Radhika Chellasamy¹, Sathish Thanikodi², Kamesh Krishnamoorthy³, Gnanavel Balakrishnan Kannaiyan⁴ , Ragavanantham Shanmugam⁵ and Monsuru Ramoni⁶

¹Department of Mechanical Engineering, Saveetha Engineering College, Thandalam, Chennai, Tamil Nadu, India.

²Department of Thermal Engineering, Saveetha School of Engineering, Chennai, Tamil Nadu, India.

³Tool and Die Making, Murugappa Polytechnic College, Chennai, Tamil Nadu, India.

⁴Department of Mechanical Engineering, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur.Tamil Nadu, India.

⁵Department of Engineering and Technology, Fairmont State University, West Virginia, United States of America.

⁶Industrial Engineering, Navajo Technical University, NM, United States of America.

Corresponding Author E-mail: radhikasky35@gmail.com

DOI : https://dx.doi.org/10.13005/bpj/2987

Abstract

To facilitate the delivery of drugs into the skin structure, microneedles play a pivotal role. Unlike conventional hypodermic syringes, microneedles penetrate only the dermis layer, avoiding nerve receptors and resulting in a painless injection. However, when a drug is administered into the skin, microneedles may undergo bending and buckling, leading to structural failure. Such failure can cause the drug to remain beneath the skin, potentially creating complications. Preventing the catastrophe of microneedle failure necessitates a close examination of parameters involved in the bending and buckling process. In this paper, we focus on buckling analysis, as the majority of microneedle failures are attributed to the buckling effect. We perform buckling analysis through finite element analysis to predict the critical buckling load (Pcr). This analysis helps determine the maximum load that a microneedle can withstand. We conduct this analysis using two modes: linear and non-linear (post-buckling analysis). By varying the tip diameter of the microneedle (20µm, 40µm, 60µm, 80µm, 100µm), we can identify the safe insertion load.

Keywords

Buckling analysis; Critical buckling load; Finite element analysis; Polycarbonate microneedle; post-buckling behavior

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Copy the following to cite this article: Chellasamy R, Thanikodi S, Krishnamoorthy K, Kannaiyan G. B, Shanmugam R, Ramoni M. Linear and Post-Buckling Analysis of Biocompatible Polymer Microneedle for Transdermal Drug Delivery. Biomed Pharmacol J 2024;17(3).

Copy the following to cite this URL: Chellasamy R, Thanikodi S, Krishnamoorthy K, Kannaiyan G. B, Shanmugam R, Ramoni M. Linear and Post-Buckling Analysis of Biocompatible Polymer Microneedle for Transdermal Drug Delivery. Biomed Pharmacol J 2024;17(3). Available from: https://bit.ly/3Y8U1xm

Introduction

Microneedles are utilized to deliver drugs through micron-sized patches. These patches are meticulously designed so that when applied to the skin, the micron-sized needles penetrate the skin to deliver the drug. The microneedles only reach up to the dermis layer, ensuring a painless dose. While a variety of microneedles are available today, the development of a painless and safe needle remains a challenging process. Microneedles are classified based on the fabrication process, shapes, types, drug delivery approaches, and materials. Regarding the fabrication process, microneedles can be categorized as in-plane and out-of-plane microneedles^{1, 2, 3, 4}. The variation depends on the needles which protrude in and out of the base surface. A variety of microneedle shapes is reported in the literature such as cylinder, cone, pyramid, tapered, and several shapes as mentioned in Table I⁵. Based on the types and drug delivery approach, the microneedles consist of solid, coated, hollow, and dissolving microneedles. The solid microneedles work by generating pores on the skin by insertion thereby applying the drug to the skin ^6,7. The coated microneedles encompass solid microneedle coated with the drug.  The coating of drugs is demonstrated by a predictable film coating process ⁸. The hollow microneedles are intended to generate a hollow path for carrying and delivering the drug ^8,9,10. The dissolving microneedles are designed in such a way the needles gets dissolved once it is injected into the skin ¹¹, ¹². 

Table 1: Classification of microneedles based on the shapes.

Geometrical shape	References
Cylinder	13, 14, 15
Cone	16, 17, 14, 18,  19, 20, 21
Pyramid	Square – 22, 20, 23, 24, 25
	Triangular – 26, 27
	Octahedral- 28
Tapered	29, 30, 31,32, 13
Spear	24, 7
Spherical pedestal	33
Candle-like	7, 34
Bullet-shaped	35, 36, 37
Spike	4, 38, 7
Lancet	14

Table 2: Material properties

Structure	Material	Young’s modulus, E	Density, ρ	Poisson ratio, ν	Ultimate stress, σut	References
Unit	–	GPa	kg/m3	–	MPa	–
Microneedle	Polycarbonate	2.4	1200	0.37	55	39
	Silicon	162	2330	0.22	700	40
		168.9	2329	0.3	–	41
Skin	Aluminium	70	2660	0.3	275	42
	Porcine skin	0.00435	–	–	–	43

 

Materials and Methods

Microneedles are made from a variety of materials, including silicon, glass, metal, composites, and polymers. The current trend in microneedle development places a strong emphasis on polymer materials to create biocompatible microneedles for safe insertion. The selection of the polymer material for microneedles is contingent upon the specific drug, the type of disease being treated, and the desired immune response. ⁴⁴, ⁴⁵. The polymer material selection and the guidelines for the appropriate fabrication process is discussed ⁴⁶.  The polycarbonate a biocompatible polymer microneedle is selected for predicting the structural behavior using the numerical technique. The geometrical dimensions of the cone-shaped microneedle is considered as a reference from the literature ⁴⁷.  The properties applied to the microneedle are listed in Table II.

Theoretical study: Microneedle Buckling Effect

The buckling behavior of a microneedle is primarily determined by its length, yield strength, and tip diameter. Longer microneedles with lower yield strength are more likely to experience buckling ⁴⁸. Once the needle starts to buckle, further increasing the applied load will make the microneedle critically buckle leading to fracture ⁴⁸.  The tip diameter as well depends on the buckling effect. Having a sharp tip, the microneedle effortlessly gets inserted into the skin thereby preventing the buckling effect ⁴⁹.  As the majority of the microneedle failure is caused by buckling, identifying the buckling causing parameters and controlling the effects will lead to a safe insertion. The theoretical study in predicting the critical buckling actions is deliberated ⁵⁰.

The bending moment equation in predicting the critical load is given as (1).

The critical buckling load (Pcr)considered for the tapered structure is given as ⁵¹ in equation (2)

The critical buckling load derived for the hollow conical structure is specified from equation (1) as ³².

Numerical Analysis

Linear Buckling Analysis

Buckling analysis of the microneedle is conducted using two methods: linear buckling mode with a linear perturbation procedure in the Abaqus module and non-linear buckling using the Static Riks algorithm. In the linear buckling analysis, the microneedle is meshed using the C3D10 – 10-node quadratic tetrahedron element, effectively discretizing the model. To apply loads consistently on the microneedle structure, a reference point is created on the top surface of the microneedle. Initially, a 1N load is applied to the top reference point, and the bottom surface is constrained to arrest all degrees of freedom. This analysis is carried out for microneedle tip diameters of 20µm, 40µm, 60µm, 80µm, and 100µm. The results obtained from the linear buckling analysis for various tip diameters are presented in Table III, which includes eigenvalues, reaction forces, displacements, and displacement rotations. As the tip diameter increases, the eigenvalue also increases, while the reaction force, displacement, and displacement rotation vary. Critical buckling loads are determined for each diameter using the linear technique: Pcr (20 µm) = 0.50183, Pcr (40 µm) = 1.7563, Pcr (60 µm) = 3.5228, Pcr (80 µm) = 5.4135, and Pcr (100 µm) = 7.2427. The findings indicate that for a 60 µm tip diameter, the reaction force is minimized, and displacement is maximized compared to other tip diameters. Mode shapes for the 60 µm tip diameter are illustrated in Figure 1. This analysis highlights the importance of ensuring that the applied load for each diameter remains below the critical load to guarantee a safe insertion.

Table 3: Linear buckling results exerted for various tip diameter

Tip Diameter (Td), µm	Eigen value	Reaction Force (RF), N	Displacement (U), µm	Displacement Rotation (UR), N
20	0.50183	2.648	501.83	2.020
40	1.7563	3.455	1067	1.442
60	3.5228	1.169	1183	2.02
80	5.4135	4.105	1040	2.199
100	7.2427	6.401	1029	1.881

 

Figure 1: Various mode shapes obtained during the linear buckling analysis for microneedle tip diameter, Td=60 µm. Click here to view Figure

Post-buckling Analysis

The non-linear buckling analysis, also known as post-buckling analysis, is conducted using the Static-Riks algorithm. The critical buckling load obtained from the linear analysis serves as the input load for the post-buckling analysis, with 1000 iterations specified. For each diameter, an individual Load Proportionality Factor (LPF) graph is generated and compared, as depicted in Figure 2. Notably, the 60 µm diameter exhibits faster convergence within minimal arc length increments compared to other diameters. The initial buckling of the 60 µm diameter microneedle occurs at the 5th iteration, with the corresponding Critical Force (CF), Reaction Force (RF), Displacement (U), and Displacement Rotation (UR) values of 0.289115, 8.20E-05, 0.007601 mm, and 0.001714 radians, respectively. At the 712th iteration, the microneedle enters a critical buckling state, with CF, RF, U, and UR values of 0.558693, 0.017281, 0.087769 mm, and 0.096524 radians. During this critical buckling stage, the specified Load Proportionality Factor (LPF) is 0.159626, representing 15.96% of the applied load. Hence, the critical buckling load is calculated as the product of the LPF and the applied load. This approach is applied consistently across all tip diameters to determine the critical load

Pcr (20ɸ) = 0.0908014x 0.50183 N = 0.0455N

Critical buckling load, Pcr(20ɸ)  = 0.05 N

Pcr (40ɸ)  = 0.19699x 1.7563 N = 0.3459N

Critical buckling load, Pcr (40ɸ)  = 0.3 N

Pcr (60ɸ)  = 0.159626x 3.5228 N               = 0.558691N

Critical buckling load, Pcr (60ɸ)         = 0.6 N

Pcr (80ɸ)  = 0.17829x 5.4135 N   = 0.965N

Critical buckling load, Pcr (80ɸ) = 1 N

Pcr (100ɸ)   = 0.184288x 7.2427 N   = 1.334N

Critical buckling load, Pcr (100ɸ) = 1.3 N

Exceeding the critical buckling load leads to structural failure in the microneedle, resulting in a severe buckling effect. Therefore, it is essential to ensure that the applied load for insertion remains below the corresponding critical buckling load obtained for each diameter.

Figure 2: Comparison plot of LPF Vs Arc length for various tip diameters of the microneedle. Click here to view Figure

Result and Discussion

Non-linear buckling analysis is performed to anticipate the post-buckling response of the microneedle under various loading conditions. Among the different tip diameters examined, only the 60 µm tip microneedle displayed superior convergence. The Load Proportionality Factor (LPF) graph for the 60 µm tip diameter microneedle is depicted in Figure 3. Initial buckling initiates at 8% of the applied load, reaching a critical buckling point at 15.9% of the applied load. The corresponding critical buckling load is calculated as 0.6N. Therefore, for safe insertion, the microneedle should not be subjected to loads exceeding 0.6N. To gain further insight, the microneedle’s behavior is scrutinized to identify the maximum failure points at the critical stage. The maximum stress and displacement, recorded at the 712th iteration, are found to be 176.483N/mm² and 0.106mm, as illustrated in Figure 4. Importantly, even at critical points, it is observed that the microneedle’s tip does not fracture but instead undergoes crushing, ultimately leading to failure.

Figure 3: The load Proportionality factor (LPF) exerted during the during post buckling behavior of microneedle Click here to view Figure

Figure 4: Maximum stress and displacement were obtained at critical buckling points. Click here to view Figure

Conclusion

The stability of microneedles is at risk when the insertion force surpasses a certain threshold, known as the critical load. To ensure their safe application, it is imperative to identify this critical load for structures that are vulnerable to buckling. This is achieved through both linear and non-linear (post-buckling) analyses using numerical Finite Element Analysis (FEA) software. These analyses reveal that the critical buckling loads for microneedles are 3.5228N for linear analysis and 0.6N for post-buckling analysis. These values are evaluated across different tip diameters, providing a comprehensive understanding of the safe insertion loads. This methodology can be extended to various structures at risk of buckling, enhancing their safety under applied loads. Additionally, these findings are pertinent to the insertion of microneedles into human skin, ensuring their effective and safe use in medical applications.

Acknowledgment

The author would like to thank, (Insert university name and Dept. name) for their guidance and support to complete this article.

Conflict of Interest

The authors do not have any conflict of interest.

Funding Sources

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Data Availability Statement

This statement does not apply to this article.

Ethics Statement

This research did not involve human participants, animal subjects, or any material that requires ethical approval.

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Nomenclature
Mn	Microneedle
E	Youngs Modulus
σ	Stress
σut	Ultimate stress
ρ	Density
ν	Poissons ratio
Td	Tip diameter
Pcr	Critical buckling load
I(z)	Moment of inertia about the centroid
M(z)	Bending moment distribution
y(z)	Deflected shape
L	Length of the column
k	Constant coefficient
di	Internal diameter
do	Outer diameter
RF	Reaction force
U	Displacement
UR	Displacement rotation
LPF	Load proportionality factor

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