# Topological Optimisation Structure Design for Personalisation of Hydrogel Controlled Drug Delivery System

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}. This novel method provides a reference for personalised structure design of CDDS in the context of precision medicine.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials Introduction

_{3}H

_{5}NO, Lot No. 20220401), sodium alginate ((C

_{6}H

_{7}NaO

_{6})

_{n}, Lot No. 20210901), N, N-methylene-bis-acrylamide (C

_{7}H

_{10}N

_{2}O

_{2}, Lot No. 20210115), ammonium persulfate ((NH

_{4})

_{2}S

_{2}O

_{8}, Lot No. 20211023) and calcium chloride anhydrous (CaCl

_{2}, Lot No. 20210710) were all purchased from Sinopharm Chemical Reagent Co., Ltd., Shanghai, China.

_{22}H

_{24}N

_{2}O

_{8}·HCl, Lot No. G2116343, Shanghai Aladdin Biochemical Technology Co., Ltd., Shanghai, China) was used as a model drug [40]. The molecular weight is 480.9 g/mol and its saturation concentration in water is 41.59 mol/m

^{3}.

#### 2.2. Forming and Preparation Methods

_{2}solution and swelled until it reached equilibrium.

#### 2.3. Optimisation Model for Hydrogel CDDS

- (1)
- Because the polyacrylamide-sodium alginate dual-network hydrogel degrades insignificantly when stored in water for 6 months [45], the effect of the degradative property of the hydrogel on drug release was ignored. During optimisation, the mechanism of drug release was diffusion, and the diffusion coefficient of the drug in the hydrogel was constant.
- (2)
- In order to meet the clinical conditions as much as possible, the parameters in the model were all values at a temperature of 37 °C.
- (3)
- The drug was only released from the top surface.

- (1)
- The drug-reservoir boundary is the red boundary shown in Figure 1, during the drug delivery, its concentration was 41.59 mol/m
^{3}, which is the saturation concentration of tetracycline hydrochloride. - (2)
- The no-flux boundary is the grey boundary shown in Figure 1, the tetracycline hydrochloride was prevented diffuse from this boundary.
- (3)
- The drug diffusion boundary is the blue boundary shown in Figure 1, the tetracycline hydrochloride diffuses into the external environment through this boundary during drug delivery. For the reason that the external environment simulates the state of body fluid circulation, if any drug diffuses through this boundary, it is removed by the circulation of body fluids. So that the concentration of this drug diffusion boundary was always 0 mol/m
^{3}. - (4)
- According to the method in Section 2.2, the diffusion coefficient of tetracycline hydrochloride in polyacrylamide-sodium alginate hydrogel was 1.8 × 10
^{−11}m^{2}/s, and diffusion coefficient of tetracycline hydrochloride in water was 7.42 × 10^{−10}m^{2}/s.

_{min}≤ x

_{i}≤ 1

_{v}is the volume factor used to limit the proportion of the flow channel in the hydrogel, and V

_{0}is the initial volume of the hydrogel.

_{obj}is the pre-specified target concentration of the hydrogel, C

_{avg}is the average concentration of the hydrogel in the current structure, and f(x) is the absolute value of the difference between the average concentration in the hydrogel and the target concentration.

#### 2.4. Key Methods and Parameters for Solving the Optimisation Model

_{i}) is the diffusion coefficient of the corresponding mesh, D

_{min}is the diffusion coefficient of the drug in the hydrogel, and D

_{max}is the diffusion coefficient of the drug in the flow channels. Ideally, when x

_{i}= 0, the diffusion coefficient of this mesh is the diffusion coefficient of the drug in the hydrogel, and when x

_{i}= 1, the diffusion coefficient of this mesh is equal to the diffusion coefficient of the drug in saline. q is the penalty coefficient.

_{min}is the filtering radius, x

_{f}is the filtered density, and $\nabla $ is the Hamiltonian counter.

_{β}is the threshold value of projection, and x

_{p}is the density value obtained after projection.

^{−3}, and the maximum number of iterations is 1000.

## 3. Results and Discussion

^{3}after 16 d, and a stable concentration gradient in the hydrogel was formed. This value is the average concentration that can be formed in the hydrogel without flow-channel. The saturation concentration of tetracycline hydrochloride in saline at 37 °C is 41.59 mol/m

^{3}. In this study, the target concentration for topological optimisation of the hydrogel CDDS was in the range of 20.79 to 41.59 mol/m

^{3}.

#### 3.1. Effect of Mesh Size on Optimisation Results

^{3}and a volume factor of 0.1, to study the effect of the mesh size on the optimisation results, mesh sizes of 0.08, 0.1, 0.2, 0.3, 0.4, and 0.5 mm were used, respectively.

^{3}can be achieved when the mesh size is less than 0.5 mm.

#### 3.2. Effect of Target Concentration on Optimisation Results

^{3}, with a mesh size of 0.1 mm and a volume factor of 0.1.

^{3}. If the target concentration keeps increasing, the optimised structures of the flow channels will remain unchanged. That means 30 mol/m

^{3}maybe the maximum concentration that can be adjusted with the current parameters.

^{3}, the average concentration in the hydrogel can reach the set value. Whereas, when the target concentrations exceed 28.08 mol/m

^{3}, the average concentration in the hydrogel is maintained at 28.08 mol/m

^{3}. So that the maximum concentration in the hydrogel which can be adjusted is 28.08 mol/m

^{3}. This is consistent with the above conclusion.

^{3}, the high-concentration region increases with the target concentration. When the target concentrations are more than 28.08 mol/m

^{3}, the concentration distributions were unchanged.

#### 3.3. Effect of Volume Factor on Optimisation Results

^{3}at a volume factor of 0.1. In order to meet a higher target concentration, the target concentration was set to 31 mol/m

^{3}, the volume factor was set to 0.2. The optimisation results showed that the average concentration in the hydrogel can reach the target concentration of 31 mol/m

^{3}. The structure of the flow channel is shown in Figure 11. The higher the proportion of flow channels in the hydrogel, the easier it is for the drugs to diffuse. So the increase in the volume factor leads to an increase in the maximum adjustable concentration in the hydrogel.

^{3}. The volume factors were set to 0.1, 0.2, 0.3, 0.4, and 0.5, respectively, the remaining parameters were unchanged for the structural optimisation.

^{3}.

^{3}. So that a reasonable adjustable range of the target concentration in hydrogel is 20.79 to 31.04 mol/m

^{3}.

#### 3.4. Hydrogel CDDS In Vitro Experiment

## 4. Conclusions

^{3}. Based on in vitro experiments, the CDDS can control drug release within 7 days, while the cumulative release curve tends to zero-order release. In order to the designed CDDS meets clinical requirements, the model parameters can be adjusted according to the drug type and dosage of specific clinical requirements. However, this study was carried out as a one-way drug release case; future studies will focus on improving the ability of the simulation model to conform to actual situations.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Numerical simulation results of the CDDS without structure optimisation: (

**a**) Drug concentration in the hydrogel. (

**b**) The curve of average hydrogel concentration with release time.

**Figure 14.**Photographs of the mould and sample used in in vitro drug release experiment: (

**a**) Mould of the hydrogel flow channels; (

**b**) Prepared topological hydrogel; (

**c**) Hydrogel CDDS sample.

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**MDPI and ACS Style**

Gao, Y.; Li, T.; Meng, F.; Hou, Z.; Xu, C.; Yang, L. Topological Optimisation Structure Design for Personalisation of Hydrogel Controlled Drug Delivery System. *Materials* **2023**, *16*, 2687.
https://doi.org/10.3390/ma16072687

**AMA Style**

Gao Y, Li T, Meng F, Hou Z, Xu C, Yang L. Topological Optimisation Structure Design for Personalisation of Hydrogel Controlled Drug Delivery System. *Materials*. 2023; 16(7):2687.
https://doi.org/10.3390/ma16072687

**Chicago/Turabian Style**

Gao, Yang, Tan Li, Fanshu Meng, Zhenzhong Hou, Chao Xu, and Laixia Yang. 2023. "Topological Optimisation Structure Design for Personalisation of Hydrogel Controlled Drug Delivery System" *Materials* 16, no. 7: 2687.
https://doi.org/10.3390/ma16072687