The Finite Element Method (FEM) has been used in a number of different areas of research, such as orthopedic implant design. Numerical analyses of hip implants and their surface topographies provide important information that can indicate if the connection between bone and implant is good. Although this approach requires less time compared to traditional in vivo studies, it is still time-consuming in situations when a large number of different models need to be created and analyzed. This is the situation with the analysis of a variety of surface topographies, which is needed to better understand the influence of each parameter on shear stress distribution. It is known that higher shear stress values lead to loosening of the contact between femoral bone and hip implant and additional surgical procedures. In order to perform shear stress classification, four algorithms have been considered. Those algorithms were: Support Vector Machines (SVM), K - Nearest Neighbor (KNN), Decision Tree (DT), and Random Forest (RF). A total of 10 model parameters have been used with the previously mentioned classification algorithms in order to obtain information if the shear stress value for the implant will be below the user-defined threshold value (0 – above threshold; 1 – below threshold). The considered parameters were: Number of different radius values (1 or 2); Radius 1 value (>0); Radius 2 value (≥0); Number of half-cylinders lengthwise (>1); Distance between half-cylinders lengthwise (≥0); Number of half-cylinder rows (≥0); Distance between half cylinders rows (≥0); Distance of the first half-cylinder from the edge where loading is defined (≥0); Distance of the last half-cylinder from the edge without loading (≥0); Half cylinder orientation (0 – half-.cylinder follows model length; 1 – half-cylinder follows model width). The database consisted of 60 models, which is the main limitation of this study. The obtained results show that classification algorithms can be useful as a way to have preliminary indications of models that should be further analyzed with FEM. SVM and RF have shown the best results out of the four considered algorithms. For those two algorithms, the following results were obtained: SVM: Precision - 93%; Recall - 92%; F1 score – 92%; RF: Precision - 90%; Recall - 86%; F1 score – 86%. KNN and DT have obtained significantly lower results.

Acknowledgment

This research is supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 952603 - SGABU. This article reflects only the author’s The Commission is not responsible for any use that may be made of the information it contains. The research was funded by the Ministry of Education, Science and Technological Development of the Republic of Serbia, contract number [451-03-68/2022-14/200107 (Faculty of Engineering, University of Kragujevac)].

Digital image processing has become increasingly widespread in biological and medical research as microscopy and screening images have become more complex. Automatic image processing plays an important role in increasing the comprehensibility of imaging data inference and reducing the amount of time and manual labor required to fulfill such tasks. One of such tasks requiring digital image processing is Traction Force Microscopy (TFM). Cells adhere to the extracellular matrix (ECM) and exert traction forces to probe the environment, migrate, maintain tissue integrity and form more complex multicellular structures. TFM has become the preferred methodology to quantify exerted forces at the cell–matrix interface and thereby provide quantitative information on cellular mechanics. Before TFM can be utilized, image processing is necessary in multiple phases of data preparation. Data used in this research was acquired from an in vitro model of sprouting angiogenesis in which Human Umbilical Vein Endothelial Cells (HUVECs) invade a polyethylene glycol (PEG) hydrogel. The data is represented as raw 3-dimensional volumes of cells before and after inhibiting their mechanical activity by means of Cytochalasin D. Currently the image processing for TFM required time consuming manual tuning of image denoising filters and tuning of an image segmentation threshold. The dataset was composed of 125 3D volumes of varying sizes, in height and width as well as in depth. These volumes consisted of 9126 total 2D slices, of which 20% was used as the test set, while 80% was used for neural network training.

In this paper we propose a methodology for automatic image segmentation which alleviates most of the manual labor required from the user. The aforementioned stacks of images contained noise caused by either the equipment used or the environment. This noise had to be reduced for the purpose of increasing the quality of training images and segmentation accuracy. The individual 2D slices of each image stack were introduced into the convolutional neural network, while the previously manually segmented images were used as training masks. The segmentation model is based on the U-Net architecture which was modified for this purpose. The model provides 2D segmented images which are concatenated into a 3D stack to reconstruct the 3D input volume. The model achieved admirable results showed by the intersection over union metric, which is greater than 80%. Future research will focus on the improvement of segmentation results through the creation of new image filtering mechanisms and the introduction of more data.

Acknowledgements: The research was funded by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia, contract number [451-03-47/2023-01/200378 (Institute for Information Technologies, University of Kragujevac)]. This research is also supported by the project that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 952603 (SGABU project). J.B-F. acknowledges the support from the Research Foundation Flanders (FW) grant n. 1259223N. This article reflects only the author's view. The Commission is not responsible for any use that may be made of the information it contains.

In the era of personalized medicine, early and accurate prediction of individuals at high risk of severe consequences of carotid artery stenosis (CAS) which is caused by the atherosclerotic plaque deposition and progression, would allow preventive, therapeutic, or surgical measures before any of life-threatening events take place. It is therefore important to integrate machine learning techniques and computational modeling that can automatically and objectively segment and afterwards mesh the carotid arteries from image data. Among various diagnostic techniques, the US is usually initially recommended CAS diagnostic examination. The US images are used in this study as this diagnostic procedure is low-cost and present at the first level of clinical care, while its improvement in view of image processing and extracted features can be beneficial for more detailed and faster analysis of patients.

Comparing with traditional Computer-Aided Diagnosis (CAD) systems where feature selection and extraction are important steps, deep learning replaces generic imaging features with processing layers that are more complex and more specific to the data. In this study, we have investigated a deep learning approach, which does not require intensity thresholds and imaging features, leading to an optimal use of information and improved prediction power. The automatic carotid artery segmentation was done using U-Net based deep convolutional network (CNN). Deep learning is combined with meshing techniques to perform 3D reconstruction of patient-specific carotid bifurcation, including extraction of atherosclerotic plaque within the arterial wall. The clinical dataset of US anonymized images was used to train and validate the U-Net CNN in automatic segmentation of carotid components (lumen, arterial wall, atherosclerotic plaque) taking into account all three arterial branches (common, internal and external carotid artery). Common classification metrics are considered for one-vs-all quantitative evaluation, including precision (P), recall (R) and F1-score. Results on the test dataset for lumen: P= 0.89, R=0.78, F1=0.83; and for wall: P=0.82 R=0.91, F1=0.85. The results of segmentation are coupled with the reconstruction software to perform a full 3D reconstruction of carotid bifurcation and generate patient-specific 3D mesh. Using the reconstruction software, it is possible to obtain 3D volume information and perform the visualization of carotid structures in different planes and from different angles.

In summary, the automatic extraction of US features related to atherosclerotic carotid artery gives the specific segmentation of individual patient-specific anatomy and can be efficiently integrated with 3D reconstruction. The obtained 3D models can be used for further computational simulations and analyses of individual patients. Integration of deep learning techniques and computer-based modelling can contribute to better risk stratification and assessment of asymptomatic patients with carotid atherosclerotic disease.

Acknowledgements: This paper is supported by the European Union’s Horizon 2020 research and innovation programme TAXINOMISIS (Grant Agreement 755320). This article reflects only the author's view. The Commission is not responsible for any use that may be made of the information it contains. The research is also funded by Serbian Ministry of Education, Science, and Technological Development, grants [451-03-47/2023-01/200378 (Institute for Information Technologies, University of Kragujevac)] and [451-03-47/2023-01/200107 (Faculty of Engineering, University of Kragujevac)].

Mathematical models for multiscale phenomena are typically based on the deduction of a set of differential equations relating the behavior at different involved scales. The number of necessary parameters and the complexity of the equations are crucial in developing effective, predictive models.

A large scientific effort in deducing sophisticated numerical techniques, in particular neural network approaches, characterized the recent literature in the field. This is due to the availability in different fields and in material science of large new data sets down to the nanoscales. New sophisticated approaches exhibit an incredible ability of fitting experimental data even when strongly multiscale nonlinear behavior is observed. The important drawback of these approaches is that typically they are based on statistical based analysis without explicit causal relations, resulting in a poor physical insight.

In this perspective, we propose the adoption of symbolic data modelling techniques, that generate mathematical expressions to fit set of data points using the evolutionary process of Genetic Programming (GP). It is ``Evolutionary Polynomial Regression’’ (EPR) approach integrating regression capability and GP paradigm.

As a result, we obtain explicit analytic formulas that represent the multiscale phenomenon model, elucidating the role of dependent and independent variables, with the important possibility to minimize the complexity of the model in a classical Pareto front.

Specifically, by focusing on the important case of hierarchical biological materials, in this work we deduce numerical techniques that recognize the role of variables in multiscale modelling. Based on a recent set of data at the micro, meso and macroscale of spider silks of different spider species, by means the EPR approach we obtained a set of equations deducing the dependence of the macroscopic thermo-hygro-mechanical behavior from low scales parameters. This set of equations
represents the multiscale model, obtained from data modelling, that we propose to describe the spider silk behavior. Such material behavior constitutes a prototypical example of a physical phenomenon deeply based on a hierarchical behavior and on a complex energetic exchange among different scales. Spider silk is an incredible example on how, based on very `weak’ material components and chemical bonds at the micro scales, it is possible to obtain material behaviors unattained by artificial materials. This is interesting not only for biological aspects, but also in the field of designing new bioinspired materials.

We propose a preliminary analysis of the possibility of adopting such techniques in material science, that in our opinion can represent an important extension of presently adopted numerical methods. As we show, this can be fundamental to gain new physical and modelling insight based on the availability of large new data sets down to the nanoscales. Moreover, we suggest that, due to the generality of our results, the proposed approach can be of interest for many other different fields where multiscale phenomena underly the observed behavior.

In recent years, the use of Artificial Intelligence (AI) models that are informed by physics has become a popular approach for creating data-efficient models in fields such as computational physics, biomedicine, and biomechanics. At the heart of these applications is the complex and adaptable nature of living matter. The adaptations occurring in living systems, such as inflammation, or mechanical changes like growth and remodeling are governed by complex cell-signaling regulatory networks and occur on multiple spatial and temporal scales.

Mechanical modeling of changes in living systems such as peripheral artery plaque progression involves constructing computational models that simulate the development and progression of plaque in the arteries. While these models offer the potential to improve understanding of the underlying mechanisms of plaque formation and to predict the progression of the disease, there are several bottlenecks that can limit their accuracy and effectiveness.

One of the primary challenges is the limited availability of high-quality clinical data including measurements of arterial geometry, blood flow characteristics, and properties of the arterial wall and plaque, all necessary for constructing high quality models. Obtaining this data is often difficult and time-consuming, thus limiting the accuracy and validity of the resulting models.

Creating models that accurately represent complex interactions such as fluid dynamics, solid mechanics, and cellular processes of biological phenomena can be challenging, and models that are too simplistic may fail to capture key aspects of the disease process. In addition, the behavior of arterial plaque is highly variable between patients, and this makes it difficult to develop models that accurately capture the full range of possible disease trajectories.

Finally, creating and running accurate models requires significant computing resources, which can limit the number of simulations that can be performed and can make it difficult to perform sensitivity analyses and explore the effects of different input parameters.

AI has the potential to significantly enhance the accuracy of peripheral artery plaque progression models. The choice of AI method depends on the specific task, available data, and considerations around patient privacy and data security. Machine learning (ML) techniques, including both supervised and unsupervised learning, can be used to predict plaque progression and identify underlying patterns in the data. Genetic Algorithms optimize model parameters for individual patient characteristics and reinforcement learning can determine optimal treatment plans, learning to maximize the reward of minimizing plaque progression. Natural Language Processing (NLP) can be used to extract relevant clinical information from unstructured data, such as clinical notes. Bayesian Networks infer the likelihood of plaque progression based on various patient features. Artificial Neural Networks (ANNs) can model complex relationships between multiple variables, while convolutional and recurrent neural networks, can analyze images or sequential data related to plaque progression.

Acknowledgements

This paper is supported by the DECODE project (www.decodeitn.eu) that has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 956470. This article reflects only the author's view. The Commission is not responsible for any use that may be made of the information it contains.

We simulate biophysical processes at various spatial and temporal scales in order to investigate muscle activity. Multiscale simulations, where Huxley's muscle contraction model defines the microscopic scale material properties of muscle, and continuum muscle mechanics is modeled using the finite element approach, can require a significant amount of computational power. The computations performed at the microscale are the most time-consuming component in these simulations. In our work, we developed a computationally more efficient surrogate model to replace the actual Huxley muscle model in order to reduce the computational demands of the simulations.

Instead of solving Huxley’s muscle contraction equation via a method of characteristics, we train a physics-informed neural network to give an approximate solution. Physics-informed neural networks can produce solutions faster than traditional numerical solvers, although these solutions can be less reliable. Once the neural network is successfully trained we use it in multi-scale simulation instead of the traditional method of characteristics. The neural network takes as an input the position of the nearest available actin-binding site relative to the equilibrium position of the myosin head, time, activation, current and previous stretch and produces the probability of cross-bridge formation. For each of the integration points within the finite element model, a large number of positions of available actin sites are observed and stresses are calculated by summing all of the calculated probabilities of the cross-bridge formation.

In our work, we also present the interface between finite elements, at the macro level, and physics-informed neural network at the micro level. The neural network architecture and weights are loaded at the beginning of the finite element simulation, along with the initialization of the neural network input tensor. The size of the neural network input tensor is dependent on the number of integration points in the model and division along the axis at which the positions of the nearest available acting sites are observed. Values of the observed positions are constant during finite element simulation, so only the values for time, activation, and stretches are changed inside the neural network input tensor. To lower time consumption, values for all of the integration points are filled-in, before the neural network’s prediction. Once the tensors are filled-in, the neural network predicts output values for all the integration points in the model. After the neural network has made its prediction, stresses are calculated based on the probabilities of the attached myosin heads, and the finite element procedure continues with the next iteration or next time step. Our physics-informed surrogate model is around two times faster than the original Huxley model solved by the method of characteristics.

This research was supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 952603 (http://sgabu.eu/). This article reflects only the author's view. The Commission is not responsible for any use that may be made of the information it contains. Research was also supported by the SILICOFCM project that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 777204. This article reflects only the authors’ views. The European Commission is not responsible for any use that may be made of the information the article contains. The research was also funded by the Ministry of Education, Science and Technological Development of the Republic of Serbia, contract numbers [451-03-68/2022-14/200107 (Faculty of Engineering, University of Kragujevac) and 451-03-68/2022-14/200378 (Institute for Information Technologies Kragujevac, University of Kragujevac)].