Conference Agenda

The segmentation of computed tomography (CT) scans allows to define patient-specific computational models for the development of targeted tissue engineering applications. However, the segmentation of these images does not provide an accurate definition of the soft tissues. For cervical spine models, this problem is observed when rebuilding intervertebral discs (IVD), facet joints and ligaments, requiring adjustments on the geometry of these structures. In the literature, there is no consensual definition of the parameters that characterise these structures, as they provide different results when compared to the benchmark experimental data. Also, recent works use non-linear material properties to achieve a better physiological cervical spine mobility. The aim of this study was to define the role of the components of the cervical spine, on a linear finite element (FE) model, and how can a combination of modelling parameters be adapted to better represent cervical spine mobility and assist on enhancing new tissue engineering strategies. Adjustments on IVD geometry, ligaments insertion and material properties were taken to evaluate if a FE model could replicate experimental data mobility without requiring non-linear material properties.

Three subject-specific models were segmented and converted to FE models in ScanIP (Synopsys, Inc.,USA). The IVD design was based on vertebrae boundaries and experimental data volumes. The segmentation of the IVD was performed by the attribution of different material properties to the Nucleus Pulposus and the Annulus Fibrosus. On Abaqus (Dassault Systèmes, USA), the model was assembled with the cervical spine ligaments. For the ligaments, two parameters were studied: insertion area and number of elements. The range of motion (RoM) of the model, measured on the superior surface of each IVD, was compared with experimental mobility data conducted in Panjabi et al. (2001). Based on the RoM, the influence of patient-specific geometrical features was evaluated.

For validation, the FE model was conditioned to a simultaneous 50N compressive load and 1Nm moment in different directions. The FE model agreed well in flexion where motion for each segment was 7.97° at C4-C5, 5.58° at C5-C6 and 2.84° at C6-C7, as well as in extension where motion for each segment was 6.80° at C4-C5, 4.65° at C5-C6 and 1.67° at C6-C7 which are within the experimental findings. For lateral bending, motion for segment at C4-C5 was 7.92° and at C5-C6 was 5.59° were in accord with the experimental data, however motion for segment at C6-C7 was 2.15° which meant an underprediction by 153%. For axial rotation, motion for segment at C4-C5 was 9.48° and at C5-C6 was 7.35° which overpredicted by 29% and 28%, respectively. For segment at C6-C7 motion was 3.60° which is within the experimental data.

Adjustments on the cervical spine components produced favorable outcomes, when compared to the experimental mobility data. The workflow followed in this study ensured uniform segmentation of cervical spine finite element models and latter adaptations of parameters. Compared to non-linear FE models, this methodology presented similar mobility results with a facilitated segmentation process and linear material properties.

Bone tissue engineering (BTE) scaffolds are used in different situations when there is a need to replace or regenerate bone tissue, such as fractures, tumor resections or joint replacement. Among biocompatible materials bio-Ceramic scaffolds represent an effective solution for BTE applications since they stimulate the bone growth thanks to their affinity with the native bone tissue. The main drawback of ceramic materials is represented by their intrinsic brittleness that makes the failure unpredictable and catastrophic. One of the key challenges in tissue engineering is to design scaffolds with appropriate mechanical properties and pore structures that can carry the load and in the meantime support cell growth and differentiation. To this purpose, we developed a numerical tool able to generate bone-like architectures with tuneable morphometric properties based on stochastic approaches. In particular, the Voronoi tessellation was used to create the three-dimensional scaffold mimicking the natural structure of bone tissue. A predefined number of seeds have been randomly distributed in a cubic domain and the Voronoi tessellation have been created. According to a statistical probability function based on the orientation of the edge of the cells, faces and edges have been removed in order to get a fully interconnected porosity. Finally, the resulting structure have been dilated to get the scaffold architecture. Taking inspiration from the trabecular bone tissue, the model was forced to have a preferential orientation of the rod-like trabeculae along a prescribed direction, no more than four trabeculae converging in one node and control the ratio between rod-like and plate like trabeculae.

The homogenized elastic properties of the scaffolds were characterized using finite element analysis on cubic domains by using the solver ParOSol. A damage-based iterative procedure has been used to assess the macroscopic strength of the scaffold.

The proposed model offers a versatile and effective method for designing ceramic scaffolds for tissue engineering applications. The ability to control the scaffold properties through the Voronoi tessellation allows for the development of customized and patient-specific scaffolds with enhanced mechanical properties, potentially leading to more effective tissue regeneration and repair. In particular, through this model we were able to control the amount of plate-like trabeculae and rod-like trabeculae, their orientation and detect their effect on the macroscopic strength of the scaffold.

In the field of bone tissue engineering (BTE), porous scaffolds gained attention due to their capability to promote tissue regeneration. Recently, triply periodic minimal surfaces (TPMS) scaffolding method became a promising candidate to aid bone tissue renewal. TPMS scaffolds allow tuning of several designing parameters, so the aim of this study was to understand the role of geometry, porosity degree and material non-linearity in the overall mechanical response of the scaffold. For this purpose, different building materials for TPMS scaffolds were simulated using the finite element (FE) method.

The TMPS scaffolds derived from a combination between geometry, Diamond (SD), Gyroid (SG) or Primitive (SP); and porosity, 60%, 70% or 80%. The nine different scaffolds (SD60, SD70, SD80, SG60, SG70, SG80, SP60, SP70 and SP80) were modelled on Abaqus (Dassault systems Simulia Corp., USA). The FE models were generated by the repetition of a cubic structural unit (1 mm side) on a 2x2x4 units configuration and modelled using two materials: VisiJet^® M3 Crystal (approximated as linear elastic, with E=1.46 GPa and ν=0.35), and a viscoelastic gelatin hydrogel (Kalyanam et al., 2009). On a first stage, the mechanical behaviour of the 16-units FE model was compared to a previous study that used FE models of 2-units (Castro et al., 2020). Preliminary results showed different mechanical behaviour on the maximum value and location of von-Mises stress, between 16- and 2- units. Thus, the 16-units scaffolds were considered for the following analysis. The mechanical loading was performed as a displacement-controlled compression along the z-direction of the FE model, applying a compression amplitude (measured along the z-direction) of up to 10% for the linear material and 2% for the hydrogel.

The scaffolds built with the linear elastic material showed a linear trend for each combination of geometry and porosity (R² coefficient from 0.99466 for SP80 to 0.99994 for SD80), in terms of equivalent strain/stress curves, revealing the absence of non-linear behaviour coming from the changes in scaffold geometry. In terms of equivalent stiffness, for each geometry, the Young’s modulus decreases with an increase in porosity, as expected. Furthermore, the SD and SP geometry corresponded to the highest and lowest Young’s Modulus, respectively, for each porosity level. The computational equivalent stiffness was compared with the stiffness values obtained from experimental tests (3D printed scaffolds in Crystal) and homogenisation method, showing considerable differences for the SD geometry and minor variations for SG and SP. However, the homogenisation method assumes an infinite periodicity of units, which probably means that, by increasing the number of units on the FE model, the outputs from these two methods could be closer.

The use of computational FE models allowed to study the mechanical behaviour under compression of TPMS scaffolds. The current outputs suggest that the non-linearities on the mechanical behaviour of TMPS scaffold are not introduced by the scaffold geometry, allowing for the exploration of non-linear building materials. Further work will include experimental tests of stress relaxation, to investigate the effect of geometry on the time-dependent behaviour of these scaffolds.

The application of computational methods to the design and testing process of Bone Tissue Engineering scaffolds is a valuable but complex approach, as the number of structures and materials that can be utilized to create these structures is constantly increasing and with it the time and costs required to accurately assess scaffold properties.

Among the different parameters that need to be defined, the macroscopic strength and the fracture mechanisms are of particular importance for ceramic-based scaffolds, as they are characterized by brittle-like failure and can undergo abrupt rupture processes. Proper assessment of scaffold strength and fracture patterns can aid the design and optimization process and therefore needs to be accurately implemented in the scaffold testing process.

Different crack propagation models exist nowadays, allowing for the computational evaluation of scaffold strength. Explicit methods can be characterized by stability issues, as convergence is conditionally achievable, and tends to limit its analyses to short transient processes. The phase-field approach, which is based on an implicit approach, models crack propagation as a gradient of element damage, allowing for the evaluation of brittle fracture as a quasi-static process. Furthermore, its versatility allows for the implementation of different phenomena, such as corrosion.

The staggered phase-field model created by Molnár et al. for modelling brittle failure was tested on hydroxyapatite-based scaffolds produced with the Robocasting technique. The results of this starting algorithm highlighted discrepancies in the failure mechanism when compared to finite element method results. While the latter displayed vertical cracks along the compression direction, suggesting that tensile stress is the dominating factor for fracture generation, the phase-field results were characterised by diagonally oriented cracks, highlighting a shear-dominated fracture process. This particular failure mode is owed to the specific function assumed for onset and progression of localised damage.

In this work, an alternative form of damage propagation is proposed with the purpose of better simulate the fracture mode observed in ceramic scaffolds subjected to compressive loads.

The aim of this alternative formulation is to account for a higher resistance of the material to shear stresses, and a much higher resistance to compression.

The final crack pattern formation more closely resembles the expected pattern and is therefore able to model the material’s behaviour more accurately, paving the way to the application of the phase-field model on bone tissue engineering scaffolds characterized by structural continuity between different layers along the loading direction, where compression stresses are transferred directly along said direction.

Skin is the body’s largest organ, composed of three layers that vary in properties across its structure and exhibit directional-dependent physical properties. Despite its exceptional healing capacity, the skin is very susceptible to full-thickness wounds that require specialized dressings to promote tissue regeneration. While there are various commercial skin grafting solutions available, they all have limitations that can result in non-native scar formation, for instance, highlighting the need for further investigation in the field. In this study, we investigate the use of fiber scaffolds with micro-scale auxetic geometries for skin tissue engineering applications. Auxetic structures are known to expand in multiple directions when stretched, enabling them to conform to different wound shapes and promote wound healing [1]. By altering the micro-geometry design, these structures can be tuned to provide tailored mechanical properties that match the unique needs of each patient’s wound, which may vary based on location of the wound or patient’s age or gender [2].

We have investigated two types of scaffold micro-scale designs, both comprising interwoven fiber networks to achieve auxetic behavior. These designs are categorized as re-entrant and chiral and exhibit distinct mechanical properties that are determined by the arrangement of interconnections between the fibers. Numerical finite element simulations of these fibrous structures were conducted to predict their mechanical behaviour prior to fabrication by means of a parametric study of each auxetic design. These simulations were generated, calculated and post-processed with a Python script-based software tool developed to automate this process. After numerical analysis, some designs were selected for fabrication and mechanical characterization with uniaxial and biaxial tensile tests to validate the numerical models. Polycaprolactone fiber scaffolds were fabricated using an in-house built melt electro-writing set-up. The multilayer structures were printed with fiber diameters of approximately 20 microns (with pore size around 300 microns) with the aim of developing microstructures that could provide adequate mechanical environment for cells.

Both numerical simulations and experimental tests have revealed that the mechanical behaviour of the printed scaffolds matches the mechanical properties [3] and behavior of skin (J-shaped stress-strain curve), as well as its auxetic behaviour [4]. Mimicking native tissue properties is essential for tissue engineering. Furthermore, comparative analysis of the results revealed differences in stiffness and auxeticity depending on the auxetic design, allowing us to tailor their properties via geometrical changes.

The combination of numerical simulations with a high-end fiber printing process and mechanical testing has enabled us to develop a platform for designing structured fiber scaffolds with tunable mechanical properties for skin tissue regeneration.

References

1. Kim et al, Materials (Basel), 14(22):6821, 2021.
2. Luebberding et al, Skin Res Technol, 20(2):127-35, 2014.
3. Joodaki et al, Proc Inst Mech Eng H, 232(4):323-343, 2018.
4. Dwivedi et al, R Soc Open Sci, 9(3):211301, 2022

Acknowledgements

The authors acknowledge the project LMP 176_21 funded by the Department of Science, University and Knowledge Society of the Government of Aragon.