Bridging finite element and machine learning modeling: stress prediction of arterial walls in atherosclerosis

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.

An integrated finite element method and machine learning algorithm for brain morphology prediction

The human brain development experiences a complex evolving cortical folding from a smooth surface to a convoluted ensemble of folds. Computational modeling of brain development has played an essential role in better understanding the process of cortical folding, but still leaves many questions to be answered. A major challenge faced by computational models is how to create massive brain developmental simulations with affordable computational sources to complement neuroimaging data and provide reliable predictions for brain folding. In this study, we leveraged the power of machine learning in data augmentation and prediction to develop a machine-learning-based finite element surrogate model to expedite brain computational simulations, predict brain folding morphology, and explore the underlying folding mechanism. To do so, massive finite element method (FEM) mechanical models were run to simulate brain development using the predefined brain patch growth models with adjustable surface curvature. Then, a GAN-based machine learning model was trained and validated with these produced computational data to predict brain folding morphology given a predefined initial configuration. The results indicate that the machine learning models can predict the complex morphology of folding patterns, including 3-hinge gyral folds. The close agreement between the folding patterns observed in FEM results and those predicted by machine learning models validate the feasibility of the proposed approach, offering a promising avenue to predict the brain development with given fetal brain configurations.

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.

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.

A likelihood swarm whale optimization based LeNet classifier approach for the prediction and diagnosis of patients with atherosclerosis disease

Coronary Artery Disease (CAD) caused by atherosclerosis is having huge impact and is considered an epidemic one in all over the world. Cardio vascular disease (CVD) in 2019 records is about 32% of global death rate. Among these deaths, 85% were caused by heart attack and stroke. Atherosclerosis is regarded as a condition at which the arteries become hardened and narrowed due to the plaque accumulation around the walls of arteries. The disease growth is slow, asymptomatic, sudden cardiac arrest, myocardial infarction and stroke. At present, medical diagnostic techniques are widely applied for the prediction of disease. However, they are uncommon in the desired sensitivity and resolution for detection. The lack of non-invasive diagnosing tool for the prediction of disease in early stage limits the treatment and prevention of patients having various degrees. This proposed research work focuses on intelligent optimization technique named Maximum Likelihood Swarm Whale Optimization (MLSWO) that is used to extract the crucial features in the Atherosclerosis (STULONG) and Kaggle datasets and predict the disease progression. The outcomes the selected features are classified using LeNet classifier for assorting the individuals. The proposed MLSWO algorithm produces higher accuracy rate of 99.2%, sensitivity rate of 98.36% and specificity of 100% compared with other state-of art techniques.

Rupture risk prediction of cerebral aneurysms using a novel convolutional neural network-based deep learning model

BACKGROUND

Cerebral aneurysms should be treated before rupture because ruptured aneurysms result in serious disability. Therefore, accurate prediction of rupture risk is important and has been estimated using various hemodynamic factors.

OBJECTIVE

To suggest a new way to predict rupture risk in cerebral aneurysms using a novel deep learning model based on hemodynamic parameters for better decision-making about treatment.

METHODS

A novel convolutional neural network (CNN) model was used for rupture risk prediction retrospectively of 123 aneurysm cases. To include the effect of hemodynamic parameters into the CNN, the hemodynamic parameters were first calculated using computational fluid dynamics and fluid-structure interaction. Then, they were converted into images for training the CNN using a novel approach. In addition, new data augmentation methods were devised to obtain sufficient training data. A total of 53,136 images generated by data augmentation were used to train and test the CNN.

RESULTS

The CNNs trained with wall shear stress (WSS), strain, and combination images had area under the receiver operating characteristics curve values of 0.716, 0.741, and 0.883, respectively. Based on the cut-off values, the CNN trained with WSS (sensitivity: 0.5, specificity: 0.79) or strain (sensitivity: 0.74, specificity: 0.71) images alone was not highly predictive. However, the CNN trained with combination images of WSS and strain showed a sensitivity and specificity of 0.81 and 0.82, respectively.

CONCLUSION

CNN-based deep learning algorithm using hemodynamic factors, including WSS and strain, could be an effective tool for predicting rupture risk in cerebral aneurysms with good predictive accuracy.

Simulation of Postoperative Facial Appearances via Geometric Deep Learning for Efficient Orthognathic Surgical Planning

Orthognathic surgery corrects jaw deformities to improve aesthetics and functions. Due to the complexity of the craniomaxillofacial (CMF) anatomy, orthognathic surgery requires precise surgical planning, which involves predicting postoperative changes in facial appearance. To this end, most conventional methods involve simulation with biomechanical modeling methods, which are labor intensive and computationally expensive. Here we introduce a learning-based framework to speed up the simulation of postoperative facial appearances. Specifically, we introduce a facial shape change prediction network (FSC-Net) to learn the nonlinear mapping from bony shape changes to facial shape changes. FSC-Net is a point transform network weakly-supervised by paired preoperative and postoperative data without point-wise correspondence. In FSC-Net, a distance-guided shape loss places more emphasis on the jaw region. A local point constraint loss restricts point displacements to preserve the topology and smoothness of the surface mesh after point transformation. Evaluation results indicate that FSC-Net achieves 15× speedup with accuracy comparable to a state-of-the-art (SOTA) finite-element modeling (FEM) method.

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.

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.

Machine Learning-Based Surrogate Model for Press Hardening Process of 22MnB5 Sheet Steel Simulation in Industry 4.0

The digitalization of manufacturing processes offers great potential in quality control, traceability, and the planning and setup of production. In this regard, process simulation is a well-known technology and a key step in the design of manufacturing processes. However, process simulations are computationally and time-expensive, typically beyond the manufacturing-cycle time, severely limiting their usefulness in real-time process control. Machine Learning-based surrogate models can overcome these drawbacks, and offer the possibility to achieve a soft real-time response, which can be potentially developed into full close-loop manufacturing systems, at a computational cost that can be realistically implemented in an industrial setting. This paper explores the novel concept of using a surrogate model to analyze the case of the press hardening of a steel sheet of 22MnB5. This hot sheet metal forming process involves a crucial heat treatment step, directly related to the final part quality. Given its common use in high-responsibility automobile parts, this process is an interesting candidate for digitalization in order to ensure production quality and traceability. A comparison of different data and model training strategies is presented. Finite element simulations for a transient heat transfer analysis are performed with ABAQUS software and they are used for the training data generation to effectively implement a ML-based surrogate model capable of predicting key process outputs for entire batch productions. The resulting final surrogate predicts the behavior and evolution of the most important temperature variables of the process in a wide range of scenarios, with a mean absolute error around 3 °C, but reducing the time four orders of magnitude with respect to the simulations. Moreover, the methodology presented is not only relevant for manufacturing purposes, but can be a technology enabler for advanced systems, such as digital twins and autonomous process control.

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.

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.

A Predictive Analysis of Wall Stress in Abdominal Aortic Aneurysms Using a Neural Network Model

Rupture risk assessment of abdominal aortic aneurysms (AAAs) by means of quantifying wall stress is a common biomechanical strategy. However, the clinical translation of this approach has been greatly limited due to the complexity associated with the computational tools required for its implementation. Thus, being able to estimate wall stress using nonbiomechanical markers that can be quantified as a direct outcome of clinical image segmentation would be advantageous in improving the potential implementation of said strategy. In the present work, we investigated the use of geometric indices to predict patient-specific AAA wall stress by means of a novel neural network (NN) modeling approach. We conducted a retrospective review of existing clinical images of two patient groups: 98 asymptomatic and 50 symptomatic AAAs. The images were subject to a protocol consisting of image segmentation, processing, volume meshing, finite element modeling, and geometry quantification, from which 53 geometric indices and the spatially averaged wall stress (SAWS) were calculated. SAWS estimated from finite element analysis was considered the gold standard for the predictions. We developed feed-forward NN models composed of an input layer, two dense layers, and an output layer using Keras, a deep learning library in python. The NN models were trained, tested, and validated independently for both AAA groups using all geometric indices, as well as a reduced set of indices resulting from a variable reduction procedure. We compared the performance of the NN models with two standard machine learning algorithms (MARS: multivariate adaptive regression splines and GAM: generalized additive model) and a linear regression model (GLM: generalized linear model). With the reduced sets of indices, the NN-based approach exhibited the highest mean goodness-of-fit (for the symptomatic group 0.71 and for the asymptomatic group 0.79) and lowest mean relative error (17% for both groups). In contrast, MARS yielded a mean goodness-of-fit of 0.59 for the symptomatic group and 0.77 for the asymptomatic group, with relative errors of 17% for the symptomatic group and 22% for the asymptomatic group. GAM had a mean goodness-of-fit of 0.70 for the symptomatic group and 0.80 for the asymptomatic group, with relative errors of 16% for the symptomatic group and 20% for the asymptomatic group. GLM did not perform as well as the other algorithms, with a mean goodness-of-fit of 0.53 for the symptomatic group and 0.70 for the asymptomatic group, with relative errors of 19% for the symptomatic group and 23% for the asymptomatic group. Nevertheless, the NN models required a reduced set of 15 and 13 geometric indices to predict SAWS for the symptomatic and asymptomatic AAA groups, respectively. This was in contrast to the reduced set of nine and eight geometric indices required to predict SAWS with the MARS and GAM algorithms for each AAA group, respectively. The use of NN modeling represents a promising alternative methodology for the estimation of AAA wall stress using geometric indices as surrogates, in lieu of finite element modeling. The performance metrics of NN models are expected to improve with significantly larger group sizes, given the suitability of NN modeling for "big data" applications.

Machine learning approaches to surrogate multifidelity Growth and Remodeling models for efficient abdominal aortic aneurysmal applications

Computational Growth and Remodeling (G&R) models have been widely used to capture the pathological development of arterial diseases and have shown promise for aiding clinical diagnosis, prognosis prediction, and staging classification. However, due to the high complexity of the arterial adaptation mechanism, high-fidelity arterial G&R simulation usually takes hours or even days, which hinders its application in clinical practice. To remedy this problem, we develop a computationally efficient arterial G&R simulation framework that comprehensively combines the physics-based G&R simulations and data-driven machine learning approaches. The proposed framework greatly enhances the computational efficiency of arterial G&R simulations, thereby enabling more time-consuming arterial applications, including personalized parameter estimation and arterial disease progression prediction. In particular, we achieve significant computational cost reduction mainly through two methods: (1) constructing a Multifidelity Surrogate (MFS) to approximate multifidelity G&R simulations by using a cokriging approach and (2) developing a novel iterative optimization algorithm for personalized parameter estimation. The proposed framework is demonstrated by estimating G&R model parameters and predicting individual aneurysm growth using follow-up CT images of Abdominal Aortic Aneurysms (AAAs) from 21 patients. Results show that the personalized parameters are satisfactorily estimated and the growth of AAAs is predicted within the clinically relevant time frame, i.e., less than 2 h, without a loss of accuracy.

Lopsided Blood-Thinning Drug Increases the Risk of Internal Flow Choking Leading to Shock Wave Generation Causing Asymptomatic Cardiovascular Disease

The discovery of Sanal flow choking in the cardiovascular-system calls for multidisciplinary and global action to develop innovative treatments and to develop new drugs to negate the risk of asymptomatic-cardiovascular-diseases. Herein, it is shown that when blood-pressure-ratio (BPR) reaches the lower-critical-hemorrhage-index (LCHI) internal-flow-choking and shock wave generation can occur in the cardiovascular-system, with sudden expansion/divergence/vasospasm or bifurcation regions, without prejudice to the percutaneous-coronary-intervention (PCI). Analytical findings reveal that the relatively high and the low blood-viscosity are cardiovascular-risk factors. In vitro studies have shown that nitrogen, oxygen, and carbon dioxide gases are dominant in fresh blood samples of humans/guinea pigs at a temperature range of 98.6-104 F. An in silico study demonstrated the Sanal flow choking phenomenon leading to shock-wave generation and pressure-overshoot in the cardiovascular-system. It has been established that disproportionate blood-thinning treatment increases the risk of the internal-flow-choking due to the enhanced boundary-layer-blockage-factor, resulting from an increase in flow-turbulence level in the cardiovascular-system, caused by an increase in Reynolds number as a consequence of low blood-viscosity. The cardiovascular-risk can be diminished by concurrently lessening the viscosity of biofluid/blood and flow-turbulence by raising the thermal-tolerance-level in terms of blood-heat-capacity-ratio (BHCR) and/or by decreasing the systolic-to-diastolic blood-pressure-ratio.

A Machine Learning Approach as a Surrogate for a Finite Element Analysis: Status of Research and Application to One Dimensional Systems

Current maintenance intervals of mechanical systems are scheduled a priori based on the life of the system, resulting in expensive maintenance scheduling, and often undermining the safety of passengers. Going forward, the actual usage of a vehicle will be used to predict stresses in its structure, and therefore, to define a specific maintenance scheduling. Machine learning (ML) algorithms can be used to map a reduced set of data coming from real-time measurements of a structure into a detailed/high-fidelity finite element analysis (FEA) model of the same system. As a result, the FEA-based ML approach will directly estimate the stress distribution over the entire system during operations, thus improving the ability to define ad-hoc, safe, and efficient maintenance procedures. The paper initially presents a review of the current state-of-the-art of ML methods applied to finite elements. A surrogate finite element approach based on ML algorithms is also proposed to estimate the time-varying response of a one-dimensional beam. Several ML regression models, such as decision trees and artificial neural networks, have been developed, and their performance is compared for direct estimation of the stress distribution over a beam structure. The surrogate finite element models based on ML algorithms are able to estimate the response of the beam accurately, with artificial neural networks providing more accurate results.

Application of feed forward and recurrent neural networks in simulation of left ventricular mechanics

An understanding of left ventricle (LV) mechanics is fundamental for designing better preventive, diagnostic, and treatment strategies for improved heart function. Because of the costs of clinical and experimental studies to treat and understand heart function, respectively, in-silico models play an important role. Finite element (FE) models, which have been used to create in-silico LV models for different cardiac health and disease conditions, as well as cardiac device design, are time-consuming and require powerful computational resources, which limits their use when real-time results are needed. As an alternative, we sought to use deep learning (DL) for LV in-silico modeling. We used 80 four-chamber heart FE models for feed forward, as well as recurrent neural network (RNN) with long short-term memory (LSTM) models for LV pressure and volume. We used 120 LV-only FE models for training LV stress predictions. The active material properties of the myocardium and time were features for the LV pressure and volume training, and passive material properties and element centroid coordinates were features of the LV stress prediction models. For six test FE models, the DL error for LV volume was 1.599 ± 1.227 ml, and the error for pressure was 1.257 ± 0.488 mmHg; for 20 LV FE test examples, the mean absolute errors were, respectively, 0.179 ± 0.050 for myofiber, 0.049 ± 0.017 for cross-fiber, and 0.039 ± 0.011 kPa for shear stress. After training, the DL runtime was in the order of seconds whereas equivalent FE runtime was in the order of several hours (pressure and volume) or 20 min (stress). We conclude that using DL, LV in-silico simulations can be provided for applications requiring real-time results.

Real-time biomechanics using the finite element method and machine learning: Review and perspective

PURPOSE

The finite element method (FEM) is the preferred method to simulate phenomena in anatomical structures. However, purely FEM-based mechanical simulations require considerable time, limiting their use in clinical applications that require real-time responses, such as haptics simulators. Machine learning (ML) approaches have been proposed to help with the reduction of the required time. The present paper reviews cases where ML could help to generate faster simulations, without considerably affecting the performance results.

METHODS

This review details the ML approaches used, considering the anatomical structures involved, the data collection strategies, the selected ML algorithms, with corresponding features, the metrics used for validation, and the resulting time gains.

RESULTS

A total of 41 references were found. ML algorithms are mainly trained with FEM-based simulations in 32 publications. The preferred ML approach is neural networks, including deep learning in 35 publications. Tissue deformation is simulated in 18 applications, but other features are also considered. The average distance error and mean squared error are the most frequently used performance metrics, in 14 and 17 publications, respectively. The time gains were considerable, going from hours or minutes for purely FEM-based simulations to milliseconds, when using ML.

CONCLUSIONS

ML algorithms can be used to accelerate FEM-based biomechanical simulations of anatomical structures, possibly reaching real-time responses. Fast and real-time simulations of anatomical structures, generated with ML algorithms, can help to reduce the time required by FEM-based simulations and accelerate their adoption in the clinical practice.

Classification of aortic stenosis using conventional machine learning and deep learning methods based on multi-dimensional cardio-mechanical signals

This paper introduces a study on the classification of aortic stenosis (AS) based on cardio-mechanical signals collected using non-invasive wearable inertial sensors. Measurements were taken from 21 AS patients and 13 non-AS subjects. A feature analysis framework utilizing Elastic Net was implemented to reduce the features generated by continuous wavelet transform (CWT). Performance comparisons were conducted among several machine learning (ML) algorithms, including decision tree, random forest, multi-layer perceptron neural network, and extreme gradient boosting. In addition, a two-dimensional convolutional neural network (2D-CNN) was developed using the CWT coefficients as images. The 2D-CNN was made with a custom-built architecture and a CNN based on Mobile Net via transfer learning. After the reduction of features by 95.47%, the results obtained report 0.87 on accuracy by decision tree, 0.96 by random forest, 0.91 by simple neural network, and 0.95 by XGBoost. Via the 2D-CNN framework, the transfer learning of Mobile Net shows an accuracy of 0.91, while the custom-constructed classifier reveals an accuracy of 0.89. Our results validate the effectiveness of the feature selection and classification framework. They also show a promising potential for the implementation of deep learning tools on the classification of AS.

Generating wall shear stress for coronary artery in real-time using neural networks: Feasibility and initial results based on idealized models

Computational fluid dynamics (CFD) and medical imaging can be integrated to derive some important hemodynamic parameters such as wall shear stress (WSS). However, CFD suffers from a relatively long computational time that usually varies from dozens of minutes to hours. Machine learning is a popular tool that has been applied to many fields, and it can predict outcomes fast and even instantaneously in most applications. This study aims to use machine learning as an alternative to CFD for generating hemodynamic parameters in real-time diagnosis during medical examinations. To perform the feasibility study, we used CFD to model the blood flow in 2000 idealized coronary arteries, and the calculated WSS values in these models were used as the dataset for training and testing. The preparation of the dataset was automated by scripts programmed in Python, and OpenFOAM was used as the CFD solver. We have explored multivariate linear regression, multi-layer perceptron, and convolutional neural network architectures to generate WSS values from coronary artery geometry directly without CFD. These architectures were implemented in TensorFlow 2.0. Our results showed that these algorithms were able to generate results in less than 1 s, proving its capability in real-time applications, in terms of computational time. Based on the accuracy, convolutional neural network outperformed the other architectures with a normalized mean absolute error of 2.5%. Although this study is based on idealized models, to the best of our knowledge, it is the first attempt to predict WSS in a stenosed coronary artery using machine learning approaches.

Prediction of Left Ventricular Mechanics Using Machine Learning

The goal of this paper was to provide a real-time left ventricular (LV) mechanics simulator using machine learning (ML). Finite element (FE) simulations were conducted for the LV with different material properties to obtain a training set. A hyperelastic fiber-reinforced material model was used to describe the passive behavior of the myocardium during diastole. The active behavior of the heart resulting from myofiber contractions was added to the passive tissue during systole. The active and passive properties govern the LV constitutive equation. These mechanical properties were altered using optimal Latin hypercube design of experiments to obtain training FE models with varied active properties (volume and pressure predictions) and varied passive properties (stress predictions). For prediction of LV pressures, we used eXtreme Gradient Boosting (XGboost) and Cubist, and XGBoost was used for predictions of LV pressures, volumes as well as LV stresses. The LV pressure and volume results obtained from ML were similar to FE computations. The ML results could capture the shape of LV pressure as well as LV pressure-volume loops. The results predicted by Cubist were smoother than those from XGBoost. The mean absolute errors were as follows: XGBoost volume: 1.734 ± 0.584 ml, XGBoost pressure: 1.544 ± 0.298 mmHg, Cubist volume: 1.495 ± 0.260 ml, Cubist pressure: 1.623 ± 0.191 mmHg, myofiber stress: 0.334 ± 0.228 kPa, cross myofiber stress: 0.075 ± 0.024 kPa, and shear stress: 0.050 ± 0.032 kPa. The simulation results show ML can predict LV mechanics much faster than the FE method. The ML model can be used as a tool to predict LV behavior. Training of our ML model based on a large group of subjects can improve its predictability for real world applications.