## Abstract

Building biomimetic neuron structures that emulate the topological features of biological neural networks at multiple scales has been an active area in neuron cell culturing, neuron-chip interface and computer chip design. However, due to the fact that biological neural networks possess extraordinary connectivity and complexity from millimeter down to nanometer scale, with different dendritic branch angles, branch lengths, and branch diameters, previous methods to reproduce the topological features of biological neural networks are either limited to two dimensions or lack of fabrication resolution in building three-dimensional (3D) structures. Here we report on the generation of 3D biomimetic neuron structures at a micrometer scale, with high mechanical stability and controlled topologies by studying the effect of 3D direct laser writing (DLW) on the capillary force. This work provides an optical technology platform to replicate the topological features of biological neural networks and paves the avenue towards more applications of using 3D direct laser writing in engineered neural networks.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Reproducing the topology of biological neural networks (BNNs) to create optimized biomimetic structures has been an active area of research over the last decade, where many fabrication approaches, such as electron beam lithography and soft lithography have been developed to build two-dimensional (2D) biomimetic neuron structures in a variety of materials including hydrogels [1], silicon wafer [2], etc. Recent development of three-dimensional (3D) additive manufacturing has showed its potential in producing 3D large scale biomimetic neuron structures using biocompatible inks [3,4]. These biomimetic structures not only provide structural supports [5] and direct neuron shapes [6], affect neuron differentiation [7], migration and proliferation [8–10], but also have been proved to reflect their involvement in different neuron functional tasks [11] because these structures provide varied mechanical and biochemical cues. However, due to the fact that BNNs possess extraordinary connectivity and complexity with different dendritic branch angles, branch lengths, and branch diameters from millimeter down to nanometer scale [12,13], previous methods to reproduce the topological features of BNNs are either limited to 2D structures or lack of fabrication resolution in building 3D structures. 3D direct laser writing (DLW) based on two-photon polymerization has been widely used to fabricate complex microstructures due to its advantages in generating arbitrary 3D geometrical configurations [14–19].

In this work, we demonstrate the ability of 3D DLW to generate 3D biomimetic neuron structures of various topologies with sub-micrometer feature size. We theoretically and experimentally demonstrate a semi-empirical theory modeling the capillary force induced during the developing process after laser fabrication. Based on our theoretical model, complicated biomimetic neuron structures are fabricated by directly implementing the neuron structural database of biological neurons with optimum laser fabrication conditions. The size of our fabricated biomimetic neuron structures is ten times smaller than their biological counterparts.

## 2. Experimental setup

The experimental set-up and schematic of our 3D biomimetic neuron structures fabricated by 3D DLW are illustrated in Figs. 1(a) and 1(b). A femtosecond laser beam operating at a wavelength of 535 nm (Fidelity), with a pulse width of 270 fs and a repetition rate of 50 MHz, was steered by a combination of a 4f imaging system and 2D galvo mirrors (Thorlabs) into a 1.4 NA × 100 oil immersion objective (Olympus), and beam delivery and power are controlled by an acoustic optical modulator (AOM). Within the focus of the laser beam, polymerization occurs when the effective laser intensity is above the threshold of the photoresist (A zirconium-based hybrid organic–inorganic photoresist [20]). Biomimetic neuron structures are written by translation of the sample on the piezoelectric nanotranslation stage (Physik Instrumente), shown in Fig. 1(b).

## 3. Branching model

Biological neuron structures are complicated multiple branches structures spinning in 3D space with a high-aspect-ratio (shown in Fig. 1(b)), and it is challenging to maintain high mechanical stability and fidelity of biomimetic neuron structures due to the detrimental effects induced by capillary force [21] during the developing process. Previous efforts, such as adopting a supercritical-point dryer [22] in eliminating these effects are too complicated and expensive.

Here, a branching model (shown in Fig. 1(c)) is introduced to demonstrate that, by carefully tuning the fabrications conditions in 3D DLW, detrimental effects induced by capillary force can be eliminated and the mechanical properties of biomimetic neuron structures can be adjusted. Biological neuron structures are constructed with individual single branch structures; each single branch structure has a certain dendritic branch angle and dendritic branch length. Similarly, our branching model constitutes both single branch structures and multiple branch structures. A single branch structure, shown in Fig. 1(c), corresponds to a single branch beam posing a certain angle$\theta $on the top of a stronger beam, at a certain branch length *L*. In multiple branch structures, shown in Fig. 1(d), single branch structures stack up into a multiple branch structure, with different branch orders ($n$= 0, 1, 2…), various branch diameter *R*, branch angle$\theta $, and branch lengths *L*.

Thus, to construct biomimetic neuron structures using 3D DLW, we start from studying the mechanical properties of single branch structures, then move to extrapolate the knowledge to multiple branch structures, and eventually demonstrate biomimetic neuron-tracing structures emulating from the biological neuron structures with different average branch angles and topologies.

#### 3.1 Influence of elastic-capillary force in fabricating single branch structure

Consider a single branch structure with branch length *L*, branch diameter *R*, branch angle$\theta $, fabricated by 3D DLW (shown in Fig. 2(a) inset top). After the laser writing, fabricated structures are dipped into a solvent to remove the un-polymerized materials. According to the semi-empirical theory discussing about the stability of piercing branch structure in [23], when the solvent (1-propanol) of the photoresist evaporates to the level of the freestanding branch tips during the developing process, capillary force *F _{c}* is yielded on this single branch structure, is given by

*γ*(for liquid 1-propanol,

*γ*= 25.26 mN/m), the branch diameter

*R*, the cosine of the contact angle

*α*(typical value: 60°) between the solvent and the surface of the branch, and disproportional to the cosine of the branch angle$\theta $.

Resistance to the capillary force is the elastic restoring force *F _{r}*, which is proportional to the Young’s modulus of the material

*E*(1-2 GPa), and the branch diameter

*R*, in proportion to the branch length

*L*, given by

when${F}_{c}={F}_{r}$, a balance between the capillary force and the elastic restoring force reaches the un-deformed shape of the single branch structures. By combining Eqs. (1) and (2), a critical diameter ${R}_{critical}$ can be derived given a single branch structure with branch angle $\theta $ and branch length $L$, and can be expressed as

The branch diameter corresponding to fabrication line width in 3D DLW, which is a parameter relying on laser power *P* and writing speed *s* described by [24], expressed as

*I*is the polymerization threshold energy of the photoresist,

_{th}*ω*

_{0}is the half width of the laser beam in the focusing region. For the convenience of our discussion and experiments, branch length is fixed to 10 μm both in our theoretical discussion and experiments.

According to this theory, stable single branch structures can be fabricated by controlling the laser power and writing speed to tune the size of branch diameter which satisfies the balance between capillary force and elastic restoring force. The criteria that we use in qualifying the deformation and un-deformed structures depend on the displacement of the tip of a branch. The structure is regarded as un-deformed if the displacement is less than the branch diameter.

Firstly, given a single branch structure, larger writing speed requires larger laser power when fabricating stable single branch structures. This is confirmed by fabricating arrays of single branch structures with varied branch angles (branch length of 10 μm) at different laser powers (from 0.5 mW to 2.0 mW) and writing speeds (from 10 μm/s to 50 μm/s). As is shown in Fig. 2(a), a single branch structure with the branch angle of 45° is fabricated by scanning laser power and writing speed. A critical line is shown in Fig. 2(a) with red circles and summarized quantitatively and fitted theoretically in Fig. 2(b). Above this critical line, un-deformed single branch structures can be achieved. Blew this line, a deformation resulting from the capillary force would happen. This is in agreement with our theory discussed above. The position of this line is influenced by the critical branch diameter *R _{critical}* of the structure itself and the laser dose required in the fabrication.

Secondly, for a fixed writing speed, single branch structures with larger branch angles require larger critical branch diameters to achieve the balance between capillary force and elastic restoring force, which corresponding to higher laser power during fabrication. Further experiments are also performed to confirm our theory by fabricating single branch structures with different branch angles. As is shown in Fig. 3(c), single branch structures with different branch angles have unique critical fabrication condition lines. As discussed above, the position of this line is influenced by the critical branch diameter required. From Fig. 3(c), for a given fabrication speed at 50 μm/s, single branch structure with a branch angle of 85° requires a fabrication laser power of 1.2 mW, while the former laser power is 1.0 mW to fabricate a single branch structure with branch angle of 30°.

Due to the reason that the photoresist in the fabrication area is only exposed once by the laser beam, the phenomenon of the deformation seen in the laser power/writing speed matrix presented in Fig. 3(c) can be explained by Eq. (4). The spatiotemporal polymerization behavior described by Eq. (4) is further confirmed by study the relationship between fabrication line width and laser power/writing speed (shown in Fig. 2(d), theoretical fitting follows the work in [24]).

#### 3.2 Fabrication of multiple branch structures

Based on the study in maintaining mechanical stability in building single branch structures, we demonstrate that multiple branch structures with average branch angle of 30°, 45°, and 60° can be fabricated under optimized fabrication conditions with laser power of 0.8 mW, 1.1 mW and 1.2 mW at the writing speed of 50 μm/s. We note that some subtle changes in our fabrication resulting from the uncontrollable microenvironment change during the drying process.

## 4. Fabrication of biomimetic neuron-tracing structures

The feasibility of 3D DLW in producing biomimetic neuron structures with high mechanical stability and desired topology were further demonstrated by building biomimetic neuron-tracing structures. We begin with extracting the morphology data of varied kinds of neurons from online database [25]. The morphology data are processed by a custom MATLAB code and a LabVIEW system to create 3D printable neuron models for our home-build 3D DLW system. By tracing out the topology of neuron structures, biomimetic neuron structures with different branch angles, branch lengths, and branch diameters can be generated through the 3D DLW. The topology of neuron structures from raw neuron morphology data and our fabricated 3D biomimetic neuron structures are shown in Fig. 4. Four selected biological neuron structures coming from different parts of neuron system in animal body are shown in the insets of Fig. 4, respectively: (a) Ganglion neuron cell from the retina of rabbit, with biological neuron size: height 302.16 μm, width 257.57 μm, depth 13 μm; (b) Pyramidal neuron cell from the neocortex of human, with biological neuron size: height 383.18 μm, width 141.25 μm, depth 51.41 μm; (c) Pyramidal neuron cell from the dorsal thalamus of rat brain, with biological neuron size: height 232.39 μm, width 256.21 μm, depth 177.1 μm; (d) Pyramidal neuron cell from the retina of human, with biological neuron size: height 245.77 μm, width 189.62 μm, depth 90.56 μm. Biomimetic neuron structures were created with sizes 10 times smaller than their original biological counterparts, scanning electron microscope (SEM) images of biomimetic neuron structures are shown in Fig. 4. Besides, in order to visualize the 3D feature of our fabricated biomimetic neuron structures with optical method, Rhodamine 6G was added into our photoresist before laser fabrication to create 3D fluorescent biomimetic neuron structures. 3D confocal fluorescent images of biomimetic neuron structure (d) after fabrication and are shown in Figs. 4(e) and 4(f), from which it is revealed that these biomimetic neuron structures maintained outstanding 3D feature at micrometer scale.

## 5. Conclusion

In summary, we have demonstrated the fabrication of biomimetic neuron structures using 3D DLW. The influence of laser power and writing speed in fabricating biomimetic neuron structures with varied topologies were studied. The quantitative experiment results revealed that neuron structures with different average branch angles requires different fabrication conditions. Based on these understandings, the first experimental realization of micrometer scale biomimetic neuron structures 10 times smaller than biological neurons has been achieved using two-photon direct laser writing in this work. Combining galvo-scanning devices, long range translational stages and nanotranslation stages can provide a potential method to replicate the topological features of biological neural networks to a larger scale and forms a new optical technology platform towards the applications of using 3D DLW in engineered neural networks.

## Funding

Australian Research Council (ARC) (Discovery Project 170101775).

## Acknowledgments

We acknowledge the technical support of RMIT Microscopy and Microanalysis Facility in SEM imaging experiments.

## References

**1. **M. Merz and P. Fromherz, “Polyester microstructures for topographical control of outgrowth and synapse formation of snail neurons,” Adv. Mater. **14**(2), 141–144 (2002). [CrossRef]

**2. **P. Fromherz, “Three levels of neuroelectronic interfacing: silicon chips with ion channels, nerve cells, and brain tissue,” Ann. N. Y. Acad. Sci. **1093**(1), 143–160 (2006). [CrossRef] [PubMed]

**3. **R. Lozano, L. Stevens, B. C. Thompson, K. J. Gilmore, R. Gorkin 3rd, E. M. Stewart, M. in het Panhuis, M. Romero-Ortega, and G. G. Wallace, “3D printing of layered brain-like structures using peptide modified gellan gum substrates,” Biomaterials **67**, 264–273 (2015). [CrossRef] [PubMed]

**4. **R. A. McDougal and G. M. Shepherd, “3D-printer visualization of neuron models,” Front. Neuroinform. **9**, 18 (2015). [CrossRef] [PubMed]

**5. **Y. Berdichevsky, K. J. Staley, and M. L. Yarmush, “Building and manipulating neural pathways with microfluidics,” Lab Chip **10**(8), 999–1004 (2010). [CrossRef] [PubMed]

**6. **S. Roth, M. Bisbal, J. Brocard, G. Bugnicourt, Y. Saoudi, A. Andrieux, S. Gory-Fauré, and C. Villard, “How morphological constraints affect axonal polarity in mouse neurons,” PLoS One **7**(3), e33623 (2012). [CrossRef] [PubMed]

**7. **D. Kleinfeld, K. H. Kahler, and P. E. Hockberger, “Controlled outgrowth of dissociated neurons on patterned substrates,” J. Neurosci. **8**(11), 4098–4120 (1988). [CrossRef] [PubMed]

**8. **H. Dermutz, R. R. Grüter, A. M. Truong, L. Demkó, J. Vörös, and T. Zambelli, “Local polymer replacement for neuron patterning and in situ neurite guidance,” Langmuir **30**(23), 7037–7046 (2014). [CrossRef] [PubMed]

**9. **Y. Yi, J. Park, J. Lim, C. J. Lee, and S. H. Lee, “Central nervous system and its disease models on a chip,” Trends Biotechnol. **33**(12), 762–776 (2015). [CrossRef] [PubMed]

**10. **C. D’Avanzo, J. Aronson, Y. H. Kim, S. H. Choi, R. E. Tanzi, and D. Y. Kim, “Alzheimer’s in 3D culture: challenges and perspectives,” BioEssays **37**(10), 1139–1148 (2015). [CrossRef] [PubMed]

**11. **M. F. Hasan and Y. Berdichevsky, “Neural circuits on a chip,” Micromachines (Basel) **7**(9), 157 (2016). [CrossRef]

**12. **J. C. Rah, L. Feng, S. Druckmann, H. Lee, and J. Kim, “From a meso- to micro-scale connectome: array tomography and mGRASP,” Front. Neuroanat. **9**, 78 (2015). [CrossRef] [PubMed]

**13. **O. Sporns, G. Tononi, and R. Kötter, “The human connectome: a structural description of the human brain,” PLOS Comput. Biol. **1**(4), e42 (2005). [CrossRef] [PubMed]

**14. **M. Straub and M. Gu, “Near-infrared photonic crystals with higher-order bandgaps generated by two-photon photopolymerization,” Opt. Lett. **27**(20), 1824–1826 (2002). [CrossRef] [PubMed]

**15. **Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. **4**(1), 2061 (2013). [CrossRef] [PubMed]

**16. **V. Schmidt and M. R. Belegratis, *Laser technology in biomimetics: Basics and applications* (Springer Science & Business Media, 2014).

**17. **X. Gou, M. Zheng, Y. Zhao, X. Dong, F. Jin, J. Xing, and X. Duan, “Mechanical property of PEG hydrogel and the 3D red blood cell microstructures fabricated by two-photon polymerization,” Appl. Surf. Sci. **416**, 273–280 (2017). [CrossRef]

**18. **V. Ajeti, C. H. Lien, S. J. Chen, P. J. Su, J. M. Squirrell, K. H. Molinarolo, G. E. Lyons, K. W. Eliceiri, B. M. Ogle, and P. J. Campagnola, “Image-inspired 3D multiphoton excited fabrication of extracellular matrix structures by modulated raster scanning,” Opt. Express **21**(21), 25346–25355 (2013). [CrossRef] [PubMed]

**19. **H. B. Sun and S. Kawata, *NMR• 3D Analysis• Photopolymerization* (Springer, 2004).

**20. **K. Terzaki, N. Vasilantonakis, A. Gaidukeviciute, C. Reinhardt, C. Fotakis, M. Vamvakaki, and M. Farsari, “3D conducting nanostructures fabricated using direct laser writing,” Opt. Mater. Express **1**(4), 586–597 (2011). [CrossRef]

**21. **Y. Hu, Z. Lao, B. P. Cumming, D. Wu, J. Li, H. Liang, J. Chu, W. Huang, and M. Gu, “Laser printing hierarchical structures with the aid of controlled capillary-driven self-assembly,” Proc. Natl. Acad. Sci. U.S.A. **112**(22), 6876–6881 (2015). [CrossRef] [PubMed]

**22. **J. M. DeSimone, “Practical approaches to green solvents,” Science **297**(5582), 799–803 (2002). [CrossRef] [PubMed]

**23. **B. Roman and J. Bico, “Elasto-capillarity: deforming an elastic structure with a liquid droplet,” J. Phys. Condens. Matter **22**(49), 493101 (2010). [CrossRef] [PubMed]

**24. **X. Zhou, Y. Hou, and J. Lin, “A review on the processing accuracy of two-photon polymerization,” AIP Adv. **5**(3), 030701 (2015). [CrossRef]

**25. **Neuron topology database: Neuromorpho.org.