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

Computational models of bone fracture healing and applications: a review

Fracture healing is a very complex physiological process involving multiple events at different temporal and spatial scales, such as cell migration and tissue differentiation, in which mechanical stimuli and biochemical factors assume key roles. With the continuous improvement of computer technology in recent years, computer models have provided excellent solutions for studying the complex process of bone healing. These models not only provide profound insights into the mechanisms of fracture healing, but also have important implications for clinical treatment strategies. In this review, we first provide an overview of research in the field of computational models of fracture healing based on CiteSpace software, followed by a summary of recent advances, and a discussion of the limitations of these models and future directions for improvement. Finally, we provide a systematic summary of the application of computational models of fracture healing in three areas: bone tissue engineering, fixator optimization and clinical treatment strategies. The application of computational models of bone healing in clinical treatment is immature, but an inevitable trend, and as these models become more refined, their role in guiding clinical treatment will become more prominent.

Material characterization of human middle ear using machine-learning-based surrogate models

This study aims to introduce a novel non-invasive method for rapid material characterization of middle-ear structures, taking into consideration the invaluable insights provided by the mechanical properties of ear tissues. Valuable insights into various ear pathologies can be gleaned from the mechanical properties of ear tissues, yet conventional techniques for assessing these properties often entail invasive procedures that preclude their use on living patients. In this study, in the first step, we developed machine-learning models of the middle ear to predict its responses with a significantly lower computational cost in comparison to finite-element models. Leveraging findings from prior research, we focused on the most influential model parameters: the Young's modulus and thickness of the tympanic membrane and the Young's modulus of the stapedial annular ligament. The eXtreme Gradient Boosting (XGBoost) method was implemented for creating the machine-learning models. Subsequently, we combined the created machine-learning models with Bayesian optimization (BoTorch) for fast and efficient estimation of the Young's moduli of the tympanic membrane and the stapedial annular ligament. We demonstrate that the resultant surrogate models can fairly represent the vibrational responses of the umbo, stapes footplate, and vibration patterns of the tympanic membrane at most frequencies. Also, our proposed material characterization approach successfully estimated the Young's moduli of the tympanic membrane and stapedial annular ligament (separately and simultaneously) with values of mean absolute percentage error of less than 7%. The remarkable accuracy achieved through the proposed material characterization method underscores its potential for eventual clinical applications of estimating mechanical properties of the middle-ear structures for diagnostic purposes.

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.

Mechanics of ascending aortic aneurysms based on a modulus of elasticity dependent on aneurysm diameter and pressure

The mechanical stresses and strains are examined, in ascending thoracic aortic aneurysm (aTAA) models, in a patient-specific aTAA as well as in healthy thoracic aortic models, via Finite Element Analysis. The aneurysms are assumed spherical, 1.5 mm thick, with diameters between 47 mm and 80 mm, eccentrically positioned. The geometry and wall thickness distribution of the aorta along its length are based on open literature data for an average patient age of 66.25 years, accounting for the Body Surface Area (BSA) parameter. The vessel wall material is assumed isotropic and incompressible, with its Young's modulus varying with the aneurysm diameter and the applied intraluminal pressure (120 mmHg to 240 mmHg). In the aTAAs, peak stresses were found to increase nonlinearly with aneurysm diameter (for a given pressure) tending to reach a plateau, appearing at the proximal area of the aneurysm, whereas lower stresses were found at its distal part and even smaller at the aneurysm maximum diameter. Regarding the patient-specific aTAA model, the peak stresses appeared at the distal part of the aneurysm where a tear of the intima layer was detected during surgical intervention. Peak strains exhibited for each pressure a maximum at a certain aneurysm diameter beyond which they dropped so that essentially the vessel wall's distensibility was thus reduced. Examining more than 100 geometry cases and employing a failure stress criterion, the rupture diameter thresholds were estimated to be 65, 52.5, 50 and 47.5 mm for a pressure of 120, 160, 200 and 240 mmHg respectively.

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%.

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.

Development of numerical model-based machine learning algorithms for different healing stages of distal radius fracture healing

BACKGROUND AND OBJECTIVES

Early therapeutic exercises are vital for the healing of distal radius fractures (DRFs) treated with the volar locking plate. However, current development of rehabilitation plans using computational simulation is normally time-consuming and requires high computational power. Thus, there is a clear need for developing machine learning (ML) based algorithms that are easy for end-users to implement in daily clinical practice. The purpose of the present study is to develop optimal ML algorithms for designing effective DRF physiotherapy programs at different stages of healing.

METHOD

First, a three-dimensional computational model for the healing of DRF was developed by integrating mechano-regulated cell differentiation, tissue formation and angiogenesis. The model is capable of predicting time-dependant healing outcomes based on different physiologically relevant loading conditions, fracture geometries, gap sizes, and healing time. After being validated using available clinical data, the developed computational model was implemented to generate a total of 3600 clinical data for training the ML models. Finally, the optimal ML algorithm for each healing stage was identified.

RESULTS

The selection of the optimal ML algorithm depends on the healing stage. The results from this study show that cubic support vector machine (SVM) has the best performance in predicting the healing outcomes at the early stage of healing, while trilayered ANN outperforms other ML algorithms in the late stage of healing. The outcomes from the developed optimal ML algorithms indicate that Smith fractures with medium gap sizes could enhance the healing of DRF by inducing larger cartilaginous callus, while Colles fractures with large gap sizes may lead to delayed healing by bringing excessive fibrous tissues.

CONCLUSIONS

ML represents a promising approach for developing efficient and effective patient-specific rehabilitation strategies. However, ML algorithms at different healing stages need to be carefully chosen before being implemented in clinical 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.

Neural operator learning of heterogeneous mechanobiological insults contributing to aortic aneurysms

Thoracic aortic aneurysm (TAA) is a localized dilatation of the aorta that can lead to life-threatening dissection or rupture. In vivo assessments of TAA progression are largely limited to measurements of aneurysm size and growth rate. There is promise, however, that computational modelling of the evolving biomechanics of the aorta could predict future geometry and properties from initiating mechanobiological insults. We present an integrated framework to train a deep operator network (DeepONet)-based surrogate model to identify TAA contributing factors using synthetic finite-element-based datasets. For training, we employ a constrained mixture model of aortic growth and remodelling to generate maps of local aortic dilatation and distensibility for multiple TAA risk factors. We evaluate the performance of the surrogate model for insult distributions varying from fusiform (analytically defined) to complex (randomly generated). We propose two frameworks, one trained on sparse information and one on full-field greyscale images, to gain insight into a preferred neural operator-based approach. We show that this continuous learning approach can predict the patient-specific insult profile associated with any given dilatation and distensibility map with high accuracy, particularly when based on full-field images. Our findings demonstrate the feasibility of applying DeepONet to support transfer learning of patient-specific inputs to predict TAA progression.

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

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