Team:KCL UK/Model

Model Overview

Finite Element Analysis (FEA) of Scaffold Macro-architecture

Please see Scaffold Modelling page for further, in-depth analysis of our Finite Element Analysis

Mechanical Simulations

Finite Element Analysis is a type of numerical method that is widely used for solving problems involving mathematical models, especially those that contain partial differential equations (PDEs). Our simulations using AutoDesk Inventor and NASTRAN serves as an exploration into the mechanical properties of different scaffold macro-architectures, utilising Finite Element Analysis, to evaluate von Mises properties. We have utilised FEA to simulate the stresses, strains and forces on our five scaffold designs. The results of the simulations are shown in the table below.

Table 1: Overall results for the simulations that were carried out
Cylinder Tube Open Path with CoreOpen Path without CoreChannel
Property Min Max Min Max Min Max Min MaxMin Max
SVM Stress (MPa) 1.11E-05 7.25E-04 1.23E-056.71E-046.61E-066.37E-041.09E-056.55E-041.01E-056.76E-05
SVM Strain 2.47E-06 1.62E-04 2.75E-06 1.50E-04 1.48E-06 1.42E-04 2.43E-06 1.46E-04 2.26E-06 1.51E-04
Displacement (mm) 0 2.30E-04 0 2.63E-04 0 3.04E-04 0 5.37E-04 0 2.60E-04
Applied Force (N) 6.13E-08 2.78E-06 4.60E-08 2.71E-06 1.24E-08 1.97E-06 2.96E-08 2.07E-06 3.56E-08 2.56E-06

Figure 1. Solid von Mises Stress of the Channel Scaffold
Figure 2. Solid von Mises Stress of the Open path without core Scaffold
Figure 3. Solid von Mises Stress of the Open path with core Scaffold
Figure 4. Solid von Mises Stress of the Cylinder Scaffold
Figure 5. Solid von Mises Stress of the Tube Scaffold

Overall, in relation to von Mises Stress, none of the scaffolds exceeded the yield strength of 17.82MPa – indicating that each scaffold is a viable candidate. Due to the large plasticity region of PCL, it is advised that the comparison is made with respect to the yield strength rather than the tensile strength (34.1MPa) (Ragaert, De Baere, Degrieck, & Cardon, 2014). Therefore, under gravitational load none of the scaffolds would be deemed unsuitable due to permanent deformation. We analysed our results and determined that the open path with core scaffold was the optimal design to choose from the five scaffolds when considering the crucial mechanical properties. Each scaffold has 4 parameters which are scored in a range between 1 and 5 with 1 being the highest rank. The lowest total score is best. The open path with core achieved a score of 7. This result agrees with Wong et al., which also found the open path with core to be the most suitable as it supported white matter tracts (central core), allowed extension of myelinated fibres, maintained the defect size in a period of 3 months and axonal regeneration was observed.

Scaffold Degradation Simulation

Please see Scaffold Degradation Modelling page for further, in-depth exploration and description of our scaffold degradation simulation

We have designed a program to model how our PCL scaffold will degrade over time. You can find our open-source MATLAB degradation code on GitHub, here

One of the crucial design parameters that we identified within our scaffold specification list is the degradation of the scaffold. Therefore, we chose to investigate this further to refine and optimise our final design such that the proposed scaffold should degrade alongside axonal regrowth as well as remaining mechanically sound throughout the regenerative stage. Following this, we carried out a literature review to determine the degradation mechanism of polycaprolactone - and found this to be bulk degradation (Woodruff and Hutmacher, 2010). Subsequently, we used the equations presented within these papers to create our own MATLAB program to simulate the degradation of a polymer scaffold - as we found there to be a lack of similar software. This program allows the user to enter an initial molecular weight to be tested against time, providing that either the degradation rate or porosity (if the material is PCL for the latter) is entered. The user interface for this program can be seen in Fig 6. However, the code is easily adjustable for other polymer porosity relations, as long as the equation relating porosity and degradation is known (through experimentation or other means); line 139 within the calRateofDegradation(e,time) function specifies the relationship between k (degradation rate) and e (porosity).

Figure 6: User Interface for degradation code

After the program receives these inputs, a graph is developed to depict the degradation prediction for a specified time frame. Due to the lack of access to the labs, we have used this program to validate our design parameters (material choice, porosity and initial molecular weight). Further information about these validations may be found on the Scaffold Degradation page here. An additional useful design feature that we implemented is the ability to add a critical molecular weight value (the minimum value such that the scaffold remains useful), and if the simulation predicts that the inputted values would decay beyond this in the desired period a warning will be shown to the user.

Most importantly, to ensure that the scaffold lasts a minimum of at least a year, with a porosity of 58%, an absolute minimum starting molecular weight of 9kDa should be used. The program has calculated this minimum value based on a porosity input and specified time frame, and subsequently produced the degradation prediction graph in Fig 7. Following this, we decided to select an initial molecular weight of 60kDa, a commonly used starting value, of which will instead last around 3.5 years and the degradation of this can be seen within Fig 8.

Figure 7: Degradation rate of PCL with a starting Molecular Weight of 9kDa over one year
Figure 8: Degradation rate of PCL with a starting Molecular Weight of 60kDa over 3-3.5 years

We have made this program open-source, so that it may be used to predict the degradation of a polymer scaffold, as we recognised a lack of experimental values within the literature, as well as a lack of a similar resource. The MATLAB code can be found on the GitHub here, and our further applications of the code can be found on the Scaffold Degradation and Contribution Pages.

Mussel Foot Protein Overview

Please see Structural Modelling for further, in-depth analysis our structural model of Pvfp-5β

To better understand and explore the adhesion of our Mussel Foot Protein, Pvfp-5β, to surfaces it is known to adhere to, and also to our prospective Polycaprolactone (PCL) scaffold. We first had to generate a working structural model. A homology model of our Pvfp-5β sequence (UniProt ID: U5Y6U9) was generated using the Phyre-2 web tool (Kelley et al., 2015), with the Human Notch-1 EGFs 11-13 protein (PDB ID: 2VJ3) used as a template sequence. The resulting Pvfp-5β model had a query coverage of 84%, and an identity confidence of 99.7%! Energy minimisation simulations using the GROMACS Molecular Dynamics package were run due to issues with elucidation of one (known) disulphide bond on our Pvfp-5β model. Residues C86-C95 are known to generate a disulphide bond, however on our resultant homology model from Phyre-2, these two residues were too far apart - at a distance of 12.7Å! Successive energy minimisations through GROMACS, and Molecular Dynamics using the YASARA graphical modelling software allowed us to impose this bond.

Our next steps involve carrying out physicochemical analysis on Pvfp-5β using YASARA during Phase II of our project, as we were unable to conduct this over the summer. This research will support our wet lab studies in the next phase as it will provide us with a deeper understanding of our proteins properties, and how it can be manipulated for maximum adhesive efficiency. Figure 9 shows the distribution of Tyrosine (Y) residues across Pvfp-5β - which are inadvertently involved in the adhesion mechanism through oxidation into DOPA. Furthermore, we will build upon our own structural model by semi-rationally designing a more thermostable protein through consensus design. By constructing phylogenetic trees and conducting extended research into the structure and function relationships of the Mfp-5 (the fifth protein to be secreted by the mussel), conducting a consensus design will aid us to improve the biological activity (adhesion), and stability of our protein.

Figure 9 A): 'Cartoon' depiction of Pvfp-5β (blue). All Tyrosine (Y) residues are shown as 'sticks' (purple).
Figure 9 B): Zoomed in 'cartoon' depiction of Pvfp-5β (blue). Tyrosine (Y) (purple) residues Y88, Y90, Y91, Y101, Y102, Y119, Y122 are shown in more clarity (as 'sticks').

In addition to structural modelling, we have conducted substantial research in the implementation of our protein into our system. We have developed a genetic system to polymerise our protein in vitro , and have also generated a genetic algorithm through the iGAM software created by iGEM Calgary 2019, to best predict which mutations will increase the adhesiveness of our protein (Pvfp-5β). Moreover, we have developed protocols for several experiments as part of our engineering cycle. More information regarding Structural Modelling and our Composite Parts can be found on their respective pages. More about Mussel Foot Proteins in general can be found Here.

References for Bioprinting Overview

  • Woodruff, M. and Hutmacher, D., 2010. The return of a forgotten polymer—Polycaprolactone in the 21st century. Progress in Polymer Science, 35(10), pp.1217-1256.

References: Mussel Foot Protein Overview

  • Kelley, L., Mezulis, S., Yates, C., Wass, M. and Sternberg, M., 2015. The Phyre2 web portal for protein modeling, prediction and analysis. Nature Protocols, 10(6), pp.845-858.