Simulation assisted design for microneedle manufacturing: Computational modeling of two-photon templated electrodeposition
Introduction
Precision metallic microneedles – fabricated by a hybrid additive manufacturing (AM) method called two-photon templated electrodeposition (2PTE) – hold great potential to enable inner ear diagnostics and drug delivery, or similar precision medical applications [1]. For inner ear diagnostics and drug delivery, the most promising portal into the inner ear is across the round window membrane (RWM), which is the only non-osseous barrier separating the fluid-filled inner ear and the air-filled middle ear [[2], [3], [4], [5]]. The RWM is a thin tissue about 1 mm across and 10−30 μm thick in guinea pigs [[6], [7], [8]], and about 2 mm across and 60 μm thick in humans [9]. Controlled perforation of the RWM with microneedles [[9], [10], [11], [12], [13], [14]] has recently been shown to increase the rate of diffusion of a fluorescent agent, Rhodamine-B, (as a proxy for Gentamicin) across the RWM [15,16] with no long-term functional or anatomical consequences [1,17].
The delivery of accurate and precise therapeutic dosages to the inner ear necessitates the accurate and precise creation of perforations through the RWM with microneedles. In the context of the RWM, a “sharp” needle must have a tip radius of curvature much less than the thickness of this tissue [10]. Polymeric and metallic microneedles with tip radius of curvature of 1 μm or less and shaft diameter of 100 μm can introduce microperforations through the RWM that largely push apart – rather than cut – connective tissue within the RWM. Thus, perforations are introduced with a minimal degree of tissue damage [10,17], which speeds healing of the RWM after perforation and with no functional consequence [17,18]. However, the fabrication of sufficiently sharp metallic microneedles is challenging.
The two-photon templated electrodeposition (2PTE) methodology is able to fabricate metallic microneedles with micrometer-scale precision, with high design freedom, and desirable mechanical properties via a hybrid additive manufacturing process [11]. This was enabled by recent progress in two‐photon based lithography that enables fabrication (or printing) of complex 3D polymeric small-scale structures. Employing a hybrid process of a single lithography step and single electrodeposition step, ultra-sharp microneedles with circular cross-sections were created. First, polymeric molds containing cavities in the desired shapes of microneedles were fabricated using the two-photon lithography (2PP) process with voxel resolution approaching 100 nm. The mold was mounted onto a rotating disk and placed into the electrolyte of an electrochemical deposition cell where copper was electrochemically deposited into the cavities in the mold. The mold was subsequently removed, thus releasing the copper microneedles. The resolution and precision of the resulting metallic 2PTE microneedles are commensurate with that of2 2PP polymeric microneedles and thus are able to perforate guinea pig RWM with minimal damage to the tissue [10,11,17]. One of the microneedles can be seen in Fig. 1, mounted on a 24-gauge blunt stainless-steel needle that itself can be mounted with a Luer lock onto a syringe.
Our 2PTE methodology allows significant freedom of design. However, given that the mold cavities have micrometer-scale dimensions, complications duriduring the electrochemical deposition step of the 2PTE process can arise from transport related phenomena inside the small cavities. Varying cross-sectional areas in the cavities cause the area of the deposition front to change by up to four orders of magnitude as the cavity is filled, leading potentially to highly nonuniform current density distributions. Further, electrolyte can become trapped in isolated regions of the mold cavities, which leads to incomplete filling of the mold [19,20].
The base part of the needle shown in Fig. 1, which mates with the blunt syringe needle for mounting, was designed under the naïve assumption that electric current distribution at the moving copper deposition front would be uniform, thus independent of position. Fig. 2 shows a yellow outline of the desired microneedle profile – and hence the shape of the mold – overlaid on a scanning electron microscope (SEM) image of the actual needle. The expected outcome is not realized because geometric obstacles in the cavities lead to nonuniform depletion of reactant (cupric ions) as well as nonuniformities in electrical fields within the cavities. While the geometry of the needle tip and shaft were successfully fabricated with sub-micrometer fidelity to the design, the design of the microneedle base and the outcome do not match. The mismatch can be seen especially in the extreme periphery of the needle base, and this offset is on the order of 30 μm. Such a mismatch shows that the constant current density assumption was incorrect for at least a portion of the deposition.
As replicating the base geometry precisely was not crucial for demonstrating function of this class of microneedle, it was possible to successfully mount these microneedles in the configuration they were made. However, for manufacturing needles or other structures using 2PTE that vitally depend on the successful replication of all geometric features, it is necessary to understand the transport behavior and electrochemical deposition behavior in detail. For this reason, we have developed a robust numerical model using COMSOL Multiphysics® software [21] that is able to accurately predict the geometry of microneedles fabricated via 2PTE. The model was validated on the preexisting geometry shown in Fig. 2 and was utilized for the successful deposition of another geometry, to be discussed later in this paper.
The theory of electrochemical deposition and effects of additives have been well explored and have been crucial in developing this model [22]. Electrodeposition into 2D structures has long been a topic of interest and design rules have been explored for such geometries [[23], [24], [25], [26], [27]]. Numerical simulations of electrodepositions of copper from acidic solutions using COMSOL have also been extensively studied [28,29].
The model developed herein demonstrates the use of a moving boundary model of the deposition front for 3D structures, both in a two-dimensional axisymmetric geometry and a full three-dimensional geometry. The purpose of this model is to serve as a tool to inform the designer on what designs are possible, while also creating the possibility of changing chemical parameters such as leveling agents and operating conditions such as applied potential to see their expected effect on outcome.
The vital need for such a tool arises from the fact that in highly three-dimensional depositions such as the ones concerning microneedles, the area of the deposition front can increase by up to four orders of magnitude within a single deposition. As a consequence, the presented model will serve as a tool that helps inform complicated micro/mesoscale design choices with 2PTE using a commercially available electrodeposition chemistry.
The goal of this paper is the introduction of a design tool for 2PTE fabrication that uses the COMSOL Multiphysics® software. Section 2 discusses the assumptions and equations utilized in the numerical modeling, Section 3 discusses the experimental process, Section 4 introduces the results derived from the numerical tool, and these results are discussed in Section 5.
Section snippets
Modeling assumptions
The deposition process is simulated by explicitly solving for the spatial and temporal variations of the concentrations of sulfate, cupric ions, protons, and when present, a leveling agent. The concentration fields are coupled through an electrical field, which is determined by satisfying an electroneutrality constraint [29]. The deposition at the cathode (i.e. working electrode) and the dissolution at the anode are assumed to take place with 100 % current efficiency, which means that the model
Experimental Methods
The 2PTE hybrid additive manufacturing process is used for fabricating ultra-sharp microneedles [11]. First, a mold containing a cavity with the desired shape of the microneedles is fabricated using 2PP lithography, a 3D printing technique that can yield polymeric structures with spatial resolution (i.e. voxel size) approaching 100 nm, using a negative-tone photoresist. Second, electrodeposition of copper is used to grow microneedle-shaped structures in the mold. Potentiostatic deposition was
Single needle axisymmetric simulation
The results from numerical simulations using the geometry shown in Fig. 2, Fig. 3 are represented in this section. First, the differences between a naïve, fully conformal simulation and a sophisticated electrochemical simulation are explored. Second, the experimentally produced microneedle geometry is simulated to a high degree of agreement using parameters outlined in Table 1, identical to the ones used in experiments. Third, the mechanism behind the production of the microneedle geometry is
Discussion
It was shown that, with appropriate parameters, the numerical model was successful in predicting the resulting geometry. Such a tool can be leveraged to accelerate the manufacturing design cycle. As evident from Fig. 6, the simulation predicts that the base of the microneedle would only be partially replicated. Depending on the application, this may be an acceptable outcome. Alternatively, changes to the mold could be made at this point to explore via simulation different geometric design
Conclusion
A numerical tool that can be used to predict the geometric growth of the deposition front during 2PTE was presented, for the purpose of manufacturing microneedles. The numerical tool is validated experimentally by comparing the results to two very different microneedle designs. Therefore, this tool can be used to predict the geometric behavior of the deposition front in a complicated mold design in which the area of the deposition front changes by up to four orders of magnitude within a single
Declaration of Competing Interest
The authors report no declarations of interest.
Acknowledgements
The authors gratefully acknowledge Prof. Elizabeth Olson, Dr. Elika Fallah, Ryan Gusley, Dr. Jonathan Vardner, Wenbin Wang, Shruti Rastogi, Dr. Miguel Arriaga, Dr. Dimitrios Fafalis, Chaoqun Zhou, Dr. Betsy Szeto, Stephen Leong, and Dr. Chris Valentini for helpful discussions. This work was performed in part at the Advanced Science Research Center NanoFabrication Facility of the Graduate Center at the City University of New York. This research was supported by National Institute on Deafness and
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