in order to assess the feasibility of the method. Finally, the predictive capability of the simulation is evaluated on a group of nine patients. The error between the final simulated and intraoperatively measured tool positions was 2.1 mm after the calibration phase on one patient. It results in a 4.6 ± 2.5 mm in average error for the blind evaluation on nine patients.