A new inverse method for estimation of in vivo mechanical properties of the aortic wall

On the Material Constitutive Behavior of the Aortic Root in Patients with Transcatheter Aortic Valve Implantation

BACKGROUND

Transcatheter aortic valve implantation (TAVI) is a minimally invasive procedure used to treat patients with severe aortic valve stenosis. However, there is limited knowledge on the material properties of the aortic root in TAVI patients, and this can impact the credibility of computer simulations. This study aimed to develop a non-invasive inverse approach for estimating reliable material constituents for the aortic root and calcified valve leaflets in patients undergoing TAVI.

METHODS

The identification of material parameters is based on the simultaneous minimization of two cost functions, which define the difference between model predictions and cardiac-gated CT measurements of the aortic wall and valve orifice area. Validation of the inverse analysis output was performed comparing the numerical predictions with actual CT shapes and post-TAVI measures of implanted device diameter.

RESULTS

A good agreement of the peak systolic shape of the aortic wall was found between simulations and imaging, with similarity index in the range in the range of 83.7% to 91.5% for n.20 patients. Not any statistical difference was observed between predictions and CT measures of orifice area for the stenotic aortic valve. After TAVI simulations, the measurements of SAPIEN 3 Ultra (S3) device diameter were in agreement with those from post-TAVI angio-CT imaging. A sensitivity analysis demonstrated a modest impact on the S3 diameters when altering the elastic material property of the aortic wall in the range of inverse analysis solution.

CONCLUSIONS

Overall, this study demonstrates the feasibility and potential benefits of using non-invasive imaging techniques and computational modeling to estimate material properties in patients undergoing TAVI.

In Vivo Material Properties of Human Common Carotid Arteries: Trends and Sex Differences

INTRODUCTION

In vivo estimation of material properties of arterial tissue can provide essential insights into the development and progression of cardiovascular diseases. Furthermore, these properties can be used as an input to finite element simulations of potential medical treatments.

MATERIALS AND METHODS

This study uses non-invasively measured pressure, diameter and wall thickness of human common carotid arteries (CCAs) acquired in 103 healthy subjects. A non-linear optimization was performed to estimate material parameters of two different constitutive models: a phenomenological, isotropic model and a structural, anisotropic model. The effect of age, sex, body mass index and blood pressure on the parameters was investigated.

RESULTS AND CONCLUSION

Although both material models were able to model in vivo arterial behaviour, the structural model provided more realistic results in the supra-physiological domain. The phenomenological model predicted very high deformations for pressures above the systolic level. However, the phenomenological model has fewer parameters that were shown to be more robust. This is an advantage when only the physiological domain is of interest. The effect of stiffening with age, BMI and blood pressure was present for women, but not always for men. In general, sex had the biggest effect on the mechanical properties of CCAs. Stiffening trends with age, BMI and blood pressure were present but not very strong. The intersubject variability was high. Therefore, it can be concluded that finding a representative set of parameters for a certain age or BMI group would be very challenging. Instead, for purposes of patient-specific modelling of surgical procedures, we currently advise the use of patient-specific parameters.

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.

Biomechanical characterization of normal and pathological human ascending aortic tissues via biaxial testing Experiment, constitutive modeling and finite element analysis

BACKGROUND

Aortic dissection and atherosclerosis are two common pathological conditions affecting the aorta. Aortic biomechanics are believed to be closely associated with the pathological development of these diseases. However, the biomechanical environment that predisposes the aortic wall to these pathological conditions remains unclear.

METHODS

Sixteen ascending aortic specimens were harvested from 16 human subjects and further categorized into three groups according to their disease states: aortic dissection group, aortic dissection with accompanied atherosclerosis group and healthy group. Experimental stress-strain data from biaxial tensile testing were used to fit the anisotropic Mooney-Rivlin model to determine material parameters. Computed tomography images or transesophageal echocardiography images were collected to construct computational models to simulate the stress/strain distributions in aortas at the pre-dissection state. Statistical analyses were performed to identify the biomechanical factors to distinguish three groups of aortic tissues.

RESULTS

Material parameters of anisotropic Mooney-Rivlin model were fitted with average R2 value 0.9749. The aortic diameter showed no significant difference among three groups. Changes of maximum and average stress values from minimum pressure to maximum pressure (△MaxStress and △AveStress) had significantly difference between dissection group and dissection with accompanied atherosclerosis group (p = 0.0201 and 0.0102). Changes of maximum and average strain values from minimum pressure to maximum pressure (△MaxStrain and △AveStrain) from dissection group were significant different from healthy group (p = 0.0171 and 0.0281).

CONCLUSION

Changes of stress and strain values during the cardiac cycle are good biomechanical factors for predicting potential aortic dissection and aortic dissection accompanied with atherosclerosis.

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.

A review on the biomechanical behaviour of the aorta

Large aortic aneurysm and acute and chronic aortic dissection are pathologies of the aorta requiring surgery. Recent advances in medical intervention have improved patient outcomes; however, a clear understanding of the mechanisms leading to aortic failure and, hence, a better understanding of failure risk, is still missing. Biomechanical analysis of the aorta could provide insights into the development and progression of aortic abnormalities, giving clinicians a powerful tool in risk stratification. The complexity of the aortic system presents significant challenges for a biomechanical study and requires various approaches to analyse the aorta. To address this, here we present a holistic review of the biomechanical studies of the aorta by categorising articles into four broad approaches, namely theoretical, in vivo, experimental and combined investigations. Experimental studies that focus on identifying mechanical properties of the aortic tissue are also included. By reviewing the literature and discussing drawbacks, limitations and future challenges in each area, we hope to present a more complete picture of the state-of-the-art of aortic biomechanics to stimulate research on critical topics. Combining experimental modalities and computational approaches could lead to more comprehensive results in risk prediction for the aortic system.

Biomechanical Characterisation of Thoracic Ascending Aorta with Preserved Pre-Stresses

Mechanical properties of an aneurysmatic thoracic aorta are potential markers of future growth and remodelling and can help to estimate the risk of rupture. Aortic geometries obtained from routine medical imaging do not display wall stress distribution and mechanical properties. Mechanical properties for a given vessel may be determined from medical images at different physiological pressures using inverse finite element analysis. However, without considering pre-stresses, the estimation of mechanical properties will lack accuracy. In the present paper, we propose and evaluate a mechanical parameter identification technique, which recovers pre-stresses by determining the zero-pressure configuration of the aortic geometry. We first validated the method on a cylindrical geometry and subsequently applied it to a realistic aortic geometry. The verification of the assessed parameters was performed using synthetically generated reference data for both geometries. The method was able to estimate the true mechanical properties with an accuracy ranging from 98% to 99%.

Inverse material parameter estimation of patient-specific finite element models at the carotid bifurcation: The impact of excluding the zero-pressure configuration and residual stress

The carotid bifurcation experiences a complex loading environment due to its anatomical structure. Previous in-vivo material parameter estimation methods often use simplified model geometries, isotropic hyperelastic constitutive equations or neglect key aspects of the vessel, such as the zero-pressure configuration or residual stress, all of which have independently been shown to alter the stress environment of the vessel wall. Characterizing the location of high stress in the vessel wall has often been proposed as a potential indicator of structural weakness. However, excluding the afore-mentioned zero-pressure configuration, residual stress and patient-specific material parameters can lead to an incorrect estimation of the true stress values observed, meaning that stress alone as a risk indicator of rupture is insufficient. In this study, we investigate how the estimated material parameters and overall stress distributions in geometries of carotid bifurcations, extracted from in-vivo MR images, alter with the inclusion of the zero-pressure configuration and residual stress. This approach consists of the following steps: (1) geometry segmentation and hexahedral meshing from in-vivo magnetic resonance images (MRI) at two known phases; (2) computation of the zero-pressure configuration and the associated residual stresses; (3) minimization of an objective function built on the difference between the stress states of an "almost true" stress field at two known phases and a "deformed" stress field by altering the input material parameters to determine patient-specific material properties; and (4) comparison of the stress distributions throughout these carotid bifurcations for all cases with estimated material parameters. This numerical approach provides insights into the need for estimation of both the zero-pressure configuration and residual stress for accurate material property estimation and stress analysis for the carotid bifurcation, establishing the reliability of stress as a rupture risk metric.

Image-Based Finite Element Modeling Approach for Characterizing In Vivo Mechanical Properties of Human Arteries

Mechanical properties of the arterial walls could provide meaningful information for the diagnosis, management and treatment of cardiovascular diseases. Classically, various experimental approaches were conducted on dissected arterial tissues to obtain their stress-stretch relationship, which has limited value clinically. Therefore, there is a pressing need to obtain biomechanical behaviors of these vascular tissues in vivo for personalized treatment. This paper reviews the methods to quantify arterial mechanical properties in vivo. Among these methods, we emphasize a novel approach using image-based finite element models to iteratively determine the material properties of the arterial tissues. This approach has been successfully applied to arterial walls in various vascular beds. The mechanical properties obtained from the in vivo approach were compared to those from ex vivo experimental studies to investigate whether any discrepancy in material properties exists for both approaches. Arterial tissue stiffness values from in vivo studies generally were in the same magnitude as those from ex vivo studies, but with lower average values. Some methodological issues, including solution uniqueness and robustness; method validation; and model assumptions and limitations were discussed. Clinical applications of this approach were also addressed to highlight their potential in translation from research tools to cardiovascular disease management.

Mechanical and histological characteristics of aortic dissection tissues

AIMS

This study investigated the association between the macroscopic mechanical response of aortic dissection (AoD) flap, its fibre features, and patient physiological features and clinical presentations.

METHODS

Uniaxial test was performed with tissue strips in both circumferential and longitudinal directions from 35 patients with (AoD:CC) and without (AoD:w/oCC) cerebral/coronary complications, and 19 patients with rheumatic or valve-related heart diseases (RH). A Bayesian inference framework was used to estimate the expectation of material constants (C₁, D₁, and D₂) of the modified Mooney-Rivlin strain energy density function. Histological examination was used to visualise the elastin and collagen in the tissue strips and image processing was performed to quantify their area percentages, fibre misalignment and waviness.

RESULTS

The elastin area percentage was negatively associated with age (p = 0.008), while collagen increased about 6% from age 40 to 70 (p = 0.03). Elastin fibre was less dispersed and wavier in old patients and no significant association was found between patient age and collagen fibre dispersion or waviness. Features of fibrous microstructures, either elastin or collagen, were comparable between AoD:CC and AoD:w/oCC group. Elastin and collagen area percentages were positively correlated with C₁ and D₂, respectively, while the elastin and collagen waviness were negatively correlated with C₁ and D₂, respectively. Elastin dispersion was negatively correlated to D₂. Multivariate analysis showed that D₂ was an effective parameter which could differentiate patient groups with different age and clinical presentations, as well as the direction of tissue strip.

CONCLUSION

Fibre dispersion and waviness in the aortic dissection flap changed with patient age and clinical presentations, and these can be captured by the material constants in the strain energy density function.

STATEMENT OF SIGNIFICANCE

Aortic dissection (AoD) is a severe cardiovascular disease. Understanding the mechanical property of intimal flap is essential for its risk evaluation. In this study, mechanical testing and histology examination were combined to quantify the relationship between mechanical presentations and microstructure features. A Bayesian inference framework was employed to estimate the expectation of the material constants in the modified Mooney-Rivlin constitutive equation. It was found that fibre dispersion and waviness in the AoD flap changed with patient age and clinical presentations, and these could be captured by the material constants. This study firstly demonstrated that the expectation of material constants can be used to characterise tissue microstructures and differentiate patients with different clinical presentations.

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.

Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications

Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.

A machine learning model to estimate myocardial stiffness from EDPVR

In-vivo estimation of mechanical properties of the myocardium is essential for patient-specific diagnosis and prognosis of cardiac disease involving myocardial remodeling, including myocardial infarction and heart failure with preserved ejection fraction. Current approaches use time-consuming finite-element (FE) inverse methods that involve reconstructing and meshing the heart geometry, imposing measured loading, and conducting computationally expensive iterative FE simulations. In this paper, we propose a machine learning (ML) model that feasibly and accurately predicts passive myocardial properties directly from select geometric, architectural, and hemodynamic measures, thus bypassing exhaustive steps commonly required in cardiac FE inverse problems. Geometric and fiber-orientation features were chosen to be readily obtainable from standard cardiac imaging protocols. The end-diastolic pressure-volume relationship (EDPVR), which can be obtained using a single-point pressure-volume measurement, was used as a hemodynamic (loading) feature. A comprehensive ML training dataset in the geometry-architecture-loading space was generated, including a wide variety of partially synthesized rodent heart geometry and myofiber helicity possibilities, and a broad range of EDPVRs obtained using forward FE simulations. Latin hypercube sampling was used to create 2500 examples for training, validation, and testing. A multi-layer feed-forward neural network (MFNN) was used as a deep learning agent to train the ML model. The model showed excellent performance in predicting stiffness parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_f$$\end{document}af and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_f$$\end{document}bf associated with fiber direction (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2_{a_f}=99.471\%$$\end{document}Raf2=99.471% and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2_{b_f}=92.837\%$$\end{document}Rbf2=92.837%). After conducting permutation feature importance analysis, the ML performance further improved for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_f$$\end{document}bf (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2_{b_f}=96.240\%$$\end{document}Rbf2=96.240%), and the left ventricular volume and endocardial area were found to be the most critical geometric features for accurate predictions. The ML model predictions were evaluated further in two cases: (i) rat-specific stiffness data measured using ex-vivo mechanical testing, and (ii) patient-specific estimation using FE inverse modeling. Excellent agreements with ML predictions were found for both cases. The trained ML model offers a feasible technology to estimate patient-specific myocardial properties, thus, bridging the gap between EDPVR, as a confounded organ-level metric for tissue stiffness, and intrinsic tissue-level properties. These properties provide incremental information relative to traditional organ-level indices for cardiac function, improving the clinical assessment and prognosis of cardiac diseases.

Uncertainty quantification in subject-specific estimation of local vessel mechanical properties

Quantitative estimation of local mechanical properties remains critically important in the ongoing effort to elucidate how blood vessels establish, maintain, or lose mechanical homeostasis. Recent advances based on panoramic digital image correlation (pDIC) have made high-fidelity 3D reconstructions of small-animal (e.g., murine) vessels possible when imaged in a variety of quasi-statically loaded configurations. While we have previously developed and validated inverse modeling approaches to translate pDIC-measured surface deformations into biomechanical metrics of interest, our workflow did not heretofore include a methodology to quantify uncertainties associated with local point estimates of mechanical properties. This limitation has compromised our ability to infer biomechanical properties on a subject-specific basis, such as whether stiffness differs significantly between multiple material locations on the same vessel or whether stiffness differs significantly between multiple vessels at a corresponding material location. In the present study, we have integrated a novel uncertainty quantification and propagation pipeline within our inverse modeling approach, relying on empirical and analytic Bayesian techniques. To demonstrate the approach, we present illustrative results for the ascending thoracic aorta from three mouse models, quantifying uncertainties in constitutive model parameters as well as circumferential and axial tangent stiffness. Our extended workflow not only allows parameter uncertainties to be systematically reported, but also facilitates both subject-specific and group-level statistical analyses of the mechanics of the vessel wall.

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.

Surrogate models based on machine learning methods for parameter estimation of left ventricular myocardium

A long-standing problem at the frontier of biomechanical studies is to develop fast methods capable of estimating material properties from clinical data. In this paper, we have studied three surrogate models based on machine learning (ML) methods for fast parameter estimation of left ventricular (LV) myocardium. We use three ML methods named K-nearest neighbour (KNN), XGBoost and multi-layer perceptron (MLP) to emulate the relationships between pressure and volume strains during the diastolic filling. Firstly, to train the surrogate models, a forward finite-element simulator of LV diastolic filling is used. Then the training data are projected in a low-dimensional parametrized space. Next, three ML models are trained to learn the relationships of pressure-volume and pressure-strain. Finally, an inverse parameter estimation problem is formulated by using those trained surrogate models. Our results show that the three ML models can learn the relationships of pressure-volume and pressure-strain very well, and the parameter inference using the surrogate models can be carried out in minutes. Estimated parameters from both the XGBoost and MLP models have much less uncertainties compared with the KNN model. Our results further suggest that the XGBoost model is better for predicting the LV diastolic dynamics and estimating passive parameters than other two surrogate models. Further studies are warranted to investigate how XGBoost can be used for emulating cardiac pump function in a multi-physics and multi-scale framework.

Assessing Patient-Specific Mechanical Properties of Aortic Wall and Peri-Aortic Structures From In Vivo DENSE Magnetic Resonance Imaging Using an Inverse Finite Element Method and Elastic Foundation Boundary Conditions

The establishment of in vivo, noninvasive patient-specific, and regionally resolved techniques to quantify aortic properties is key to improving clinical risk assessment and scientific understanding of vascular growth and remodeling. A promising and novel technique to reach this goal is an inverse finite element method (FEM) approach that utilizes magnetic resonance imaging (MRI)-derived displacement fields from displacement encoding with stimulated echoes (DENSE). Previous studies using DENSE MRI suggested that the infrarenal abdominal aorta (IAA) deforms heterogeneously during the cardiac cycle. We hypothesize that this heterogeneity is driven in healthy aortas by regional adventitial tethering and interaction with perivascular tissues, which can be modeled with elastic foundation boundary conditions (EFBCs) using a collection of radially oriented springs with varying stiffness with circumferential distribution. Nine healthy IAAs were modeled using previously acquired patient-specific imaging and displacement fields from steady-state free procession (SSFP) and DENSE MRI, followed by assessment of aortic wall properties and heterogeneous EFBC parameters using inverse FEM. In contrast to traction-free boundary condition, prescription of EFBC reduced the nodal displacement error by 60% and reproduced the DENSE-derived heterogeneous strain distribution. Estimated aortic wall properties were in reasonable agreement with previously reported experimental biaxial testing data. The distribution of normalized EFBC stiffness was consistent among all patients and spatially correlated to standard peri-aortic anatomical features, suggesting that EFBC could be generalized for human adults with normal anatomy. This approach is computationally inexpensive, making it ideal for clinical research and future incorporation into cardiovascular fluid-structure analyses.

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.

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 COUPLED EXPERIMENTAL AND NUMERICAL APPROACH TO CHARACTERIZE THE ANISOTROPIC MECHANICAL BEHAVIOR OF AORTIC TISSUES

Nowadays, the investigation of aortic wall biomechanics is a fundamental tool in clinical research and vascular prosthesis design. This study aims at analyzing the biomechanical behavior of aortic tissues using a coupled experimental and computational approach. Considering the typical fiber-reinforced configuration of aortic tissues, uni-axial tensile tests along six different loading directions were performed on specimens from pig aorta. Starting from the obtained experimental data, a suitable constitutive framework was defined and a methodology for the identification of the constitutive parameters was developed using the inverse analysis of mechanical tests. Transversal stretch versus loading stretch and nominal stress versus loading stretch curves were evaluated, showing the anisotropic and nonlinear mechanical behavior determined by tissue conformation with fibers distributed along preferential directions. In detail, experimental data showed different mechanical responses between longitudinal and circumferential directions, with a greater tissue stiffness along the longitudinal one. The reliability of the developed constitutive framework was evaluated by the comparison between experimental data and model results. The mentioned analysis can be considered as a useful tool for the development of reliable computational models, which allow a better understanding of the pathophysiology of cardiovascular diseases and can be applied for a proper planning of surgical procedures.

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.

A Comprehensive Engineering Analysis of Left Heart Dynamics After MitraClip in a Functional Mitral Regurgitation Patient

Percutaneous edge-to-edge mitral valve (MV) repair using MitraClip has been recently established as a treatment option for patients with heart failure and functional mitral regurgitation (MR), which significantly expands the number of patients that can be treated with this device. This study aimed to quantify the morphologic, hemodynamic and structural changes, and evaluate the biomechanical interaction between the MitraClip and the left heart (LH) complex of a heart failure patient with functional MR using a fluid-structure interaction (FSI) modeling framework. MitraClip implantation using lateral, central and double clip positions, as well as combined annuloplasty procedures were simulated in a patient-specific LH model that integrates detailed anatomic structures, incorporates age- and gender-matched non-linear elastic material properties, and accounts for mitral chordae tethering. Our results showed that antero-posterior distance, mitral annulus spherecity index, anatomic regurgitant orifice area, and anatomic opening orifice area decreased by up to 28, 39, 52, and 71%, respectively, when compared to the pre-clip model. MitraClip implantation immediately decreased the MR severity and improved the hemodynamic profile, but imposed a non-physiologic configuration and loading on the mitral apparatus, with anterior and posterior leaflet stress significantly increasing up to 210 and 145% during diastole, respectively. For this patient case, while implanting a combined central clip and ring resulted in the highest reduction in the regurgitant volume (46%), this configuration also led to mitral stenosis. Patient-specific computer simulations as used here can be a powerful tool to examine the complex device-host biomechanical interaction, and may be useful to guide device positioning for potential favorable clinical outcomes.

The Impact of Self-Expandable Transcatheter Aortic Valve Replacement on Concomitant Functional Mitral Regurgitation: A Comprehensive Engineering Analysis

Background

Mitral regurgitation (MR) is present in a large proportion of patients who undergo transcatheter aortic valve replacement (TAVR). However, existing clinical data on the impact of TAVR on early post-procedural MR severity are contradictory. Using a comprehensive computational engineering methodology, this study aimed to evaluate quantitatively the structural and hemodynamic impact of TAVR on aortic-mitral continuity and MR severity in a rigorously developed and validated patient-specific left heart (LH) computer model with aortic stenosis and concomitant functional MR.

Methods

TAVR procedure was virtually simulated using a self-expandable valve (SEV) at three implantation heights. Pre- and post-TAVR LH dynamics as well as intra-operative biomechanics were analyzed.

Results

No significant differences in early MR improvement (<10%) were noted at the three implantation depths when compared to the pre-TAVR state. The high deployment model resulted in the highest stress in the native aortic leaflets, lowest stent-tissue contact force, highest aortic-mitral angle, and highest MR reduction for this patient case. When comparing SEV vs. balloon-expandable valve (BEV) performance at an optimal implantation height, the SEV gave a higher regurgitant volume ⋅ than the pre-TAVR model (40.49 vs 37.59 ml), while the BEV model gave the lowest regurgitant volume (33.84 vs 37.59 ml).

Conclusions

Contact force, aortic-mitral angle, and valve annuli compression were identified as possible mechanistic parameters that may suggest avenues for acute MR improvement. Albeit a single patient parametric study, it is our hope that such detailed engineering analysis could shed some light into the underlying biomechanical mechanisms of TAVR impact on MR.

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.

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.

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.

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.

Material characterization of cardiovascular biomaterials using an inverse finite-element method and an explicit solver

The ability to accurately model soft tissue behavior, such as that of heart valve tissue, is essential for developing reliable numerical simulations and determining patient-specific care options. Although several material models can predict soft tissue behavior, complications may arise when these models are implemented into finite element (FE) programs, due to the addition of an arbitrary penalty parameter for numerically enforcing material incompressibility. Herein, an inverse methodology was developed in MATLAB to use previously published stress-strain data from experimental planar equibiaxial testing of five biomaterials used in heart valve cusp replacements, in conjunction with commercial explicit FE solver LS-DYNA, to optimize the material parameters and the penalty parameter for an anisotropic hyperelastic strain energy function. A two-parameter optimization involving the scaling constant of the strain energy function and the penalty parameter proved sufficient to produce acceptable material responses when compared with experimental behaviors under the same testing conditions, as long as analytically derived material constants were available for the other non-optimized parameters and the actual tissue thickness was not much less than 1 mm. Variations in the penalty parameter had a direct effect on the accuracy of the simulated responses, with a practical range determined to be 5×10⁸-9×10⁸ times the scaling constant of the strain energy function.

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.

Estimation of in vivo mechanical properties of the aortic wall: A multi-resolution direct search approach

The patient-specific biomechanical analysis of the aorta requires in vivo mechanical properties of individual patients. Existing approaches for estimating in vivo material properties often demand high computational cost and mesh correspondence of the aortic wall between different cardiac phases. In this paper, we propose a novel multi-resolution direct search (MRDS) approach for estimation of the nonlinear, anisotropic constitutive parameters of the aortic wall. Based on the finite element (FE) updating scheme, the MRDS approach consists of the following three steps: (1) representing constitutive parameters with multiple resolutions using principal component analysis (PCA), (2) building links between the discretized PCA spaces at different resolutions, and (3) searching the PCA spaces in a 'coarse to fine' fashion following the links. The estimation of material parameters is achieved by minimizing a node-to-surface error function, which does not need mesh correspondence. The method was validated through a numerical experiment by using the in vivo data from a patient with ascending thoracic aortic aneurysm (ATAA), the results show that the number of FE iterations was significantly reduced compared to previous methods. The approach was also applied to the in vivo CT data from an aged healthy human patient, and using the estimated material parameters, the FE-computed geometry was well matched with the image-derived geometry. This novel MRDS approach may facilitate the personalized biomechanical analysis of aortic tissues, such as the rupture risk analysis of ATAA, which requires fast feedback to clinicians.

A deep learning approach to estimate chemically-treated collagenous tissue nonlinear anisotropic stress-strain responses from microscopy images

Biological collagenous tissues comprised of networks of collagen fibers are suitable for a broad spectrum of medical applications owing to their attractive mechanical properties. In this study, we developed a noninvasive approach to estimate collagenous tissue elastic properties directly from microscopy images using Machine Learning (ML) techniques. Glutaraldehyde-treated bovine pericardium (GLBP) tissue, widely used in the fabrication of bioprosthetic heart valves and vascular patches, was chosen to develop a representative application. A Deep Learning model was designed and trained to process second harmonic generation (SHG) images of collagen networks in GLBP tissue samples, and directly predict the tissue elastic mechanical properties. The trained model is capable of identifying the overall tissue stiffness with a classification accuracy of 84%, and predicting the nonlinear anisotropic stress-strain curves with average regression errors of 0.021 and 0.031. Thus, this study demonstrates the feasibility and great potential of using the Deep Learning approach for fast and noninvasive assessment of collagenous tissue elastic properties from microstructural images.

STATEMENT OF SIGNIFICANCE

In this study, we developed, to our best knowledge, the first Deep Learning-based approach to estimate the elastic properties of collagenous tissues directly from noninvasive second harmonic generation images. The success of this study holds promise for the use of Machine Learning techniques to noninvasively and efficiently estimate the mechanical properties of many structure-based biological materials, and it also enables many potential applications such as serving as a quality control tool to select tissue for the manufacturing of medical devices (e.g. bioprosthetic heart valves).