Validation of the computational model of a coronary stent: a fundamental step towards in silico trials

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.

An integrated mechanical degradation model to explore the mechanical response of a bioresorbable polymeric scaffold

Simulation of bioresorbable medical devices is hindered by the limitations of current material models. Useful simulations require that both the short- and long-term response must be considered; existing models are not physically-based and provide limited insight to guide performance improvements. This study presents an integrated degradation framework which couples a physically-based degradation model, which predicts changes in both crystallinity (Xc) and molecular weight (Mn), with the results of a micromechanical model, which predicts the effective properties of the semicrystalline polymer. This degradation framework is used to simulate the deployment of a bioresorbable PLLA (Poly (L-lactide) stent into a mock vessel and the subsequent mechanical response during degradation under different diffusion boundary conditions representing neointimal growth. A workflow is established in a commercial finite element code that couples both the immediate and long-term responses. Clinically relevant lumen loss is reported and used to compare different responses and the effect of neo-intimal tissue regrowth post-implantation on degradation and on the mechanical response is assessed. In addition, the effects of possible changes in Xc, which could occur during processing and stent deployment, are explored.

Multi-objective design optimization of bioresorbable braided stents

BACKGROUND AND OBJECTIVES

Bioresorbable braided stents, typically made of bioresorbable polymers such as poly-l-lactide (PLLA), have great potential in the treatment of critical limb ischemia, particularly in cases of long-segment occlusions and lesions with high angulation. However, the successful adoption of these devices is limited by their low radial stiffness and reduced elastic modulus of bioresorbable polymers. This study proposes a computational optimization procedure to enhance the mechanical performance of bioresorbable braided stents and consequently improve the treatment of critical limb ischemia.

METHODS

Finite element analyses were performed to replicate the radial crimping test and investigate the implantation procedure of PLLA braided stents. The stent geometry was characterized by four design parameters: number of wires, wire diameter, initial stent diameter, and braiding angle. Manufacturing constraints were considered to establish the design space. The mechanical performance of the stent was evaluated by defining the radial force, foreshortening, and peak maximum principal stress of the stent as objectives and constraint functions in the optimization problem. An approximate relationship between the objectives, constraint, and the design parameters was defined using design of experiment coupled with surrogate modelling. Surrogate models were then interrogated within the design space, and a multi-objective design optimization was conducted.

RESULTS

The simulation of radial crimping was successfully validated against experimental data. The radial force was found to be primarily influenced by the number of wires, wire diameter, and braiding angle, with the wire diameter having the most significant impact. Foreshortening was predominantly affected by the braiding angle. The peak maximum principal stress exhibited contrasting behaviour compared to the radial force for all parameters, with the exception of the number of wires. Among the Pareto-optimal design candidates, feasible peak maximum principal stress values were observed, with the braiding angle identified as the differentiating factor among these candidates.

CONCLUSIONS

The exploration of the design space enabled both the understanding of the impact of design parameters on the mechanical performance of bioresorbable braided stents and the successful identification of optimal design candidates. The optimization framework contributes to the advancement of innovative bioresorbable braided stents for the effective treatment of critical limb ischemia.

Investigating Balloon-Vessel Contact Pressure Patterns in Angioplasty: In Silico Insights for Drug-Coated Balloons

Drug-Coated Balloons have shown promising results as a minimally invasive approach to treat stenotic arteries, but recent animal studies have revealed limited, non-uniform coating transfer onto the arterial lumen. In vitro data suggested that local coating transfer tracks the local Contact Pressure (CP) between the balloon and the endothelium. Therefore, this work aimed to investigate in silico how different interventional and device parameters may affect the spatial distribution of CP during the inflation of an angioplasty balloon within idealized vessels that resemble healthy femoral arteries in size and compliance. An angioplasty balloon computational model was developed, considering longitudinal non-uniform wall thickness, due to its forming process, and the folding procedure of the balloon. To identify the conditions leading to non-uniform CP, sensitivity finite element analyses were performed comparing different values for balloon working length, longitudinally varying wall thickness, friction coefficient on the balloon-vessel interface, vessel wall stiffness and thickness, and balloon-to-vessel diameter ratio. Findings indicate a significant irregularity of contact between the balloon and the vessel, mainly affected by the balloon's unfolding and longitudinal thickness variation. Mirroring published data on coating transfer distribution in animal studies, the interfacial CP distribution was maximal at the middle of the balloon treatment site, while exhibiting a circumferential pattern of linear peaks as a consequence of the particular balloon-vessel interaction during unfolding. A high ratio of balloon-to-vessel diameter, higher vessel stiffness, and thickness was found to increase significantly the amplitude and spatial distribution of the CP, while a higher friction coefficient at the balloon-to-vessel interface further exacerbated the non-uniformity of CP. Evaluation of balloon design effects revealed that the thicker tapered part caused CP reduction in the areas that interacted with the extremities of the balloon, whereas total length only weakly impacted the CP. Taken together, this study offers a deeper understanding of the factors influencing the irregularity of balloon-tissue contact, a key step toward uniformity in drug-coating transfer and potential clinical effectiveness.

An in silico trials platform for the evaluation of stent design effect in post-implantation outcomes

Bioresorbable Vascular Scaffolds (BVS), developed to allow drug deliver and mechanical support, followed by complete resorption, have revolutionized atherosclerosis treatment. InSilc is a Cloud platform for in silico clinical trials (ISCT) used in the design, development and evaluation pipeline of stents. The platform integrates beyond the state-of-the-art multi-disciplinary and multiscale models, which predict the scaffold's performance in the short/acute and medium/long term. In this study, a use case scenario of two Bioabsorbable Vascular Stents (BVSs) implanted in the same arterial anatomy is presented, allowing the whole InSilc in silico pipeline to be applied and predict how the different aspects of this intervention affect the success of stenting process.

Introduction of a Novel Image-Based and Non-Invasive Method for the Estimation of Local Elastic Properties of Great Vessels

Background: In the context of a growing demand for the use of in silico models to meet clinical requests, image-based methods play a crucial role. In this study, we present a parametric equation able to estimate the elasticity of vessel walls, non-invasively and indirectly, from information uniquely retrievable from imaging. Methods: A custom equation was iteratively refined and tuned from the simulations of a wide range of different vessel models, leading to the definition of an indirect method able to estimate the elastic modulus E of a vessel wall. To test the effectiveness of the predictive capability to infer the E value, two models with increasing complexity were used: a U-shaped vessel and a patient-specific aorta. Results: The original formulation was demonstrated to deviate from the ground truth, with a difference of 89.6%. However, the adoption of our proposed equation was found to significantly increase the reliability of the estimated E value for a vessel wall, with a mean percentage error of 9.3% with respect to the reference values. Conclusion: This study provides a strong basis for the definition of a method able to estimate local mechanical information of vessels from data easily retrievable from imaging, thus potentially increasing the reliability of in silico cardiovascular models.

Towards a Digital Twin of Coronary Stenting: A Suitable and Validated Image-Based Approach for Mimicking Patient-Specific Coronary Arteries

Considering the field of application involving stent deployment simulations, the exploitation of a digital twin of coronary stenting that can reliably mimic the patient-specific clinical reality could lead to improvements in individual treatments. A starting step to pursue this goal is the development of simple, but at the same time, robust and effective computational methods to obtain a good compromise between the accuracy of the description of physical phenomena and computational costs. Specifically, this work proposes an approach for the development of a patient-specific artery model to be used in stenting simulations. The finite element model was generated through a 3D reconstruction based on the clinical imaging (coronary Optical Coherence Tomography (OCT) and angiography) acquired on the pre-treatment patient. From a mechanical point of view, the coronary wall was described with a suitable phenomenological model, which is consistent with more complex constitutive approaches and accounts for the in vivo pressurization and axial pre-stretch. The effectiveness of this artery modeling method was tested by reproducing in silico the stenting procedures of two clinical cases and comparing the computational results with the in vivo lumen area of the stented vessel.

How to Validate in silico Deployment of Coronary Stents: Strategies and Limitations in the Choice of Comparator

This study aims at proposing and discussing useful indications to all those who need to validate a numerical model of coronary stent deployment. The proof of the reliability of a numerical model is becoming of paramount importance in the era of in silico trials. Recently, the ASME V&V Standard Committee for medical devices prepared the V&V 40 standard document that provides a framework that guides users in establishing and assessing the relevance and adequacy of verification and validation activities performed for proving the credibility of models. To the knowledge of the authors, only a few examples of the application of the V&V 40 framework to medical devices are available in the literature, but none about stents. Specifically, in this study, the authors wish to emphasize the choice of a relevant set of experimental activities to provide data for the validation of computational models aiming to predict coronary stent deployment. Attention is focused on the use of ad hoc 3D-printed mock vessels in the validation plan, which could allow evaluating aspects of clinical relevance in a representative but controlled environment.