The role of anatomic shape features in the prognosis of uncomplicated type B aortic dissection initially treated with optimal medical therapy.

OBJECTIVE: Currently, the long-term outcomes of uncomplicated type B aortic dissection (TBAD) patients managed with optimal medical therapy (OMT) remain poor. Aortic expansion is a major factor that determines patient long-term survival. The objective of this study was to investigate the association between anatomic shape features and (i) OMT outcome; (ii) aortic growth rate for TBAD patients initially treated with OMT. METHODS: 108 CT images of TBAD in the acute and chronic phases were collected from 46 patients who were initially treated with OMT. Statistical shape models (SSM) of TBAD were constructed to extract shape features from the earliest initial CT scans of each patient by using principal component analysis (PCA) and partial least square (PLS) regression. Additionally, conventional shape features (e.g., aortic diameter) were quantified from the earliest CT scans as a baseline for comparison. We identified conventional and SSM features that were significant in separating OMT "success" and failure patients. Moreover, the aortic growth rate was predicted by SSM and conventional features using linear and nonlinear regression with cross-validations. RESULTS: Size-related SSM and conventional features (mean aortic diameter: p=0.0484, centerline length: p=0.0112, PCA score c1: p=0.0192, and PLS scores t1: p=0.0004, t2: p=0.0274) were significantly different between OMT success and failure groups, but these features were incapable of predicting the aortic growth rate. SSM shape features showed superior results in growth rate prediction compared to conventional features. Using multiple linear regression, the conventional, PCA, and PLS shape features resulted in root mean square errors (RMSE) of 1.23, 0.85, and 0.84 mm/year, respectively, in leave-one-out cross-validations. Nonlinear support vector regression (SVR) led to improved RMSE of 0.99, 0.54, and 0.43 mm/year, for the conventional, PCA, and PLS features, respectively. CONCLUSION: Size-related shape features of the earliest scan were correlated with OMT failure but led to large errors in the prediction of the aortic growth rate. SSM features in combination with nonlinear regression could be a promising avenue to predict the aortic growth rate.

Patient-Specific Heart Geometry Modeling for Solid Biomechanics Using Deep Learning.

Automated volumetric meshing of patient-specific heart geometry can help expedite various biomechanics studies, such as post-intervention stress estimation. Prior meshing techniques often neglect important modeling characteristics for successful downstream analyses, especially for thin structures like the valve leaflets. In this work, we present DeepCarve (Deep Cardiac Volumetric Mesh): a novel deformation-based deep learning method that automatically generates patient-specific volumetric meshes with high spatial accuracy and element quality. The main novelty in our method is the use of minimally sufficient surface mesh labels for precise spatial accuracy and the simultaneous optimization of isotropic and anisotropic deformation energies for volumetric mesh quality. Mesh generation takes only 0.13 seconds/scan during inference, and each mesh can be directly used for finite element analyses without any manual post-processing. Calcification meshes can also be subsequently incorporated for increased simulation accuracy. Numerous stent deployment simulations validate the viability of our approach for large-batch analyses. Our code is available at https://github.com/danpak94/Deep-Cardiac-Volumetric-Mesh.

Effect of Aging, Sex, and Gene (Fbln5) on Arterial Stiffness of Mice: 20 Weeks Adult Fbln5-knockout Mice Have Older Arteries than 100 Weeks Wild-Type Mice.

The arterial stiffening is a strong independent predictor of cardiovascular risk and has been used to characterize the biological age of arteries ('arterial age'). Here we revealed that the Fbln5 gene knockout (Fbln5 -/- ) significantly increases the arterial stiffening for both male and female mice. We also showed that the arterial stiffening increases with natural aging, but the stiffening effect of Fbln5 -/- is much more severe than aging. The arterial stiffening of 20 weeks old mice with Fbln5 -/- is much higher than that at 100 weeks in wild-type (Fbln5 +/+ ) mice, which indicates that 20 weeks mice (equivalent to ∼26 years old humans) with Fbln5 -/- have older arteries than 100 weeks wild-type mice (equivalent to ∼77 years humans). Histological microstructure changes of elastic fibers in the arterial tissue elucidate the underlying mechanism of the increase of arterial stiffening due to Fbln5-knockout and aging. These findings provide new insights to reverse 'arterial age' due to abnormal mutations of Fbln5 gene and natural aging. This work is based on a total of 128 biaxial testing samples of mouse arteries and our recently developed unified-fiber-distribution (UFD) model. The UFD model considers the fibers in the arterial tissue as a unified distribution, which is more physically consistent with the real fiber distribution of arterial tissues than the popular fiber-family-based models (e.g., the well-know Gasser-Ogden-Holzapfel [GOH] model) that separate the fiber distribution into several fiber families. Thus, the UFD model achieves better accuracies with less material parameters. To our best knowledge, the UFD model is the only existing accurate model that could capture the property/stiffness differences between different groups of the experimental data discussed here.

Effect of Nonlinear Hyperelastic Property of Arterial Tissues on the Pulse Wave Velocity Based on the Unified-Fiber-Distribution (UFD) Model.

Pulse wave velocity (PWV) is a key, independent risk factor for future cardiovascular events. The Moens-Korteweg equation describes the relation between PWV and the stiffness of arterial tissue with an assumption of isotopic linear elastic property of the arterial wall. However, the arterial tissue exhibits highly nonlinear and anisotropic mechanical behaviors. There is a limited study regarding the effect of arterial nonlinear and anisotropic properties on the PWV. In this study, we investigated the impact of the arterial nonlinear hyperelastic properties on the PWV, based on our recently developed unified-fiber-distribution (UFD) model. The UFD model considers the fibers (embedded in the matrix of the tissue) as a unified distribution, which expects to be more physically consistent with the real fiber distribution than existing models that separate the fiber distribution into two/several fiber families. With the UFD model, we fitted the measured relation between the PWV and blood pressure which obtained a good accuracy. We also modeled the aging effect on the PWV based on observations that the stiffening of arterial tissue increases with aging, and the results agree well with experimental data. In addition, we did parameter studies on the dependence of the PWV on the arterial properties of fiber initial stiffness, fiber distribution, and matrix stiffness. The results indicate the PWV increases with increasing overall fiber component in the circumferential direction. The dependences of the PWV on the fiber initial stiffness, and matrix stiffness are not monotonic and change with different blood pressure. The results of this study could provide new insights into arterial property changes and disease information from the clinical measured PWV data.

PyTorch-FEA: Autograd-enabled finite element analysis methods with applications for biomechanical analysis of human aorta.

BACKGROUND AND OBJECTIVES: Finite-element analysis (FEA) is widely used as a standard tool for stress and deformation analysis of solid structures, including human tissues and organs. For instance, FEA can be applied at a patient-specific level to assist in medical diagnosis and treatment planning, such as risk assessment of thoracic aortic aneurysm rupture/dissection. These FEA-based biomechanical assessments often involve both forward and inverse mechanics problems. Current commercial FEA software packages (e.g., Abaqus) and inverse methods exhibit performance issues in either accuracy or speed. METHODS: In this study, we propose and develop a new library of FEA code and methods, named PyTorch-FEA, by taking advantage of autograd, an automatic differentiation mechanism in PyTorch. We develop a class of PyTorch-FEA functionalities to solve forward and inverse problems with improved loss functions, and we demonstrate the capability of PyTorch-FEA in a series of applications related to human aorta biomechanics. In one of the inverse methods, we combine PyTorch-FEA with deep neural networks (DNNs) to further improve performance. RESULTS: We applied PyTorch-FEA in four fundamental applications for biomechanical analysis of human aorta. In the forward analysis, PyTorch-FEA achieved a significant reduction in computational time without compromising accuracy compared with Abaqus, a commercial FEA package. Compared to other inverse methods, inverse analysis with PyTorch-FEA achieves better performance in either accuracy or speed, or both if combined with DNNs. CONCLUSIONS: We have presented PyTorch-FEA, a new library of FEA code and methods, representing a new approach to develop FEA methods to forward and inverse problems in solid mechanics. PyTorch-FEA eases the development of new inverse methods and enables a natural integration of FEA and DNNs, which will have numerous potential applications.

Synergistic Integration of Deep Neural Networks and Finite Element Method with Applications for Biomechanical Analysis of Human Aorta.

Motivation: Patient-specific finite element analysis (FEA) has the potential to aid in the prognosis of cardiovascular diseases by providing accurate stress and deformation analysis in various scenarios. It is known that patient-specific FEA is time-consuming and unsuitable for time-sensitive clinical applications. To mitigate this challenge, machine learning (ML) techniques, including deep neural networks (DNNs), have been developed to construct fast FEA surrogates. However, due to the data-driven nature of these ML models, they may not generalize well on new data, leading to unacceptable errors. Methods: We propose a synergistic integration of DNNs and finite element method (FEM) to overcome each other’s limitations. We demonstrated this novel integrative strategy in forward and inverse problems. For the forward problem, we developed DNNs using state-of-the-art architectures, and DNN outputs were then refined by FEM to ensure accuracy. For the inverse problem of heterogeneous material parameter identification, our method employs a DNN as regularization for the inverse analysis process to avoid erroneous material parameter distribution. Results: We tested our methods on biomechanical analysis of the human aorta. For the forward problem, the DNN-only models yielded acceptable stress errors in majority of test cases; yet, for some test cases that could be out of the training distribution (OOD), the peak stress errors were larger than 50%. The DNN-FEM integration eliminated the large errors for these OOD cases. Moreover, the DNN-FEM integration was magnitudes faster than the FEM-only approach. For the inverse problem, the FEM-only inverse method led to errors larger than 50%, and our DNN-FEM integration significantly improved performance on the inverse problem with errors less than 1%.

PyTorch-FEA: Autograd-enabled Finite Element Analysis Methods with Applications for Biomechanical Analysis of Human Aorta.

Motivation: Finite-element analysis (FEA) is widely used as a standard tool for stress and deformation analysis of solid structures, including human tissues and organs. For instance, FEA can be applied at a patient-specific level to assist in medical diagnosis and treatment planning, such as risk assessment of thoracic aortic aneurysm rupture/dissection. These FEA-based biomechanical assessments often involve both forward and inverse mechanics problems. Current commercial FEA software packages (e.g., Abaqus) and inverse methods exhibit performance issues in either accuracy or speed. Methods: In this study, we propose and develop a new library of FEA code and methods, named PyTorch-FEA, by taking advantage of autograd, an automatic differentiation mechanism in PyTorch. We develop a class of PyTorch-FEA functionalities to solve forward and inverse problems with improved loss functions, and we demonstrate the capability of PyTorch-FEA in a series of applications related to human aorta biomechanics. In one of the inverse methods, we combine PyTorch-FEA with deep neural networks (DNNs) to further improve performance. Results: We applied PyTorch-FEA in four fundamental applications for biomechanical analysis of human aorta. In the forward analysis, PyTorch-FEA achieved a significant reduction in computational time without compromising accuracy compared with Abaqus, a commercial FEA package. Compared to other inverse methods, inverse analysis with PyTorch-FEA achieves better performance in either accuracy or speed, or both if combined with DNNs.

Synergistic Integration of Deep Neural Networks and Finite Element Method with Applications of Nonlinear Large Deformation Biomechanics.

Patient-specific finite element analysis (FEA) holds great promise in advancing the prognosis of cardiovascular diseases by providing detailed biomechanical insights such as high-fidelity stress and deformation on a patient-specific basis. Albeit feasible, FEA that incorporates three-dimensional, complex patient-specific geometry can be time-consuming and unsuitable for time-sensitive clinical applications. To mitigate this challenge, machine learning (ML) models, e.g., deep neural networks (DNNs), have been increasingly utilized as potential alternatives to finite element method (FEM) for biomechanical analysis. So far, efforts have been made in two main directions: (1) learning the input-to-output mapping of traditional FEM solvers and replacing FEM with data-driven ML surrogate models; (2) solving equilibrium equations using physics-informed loss functions of neural networks. While these two existing strategies have shown improved performance in terms of speed or scalability, ML models have not yet provided practical advantages over traditional FEM due to generalization issues. This has led us to the question: instead of abandoning or replacing the traditional FEM framework that can reliably solve biomechanical problems, can we integrate FEM and DNNs to enhance performance? In this study, we propose a synergistic integration of DNNs and FEM to overcome their individual limitations. Using biomechanical analysis of the human aorta as the test bed, we demonstrated two novel integrative strategies in forward and inverse problems. For the forward problem, we developed DNNs with state-of-the-art architectures to predict a nodal displacement field, and this initial DNN solution was then updated by a FEM-based refinement process, yielding a fast and accurate computing framework. For the inverse problem of heterogeneous material parameter identification, our method employs DNN as a regularizer of the spatial distribution of material parameters, aiding the optimizer in locating the optimal solution. In our demonstrative examples, despite that the DNN-only forward models yielded small displacement errors in most test cases; stress errors were considerably large, and for some test cases, the peak stress errors were greater than 50%. Our DNN-FEM integration eliminated these non-negligible errors in DNN-only models and was magnitudes faster than the FEM-only approach. Additionally, compared to FEM-only inverse method with errors greater than 50%, our DNN-FEM inverse approach significantly improved the parameter identification accuracy and reduced the errors to less than 1%.

Engineering analysis of aortic wall stress and root dilatation in the V-shape surgery for treatment of ascending aortic aneurysms.

OBJECTIVES: The study objective was to evaluate the aortic wall stress and root dilatation before and after the novel V-shape surgery for the treatment of ascending aortic aneurysms and root ectasia. METHODS: Clinical cardiac computed tomography images were obtained for 14 patients [median age, 65 years (range, 33-78); 10 (71%) males] who underwent the V-shape surgery. For 10 of the 14 patients, the computed tomography images of the whole aorta pre- and post-surgery were available, and finite element simulations were performed to obtain the stress distributions of the aortic wall at pre- and post-surgery states. For 6 of the 14 patients, the computed tomography images of the aortic root were available at 2 follow-up time points post-surgery (Post 1, within 4 months after surgery and Post 2, about 20-52 months from Post 1). We analysed the root dilatation post-surgery using change of the effective diameter of the root at the two time points and investigated the relationship between root wall stress and root dilatation. RESULTS: The mean and peak max-principal stresses of the aortic root exhibit a significant reduction, P=0.002 between pre- and post-surgery for both root mean stress (median among the 10 patients presurgery, 285.46 kPa; post-surgery, 199.46 kPa) and root peak stress (median presurgery, 466.66 kPa; post-surgery, 342.40 kPa). The mean and peak max-principal stresses of the ascending aorta also decrease significantly from pre- to post-surgery, with P=0.004 for the mean value (median presurgery, 296.48 kPa; post-surgery, 183.87 kPa), and P=0.002 for the peak value (median presurgery, 449.73 kPa; post-surgery, 282.89 kPa), respectively. The aortic root diameter after the surgery has an average dilatation of 5.01% in total and 2.15%/year. Larger root stress results in larger root dilatation. CONCLUSIONS: This study marks the first biomechanical analysis of the novel V-shape surgery. The study has demonstrated significant reduction in wall stress of the aortic root repaired by the surgery. The root was able to dilate mildly post-surgery. Wall stress could be a critical factor for the dilatation since larger root stress results in larger root dilatation. The dilated aortic root within 4 years after surgery is still much smaller than that of presurgery.

A novel computational growth framework for biological tissues: Application to growth of aortic root aneurysm repaired by the V-shape surgery.

Ascending aortic aneurysms (AsAA) often include the dilatation of sinotubular junction (STJ) and extend proximally into the aortic root, which usually leads to aortic insufficiency. The novel surgery of the V-shape resection of the noncoronary sinus, for treatment of AsAA with root ectasia, has been shown to be a simpler procedure compared to traditional surgeries. Our previous study showed that the repaired aortic root aneurysms grew after the surgery. In this study, we developed a novel computational growth framework to model the growth of the aortic root repaired by the V-shape surgery. Specifically, the unified-fiber-distribution (UFD) model was applied to describe the hyperelastic deformation of the aortic tissue. A novel kinematic growth evolution law was proposed based on existing observations that the growth rate is linearly dependent on the wall stress. Moreover, we also obtained patient-specific geometries of the repaired aortic root post-surgery at two follow-up time points (Post-1 and Post-2) for 5 patients, based on clinical CT images. The novel computational growth framework was implemented into the Abaqus UMAT user subroutine and applied to model the growth of the aortic root from Post-1 to Post-2. Patient-specific growth parameters were obtained by an optimization procedure. The predicted geometry and stress of the aortic root at Post-2 agree well with the in vivo results. The novel computational growth framework and the optimized growth parameters could be applied to predict the growth of repaired aortic root aneurysms for new patients and to optimize repair strategies for AsAA.

Computation of a probabilistic and anisotropic failure metric on the aortic wall using a machine learning-based surrogate model.

Scalar-valued failure metrics are commonly used to assess the risk of aortic aneurysm rupture and dissection, which occurs under hypertensive blood pressures brought on by extreme emotional or physical stress. To compute failure metrics under an elevated blood pressure, a classical patient-specific computer model consists of multiple computation steps involving inverse and forward analyses. These classical procedures may be impractical for time-sensitive clinical applications that require prompt feedback to clinicians. In this study, we developed a machine learning-based surrogate model to directly predict a probabilistic and anisotropic failure metric, namely failure probability (FP), on the aortic wall using aorta geometries at the systolic and diastolic phases. Ascending thoracic aortic aneurysm (ATAA) geometries of 60 patients were obtained from their CT scans, and biaxial mechanical testing data of ATAA tissues from 79 patients were collected. Finite element simulations were used to generate datasets for training, validation, and testing of the ML-surrogate model. The testing results demonstrated that the ML-surrogate can compute the maximum FP failure metric, with 0.42% normalized mean absolute error, in 1 s. To compare the performance of the ML-predicted probabilistic FP metric with other isotropic or deterministic metrics, a numerical case study was performed using synthetic "baseline" data. Our results showed that the probabilistic FP metric had more discriminative power than the deterministic Tsai-Hill metric, isotropic maximum principal stress, and aortic diameter criterion.

A Novel Anisotropic Failure Criterion With Dispersed Fiber Orientations for Aortic Tissues.

Accurate failure criteria play a fundamental role in biomechanical analyses of aortic wall rupture and dissection. Experimental investigations have demonstrated a significant difference of aortic wall strengths in the circumferential and axial directions. Therefore, the isotropic von Mises stress and maximum principal stress, commonly used in computational analysis of the aortic wall, are inadequate for modeling of anisotropic failure properties. In this study, we propose a novel stress-based anisotropic failure criterion with dispersed fiber orientations. In the new failure criterion, the overall failure metric is computed by using angular integration (AI) of failure metrics in all directions. Affine rotations of fiber orientations due to finite deformation are taken into account in an anisotropic hyperelastic constitutive model. To examine fitting capability of the failure criterion, a set of off-axis uniaxial tension tests were performed on aortic tissues of four porcine individuals and 18 human ascending thoracic aortic aneurysm (ATAA) patients. The dispersed fiber failure criterion demonstrates a good fitting capability with the off-axis testing data. Under simulated biaxial stress conditions, the dispersed fiber failure criterion predicts a smaller failure envelope comparing to those predicted by the traditional anisotropic criteria without fiber dispersion, which highlights the potentially important role of fiber dispersion in the failure of the aortic wall. Our results suggest that the deformation-dependent fiber orientations need to be considered when wall strength determined from uniaxial tests are used for in vivo biomechanical analysis. More investigations are needed to determine biaxial failure properties of the aortic wall.

A generic physics-informed neural network-based constitutive model for soft biological tissues.

Constitutive modeling is a cornerstone for stress analysis of mechanical behaviors of biological soft tissues. Recently, it has been shown that machine learning (ML) techniques, trained by supervised learning, are powerful in building a direct linkage between input and output, which can be the strain and stress relation in constitutive modeling. In this study, we developed a novel generic physics-informed neural network material (NNMat) model which employs a hierarchical learning strategy by following the steps: (1) establishing constitutive laws to describe general characteristic behaviors of a class of materials; (2) determining constitutive parameters for an individual subject. A novel neural network structure was proposed which has two sets of parameters: (1) a class parameter set for characterizing the general elastic properties; and (2) a subject parameter set (three parameters) for describing individual material response. The trained NNMat model may be directly adopted for a different subject without re-training the class parameters, and only the subject parameters are considered as constitutive parameters. Skip connections are utilized in the neural network to facilitate hierarchical learning. A convexity constraint was imposed to the NNMat model to ensure that the constitutive model is physically relevant. The NNMat model was trained, cross-validated and tested using biaxial testing data of 63 ascending thoracic aortic aneurysm tissue samples, which was compared to expert-constructed models (Holzapfel-Gasser-Ogden, Gasser-Ogden-Holzapfel, and four-fiber families) using the same fitting and testing procedure. Our results demonstrated that the NNMat model has a significantly better performance in both fitting (R2 value of 0.9632 vs 0.9019, p=0.0053) and testing (R2 value of 0.9471 vs 0.8556, p=0.0203) than the Holzapfel-Gasser-Ogden model. The proposed NNMat model provides a convenient and general methodology for constitutive modeling.

Identification of in vivo nonlinear anisotropic mechanical properties of ascending thoracic aortic aneurysm from patient-specific CT scans.

Accurate identification of in vivo nonlinear, anisotropic mechanical properties of the aortic wall of individual patients remains to be one of the critical challenges in the field of cardiovascular biomechanics. Since only the physiologically loaded states of the aorta are given from in vivo clinical images, inverse approaches, which take into account of the unloaded configuration, are needed for in vivo material parameter identification. Existing inverse methods are computationally expensive, which take days to weeks to complete for a single patient, inhibiting fast feedback for clinicians. Moreover, the current inverse methods have only been evaluated using synthetic data. In this study, we improved our recently developed multi-resolution direct search (MRDS) approach and the computation time cost was reduced to 1~2 hours. Using the improved MRDS approach, we estimated in vivo aortic tissue elastic properties of two ascending thoracic aortic aneurysm (ATAA) patients from pre-operative gated CT scans. For comparison, corresponding surgically-resected aortic wall tissue samples were obtained and subjected to planar biaxial tests. Relatively close matches were achieved for the in vivo-identified and ex vivo-fitted stress-stretch responses. It is hoped that further development of this inverse approach can enable an accurate identification of the in vivo material parameters from in vivo image data.

Estimation of in vivo constitutive parameters of the aortic wall using a machine learning approach.

The patient-specific biomechanical analysis of the aorta requires the quantification of the in vivo mechanical properties of individual patients. Current inverse approaches have attempted to estimate the nonlinear, anisotropic material parameters from in vivo image data using certain optimization schemes. However, since such inverse methods are dependent on iterative nonlinear optimization, these methods are highly computation-intensive. A potential paradigm-changing solution to the bottleneck associated with patient-specific computational modeling is to incorporate machine learning (ML) algorithms to expedite the procedure of in vivo material parameter identification. In this paper, we developed an ML-based approach to estimate the material parameters from three-dimensional aorta geometries obtained at two different blood pressure (i.e., systolic and diastolic) levels. The nonlinear relationship between the two loaded shapes and the constitutive parameters are established by an ML-model, which was trained and tested using finite element (FE) simulation datasets. Cross-validations were used to adjust the ML-model structure on a training/validation dataset. The accuracy of the ML-model was examined using a testing dataset.

Finite element simulation of three dimensional residual stress in the aortic wall using an anisotropic tissue growth model.

Residual stress is believed to play a significant role in the in vivo stress state of the arterial wall, but quantifying residual stress in vivo is challenging. Based on the well-known assumptions that residual stress is a result of heterogeneous arterial growth and that it homogenizes the transmural distribution of arterial wall stress, we propose a new anisotropic tissue growth model for the aorta to recover the three-dimensional residual stress field in a bi-layer human aortic wall. Finite element simulations showed that the predicted residual stress magnitude with this method are within the documented range for human aorta. Particularly, the homeostatic inter-layer stress difference is identified as a key parameter to quantify the opening angle. To the authors' knowledge, this is the first finite element study employing anisotropic growth of aortic tissue in a bi-layer model to generate three-dimensional residual stress field, and the resultant opening angle can match with the experiments. A parametric study found that inter-layer stress homogeneity, arterial blood pressure, axial pre-stretch, and material stiffness strongly affect the residual stress field.

On the computation of in vivo transmural mean stress of patient-specific aortic wall.

It is well known that residual deformations/stresses alter the mechanical behavior of arteries, e.g., the pressure-diameter curves. In an effort to enable personalized analysis of the aortic wall stress, approaches have been developed to incorporate experimentally derived residual deformations into in vivo loaded geometries in finite element simulations using thick-walled models. Solid elements are typically used to account for "bending-like" residual deformations. Yet, the difficulty in obtaining patient-specific residual deformations and material properties has become one of the biggest challenges of these thick-walled models. In thin-walled models, fortunately, static determinacy offers an appealing prospect that allows for the calculation of the thin-walled membrane stress without patient-specific material properties. The membrane stress can be computed using forward analysis by enforcing an extremely stiff material property as penalty treatment, which is referred to as the forward penalty approach. However, thin-walled membrane elements, which have zero bending stiffness, are incompatible with the residual deformations, and therefore, it is often stated as a limitation of thin-walled models. In this paper, by comparing the predicted stresses from thin-walled models and thick-walled models, we demonstrate that the transmural mean stress is approximately the same for the two models and can be readily obtained from in vivo clinical images without knowing the patient-specific material properties and residual deformations. Computation of patient-specific mean stress can be greatly simplified by using the forward penalty approach, which may be clinically valuable.

A machine learning approach as a surrogate of finite element analysis-based inverse method to estimate the zero-pressure geometry of human thoracic aorta.

Advances in structural finite element analysis (FEA) and medical imaging have made it possible to investigate the in vivo biomechanics of human organs such as blood vessels, for which organ geometries at the zero-pressure level need to be recovered. Although FEA-based inverse methods are available for zero-pressure geometry estimation, these methods typically require iterative computation, which are time-consuming and may be not suitable for time-sensitive clinical applications. In this study, by using machine learning (ML) techniques, we developed an ML model to estimate the zero-pressure geometry of human thoracic aorta given 2 pressurized geometries of the same patient at 2 different blood pressure levels. For the ML model development, a FEA-based method was used to generate a dataset of aorta geometries of 3125 virtual patients. The ML model, which was trained and tested on the dataset, is capable of recovering zero-pressure geometries consistent with those generated by the FEA-based method. Thus, this study demonstrates the feasibility and great potential of using ML techniques as a fast surrogate of FEA-based inverse methods to recover zero-pressure geometries of human organs.

A deep learning approach to estimate stress distribution: a fast and accurate surrogate of finite-element analysis.

Structural finite-element analysis (FEA) has been widely used to study the biomechanics of human tissues and organs, as well as tissue-medical device interactions, and treatment strategies. However, patient-specific FEA models usually require complex procedures to set up and long computing times to obtain final simulation results, preventing prompt feedback to clinicians in time-sensitive clinical applications. In this study, by using machine learning techniques, we developed a deep learning (DL) model to directly estimate the stress distributions of the aorta. The DL model was designed and trained to take the input of FEA and directly output the aortic wall stress distributions, bypassing the FEA calculation process. The trained DL model is capable of predicting the stress distributions with average errors of 0.492% and 0.891% in the Von Mises stress distribution and peak Von Mises stress, respectively. This study marks, to our knowledge, the first study that demonstrates the feasibility and great potential of using the DL technique as a fast and accurate surrogate of FEA for stress analysis.