## Introduction

The length of time the scaffold needs to remain inside the body depends on the patient’s condition. In other words, the scaffold durability will need to be estimated through the simulation of its degradation inside the body to obtain a lifespan adaptable to the patient´s needs. To carry out this simulation, we required knowledge of the factors influencing the degradation of PCL within the spinal cord. Subsequently, we executed a literature search about the degradative effects of enzymatic activity and chemical medium on the scaffold.

When researching the enzymatic activity that would influence the degradation of PCL in the spinal cord, we found the enzymes NADPH oxidase and NAPD oxidase to be involved in the first step of the oxidative burst, which forms of free radicals by oxidative burst, that damages the surface of the polymer (Ali, Zhong, Doherty and Williams, 1993).

However, we concluded that the enzymatic degradation rate was small enough to be negligible, due to the lack of human enzymes specialised in hydrolysing PCL (Bartnikowski, Dargaville, Ivanovski and Hutmacher, 2019). Furthermore, by exploring the paper “The return of a forgotten polymer—Polycaprolactone in the 21st century” (Woodruff and Hutmacher, 2010) we concluded that the bioabsorbable polymer would break down by ‘Bulk Degradation’. Bulk degradation happens when the water has infiltrated all the polymer structure from a very early stage of the implantation - which it will in the case of our scaffold due to the high porosity, and therefore the random chain scissions of ester linkages begin throughout the whole structure at the same rate (Woodruff and Hutmacher, 2010). This degradative process is not enzyme driven since the carboxylic acid end groups of the PCL autocatalyze the reaction (Ali, Zhong, Doherty and Williams, 1993). When the molecular weight of the structure has reached its critical molecular weight, which in the case of PCL is 5kDa (Hoque et al., 2012), it begins to be degraded intracellularly, since the polymer chains are small enough to be bioabsorbed.

Concerning the chemical medium, overall, non-enzymatic, random chain scission has been described as a dominant driver of PCL degradation and can proceed through both acid and base catalysed ester hydrolysis. We considered the Fenton Reaction as the main cause of PCL degradation inside the spinal cord. The Fenton reaction occurs in the presence of iron and causes the formation of hydroxyl radicals, which highly contribute to the damage of the polymer (Ali, Zhong, Doherty and Williams, 1993). This process occurs after a spinal cord injury due to the accumulation of reactive oxygen species and the presence of iron in large amounts (due to the haemorrhage) and promotes ferroptosis; an iron dependant cell death (Feng et al., 2019).

The next essential step in creating a simulation is to choose the most appropriate method. Initially, the simulation method chosen was to create a virtual 3D model that would show the different phases of the degradation by considering the macro-architecture as well as the micro-architecture. After consulting Dr. Jack Lee, a lecturer at KCL and expert in computational modelling and patient-specific simulations for clinical translation, we realised an accurate computational simulation would be too complex to develop as it required many material and structural properties, difficult to acquire even in a lab. Therefore, we focused on an approximate mathematical set of equations that would describe the degradation of the scaffold over time. From our literature research on degradation of polymers inside the body, Vieira et al., (2011), suggested that if the water is uniformly diffused within the polymer the following set of equations could be used to model the change in molecular weight:

$\frac{dC}{dt} = kEwC = u_mC$

$Mn_t = Mn_0e^(-u_mt)$

Where E is the concentration of ester groups, C is the concentration of carboxyl groups and w is the concentration of water of the polymer. k is the hydrolysis kinetic constant and um is the hydrolysis rate (Vieira et al., 2011).

From our previous conclusion we know our scaffold would degrade by bulk degradation, therefore, the water is uniformly diffused across the structure and this set of equations can be used. However, the equations make use of data that we could only acquire in the lab.

After studying the paper “Effect of porosity on long-term degradation of poly (ε-caprolactone) scaffolds and their cellular response” (Zhang et al., 2013), we concluded their method to obtain an approximative degradation constant was accurate to be used in our research, because it is based on the porosity of the scaffold, an element that we were able to model. The equation in question is, which can be determined experimentally:

$\lambda = A\frac{\varepsilon ^3}{(1-\varepsilon )^2} + B$

Where λ is the degradation rate, ε is the porosity and A and B are constants obtained from the graph below, which correspond to 1.85E-4 and 1.3E-2 respectively (Zhang et al., 2013).

### Simulation and Results

Therefore, using these equations and relations, we created an open-source MATLAB program that allows the user to obtain an estimation of data about the degradation of their scaffold. This was especially useful as we were unable to validate our design due to the lack of lab access. The code has several options to simulate the degradation: using a known initial molecular weight and degradation rate, using a known initial molecular weight and porosity, and an estimation of initial molecular weight based on the required length of time before critical molecular weight is reached. This code may be found here.

Initially, we planned to simulate the degradation of the scaffold, while considering the mussel foot protein coating. However, upon discussion with Dr. Jack Lee, we were advised that due to the coating being a thin layer, it would have a negligible influence on the degradation of the polymer scaffold. Therefore we decided to remove it from the factors defining the degradation. Subsequently, it means that our open-source degradation code is widely applicable beyond our specific use with the mussel foot protein. Conversely, the assumptions that we made were that the scaffold would degrade uniformly via bulk degradation and, following Hoque (2012), was that the material was dissolved and dried.

In our case we ran the simulation to find the molecular weight and degradation rate required for our scaffold. We know the critical molecular mass of PCL is 5kDa (Hoque et al., 2012) - i.e. this is the limit of the molecular weight such that the scaffold remains useful. Linked to the microarchitecture research, the ideal porosity was between 50-70%. Our modelling of such microarchitecture was done with a 58% porosity, therefore, to be coherent, we have chosen to use a porosity of 58% in the simulation (Bayram et al., 2019) (Shahriari et al., 2017).

The Spinal Cord Injury research team found that, in general, a patient takes between 6 to 12 months to stabilise (Alizadeh, Dyck and Karimi-Abdolrezaee, 2019). However, this does not mean that the lesion has fully healed within this time frame. Following this knowledge, our simulation was based on a 12 months period to mimic the natural recovery process and to ensure the scaffold remains structurally sound, providing sustained mechanical support.

Below you can find the results we obtained from the simulation - the output of our program:

The calculated degradation rate based on our porosity is of ~0.013 Daltons per week. Furthermore, based on the requested 12 months (52 weeks) duration requirement, the simulation suggests that our scaffold should have an absolute minimum molecular weight of 9.9351 kilo Daltons initially so that the critical molecular weight is only reached after the 12 months.

### Further Validation Using our Simulation

#### Material validation

The graph above shows the degradation of PLGA (polylactide-co-glycolide) which has a starting molecular weight of 60 kDa that has to last for at least 1 year (8760 hours) to facilitate sufficient axonal regrowth. A PLGA scaffold has a critical molecular weight of 1.2 kDa. Running the simulation produces the following warning error.

By conducting simulations of potential biomaterials such as PCL and PLGA we can design and optimise for the best material type for our scenario. Assumptions that have been made in this simulation are that the samples of PCL and PLGA are dissolved and dried (Hoque, 2012). PLGA is a polymer made of both PGA and PLA, with PGA being a highly crystalline, hydrophilic, aliphatic polyester. Therefore it has a high melting point of 230 °C. PLGA undergoes a process called autocatalysis whereby the carboxylic group causes further degradation. As you can see from our results, a proposed PLGA scaffold will only last approximately 83 days, this is clearly not long enough to be useful.

As you can see from the graph the PLGA scaffold will degrade beyond the critical weight in approximately 2000 hours which is ~83 days. This is an extremely short lifespan. This result led to the ruling out of PLGA as a potential biomaterial and the choosing of PCL as detailed above.

#### Porosity validation

One of the parameters that can be tested within the simulation is porosity – as a percentage of the volume of the scaffold. In order to further the design process and verify our choice of parameters, we investigated the effect of higher porosity on the degradation, using the porosity feature of our software based upon the relation found by Zhang et al. (2013). As depicted in Fig. 6, a rise in porosity between 50-70% shows a shallower decrease in time taken to degrade, but the values beyond this (80-90%) show a much larger acceleration in degradation. This trend opposes that of other materials, such as PLGA scaffolds, that demonstrate a quicker acceleration with lower porosity (Lu et al., 2000) - which may have proved to be a benefit as, typically, a greater porosity, results in more growth. However, as previously discussed (and further demonstrated), PLGA decays at a much greater rate than PCL and so was deemed unsuitable as a material choice.

This range of 50-70% porosity for best degradation, follows the optimum range for regrowth as discussed within literature (Bayram et al., 2019). Conclusively, we selected a scaffold porosity percentage of 58%, to be a good balance between longer degradation rate, mechanical integrity and axonal regrowth.

# References:

• Ali, S., Zhong, S., Doherty, P. and Williams, D., 1993. Mechanisms of polymer degradation in implantable devices. Biomaterials, 14(9), pp.648-656.
• Alizadeh, A., Dyck, S. and Karimi-Abdolrezaee, S., 2019. Traumatic Spinal Cord Injury: An Overview of Pathophysiology, Models and Acute Injury Mechanisms. Frontiers in Neurology, 10.
• Bartnikowski, M., Dargaville, T., Ivanovski, S. and Hutmacher, D., 2019. Degradation mechanisms of polycaprolactone in the context of chemistry, geometry and environment. Progress in Polymer Science, 96, pp.1-20.
• Bayram, C. et al. (2019) ‘Biofaliication of Gelatin Tissue Scaffolds with Uniform Pore Size via Microbubble Assembly’, Macromolecular Materials and Engineering, 304(11), p. 1900394. doi: 10.1002/mame.201900394.
• Feng, S., Yao, X., Zhang, Y., Hao, J., Duan, H., Zhao, C., Sun, C., Li, B., Fan, B., Wang, X., Li, W., Fu, X., Hu, Y., Liu, C. and Kong, X., 2019. Deferoxamine promotes recovery of traumatic spinal cord injury by inhibiting ferroptosis. Neural Regeneration Research, 14(3), p.532.
• Hoque, M., Yong, L. and Ian, P. (2012) ‘MATHEMATICAL MODELING ON DEGRADATION OF 3D TISSUE ENGINEERING SCAFFOLD MATERIALS’, Official Journal of Tissue Engineering and Regenerative Medicine Society of Malaysia, 1(1), pp. 58–61.
• Lu, L. et al. (2000) ‘In vitro and in vivo degradation of porous poly(dl-lactic-co-glycolic acid) foams’, Biomaterials, 21(18), pp. 1837–1845. doi: 10.1016/S0142-9612(00)00047-8.
• Shahriari, D. et al. (2017) ‘Hierarchically Ordered Porous and High-Volume Polycaprolactone Microchannel Scaffolds Enhanced Axon Growth in Transected Spinal Cords’, Tissue Engineering Part A, 23(9–10), pp. 415–425. doi: 10.1089/ten.tea.2016.0378.
• Sun, H., Mei, L., Song, C., Cui, X. and Wang, P., 2006. The in vivo degradation, absorption and excretion of PCL-based implant. Biomaterials, 27(9), pp.1735-1740.
• Vieira, A., Vieira, J., Ferra, J., Magalhães, F., Guedes, R. and Marques, A., 2011. Mechanical study of PLA–PCL fibers during in vitro degradation. Journal of the Mechanical Behavior of Biomedical Materials, 4(3), pp.451-460.
• 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.
• Zhang, Q., Jiang, Y., Zhang, Y., Ye, Z., Tan, W. and Lang, M., 2013. Effect of porosity on long-term degradation of poly (ε-caprolactone) scaffolds and their cellular response. Polymer Degradation and Stability, 98(1), pp.209-218