Automated generation of tissue-specific three-dimensional finite element meshes containing ellipsoidal cellular inclusions

Contributions of deep learning to automated numerical modelling of the interaction of electric fields and cartilage tissue based on 3D images

Electric fields find use in tissue engineering but also in sensor applications besides the broad classical application range. Accurate numerical models of electrical stimulation devices can pave the way for effective therapies in cartilage regeneration. To this end, the dielectric properties of the electrically stimulated tissue have to be known. However, knowledge of the dielectric properties is scarce. Electric field-based methods such as impedance spectroscopy enable determining the dielectric properties of tissue samples. To develop a detailed understanding of the interaction of the employed electric fields and the tissue, fine-grained numerical models based on tissue-specific 3D geometries are considered. A crucial ingredient in this approach is the automated generation of numerical models from biomedical images. In this work, we explore classical and artificial intelligence methods for volumetric image segmentation to generate model geometries. We find that deep learning, in particular the StarDist algorithm, permits fast and automatic model geometry and discretisation generation once a sufficient amount of training data is available. Our results suggest that already a small number of 3D images (23 images) is sufficient to achieve 80% accuracy on the test data. The proposed method enables the creation of high-quality meshes without the need for computer-aided design geometry post-processing. Particularly, the computational time for the geometrical model creation was reduced by half. Uncertainty quantification as well as a direct comparison between the deep learning and the classical approach reveal that the numerical results mainly depend on the cell volume. This result motivates further research into impedance sensors for tissue characterisation. The presented approach can significantly improve the accuracy and computational speed of image-based models of electrical stimulation for tissue engineering applications.

Numerical Simulations as Means for Tailoring Electrically Conductive Hydrogels Towards Cartilage Tissue Engineering by Electrical Stimulation

Cartilage regeneration is a clinical challenge. In recent years, hydrogels have emerged as implantable scaffolds in cartilage tissue engineering. Similarly, electrical stimulation has been employed to improve matrix synthesis of cartilage cells, and thus to foster engineering and regeneration of cartilage tissue. The combination of hydrogels and electrical stimulation may pave the way for new clinical treatment of cartilage lesions. To find the optimal electric properties of hydrogels, theoretical considerations and corresponding numerical simulations are needed to identify well-suited initial parameters for experimental studies. We present the theoretical analysis of a hydrogel in a frequently used electrical stimulation device for cartilage regeneration and tissue engineering. By means of equivalent circuits, finite element analysis, and uncertainty quantification, we elucidate the influence of the geometric and dielectric properties of cell-seeded hydrogels on the capacitive-coupling electrical field stimulation. Moreover, we discuss the possibility of cellular organisation inside the hydrogel due to forces generated by the external electric field. The introduced methodology is easily reusable by other researchers and allows to directly develop novel electrical stimulation study designs. Thus, this study paves the way for the design of future experimental studies using electrically conductive hydrogels and electrical stimulation for tissue engineering.

The potential for intercellular mechanical interaction: simulations of single chondrocyte versus anatomically based distribution

Computational studies of chondrocyte mechanics, and cell mechanics in general, have typically been performed using single cell models embedded in an extracellular matrix construct. The assumption of a single cell microstructural model may not capture intercellular interactions or accurately reflect the macroscale mechanics of cartilage when higher cell concentrations are considered, as may be the case in many instances. Hence, the goal of this study was to compare cell-level response of single and eleven cell biphasic finite element models, where the latter provided an anatomically based cellular distribution representative of the actual number of cells for a commonly used [Formula: see text] edge cubic representative volume in the middle zone of cartilage. Single cell representations incorporated a centered single cell model and eleven location-corrected single cell models, the latter to delineate the role of cell placement in the representative volume element. A stress relaxation test at 10% compressive strain was adopted for all simulations. During transient response, volume- averaged chondrocyte mechanics demonstrated marked differences (up to 60% and typically greater than 10%) for the centered single versus the eleven cell models, yet steady-state loading was similar. Cell location played a marked role, due to inhomogeneity of the displacement and fluid pressure fields at the macroscopic scale. When the single cell representation was corrected for cell location, the transient response was consistent, while steady-state differences on the order of 1-4% were realized, which may be attributed to intercellular mechanical interactions. Anatomical representations of the superficial and deep zones, where cells reside in close proximity, may exhibit greater intercellular interactions, but these have yet to be explored.

Multiscale cartilage biomechanics: technical challenges in realizing a high-throughput modelling and simulation workflow

Understanding the mechanical environment of articular cartilage and chondrocytes is of the utmost importance in evaluating tissue damage which is often related to failure of the fibre architecture and mechanical injury to the cells. This knowledge also has significant implications for understanding the mechanobiological response in healthy and diseased cartilage and can drive the development of intervention strategies, ranging from the design of tissue-engineered constructs to the establishment of rehabilitation protocols. Spanning multiple spatial scales, a wide range of biomechanical factors dictate this mechanical environment. Computational modelling and simulation provide descriptive and predictive tools to identify multiscale interactions, and can lead towards a greater comprehension of healthy and diseased cartilage function, possibly in an individualized manner. Cartilage and chondrocyte mechanics can be examined in silico, through post-processing or feed-forward approaches. First, joint-tissue level simulations, typically using the finite-element method, solve boundary value problems representing the joint articulation and underlying tissue, which can differentiate the role of compartmental joint loading in cartilage contact mechanics and macroscale cartilage field mechanics. Subsequently, tissue-cell scale simulations, driven by the macroscale cartilage mechanical field information, can predict chondrocyte deformation metrics along with the mechanics of the surrounding pericellular and extracellular matrices. A high-throughput modelling and simulation framework is necessary to develop models representative of regional and population-wide variations in cartilage and chondrocyte anatomy and mechanical properties, and to conduct large-scale analysis accommodating a multitude of loading scenarios. However, realization of such a framework is a daunting task, with technical difficulties hindering the processes of model development, scale coupling, simulation and interpretation of the results. This study aims to summarize various strategies to address the technical challenges of post-processing-based simulations of cartilage and chondrocyte mechanics with the ultimate goal of establishing the foundations of a high-throughput multiscale analysis framework. At the joint-tissue scale, rapid development of regional models of articular contact is possible by automating the process of generating parametric representations of cartilage boundaries and depth-dependent zonal delineation with associated constitutive relationships. At the tissue-cell scale, models descriptive of multicellular and fibrillar architecture of cartilage zones can also be generated in an automated fashion. Through post-processing, scripts can extract biphasic mechanical metrics at a desired point in the cartilage to assign loading and boundary conditions to models at the lower spatial scale of cells. Cell deformation metrics can be extracted from simulation results to provide a simplified description of individual chondrocyte responses. Simulations at the tissue-cell scale can be parallelized owing to the loosely coupled nature of the feed-forward approach. Verification studies illustrated the necessity of a second-order data passing scheme between scales and evaluated the role that the microscale representative volume size plays in appropriately predicting the mechanical response of the chondrocytes. The tools summarized in this study collectively provide a framework for high-throughput exploration of cartilage biomechanics, which includes minimally supervised model generation, and prediction of multiscale biomechanical metrics across a range of spatial scales, from joint regions and cartilage zones, down to that of the chondrocytes.