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

Review of Machine Learning Techniques in Soft Tissue Biomechanics and Biomaterials

BACKGROUND AND OBJECTIVE

Advanced material models and material characterization of soft biological tissues play an essential role in pre-surgical planning for vascular surgeries and transcatheter interventions. Recent advances in heart valve engineering, medical device and patch design are built upon these models. Furthermore, understanding vascular growth and remodeling in native and tissue-engineered vascular biomaterials, as well as designing and testing drugs on soft tissue, are crucial aspects of predictive regenerative medicine. Traditional nonlinear optimization methods and finite element (FE) simulations have served as biomaterial characterization tools combined with soft tissue mechanics and tensile testing for decades. However, results obtained through nonlinear optimization methods are reliable only to a certain extent due to mathematical limitations, and FE simulations may require substantial computing time and resources, which might not be justified for patient-specific simulations. To a significant extent, machine learning (ML) techniques have gained increasing prominence in the field of soft tissue mechanics in recent years, offering notable advantages over conventional methods. This review article presents an in-depth examination of emerging ML algorithms utilized for estimating the mechanical characteristics of soft biological tissues and biomaterials. These algorithms are employed to analyze crucial properties such as stress-strain curves and pressure-volume loops. The focus of the review is on applications in cardiovascular engineering, and the fundamental mathematical basis of each approach is also discussed.

METHODS

The review effort employed two strategies. First, the recent studies of major research groups actively engaged in cardiovascular soft tissue mechanics are compiled, and research papers utilizing ML and deep learning (DL) techniques were included in our review. The second strategy involved a standard keyword search across major databases. This approach provided 11 relevant ML articles, meticulously selected from reputable sources including ScienceDirect, Springer, PubMed, and Google Scholar. The selection process involved using specific keywords such as "machine learning" or "deep learning" in conjunction with "soft biological tissues", "cardiovascular", "patient-specific," "strain energy", "vascular" or "biomaterials". Initially, a total of 25 articles were selected. However, 14 of these articles were excluded as they did not align with the criteria of focusing on biomaterials specifically employed for soft tissue repair and regeneration. As a result, the remaining 11 articles were categorized based on the ML techniques employed and the training data utilized.

RESULTS

ML techniques utilized for assessing the mechanical characteristics of soft biological tissues and biomaterials are broadly classified into two categories: standard ML algorithms and physics-informed ML algorithms. The standard ML models are then organized based on their tasks, being grouped into Regression and Classification subcategories. Within these categories, studies employ various supervised learning models, including support vector machines (SVMs), bagged decision trees (BDTs), artificial neural networks (ANNs) or deep neural networks (DNNs), and convolutional neural networks (CNNs). Additionally, the utilization of unsupervised learning approaches, such as autoencoders incorporating principal component analysis (PCA) and/or low-rank approximation (LRA), is based on the specific characteristics of the training data. The training data predominantly consists of three types: experimental mechanical data, including uniaxial or biaxial stress-strain data; synthetic mechanical data generated through non-linear fitting and/or FE simulations; and image data such as 3D second harmonic generation (SHG) images or computed tomography (CT) images. The evaluation of performance for physics-informed ML models primarily relies on the coefficient of determinationR 2 . In contrast, various metrics and error measures are utilized to assess the performance of standard ML models. Furthermore, our review includes an extensive examination of prevalent biomaterial models that can serve as physical laws for physics-informed ML models.

CONCLUSION

ML models offer an accurate, fast, and reliable approach for evaluating the mechanical characteristics of diseased soft tissue segments and selecting optimal biomaterials for time-critical soft tissue surgeries. Among the various ML models examined in this review, physics-informed neural network models exhibit the capability to forecast the mechanical response of soft biological tissues accurately, even with limited training samples. These models achieve highR 2 values ranging from 0.90 to 1.00. This is particularly significant considering the challenges associated with obtaining a large number of living tissue samples for experimental purposes, which can be time-consuming and impractical. Additionally, the review not only discusses the advantages identified in the current literature but also sheds light on the limitations and offers insights into future perspectives.

Implementing Machine Learning approaches for accelerated prediction of bone strain in acetabulum of a hip joint

The Finite Element (FE) methods for biomechanical analysis involving implant design and subject parameters for musculoskeletal applications are extensively reported in literature. Such an approach is manually intensive and computationally expensive with longer simulations times. Although Artificial Intelligence (AI) based approaches are implemented to a limited extent in biomechanics, such approaches to predict bone strain in acetabulum of a hip joint, are hardly explored. In this context, the primary objective of this paper is to evaluate machine learning (ML) models in tandem with high-fidelity FEA data for the accelerated prediction of the biomechanical response in the acetabulum of the human hip joint, during the walking gait. The parameters used in the FEA study included the subject weight, number and distribution of fins on the periphery of the acetabular shell, bone condition and phases of the gait cycle. The biomechanical response has also been evaluated using three different acetabular liners, including pre-clinically validated HDPE-20% HA-20% Al2O3, highly-crosslinked ultrahigh molecular weight polyethylene (HC-UHMWPE) and ZrO2-toughened Al2O3 (ZTA). Such parametric variation in FEA analysis, involving 26 variables and a full factorial design resulted in 10,752 datasets for spatially varying bone strains. The bone condition, as opposed to subject weight, was found to play a statistically significant role in determining the strain response in the periprosthetic bone of the acetabulum. While utilising hyperparameter tuning, K-fold cross validation and statistical learning approaches, a number of ML models were trained on the FEA dataset, and the Random Forest model performed the best with a coefficient of determination (R2) value of 0.99/0.97 and Root Mean Square Error (RMSE) of 0.02/0.01 on the training/test dataset. Taken together, this study establishes the potential of ML approach as a fast surrogate of FEA for implant biomechanics analysis, in less than a minute.

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.

Predicting shock-induced cavitation using machine learning: implications for blast-injury models

While cavitation has been suspected as a mechanism of blast-induced traumatic brain injury (bTBI) for a number of years, this phenomenon remains difficult to study due to the current inability to measure cavitation in vivo. Therefore, numerical simulations are often implemented to study cavitation in the brain and surrounding fluids after blast exposure. However, these simulations need to be validated with the results from cavitation experiments. Machine learning algorithms have not generally been applied to study blast injury or biological cavitation models. However, such algorithms have concrete measures for optimization using fewer parameters than those of finite element or fluid dynamics models. Thus, machine learning algorithms are a viable option for predicting cavitation behavior from experiments and numerical simulations. This paper compares the ability of two machine learning algorithms, k-nearest neighbor (kNN) and support vector machine (SVM), to predict shock-induced cavitation behavior. The machine learning models were trained and validated with experimental data from a three-dimensional shock tube model, and it has been shown that the algorithms could predict the number of cavitation bubbles produced at a given temperature with good accuracy. This study demonstrates the potential utility of machine learning in studying shock-induced cavitation for applications in blast injury research.

Artificial Intelligence in Transcatheter Aortic Valve Replacement: Its Current Role and Ongoing Challenges

Transcatheter aortic valve replacement (TAVR) has emerged as a viable alternative to surgical aortic valve replacement, as accumulating clinical evidence has demonstrated its safety and efficacy. TAVR indications have expanded beyond high-risk or inoperable patients to include intermediate and low-risk patients with severe aortic stenosis. Artificial intelligence (AI) is revolutionizing the field of cardiology, aiding in the interpretation of medical imaging and developing risk models for at-risk individuals and those with cardiac disease. This article explores the growing role of AI in TAVR procedures and assesses its potential impact, with particular focus on its ability to improve patient selection, procedural planning, post-implantation monitoring and contribute to optimized patient outcomes. In addition, current challenges and future directions in AI implementation are highlighted.

Machine learning modeling of lung mechanics: Assessing the variability and propagation of uncertainty in respiratory-system compliance and airway resistance

BACKGROUND AND OBJECTIVE

Traditional assessment of patient response in mechanical ventilation relies on respiratory-system compliance and airway resistance. Clinical evidence has shown high variability in these parameters, highlighting the difficulty of predicting them before the start of ventilation therapy. This motivates the creation of computational models that can connect structural and tissue features with lung mechanics. In this work, we leverage machine learning (ML) techniques to construct predictive lung function models informed by non-linear finite element simulations, and use them to investigate the propagation of uncertainty in the lung mechanical response.

METHODS

We revisit a continuum poromechanical formulation of the lungs suitable for determining patient response. Based on this framework, we create high-fidelity finite element models of human lungs from medical images. We also develop a low-fidelity model based on an idealized sphere geometry. We then use these models to train and validate three ML architectures: single-fidelity and multi-fidelity Gaussian process regression, and artificial neural networks. We use the best predictive ML model to further study the sensitivity of lung response to variations in tissue structural parameters and boundary conditions via sensitivity analysis and forward uncertainty quantification. Codes are available for download at https://github.com/comp-medicine-uc/ML-lung-mechanics-UQ RESULTS: The low-fidelity model delivers a lung response very close to that predicted by high-fidelity simulations and at a fraction of the computational time. Regarding the trained ML models, the multi-fidelity GP model consistently delivers better accuracy than the single-fidelity GP and neural network models in estimating respiratory-system compliance and resistance (R2∼0.99). In terms of computational efficiency, our ML model delivers a massive speed-up of ∼970,000× with respect to high-fidelity simulations. Regarding lung function, we observed an almost matched and non-linear behavior between specific structural parameters and chest wall stiffness with compliance. Also, we observed a strong modulation of airways resistance with tissue permeability.

CONCLUSIONS

Our findings unveil the relevance of specific lung tissue parameters and boundary conditions in the respiratory-system response. Furthermore, we highlight the advantages of adopting a multi-fidelity ML approach that combines data from different levels to yield accurate and efficient estimates of clinical mechanical markers. We envision that the methods presented here can open the way to the development of predictive ML models of the lung response that can inform clinical decisions.

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%.

Stress Distribution Prediction of Circular Hollow Section Tube in Flexible High-Neck Flange Joints Based on the Hybrid Machine Learning Model

The flexible high-neck flange is connected to the circular hollow section (CHS) tube through welding, and the placement of the weld seam and corresponding stress concentration factor (SCF) are crucial determinants of the joint's fatigue performance. In this study, three hybrid models combining ant colony optimization (ACO), a genetic algorithm (GA), and grey wolf optimization (GWO) with a random forest (RF) model were developed to predict the stress distribution on the inner and outer walls of the CHS tube under different flange parameter combinations. To achieve this, an automated finite element (FE) analysis program for flexible high-neck flange joints was initially developed based on ABAQUS 2020 software. Parameter combinations were randomly selected within a reasonable range to simulate the nonlinear mechanical behavior of the joint under uniform tension, generating a dataset comprising 5417 sets of data. The accuracy of the FE model was validated through experimental data from the literature. Based on this, feature importance analysis was conducted to reveal the influence of different variable parameters on the stress distribution in the tube of the joint. The flange parameters and tube stress distribution are considered as inputs and outputs, respectively. Three hybrid RF models, specifically ant colony optimization-based random forest (ACO-RF), genetic algorithm-based random forest (GA-RF), and grey wolf optimization-based random forest (GWO-RF), are trained for regression prediction. The results demonstrate that the three hybrid models outperform the original machine learning model in predictive accuracy. The ACO-RF model achieved the highest accuracy with average coefficients of determination (Rmean2) of 0.9983 and 0.9865 on the testing and training sets, respectively. Building upon this foundation, the study developed a corresponding open-source graphical user interface (GUI) as a tool for facilitating computations and visualizing results. Finally, a case study on fatigue damage assessment of a flexible high-neck flange joint in a wind-turbine tower is presented to demonstrate the application of the proposed model in this study.

Physics-informed neural networks (PINNs) for 4D hemodynamics prediction: An investigation of optimal framework based on vascular morphology

Hemodynamic parameters are of great significance in the clinical diagnosis and treatment of cardiovascular diseases. However, noninvasive, real-time and accurate acquisition of hemodynamics remains a challenge for current invasive detection and simulation algorithms. Here, we integrate computational fluid dynamics with our customized analysis framework based on a multi-attribute point cloud dataset and physics-informed neural networks (PINNs)-aided deep learning modules. This combination is implemented by our workflow that generates flow field datasets within two types of patient personalized models - aorta with fine coronary branches and abdominal aorta. Deep learning modules with or without an antecedent hierarchical structure model the flow field development and complete the mapping from spatial and temporal dimensions to 4D hemodynamics. 88,000 cases on 4 randomized partitions in 16 controlled trials reveal the hemodynamic landscape of spatio-temporal anisotropy within two types of personalized models, which demonstrates the effectiveness of PINN in predicting the space-time behavior of flow fields and gives the optimal deep learning framework for different blood vessels in terms of balancing the training cost and accuracy dimensions. The proposed framework shows intentional performance in computational cost, accuracy and visualization compared to currently prevalent methods, and has the potential for generalization to model flow fields and corresponding clinical metrics within vessels at different locations. We expect our framework to push the 4D hemodynamic predictions to the real-time level, and in statistically significant fashion, applicable to morphologically variable vessels.

Latest Developments in Adapting Deep Learning for Assessing TAVR Procedures and Outcomes

Aortic valve defects are among the most prevalent clinical conditions. A severely damaged or non-functioning aortic valve is commonly replaced with a bioprosthetic heart valve (BHV) via the transcatheter aortic valve replacement (TAVR) procedure. Accurate pre-operative planning is crucial for a successful TAVR outcome. Assessment of computational fluid dynamics (CFD), finite element analysis (FEA), and fluid-solid interaction (FSI) analysis offer a solution that has been increasingly utilized to evaluate BHV mechanics and dynamics. However, the high computational costs and the complex operation of computational modeling hinder its application. Recent advancements in the deep learning (DL) domain can offer a real-time surrogate that can render hemodynamic parameters in a few seconds, thus guiding clinicians to select the optimal treatment option. Herein, we provide a comprehensive review of classical computational modeling approaches, medical imaging, and DL approaches for planning and outcome assessment of TAVR. Particularly, we focus on DL approaches in previous studies, highlighting the utilized datasets, deployed DL models, and achieved results. We emphasize the critical challenges and recommend several future directions for innovative researchers to tackle. Finally, an end-to-end smart DL framework is outlined for real-time assessment and recommendation of the best BHV design for TAVR. Ultimately, deploying such a framework in future studies will support clinicians in minimizing risks during TAVR therapy planning and will help in improving patient care.

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

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

Theoretical study of effect of the geometrical parameters on the dynamic properties of the elastic rings of an air journal bearing

The paper investigates theoretically the effect of the geometry of the elastic rings of an air journal bearing on the elastic rings dynamic coefficients. The physical finite element method (FEM) model used to obtain the dynamic coefficients of the rings is discussed. A theoretical model is implemented to predict the effect of the geometrical parameters on the dynamic coefficients of the elastic rings. The effect of the geometrical parameters on the dynamic coefficients at different frequencies is studied using FEM. The elastic geometry that result in desired dynamic coefficients is demonstrated. Since predicting the dynamic coefficients for all possible ring geometries using FEM would be computationally expensive. A neural network (NN) is trained to predict the dynamic coefficients for all possible ring geometries generated by the different ring geometrical parameters within a given input domain. The NN results are compared to the experimentally verified FEM results and the results are in good agreement.

A neural network framework for immediate temperature prediction of surgical hand-held drilling

BACKGROUND AND OBJECTIVE

Heat generation and associated temperature rise in surgical drilling can cause irreversible tissue damage. It is nearly impossible to provide immediate temperature prediction for a hand-held drilling process since both feed rate and motion vary with time. The objective of this study is to present and test a framework for immediate bone drilling temperature visualization based on a neural network (NN) model and a linear time-invariant (LTI) model.

METHODS

In this study, the finite element analysis (FEA) model is used as the ground truth. The NN model is used to predict the location-dependent thermal responses of FEA, while LTI is used to superimpose these responses based on the location history of the heat source. The use of LTI can eliminate the uncertainty of the unlimited possibility in the time domain. To test the framework, two three-dimensional drilling cases are studied, one with a constant drilling feed and straight path and the other with a varying feed and a varying path.

RESULTS

The NN model using U-net architecture can achieve the predicted correlation of over 97% with only 1% of the total number of data points. Using the framework with U-net and LTI, both case studies show good agreement in temporal and spatial temperature distributions with the ground truth. The average error near the drilling path is less than 10%. Discrepancies are mainly found near the heat source and the regions near the removed material.

CONCLUSIONS

An FEA surrogate model for rapid and accurate prediction of 3D temperature during arbitrary bone drilling is successfully made. The overall error is less than 5% on average in the two case studies. Future improvements include strategies for training data selection and data formating.

Investigation on aortic hemodynamics based on physics-informed neural network

Pressure in arteries is difficult to measure non-invasively. Although computational fluid dynamics (CFD) provides high-precision numerical solutions according to the basic physical equations of fluid mechanics, it relies on precise boundary conditions and complex preprocessing, which limits its real-time application. Machine learning algorithms have wide applications in hemodynamic research due to their powerful learning ability and fast calculation speed. Therefore, we proposed a novel method for pressure estimation based on physics-informed neural network (PINN). An ideal aortic arch model was established according to the geometric parameters from human aorta, and we performed CFD simulation with two-way fluid-solid coupling. The simulation results, including the space-time coordinates, the velocity and pressure field, were obtained as the dataset for the training and validation of PINN. Nondimensional Navier-Stokes equations and continuity equation were employed for the loss function of PINN, to calculate the velocity and relative pressure field. Post-processing was proposed to fit the absolute pressure of the aorta according to the linear relationship between relative pressure, elastic modulus and displacement of the vessel wall. Additionally, we explored the sensitivity of the PINN to the vascular elasticity, blood viscosity and blood velocity. The velocity and pressure field predicted by PINN yielded good consistency with the simulated values. In the interested region of the aorta, the relative errors of maximum and average absolute pressure were 7.33% and 5.71%, respectively. The relative pressure field was found most sensitive to blood velocity, followed by blood viscosity and vascular elasticity. This study has proposed a method for intra-vascular pressure estimation, which has potential significance in the diagnosis of cardiovascular diseases.

Human-Centric Digital Twins in Industry: A Comprehensive Review of Enabling Technologies and Implementation Strategies

The last decade saw the emergence of highly autonomous, flexible, re-configurable Cyber-Physical Systems. Research in this domain has been enhanced by the use of high-fidelity simulations, including Digital Twins, which are virtual representations connected to real assets. Digital Twins have been used for process supervision, prediction, or interaction with physical assets. Interaction with Digital Twins is enhanced by Virtual Reality and Augmented Reality, and Industry 5.0-focused research is evolving with the involvement of the human aspect in Digital Twins. This paper aims to review recent research on Human-Centric Digital Twins (HCDTs) and their enabling technologies. A systematic literature review is performed using the VOSviewer keyword mapping technique. Current technologies such as motion sensors, biological sensors, computational intelligence, simulation, and visualization tools are studied for the development of HCDTs in promising application areas. Domain-specific frameworks and guidelines are formed for different HCDT applications that highlight the workflow and desired outcomes, such as the training of AI models, the optimization of ergonomics, the security policy, task allocation, etc. A guideline and comparative analysis for the effective development of HCDTs are created based on the criteria of Machine Learning requirements, sensors, interfaces, and Human Digital Twin inputs.

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%.

Machine learning used for simulation of MitraClip intervention: A proof-of-concept study

Introduction: Severe mitral regurgitation (MR) is a mitral valve disease that can lead to lifethreatening complications. MitraClip (MC) therapy is a percutaneous solution for patients who cannot tolerate surgical solutions. In MC therapy, a clip is implanted in the heart to reduce MR. To achieve optimal MC therapy, the cardiologist needs to foresee the outcomes of different scenarios for MC implantation, including the location of the MC. Although finite element (FE) modeling can simulate the outcomes of different MC scenarios, it is not suitable for clinical usage because it requires several hours to complete.

Methods: In this paper, we used machine learning (ML) to predict the outcomes of MC therapy in less than 1 s. Two ML algorithms were used: XGBoost, which is a decision tree model, and a feed-forward deep learning (DL) model. The MC location, the geometrical attributes of the models and baseline stress and MR were the features of the ML models, and the predictions were performed for MR and maximum von Mises stress in the leaflets. The parameters of the ML models were determined to achieve the minimum errors obtained by applying the ML models on the validation set.

Results: The results for the test set (not used during training) showed relative agreement between ML predictions and ground truth FE predictions. The accuracy of the XGBoost models were better than DL models. Mean absolute percentage error (MAPE) for the XGBoost predictions were 0.115 and 0.231, and the MAPE for DL predictions were 0.154 and 0.310, for MR and stress, respectively.

Discussion: The ML models reduced the FE runtime from 6 hours (on average) to less than 1 s. The accuracy of ML models can be increased by increasing the dataset size. The results of this study have important implications for improving the outcomes of MC therapy by providing information about the outcomes of MC implantation in real-time.

Prediction of Bone Healing around Dental Implants in Various Boundary Conditions by Deep Learning Network

Tissue differentiation varies based on patients' conditions, such as occlusal force and bone properties. Thus, the design of the implants needs to take these conditions into account to improve osseointegration. However, the efficiency of the design procedure is typically not satisfactory and needs to be significantly improved. Thus, a deep learning network (DLN) is proposed in this study. A data-driven DLN consisting of U-net, ANN, and random forest models was implemented. It serves as a surrogate for finite element analysis and the mechano-regulation algorithm. The datasets include the history of tissue differentiation throughout 35 days with various levels of occlusal force and bone properties. The accuracy of day-by-day tissue differentiation prediction in the testing dataset was 82%, and the AUC value of the five tissue phenotypes (fibrous tissue, cartilage, immature bone, mature bone, and resorption) was above 0.86, showing a high prediction accuracy. The proposed DLN model showed the robustness for surrogating the complex, time-dependent calculations. The results can serve as a design guideline for dental implants.

A low dimensional surrogate model for a fast estimation of strain in the thrombus during a thrombectomy procedure

BACKGROUND

Intra-arterial thrombectomy is the main treatment for acute ischemic stroke due to large vessel occlusions and can consist in mechanically removing the thrombus with a stent-retriever. A cause of failure of the procedure is the fragmentation of the thrombus and formation of micro-emboli, difficult to remove. This work proposes a methodology for the creation of a low-dimensional surrogate model of the mechanical thrombectomy procedure, trained on realizations from high-fidelity simulations, able to estimate the evolution of the maximum first principal strain in the thrombus.

METHOD

A parametric finite-element model was created, composed of a tapered vessel, a thrombus, a stent-retriever and a catheter. A design of experiments was conducted to sample 100 combinations of the model parameters and the corresponding thrombectomy simulations were run and post-processed to extract the maximum first principal strain in the thrombus during the procedure. Then, a surrogate model was built with a combination of principal component analysis and Kriging.

RESULTS

The surrogate model was chosen after a sensitivity analysis on the number of principal components and was tested with 10 additional cases. The model provided predictions of the strain curves with correlation above 0.9 and a maximum error of 28%, with an error below 20% in 60% of the test cases.

CONCLUSIONS

The surrogate model provides nearly instantaneous estimates and constitutes a valuable tool for evaluating the risk of thrombus rupture during pre-operative planning for the treatment of acute ischemic stroke.

Predicting stress, strain and deformation fields in materials and structures with graph neural networks

Developing accurate yet fast computational tools to simulate complex physical phenomena is a long-standing problem. Recent advances in machine learning have revolutionized the way simulations are approached, shifting from a purely physics- to AI-based paradigm. Although impressive achievements have been reached, efficiently predicting complex physical phenomena in materials and structures remains a challenge. Here, we present an AI-based general framework, implemented through graph neural networks, able to learn complex mechanical behavior of materials from a few hundreds data. Harnessing the natural mesh-to-graph mapping, our deep learning model predicts deformation, stress, and strain fields in various material systems, like fiber and stratified composites, and lattice metamaterials. The model can capture complex nonlinear phenomena, from plasticity to buckling instability, seemingly learning physical relationships between the predicted physical fields. Owing to its flexibility, this graph-based framework aims at connecting materials' microstructure, base materials' properties, and boundary conditions to a physical response, opening new avenues towards graph-AI-based surrogate modeling.

A Surrogate Model Based on a Finite Element Model of Abdomen for Real-Time Visualisation of Tissue Stress during Physical Examination Training

Robotic patients show great potential for helping to improve medical palpation training, as they can provide feedback that cannot be obtained in a real patient. They provide information about internal organ deformation that can significantly enhance palpation training by giving medical trainees visual insight based on the pressure they apply for palpation. This can be achieved by using computational models of abdomen mechanics. However, such models are computationally expensive, and thus unable to provide real-time predictions. In this work, we proposed an innovative surrogate model of abdomen mechanics by using machine learning (ML) and finite element (FE) modelling to virtually render internal tissue deformation in real time. We first developed a new high-fidelity FE model of the abdomen mechanics from computerized tomography (CT) images. We performed palpation simulations to produce a large database of stress distribution on the liver edge, an area of interest in most examinations. We then used artificial neural networks (ANNs) to develop the surrogate model and demonstrated its application in an experimental palpation platform. Our FE simulations took 1.5 h to predict stress distribution for each palpation while this only took a fraction of a second for the surrogate model. Our results show that our artificial neural network (ANN) surrogate has an accuracy of 92.6%. We also showed that the surrogate model is able to use the experimental input of palpation location and force to provide real-time projections onto the robotics platform. This enhanced robotics platform has the potential to be used as a training simulator for trainees to hone their palpation skills.

An artificial intelligence-based platform for automatically estimating time-averaged wall shear stress in the ascending aorta

Aims

Aortopathies are a series of disorders requiring multiple indicators to assess risk. Time-averaged wall shear stress (TAWSS) is currently considered as the primary indicator of aortopathies progression, which can only be calculated by Computational Fluid Dynamics (CFD). However, CFD's complexity and high computational cost, greatly limit its application. The study aimed to construct a deep learning platform which could accurately estimate TAWSS in ascending aorta.

Methods and results

A total of 154 patients who had thoracic computed tomography angiography were included and randomly divided into two parts: training set (90%, n = 139) and testing set (10%, n = 15). TAWSS were calculated via CFD. The artificial intelligence (AI)-based model was trained and assessed using the dice coefficient (DC), normalized mean absolute error (NMAE), and root mean square error (RMSE). Our AI platform brought into correspondence with the manual segmentation (DC = 0.86) and the CFD findings (NMAE, 7.8773% ± 4.7144%; RMSE, 0.0098 ± 0.0097), while saving 12000-fold computational cost.

Conclusion

The high-efficiency and robust AI platform can automatically estimate value and distribution of TAWSS in ascending aorta, which may be suitable for clinical applications and provide potential ideas for CFD-based problem solving.

Transient wall shear stress estimation in coronary bifurcations using convolutional neural networks

BACKGROUND AND OBJECTIVE

Haemodynamic metrics, such as blood flow induced shear stresses at the inner vessel lumen, are associated with the development and progression of coronary artery disease. Understanding these metrics may therefore improve the assessment of an individual's coronary disease risk. However, the calculation of such luminal Wall Shear Stress (WSS) using traditional Computational Fluid Dynamics (CFD) methods is relatively slow and computationally expensive. As a result, CFD based haemodynamic computation is not suitable for integrated and large-scale use in clinical settings.

METHODS

In this work, deep learning techniques are proposed as an alternative method to CFD, whereby luminal WSS magnitude can be predicted in coronary bifurcations throughout the cardiac cycle based on the steady state solution (which takes <120 seconds to calculate including preprocessing), vessel geometry and additional global features. The deep learning model is trained on a dataset of 101 patient-specific and 2626 synthetic left main bifurcation models with 26 separate patient-specific cases used as the test set.

RESULTS

The model showed high fidelity predictions with <5% (normalised against mean WSS magnitude) deviation to CFD derived values as the gold-standard method, while being orders of magnitude faster with on average <2 minutes versus 3 hours computation for transient CFD.

CONCLUSIONS

This method therefore offers a new approach to substantially reduce the computational cost involved in, for example, large-scale population studies of coronary haemodynamic metrics, and may therefore open the pathway for future clinical integration.

Interplay between Artificial Intelligence and Biomechanics Modeling in the Cardiovascular Disease Prediction

Cardiovascular disease (CVD) is the most common cause of morbidity and mortality worldwide, and early accurate diagnosis is the key point for improving and optimizing the prognosis of CVD. Recent progress in artificial intelligence (AI), especially machine learning (ML) technology, makes it possible to predict CVD. In this review, we first briefly introduced the overview development of artificial intelligence. Then we summarized some ML applications in cardiovascular diseases, including ML-based models to directly predict CVD based on risk factors or medical imaging findings and the ML-based hemodynamics with vascular geometries, equations, and methods for indirect assessment of CVD. We also discussed case studies where ML could be used as the surrogate for computational fluid dynamics in data-driven models and physics-driven models. ML models could be a surrogate for computational fluid dynamics, accelerate the process of disease prediction, and reduce manual intervention. Lastly, we briefly summarized the research difficulties and prospected the future development of AI technology in cardiovascular diseases.

Predicting the effective compressive modulus of human cancellous bone using the convolutional neural network method

The efficient prediction of biomechanical properties of bone plays an important role in the assessment of bone quality. However, the present techniques are either of low accuracy or of high complexity for the clinical application. The present study aims to investigate the predictive ability of the evolving convolutional neural network (CNN) technique in predicting the effective compressive modulus of porous bone structures. The T11/T12/L1 segments of thirty-five female cadavers were scanned using the HR-pQCT scanner and the images obtained from it were used to generate 10896 2 D bone samples, in which only the cancellous bony parts were processed and investigated. The corresponding 10896 heterogeneous finite-element (FE) models were generated, and then a CNN model was constructed and trained using the predictions of the FE analysis as the ground truths. Then the remaining 260 bone samples generated from the initial HR-pQCT images were used to test the predictive power of the CNN model. The results show that the coefficient of the determinant (R²) from the linear correlation between the CNN and FE predicted elastic modulus is 0.95, which is much higher than that from the correlation between the BMD and the FE predictions (R² = 0.65). Furthermore, the 95th and 50th percentiles of relative prediction error are below 0.28 and 0.09, respectively. In the conclusion, the CNN model can efficiently predict the effective compressive modulus of human cancellous bone and can be used as a promising and clinically applicable method to evaluate the mechanical quality of porous bone.

Rapid Prediction of Retina Stress and Strain Patterns in Soccer-Related Ocular Injury: Integrating Finite Element Analysis with Machine Learning Approach

Soccer-related ocular injuries, especially retinal injuries, have attracted increasing attention. The mechanics of a flying soccer ball have induced abnormally higher retinal stresses and strains, and their correlation with retinal injuries has been characterized using the finite element (FE) method. However, FE simulations demand solid mechanical expertise and extensive computational time, both of which are difficult to adopt in clinical settings. This study proposes a framework that combines FE analysis with a machine learning (ML) approach for the fast prediction of retina mechanics. Different impact scenarios were simulated using the FE method to obtain the von Mises stress map and the maximum principal strain map in the posterior retina. These stress and strain patterns, along with their input parameters, were used to train and test a partial least squares regression (PLSR) model to predict the soccer-induced retina stress and strain in terms of distributions and peak magnitudes. The peak von Mises stress and maximum principal strain prediction errors were 3.03% and 9.94% for the frontal impact and were 9.08% and 16.40% for the diagonal impact, respectively. The average prediction error of von Mises stress and the maximum principal strain were 15.62% and 21.15% for frontal impacts and were 10.77% and 21.78% for diagonal impacts, respectively. This work provides a surrogate model of FE analysis for the fast prediction of the dynamic mechanics of the retina in response to the soccer impact, which could be further utilized for developing a diagnostic tool for soccer-related ocular trauma.

Blood flow analysis with computational fluid dynamics and 4D-flow MRI for vascular diseases

Both computational fluid dynamics (CFD) and time-resolved, three-dimensional, phase-contrast, magnetic resonance imaging (4D-flow MRI) enable visualization of time-varying blood flow structures and quantification of blood flow in vascular diseases. However, they are totally different. CFD is a method to calculate blood flow by solving the governing equations of fluid mechanics, so the obtained flow field is somewhat virtual. On the other hand, 4D-flow MRI measures blood flow in vivo, thus the flow is real. Recently, with the development and enhancement of computers, medical imaging techniques, and related software, blood flow analysis has become more accessible to clinicians and its usefulness in vascular diseases has been demonstrated. In this review, we have outlined the methods and characteristics of CFD and 4D-flow MRI, respectively. We have discussed the differences in the characteristics between both methods; reviewed the milestones achieved by blood flow analysis in various vascular diseases; and discussed the usefulness, challenges, and limitations of blood flow analysis. We have discussed the difficulties and limitations of current blood flow analysis. We have also discussed our views on future directions.

Multi-fidelity surrogate modeling through hybrid machine learning for biomechanical and finite element analysis of soft tissues

Biomechanical simulation enables medical researchers to study complex mechano-biological conditions, although for soft tissue modeling, it may apply highly nonlinear multi-physics theories commonly implemented by expensive finite element (FE) solvers. This is a significantly time-consuming process on a regular computer and completely inefficient in urgent situations. One remedy is to first generate a dataset of the possible inputs and outputs of the solver in order to then train an efficient machine learning (ML) model, i.e., the supervised ML-based surrogate, replacing the expensive solver to speed up the simulation. But it still requires a large number of expensive numerical samples. In this regard, we propose a hybrid ML (HML) method that uses a reduced-order model defined by the simplification of the complex multi-physics equations to produce a dataset of the low-fidelity (LF) results. The surrogate then has this efficient numerical model and an ML model that should increase the fidelity of its outputs to the level of high-fidelity (HF) results. Based on our empirical tests via a group of diverse training and numerical modeling conditions, the proposed method can improve training convergence for very limited training samples. In particular, while considerable time gains comparing to the HF numerical models are observed, training of the HML models is also significantly more efficient than the purely ML-based surrogates. From this, we conclude that this non-destructive HML implementation may increase the accuracy and efficiency of surrogate modeling of soft tissues with complex multi-physics properties in small data regimes.

Deep Learning for Computational Hemodynamics: A Brief Review of Recent Advances

Computational fluid dynamics (CFD) modeling of blood flow plays an important role in better understanding various medical conditions, designing more effective drug delivery systems, and developing novel diagnostic methods and treatments. However, despite significant advances in computational technology and resources, the expensive computational cost of these simulations still hinders their transformation from a research interest to a clinical tool. This bottleneck is even more severe for image-based, patient-specific CFD simulations with realistic boundary conditions and complex computational domains, which make such simulations excessively expensive. To address this issue, deep learning approaches have been recently explored to accelerate computational hemodynamics simulations. In this study, we review recent efforts to integrate deep learning with CFD and discuss the applications of this approach in solving hemodynamics problems, such as blood flow behavior in aorta and cerebral arteries. We also discuss potential future directions in the field. In this review, we suggest that incorporating physiologic understandings and underlying fluid mechanics laws in deep learning models will soon lead to a paradigm shift in the development novel non-invasive computational medical decisions.

Performance Prediction of Induction Motor Due to Rotor Slot Shape Change Using Convolution Neural Network

We propose a method to predict performance variables according to the rotor slot shape of a three-phase squirrel cage induction motor using a convolution neural network (CNN) algorithm suitable for utilizing image data. The set of performance variables was labeled according to the images of each training dataset, and this set was generated from the efficiency, power factor, starting torque, and average torque. To verify the accuracy of the trained deep learning model, the analysis and prediction results of the CNN model were compared and verified with nine untrained double cage slot shapes and shapes optimized based on the root mean square error (RMSE). Although a large number of training data are required for high accuracy in the existing image processing deep learning model, the proposed deep learning method can predict the performance variables for various shapes with the same level of accuracy as the finite element analysis results using a small number of training data. Therefore, it is expected to be applied in various engineering fields.

Machine Learning for Cardiovascular Biomechanics Modeling: Challenges and Beyond

Recent progress in machine learning (ML), together with advanced computational power, have provided new research opportunities in cardiovascular modeling. While classifying patient outcomes and medical image segmentation with ML have already shown significant promising results, ML for the prediction of biomechanics such as blood flow or tissue dynamics is in its infancy. This perspective article discusses some of the challenges in using ML for replacing well-established physics-based models in cardiovascular biomechanics. Specifically, we discuss the large landscape of input features in 3D patient-specific modeling as well as the high-dimensional output space of field variables that vary in space and time. We argue that the end purpose of such ML models needs to be clearly defined and the tradeoff between the loss in accuracy and the gained speedup carefully interpreted in the context of translational modeling. We also discuss several exciting venues where ML could be strategically used to augment traditional physics-based modeling in cardiovascular biomechanics. In these applications, ML is not replacing physics-based modeling, but providing opportunities to solve ill-defined problems, improve measurement data quality, enable a solution to computationally expensive problems, and interpret complex spatiotemporal data by extracting hidden patterns. In summary, we suggest a strategic integration of ML in cardiovascular biomechanics modeling where the ML model is not the end goal but rather a tool to facilitate enhanced modeling.

Biomaterialomics: Data science-driven pathways to develop fourth-generation biomaterials

Conventional approaches to developing biomaterials and implants require intuitive tailoring of manufacturing protocols and biocompatibility assessment. This leads to longer development cycles, and high costs. To meet existing and unmet clinical needs, it is critical to accelerate the production of implantable biomaterials, implants and biomedical devices. Building on the Materials Genome Initiative, we define the concept 'biomaterialomics' as the integration of multi-omics data and high-dimensional analysis with artificial intelligence (AI) tools throughout the entire pipeline of biomaterials development. The Data Science-driven approach is envisioned to bring together on a single platform, the computational tools, databases, experimental methods, machine learning, and advanced manufacturing (e.g., 3D printing) to develop the fourth-generation biomaterials and implants, whose clinical performance will be predicted using 'digital twins'. While analysing the key elements of the concept of 'biomaterialomics', significant emphasis has been put forward to effectively utilize high-throughput biocompatibility data together with multiscale physics-based models, E-platform/online databases of clinical studies, data science approaches, including metadata management, AI/ Machine Learning (ML) algorithms and uncertainty predictions. Such integrated formulation will allow one to adopt cross-disciplinary approaches to establish processing-structure-property (PSP) linkages. A few published studies from the lead author's research group serve as representative examples to illustrate the formulation and relevance of the 'Biomaterialomics' approaches for three emerging research themes, i.e. patient-specific implants, additive manufacturing, and bioelectronic medicine. The increased adaptability of AI/ML tools in biomaterials science along with the training of the next generation researchers in data science are strongly recommended. STATEMENT OF SIGNIFICANCE: This leading opinion review paper emphasizes the need to integrate the concepts and algorithms of the data science with biomaterials science. Also, this paper emphasizes the need to establish a mathematically rigorous cross-disciplinary framework that will allow a systematic quantitative exploration and curation of critical biomaterials knowledge needed to drive objectively the innovation efforts within a suitable uncertainty quantification framework, as embodied in 'biomaterialomics' concept, which integrates multi-omics data and high-dimensional analysis with artificial intelligence (AI) tools, like machine learning. The formulation of this approach has been demonstrated for patient-specific implants, additive manufacturing, and bioelectronic medicine.

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.

Predicting the trabecular bone apparent stiffness tensor with spherical convolutional neural networks

The apparent stiffness tensor is relevant for characterizing trabecular bone quality. Previous studies have used morphology-stiffness relationships for estimating the apparent stiffness tensor. In this paper, we propose to train spherical convolutional neural networks (SphCNNs) to estimate this tensor. Information of the edges, trabecular thickness, and spacing are summarized in functions on the unitary sphere used as inputs for the SphCNNs. The concomitant dimensionality reduction makes it possible to train neural networks on relatively small datasets. The predicted tensors were compared to the stiffness tensors computed by using the micro-finite element method (μFE), which was considered as the gold standard, and models based on fourth-order fabric tensors. Combining edges and trabecular thickness yields significant improvements in the accuracy compared to the methods based on fourth-order fabric tensors. From the results, SphCNNs are promising for replacing the more expensive μFE stiffness estimations.

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Characteristic stiffness tensors are derived from trabecular bone micro-CT samples.

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Previous approximation methods fall short on heterogeneous data-sets.

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The gradient, trabecular thickness and spacing are mapped to a spherical domain.

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Spherical convolutional neural networks are used for the prediction.

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The prediction error is significantly reduced compared to the state-of-the-art.

Personalized Pre- and Post-Operative Hemodynamic Assessment of Aortic Coarctation from 3D Rotational Angiography

PURPOSE

Coarctation of Aorta (CoA) is a congenital disease consisting of a narrowing that obstructs the systemic blood flow. This proof-of-concept study aimed to develop a framework for automatically and robustly personalizing aortic hemodynamic computations for the assessment of pre- and post-intervention CoA patients from 3D rotational angiography (3DRA) data.

METHODS

We propose a framework that combines hemodynamic modelling and machine learning (ML) based techniques, and rely on 3DRA data for non-invasive pressure computation in CoA patients. The key features of our framework are a parameter estimation method for calibrating inlet and outlet boundary conditions, and regional mechanical wall properties, to ensure that the computational results match the patient-specific measurements, and an improved ML based pressure drop model capable of predicting the instantaneous pressure drop for a wide range of flow conditions and anatomical CoA variations.

RESULTS

We evaluated the framework by investigating 6 patient datasets, under pre- and post-operative setting, and, since all calibration procedures converged successfully, the proposed approach is deemed robust. We compared the peak-to-peak and the cycle-averaged pressure drop computed using the reduced-order hemodynamic model with the catheter based measurements, before and after virtual and actual stenting. The mean absolute error for the peak-to-peak pressure drop, which is the most relevant measure for clinical decision making, was 2.98 mmHg for the pre- and 2.11 mmHg for the post-operative setting. Moreover, the proposed method is computationally efficient: the average execution time was of only [Formula: see text] minutes on a standard hardware configuration.

CONCLUSION

The use of 3DRA for hemodynamic modelling could allow for a complete hemodynamic assessment, as well as virtual interventions or surgeries and predictive modeling. However, before such an approach can be used routinely, significant advancements are required for automating the workflow.

WSSNet: Aortic Wall Shear Stress Estimation Using Deep Learning on 4D Flow MRI

Wall shear stress (WSS) is an important contributor to vessel wall remodeling and atherosclerosis. However, image-based WSS estimation from 4D Flow MRI underestimates true WSS values, and the accuracy is dependent on spatial resolution, which is limited in 4D Flow MRI. To address this, we present a deep learning algorithm (WSSNet) to estimate WSS trained on aortic computational fluid dynamics (CFD) simulations. The 3D CFD velocity and coordinate point clouds were resampled into a 2D template of 48 × 93 points at two inward distances (randomly varied from 0.3 to 2.0 mm) from the vessel surface (“velocity sheets”). The algorithm was trained on 37 patient-specific geometries and velocity sheets. Results from 6 validation and test cases showed high accuracy against CFD WSS (mean absolute error 0.55 ± 0.60 Pa, relative error 4.34 ± 4.14%, 0.92 ± 0.05 Pearson correlation) and noisy synthetic 4D Flow MRI at 2.4 mm resolution (mean absolute error 0.99 ± 0.91 Pa, relative error 7.13 ± 6.27%, and 0.79 ± 0.10 Pearson correlation). Furthermore, the method was applied on in vivo 4D Flow MRI cases, effectively estimating WSS from standard clinical images. Compared with the existing parabolic fitting method, WSSNet estimates showed 2–3 × higher values, closer to CFD, and a Pearson correlation of 0.68 ± 0.12. This approach, considering both geometric and velocity information from the image, is capable of estimating spatiotemporal WSS with varying image resolution, and is more accurate than existing methods while still preserving the correct WSS pattern distribution.

How Artificial Intelligence and Machine Learning Is Assisting Us to Extract Meaning from Data on Bone Mechanics?

Dramatic advancements in interdisciplinary research with the fourth paradigm of science, especially the implementation of computer science, nourish the potential for artificial intelligence (AI), machine learning (ML), and artificial neural network (ANN) algorithms to be applied to studies concerning mechanics of bones. Despite recent enormous advancement in techniques, gaining deep knowledge to find correlations between bone shape, material, mechanical, and physical responses as well as properties is a daunting task. This is due to both complexity of the material itself and the convoluted shapes that this complex material forms. Moreover, many uncertainties and ambiguities exist concerning the use of traditional computational techniques that hinders gaining a full comprehension of this advanced biological material. This book chapter offers a review of literature on the use of AI, ML, and ANN in the study of bone mechanics research. A main question as to why to implement AI and ML in the mechanics of bones is fully addressed and explained. This chapter also introduces AI and ML and elaborates on the main features of ML algorithms such as learning paradigms, subtypes, main ideas with examples, performance metrics, training algorithms, and training datasets. As a frequently employed ML algorithm in bone mechanics, feedforward ANNs are discussed to make their taxonomy and working principles more readily comprehensible to researchers. A summary as well as detailed review of papers that employed ANNs to learn from collected data on bone mechanics are presented. Reviewing literature on the use of these data-driven tools is essential since their wider application has the potential to: improve clinical assessments enabling real-time simulations; avoid and/or minimize injuries; and, encourage early detection of such injuries in the first place.

Atlas-Based Evaluation of Hemodynamic in Ascending Thoracic Aortic Aneurysms

Atlas-based analyses of patients with cardiovascular diseases have recently been explored to understand the mechanistic link between shape and pathophysiology. The construction of probabilistic atlases is based on statistical shape modeling (SSM) to assess key anatomic features for a given patient population. Such an approach is relevant to study the complex nature of the ascending thoracic aortic aneurysm (ATAA) as characterized by different patterns of aortic shapes and valve phenotypes. This study was carried out to develop an SSM of the dilated aorta with both bicuspid aortic valve (BAV) and tricuspid aortic valve (TAV), and then assess the computational hemodynamic of virtual models obtained by the deformation of the mean template for specific shape boundaries (i.e., ±1.5 standard deviation, σ). Simulations demonstrated remarkable changes in the velocity streamlines, blood pressure, and fluid shear stress with the principal shape modes such as the aortic size (Mode 1), vessel tortuosity (Mode 2), and aortic valve morphologies (Mode 3). The atlas-based disease assessment can represent a powerful tool to reveal important insights on ATAA-derived hemodynamic, especially for aneurysms which are considered to have borderline anatomies, and thus challenging decision-making. The utilization of SSMs for creating probabilistic patient cohorts can facilitate the understanding of the heterogenous nature of the dilated ascending aorta.

Mitral Valve Atlas for Artificial Intelligence Predictions of MitraClip Intervention Outcomes

Severe mitral regurgitation (MR) is a cardiac disease that can lead to fatal consequences. MitraClip (MC) intervention is a percutaneous procedure whereby the mitral valve (MV) leaflets are connected along the edge using MCs. The outcomes of the MC intervention are not known in advance, i.e., the outcomes are quite variable. Artificial intelligence (AI) can be used to guide the cardiologist in selecting optimal MC scenarios. In this study, we describe an atlas of shapes as well as different scenarios for MC implantation for such an AI analysis. We generated the MV geometrical data from three different sources. First, the patients' 3-dimensional echo images were used. The pixel data from six key points were obtained from three views of the echo images. Using PyGem, an open-source morphing library in Python, these coordinates were used to create the geometry by morphing a template geometry. Second, the dimensions of the MV, from the literature were used to create data. Third, we used machine learning methods, principal component analysis, and generative adversarial networks to generate more shapes. We used the finite element (FE) software ABAQUS to simulate smoothed particle hydrodynamics in different scenarios for MC intervention. The MR and stresses in the leaflets were post-processed. Our physics-based FE models simulated the outcomes of MC intervention for different scenarios. The MR and stresses in the leaflets were computed by the FE models for a single clip at different locations as well as two and three clips. Results from FE simulations showed that the location and number of MCs affect subsequent residual MR, and that leaflet stresses do not follow a simple pattern. Furthermore, FE models need several hours to provide the results, and they are not applicable for clinical usage where the predicted outcomes of MC therapy are needed in real-time. In this study, we generated the required dataset for the AI models which can provide the results in a matter of seconds.

Increasing efficiency and accuracy of magnetic interaction calculations in colloidal simulation through machine learning

Calculating the magnetic interaction between magnetic particles that are positioned in close proximity to one another is a surprisingly challenging task. Exact solutions for this interaction exist either through numerical expansion of multipolar interactions or through solving Maxwell's equations with a finite element solver. These approaches can take hours for simple configurations of three particles. Meanwhile, across a range of scientific and engineering problems, machine learning approaches have been developed as fast computational platforms for solving complex systems of interest when large data sets are available. In this paper, we bring the touted benefits of recent advances in science-based machine learning algorithms to bear on the problem of modeling the magnetic interaction between three particles. We investigate this approach using diverse machine learning systems including physics informed neural networks. We find that once the training data has been collected and the model has been initiated, simulation times are reduced from hours to mere seconds while maintaining remarkable accuracy. Despite this promise, we also try to lay bare the current challenges of applying machine learning to these and more complex colloidal systems.

The biomechanical influence of facet joint parameters on corresponding segment in the lumbar spine: a new visualization method

BACKGROUND CONTEXT

Facet joints have been discussed as influential factors in the development of lumbar degeneration, which includes disc herniation and degenerative lumbar spondylolisthesis. Facet orientation (FO) and facet tropism (FT) are two important structural parameters of the lumbar facet joints. Many previous studies have focused on single parameter analysis of the lumbar spine. Owing to the correlation between independent variables, single-factor analysis cannot reflect the interaction between variables; however, there has been no corresponding biomechanical method developed to address this problem.

PURPOSE

To investigate the complex biomechanical influences on the lumbar spine when vertebral FO and FT are varied using finite element analysis (FEA) and contour maps visualization, and analyze the biomechanical role of facet joint structural parameters in the process of lumbar degenerative diseases.

STUDY DESIGN

A biomechanical modelling, analysis, and verification study was performed.

METHODS

A three-dimensional non-linear FEA model of 3 denucleated intervertebral discs (L2-3, L3-4, L4-5) with adjacent vertebral bodies (L2-L5) was created. Previously performed in vitro experiments provided experimental data for the range of motion in each load direction that was used for calibration. For 12 lumbar models, different facet joint angles relative to the sagittal plane at both L3-4 facet joints were simulated for 35°≤FO≤50° and 0°≤FT≤15°. By modifying different values of FO and FT, FEA simulation of different lumbar spine models was performed. Contour maps were used to visualize the FO- and FT-relevant data.

RESULTS

Under flexion, extension, and torsion moments, facet joint contact force and intradiscal stress increased with increasing FT. In the condition where FT remained 0° and increasing FO values, facet joint contact force and intradiscal stress remained low with no apparent increasing or decreasing trend when the model was under flexion, extension, and torsion moments. In the condition where FO and the FT values were varied at the same time, the highest force and stress regions in the contour maps were observed when all three types of moments were applied. Stress distributions of the L3-4 disc with different FT and FO values showed disc stress increased significantly with increases of FT and was concentrated on the ipsilateral region of the facet joint with the more sagittal orientation.

CONCLUSIONS

The combination of FO and FT has an important impact on the corresponding disc and facet joints, but FT played a more significant role. Moreover, disc stress was concentrated on the ipsilateral region of facet joint with greater sagittal orientation when FT existed. FT with high sagittal orientation may increase risk of recurrent LDH due to increase ipsilateral disc pressure.

CLINICAL SIGNIFICANCE

These biomechanical findings may help clinicians to understand the prognosis of some lumbar degenerative conditions.

Predicting Nonlinear and Anisotropic Mechanics of Metal Rubber Using a Combination of Constitutive Modeling, Machine Learning, and Finite Element Analysis

Metal rubber (MR) is an entangled fibrous functional material, and its mechanical properties are crucial for its applications; however, numerical constitutive models of MR for prediction and calculation are currently undeveloped. In this work, we provide a numerical constitutive model to express the mechanics of MR materials and develop an efficient finite elements method (FEM) to calculate the performance of MR components. We analyze the nonlinearity and anisotropy characteristics of MR during the deformation process. The elasticity matrix is adopted to express the nonlinearity and anisotropy of MR. An artificial neural network (ANN) model is built, trained, and tested to output the current elastic moduli for the elasticity matrix. Then, we combine the constitutive ANN model with the finite element method simulation to calculate the mechanics of the MR component. Finally, we perform a series of static and shock experiments and finite element simulations of an MR isolator. The results demonstrate the feasibility and accuracy of the numerical constitutive MR model. This work provides an efficient and convenient method for the design and analysis of MR components.

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.

Deep Simulation of Facial Appearance Changes Following Craniomaxillofacial Bony Movements in Orthognathic Surgical Planning

Facial appearance changes with the movements of bony segments in orthognathic surgery of patients with craniomaxillofacial (CMF) deformities. Conventional bio-mechanical methods, such as finite element modeling (FEM), for simulating such changes, are labor intensive and computationally expensive, preventing them from being used in clinical settings. To overcome these limitations, we propose a deep learning framework to predict post-operative facial changes. Specifically, FC-Net, a facial appearance change simulation network, is developed to predict the point displacement vectors associated with a facial point cloud. FC-Net learns the point displacements of a pre-operative facial point cloud from the bony movement vectors between pre-operative and simulated post-operative bony models. FC-Net is a weakly-supervised point displacement network trained using paired data with strict point-to-point correspondence. To preserve the topology of the facial model during point transform, we employ a local-point-transform loss to constrain the local movements of points. Experimental results on real patient data reveal that the proposed framework can predict post-operative facial appearance changes remarkably faster than a state-of-the-art FEM method with comparable prediction accuracy.

Classification of Textile Polymer Composites: Recent Trends and Challenges

Polymer based textile composites have gained much attention in recent years and gradually transformed the growth of industries especially automobiles, construction, aerospace and composites. The inclusion of natural polymeric fibres as reinforcement in carbon fibre reinforced composites manufacturing delineates an economic way, enhances their surface, structural and mechanical properties by providing better bonding conditions. Almost all textile-based products are associated with quality, price and consumer’s satisfaction. Therefore, classification of textiles products and fibre reinforced polymer composites is a challenging task. This paper focuses on the classification of various problems in textile processes and fibre reinforced polymer composites by artificial neural networks, genetic algorithm and fuzzy logic. Moreover, their limitations associated with state-of-the-art processes and some relatively new and sequential classification methods are also proposed and discussed in detail in this paper.