Computational study of mechanical stresses in a cell interacting with micromechanical cues and microfabrication of such cues in Nervous system-on-Chips

Organ-on-Chips (OoCs) are recognized as a disruptive in vitro technology for the efficient mimicry of complex human organ functions.^1,2 To this end, they have attracted significant interest in drug discovery studies by facilitating fast and patient specific drug efficacy evaluation.³ Combining microfluidic devices with advanced stem cell technologies, an OoC offers novel technical solutions for the study of organ physiology and disease modeling.⁴ By using human induced pluripotent stem cell-derived neuronal cell culture in OoC platforms, it is possible to emulate the microscale processes occurring in the human nervous system in vitro and potentially make a better prediction about the efficacy of a drug or novel treatment method for neurodegenerative diseases.⁵ OoC platforms can be engineered in a way that provides an in vivo like microenvironment, which mimics an extracellular matrix (ECM).⁶ 

The ECM is the structure around the cells, which is present in all forms of tissues. It provides the physical scaffold for (bio)molecular and cellular constituents and is of importance for many processes, including tissue morphogenesis and cellular differentiation.⁷ In this paper, we designed, realized, and investigated an OoC with instructive micromechanical cues meant to be utilized in a culture of neuronal cell networks, i.e., a microsieve of which the micropores have a three-dimensional (3D) microtopography. Such a microsieve could offer a highly simplified but effective scaffolding construct for the complex interactions taking place in the ECM of real connected nervous system tissues. Since this approach falls into the research domain of OoC platforms with a dedication to functional elements of the human nervous system, this microphysiological system is called a Nervous system-on-Chip (NoC).

We hypothesize that the features of a laser micromachined microtopography inside of a 3D micropore could act as physical cues to instruct stem cell-derived neurons residing inside of such pores, to develop a specific network topology. This hypothesis is supported by the literature stating that the material’s properties and the microenvironment are important factors in cell differentiation.^8–10 Although it is known that topography influences the intracellular processes and eventually the cell’s morphology, it is not yet known how this happens exactly. There are indications that neurons are most likely to form connections from the point where they experience the most mechanical stress.¹¹ Following-up a preliminary numerical modeling approach for the estimation of such a stress distribution in a cell interacting with a unique 3D shape at the same length scale as the cell soma,¹² here, we describe the methods for the design and realization of the numerical and experimental models required to develop a novel microsieve scaffold-assisted NoC concept in Sec. II and present the results and discussion toward the demonstration of these models in Sec. III. Potentially, these models aid in the design process of novel NoCs, which allows us to explore how instructive cues in NoC-based cultures influence the forming of in vitro neural circuits potentially dedicated in disease modeling. Finally, we summarize and conclude our findings in Sec. IV.

In this study, the fabrication of microsieves is based on the fabrication procedure described earlier by us^13,14 with a few improvements. The desired 3D micropores were made by two main steps: (1) preparing a polymeric foil containing an array of microcavities and (2) adding the 3D topographies in the individual cavities. These two main process steps are described in detail in Secs. II A 1 and II A 2, respectively.

In this work, the microsieves are made of Norland Optical Adhesive 81 (NOA81), which is a single component adhesive and is applied in liquid form. It subsequently cures under ultraviolet (UV) light within a few seconds; therefore, it is a fast curable material that can be used in replica molding processes. Furthermore, it can be handled as a robust foil substrate, which is desired in this work to be around 20 μm thick (for good optical performance in high-resolution microscopy). Moreover, NOA81 is biocompatible^13,15 and could be useful as an alternative for polydimethyl-siloxane (PDMS) in Nervous system-on-Chip applications, since it does not trap small molecules which would be undesirable in a pharmaceutical workflow. In addition, NOA81 demonstrated to be a useful filling material for the production of large aspect ratio structures even with nano scale size,¹⁶ as well as in microtransfer molding technique in the fabrication of nanogroove thin-films.¹⁷ Benefitting from our previous experience for laser ablation from the top of the cavities using laser ablation in this material, i.e., NOA81, we now expanded the library of patterns and thoroughly characterized the pattern fidelity in this fabrication process of a polymer-based micropore array with predefined geometries in order to enable the proposed cell-substrate interaction studies.

Double replica molding to fabricate a NOA81 microcavity foil was introduced by Moonen et al.,¹³ and its optimization by spin-coating rather than drop-casting was also previously published by our research group.¹⁴ In brief, a PDMS negative mold was made using replica molding from the original micro-Sieve Electrode Array (μSEA) silicon mold, which was originally fabricated and received by Schurink at the University of Twente.¹⁸ For the replica step into NOA81, the surface of the PDMS mold was made hydrophilic by a plasma oxidation step at 10 W for 30 s using a plasma asher (EMITECHK1050X, Quorum, Laughton, UK). To improve durability of the PDMS mold through multiple uses of inverting its pyramidal shapes into a NOA81 foil, we here reduced the plasma treatment power to 3 W and optimized the exposure settings. After that, NOA81 was spin-coated onto the PDMS mold in three consecutive steps: (1) 500 rpm for 30 s with an acceleration of 200 rpm/s, (2) 800 rpm for 60 s with an acceleration of 300 rpm/s, and (3) decelerated by 300 rpm/s until it stopped. The PDMS mold with NOA81 atop was then placed inside a UV-LED exposure system (IDONUS, UV-EXP 150R, Neuchatel, Switzerland) to receive a UV dosage for curing. We exposed the foil with a first dose of 6000 mJ/cm² at an intensity of 15 mW/cm² prior to peeling-off and with another dose of 12 000 mJ/cm² in two consecutive exposure steps of 6000 mJ/cm², each after releasing the foil from the mold. Next, the second main step, which is utilizing laser ablation, took place as described in Sec. II A 2.

Like in the process described by Sabahi-Kaviani and Luttge,¹⁴ the NOA81 microcavity foils were mounted on a PMMA holder and inserted in the Optec MicroMaster KrF-Laser setup (Optec S.A., Frameries, Belgium). The tool provides UV light at a wavelength of 248 nm and is equipped with a LightDeck camera system to facilitate focusing of invisible laser light on the ablation surface. The light source was moved vertically so that the off-axis light source was focused on the NOA81 foil surface and Z was set to 0. To achieve uniform final aperture shapes, the laser ablation process in all experiments discussed in this work was performed at Z = 0. Using the built-in servo motor with movement steps of 1 μm, the focused laser point was moved to the center of the inverted pyramids to ablate a hole in the center. To execute ablation in a position on the pyramidal slope, the stage was moved 6 μm in either the X- or Y-direction, after the laser was initially focused on the center of the pyramids. And finally, to create through-holes in the corner of the pyramid, the stage was moved 6 μm in both directions, i.e., X- and Y-directions, in the horizontal plane. In this case, the through-hole had a horizontal distance of approximately 8.5 μm from the center of the pyramids. In the corner and slope configurations, it is important to have the microcavity foil center lines aligned with the direction of the servo motor drives. In other words, the arrays of cavities must be aligned with the directions of the stage movement in the horizontal plane, because if that fails, moving the stage would not end up in the desired slope or corner spots. In all the desired configurations, the laser operates at the pulse repetition rate of 150 Hz, and in the series of experiments performed in this work, a range of 600–1800 pulses were used depending on the selected configuration. By changing the position of the laser beam spot on the cavities (center, slope, or corner) as well as the direction of the laser beam with respect to the NOA 81 microcavity foil (top side or back side), different ablation configurations can be executed to yield a variety of 3D micropore topographies. The design space and the design process for these topographies are consequently described in Secs. II B and II C.

To realize a NoC technology with a microsieve scaffold for cells to retain their 3D shapes, we start from the original silicon microsieve arrangement with columns and rows of 900 pyramidal-shaped micropores. This pore shape of the silicon microsieves was proven to form neural networks upon gentle microfluidic cell capture. Figure 1 shows an example of such a cell culture, where cell bodies (recognized by the blue-stained nuclei) can also be observed in between the micropores of the microsieve scaffold [Fig. 1(a)]. Interestingly, when culturing took place with excess cells seeded on the microsieves, maturing neural cultures were developed already at 12 days in vitro on the patterned substrate as indicated by MAP2 staining [Fig. 1(b)]. While a detailed biological validation has not yet been performed, it is specifically noticeable that a high level of MAP2 seems to indicate a dense network of dendritic neural processes around the micropores revealing the enhanced neuronal identity of SH-SY5Y cells.

Hence, we transferred this design concept into the optical adhesive polymer using soft lithography.^13,19 With just a subset of the resulting 900 cavities opened by laser ablation, these polymer microsieves were also proven to capture cells and form networks.¹³ 

Initially, ablation of the through-holes was performed from the base of the pyramidal cavity (the so-called top shot) in the polymeric foil focusing the laser beam at the center of the pyramid only. Thanks to Siemens NX CAD modeling, Fig. 2 depicts the resulting 3D micropore geometry, i.e., microtopography, from the superposition of the molded inverted pyramid and the conical hole drilled by the laser.

After initial validation of the fabrication process,¹⁴ this platform technology now allows us to produce microsieves in a large enough number to support biological and technical replicas for NoC culture experiments.

Our initial observations led us to the question: “Can the cells’ physiological behavior be influenced by micromechanical cues that the cells receive during capturing in the 3D micropores?” To investigate this question, we aim to use the microsieve fabrication approach introduced in this paper. The cells can connect to each other after capture and differentiation in a systematic fashion, but now, they will also be manipulated by a specific micropore’s topography. These mechanical cues could influence the direction of neurite outgrowths at the level of the individual cells that remain in the pores. By doing so, consistent neural network structures could be created each time upon seeding the cells on such a microsieve scaffold. This microsieve scaffold-assisted NoC concept potentially reduces the number of variables, when researching the effects of drugs on such a minimalistic nervous system model.

In Secs. II C 1–II C 4, we present how choosing direct-write laser micromachining for drilling the through-holes offers us a new opportunity in fabricating micropore shapes. To generate various geometries, we can select the side of laser ablation relative to the pyramids’ geometry in the substrate, i.e., either from the tip or the base of the pyramid, as well as the position and number of holes. Consequently, the selection yields 3D micropores with unique shapes emulating a cellular microenvironment. However, not all of the possible configurations are further considered for experimental modeling. In more detail, Sec. II C provides an overview of the options and selection criteria.

Figure 3 shows four of the 900 microcavities formed in a NOA81 foil. As mentioned previously, for our experimental model, we open only a subset of 10 × 10 cavities using the excimer laser according to the processing details given in Sec. II A 2. Shots can be located at different positions and the number of holes can be varied. Next in the design process, we explored resulting shapes for the ablation of one, two, or three holes in the same cavity in Secs. II C 1–II C 3.

An overview of the proposed configuration for the laser ablation process for one hole is shown in Table S1 in the supplementary material.³⁶ The ablation process alone results in a conical shape. Cells are easily deformable, so when the hole is shot from the top, the entire cell might end up in the cone, thereby still being subjected to symmetric mechanical cues. However, when a hole is laser-drilled from the back, the resulting opening is far smaller due to super-positioning the drilling from the back side with the walls of the inverted pyramid. Then, cells may only experience very minor deformational stress from trying to squeeze into the aperture of the micropore, and still, receive a symmetrically distributed stress pattern overall. To estimate the cell’s stress distribution, a simple gravitational force is assumed to assess the cell body membrane deformation upon interacting with ablated topographies.

When considering micropores with two laser-drilled holes, the six possible positions in Table S1 in the supplementary material³⁶ result in 8 different configurations of the micropores, and 32, when the laser entry point is included. An overview of the configurations considered for two ablated holes is depicted in Fig. S1 in the supplementary material.³⁶ 

When ablating three holes in one microcavity, 16 different configurations are possible, and 128, when the laser entry point from either the top or the back side is included. An overview of the configurations considered for three ablated holes is depicted in Fig. S2 in the supplementary material.³⁶ 

To narrow down the number of experimental conditions introduced in Secs. II C 1–II C 3, configurations are dismissed because of three reasons: (1) mirrored duplications [Fig. 4(a)], (2) no clear directional mechanical cue due to symmetry or complete lack thereof [Fig. 4(b)], and (3) complexity. With those three criteria for exclusion, combinations from the top and back sides in an alternated fashion for three-hole micropores are also not yet considered for ablation testing [Fig. 4(c)].

After dismissing configurations using the above three criteria, 38 configurations are promising to be investigated experimentally [Fig. 5(a)]. To get a better idea of what their geometry would look like, 3D models are made of each of the shapes using Siemens NX 12.0 [Fig. 5(b)].

Although 38 different configurations were identified to be worthwhile exploring, many configurations give similar results and have similar reasons on why they would not make good configurations for influencing the polarization process of the neurons. Some cases were dismissed due to the conditions of the cell slipping through. In this case, those multiple holes create one big hole in the micropore already in the CAD model; hence, the cell is able to slip through. Therefore, it counts as a failure mechanism for the NoC. Another failure mechanism is due to position uncertainty. In this case, when there are multiple holes ablated from the top, it is not possible to predict, where the cell will come to sit. This can depend on the side from which the cell approaches the micropore during the hydrodynamic flow. In some other cases, it is possible that cells entirely enter the laser ablated cone, rather than receiving any directional mechanical cues from the overlaying pyramidal shape. Six remaining configurations were labeled as promising configurations for influencing the polarization process of the cell. These cases are depicted, thanks to Siemens NX CAD modeling, in Fig. 6 (red arrows indicated our assumption for the predicted outgrowth direction).

We further elaborate on the details of the numerical modeling of the mechano-induced stress in cells, in Sec. II D. Independent of speculating about the cell’s behavior upon the presentation of cues, however, our focus here is on the exploration of fabrication capabilities for these various configurations, and the results thereof are discussed in Sec. III B.

A method to numerically model a cell’s mechanical stress response to different surface topographies was developed recently by van Boekel.¹² It is based on earlier atomic force microscopy (AFM) indentation finite element method (FEM) modeling methods, where the cell is already connected to the substrate.^20–24 For this paper, the most relevant conclusions over the earlier cited works on cell stress modeling are that we have incorporated the influence of gravity and friction, allowing the cell to move freely in all six degrees of freedom before it is in steady state with the exposed surface of a 3D geometry, of which the most simple 3D shape could be an open cylinder which has a diameter of about the same length scale or slightly smaller than the cell body. When the cylinder has a bottom, like in round wells of a micromanufactured well-plate, interaction with the cell leading to a certain mechanical stress distribution in the cells gets already more complicated. Here, we aimed for the analysis of such geometries, including the 3D geometries of the type of micropores of our NOA81 microsieves, of which we demonstrated their feasibility of fabrication in this work.

While details on building the numerical model can be found in van Boekel,¹² it consists of two components, a continuous and a tensegrity structural component. The continuous component is defined by a mesh of finite elements.^25–27 There are three distinct parts of the continuous component into which the cell is divided. These are (1) the membrane, (2) the cytoplasm, and (3) the nucleus of which the mechanical parameters are inspired by other works cited elsewhere^20–24 and are summarized in Sec. II D 2. The tensegrity component of the numerical model is used to describe the intricate polymer network within a cell as a simplified network of struts and cables²⁸ and includes a different network for the cytoskeleton (CSK), nucleoskeleton (NSK), and intermediate filaments (IFs), respectively. The tensegrity components are also derived from the literature and summarized in Sec. II D 3. While the continuous component of the model gives an impression of the local deformation of a cell upon contact with a substrate, the tensegrity part simulates how the local forces spread throughout the cell via the respective skeletal polymeric networks.

The continuous component of the model incorporates the membrane, cytoplasm, and nucleus [Fig. 7(a)]. Using marc mentat 2018.1.0 software, which is chosen for its compatibility with large strain nonlinear analyses,²⁹ the components are modeled and meshed into elements [Fig. 7(b)].

The nucleus was meshed into 929 linear tetra4 elements, the cytoplasm into 3425 linear tetra4 elements, and the membrane was modeled as a shell with 1644 quadratic tria6 elements.

The tensegrity cell model, which incorporates the CSK, NSK, and IFs as struts and cables, is added to the continuous cell model (Fig. 8).

As a basis for the tensegrity model, the approach by Xue et al.²² was used. This approach incorporates one spherical tensegrity model consisting of microtubules and actin for the CSK, and another smaller spherical tensegrity model consisting of nuclear lamina and chromatin for the NSK. These two structures were then connected to each other by the IFs. The implementation of the tensegrity model into the continuous model was done by the following four steps,

1. To create the CSK, six microtubules (struts) are attached to the nodes at the vertices of the elements of the membrane. Between those 6 nodes, another 24 elements are added forming actin cables [Fig. 8(a)].

2. To create the NSK, six laminas (struts) are attached to nodes at the surface of the nucleus. Between those 6 nodes, another 24 elements are added, forming chromatin cables [Fig. 8(b)].

3. For IFs, 12 elements are added between the closest nodes from the CSK and NSK [Fig. 8(c)]. This is what connects the CSK and NSK and thereby anchors the nucleus within the cell.

4. To make sure that the model behaves symmetrically when loaded from different directions, the model of Fig. 8(c) is duplicated twice. These two copies are then rotated 60° and 120°, respectively, around their Z-axis [Fig. 8(d)]. The three structures were not connected to one another, as this would significantly influence the mechanical behavior of the model.

Both the continuous and tensegrity elements were modeled as linear elastic elements. Although, in an actual cell, the continuous parts of the cell will behave more like viscoelastic elements. The approach of linear elastic elements was chosen because of the following two reasons:

1. There is very little information, yet, on the viscoelastic mechanical properties of cells, especially of their individual components. In the literature related to 3D FEM models of cells, generally linear elastic models are used.

2. When a force is subjected to the linear elastic model, it will reach its steady state almost instantly. In viscoelastic models, there is relaxation time, but in the steady state, the outcome will be the same or at least very similar to the linear elastic model.³⁰ Moreover, specifically for 3D FEM models of cells, this approach has also been validated.²⁵ 

With the FEM model of the cell, the goal is to find out how the cell settles on a substrate. Since these simplifications are more computationally efficient, a linear elastic model was used. When considering the values of Young’s moduli of the continuous parts of the cell model in the AFM indentation FEM model literature, these values are very low. This is because these models do not include gravity. In Fig. 9, using material properties from Wang et al.²⁰ results in spikes in the tensegrity structure, once a gravity load of only 20% is applied [Fig. 9(b)]. Besides the fact that this is not what cells look like, it also means that the continuous cell component cannot spread the influence of the tensegrity structure throughout the model of the cell body.

For the values of the mechanical properties of the membrane, cytoplasm, and nucleus, first, Poisson’s ratio was chosen to be 0.49 and thereby incompressible.^23,31,32 In the literature, it was found that in most cases, Young’s moduli of the membrane, cytoplasm, and nucleus have a respective ratio of 1000:100:400. This ratio was multiplied with different factors to evaluate the final shape of the continuous cell model after a gravity load was applied, and then compared to the shape of a cell on a glass substrate after 3 h.³³ Figure 10 visualizes the results of this analysis. The multiplication factor of 350 best replicates the experimentally measured cell shape.

For the bulk properties of the CSK, IFs, and NSK, a similar approach was taken. For all parts, Poisson’s ratios were kept at 0.30, as derived from the literature.^20–22,24 The multiplication factor was determined in accordance with the following two criteria:

1. The cell should not slip through a hole with a bottom aperture of 3.5 μm.^13,34

2. The continuous parts of the cell should not have obvious spikes as shown in Fig. 9(b).

This approach led to a multiplication factor of 2, and a final overview of all the bulk properties can be found in Table S2 in the supplementary material.³⁶ The factor of 2 seems low compared to the factor of 350 of a continuous cell model. The reason for this is that the cross sections of the CSK, IFs, and NSK are thin, in the order of nm², and therefore, these elements are barely influenced by the gravity load.

Using this combined model is subsequently applied to our specific cases shown in Fig. 5 for modeling the interaction of a cell with microtopography, resulting from the superposition of the replica molded inverted pyramid and the laser ablation process.

Consequently, the micropores were modeled in Siemens NX 12.0. Figure 2 (Sec. II B) shows an example of such a 3D model. This particular micropore is ablated in the center from the top side. Other configurations and sizes of the holes were modeled in accordance with the experimental part of this work. For simplicity, the laser ablated holes have a draft of 18°, as estimated based on the cross-sectional images presented in Sabahi-Kaviani and Luttge.¹⁴ From the paper, it was also concluded that the corners were not sharp; hence, a corner blend of 0.5 μm was applied to them. In the simulations, the micropore is modeled as an incompressible element. This was done because of Young’s modulus of the polymeric foil, i.e., here, the optical adhesive NOA81 (details of materials and fabrication processes are provided in Sec. II A) is 1.38 × 10⁹ Pa,³⁵ which is several orders of magnitude higher than that of the continuous cell components (Table S2 in the supplementary material).³⁶ The results of applying this method of numerical modeling of the mechanical stress distribution to a cell interacting with specific geometrical cases are further depicted and discussed in Sec. III A.

The numerical modeling method as described in Sec. II D was applied to a subset of microsieve configurations. To make sure that the modeled cell would reach a steady state, a 30 s time window is selected as an end point for the simulation. The color coding used in all subsequent figures presents some interesting modeling cases from Secs. III A 1–III A 3, indicating a von-Mises stress distribution pattern, with deep red for the highest and dark blue for the lowest local stresses. Section III A 1 elaborates on the simplest case of applying the numerical model to a cell inserted into a conical hole. Section III A 2 refers to the experimental cases for the top side and back side ablation of a single centered laser ablated hole, i.e., two of the simplest configurations that are also realized experimentally in Sec. III B 1 and depicted in Figs. 17(b) and 17(f). Section III A 3 provides an example of the limitations of the current tensegrity model applied in this work for the more complex shapes, also experimentally realized in Sec. III B.

The conical shape on which our numerical model is validated has a bottom diameter of 4 μm, a draft angle of 18°, and a depth of 20 μm. The cell experiences a symmetric amount of stress all around, but does not slip through the pore completely (Figure 11).

In Fig. 12, the simulation results for a micropore ablated from the top side and the back side can be seen. Moreover, Fig. 13 compares the cross section of the cell models in these two different microenvironments. At the micropore ablated from the top, it can be seen that the stresses are symmetrically the highest around the middle of the cell. For the cell in the micropore which is ablated from the back, there are clear stress concentrations at the corners of the pyramidal shape.

A clear difference between the two results is that in Figs. 12(a) and 13(a), the cell is positioned entirely within the cone-structure that is created by the laser ablation. The cell in Figs. 12(b) and 13(b) is still almost completely within the pyramidal part of the micropore and has a morphology that is closer to spherical. When the cell sits completely within the cone-structure of the laser ablation, it experiences a symmetric environment from all sides.

In some configurations, the cell model will take on the inverted concave shape of the pore (Fig. 14). If so, it can occur that the tensegrity model does not stay within the cell membrane. This behavior only happens in a few of the configurations which were tested. Nevertheless, it is something that should be kept in mind and validated in more detail, when simulating other configurations, as this is not in accordance with the regular cell behavior.

To make full use of the scope of the developed numerical model and guide design choices as well as fabrication methods of microsieves applied in NoCs with a higher predictive power, it is worthwhile to investigate our numerical model by modeling experts for refinement. Potentially, such a numerical model would also allow an accurate prediction of the stress distribution patterns in a more complex microtopography.

Starting from our previous work on NOA81 microsieves,¹⁴ initially, the 3D micropores only contain one top side ablated conical hole superimposed with the inverted pyramids center (Sec. II C 1). In addition to these relatively simple pore geometries, more complex topographies can be formed, when multiple holes are drilled per cavity (Secs. II C 2 and II C 3). While the feasibility of the fabrication process has already been presented by van Boekel,¹² here, we investigated these different configurations in detail by means of scanning electron microscopy (SEM) and imagej® analysis of the resulting micrographs.

For the realization of our experimental NoC models, six configurations are investigated (Sec. II C 1 and Table S1 in the supplementary material).³⁶ The physical condition at each position such as the thickness of the material or the slope of the surface and focal distance influences the resulting shape. First, for each case, the number of pulses was found by experiment.

Figures 15 and 16 depict micrographs, where the laser ablation has been executed against the number of pulses from the top side and the back side of the NOA81 foil, respectively. The laser beam is focused at the center [Figs. 15(a), 15(b), 16(a), and 16(b)], corner [Figs. 15(c), 15(d), 16(c), and 16(d)], or slope [Figs. 15(e),15(f), 16(e), and 16(f)] of the pyramidal cavities. An intact cavity is presented for comparison.

When ablating from the top in the center and off-center in the pyramidal shape, the focal distance varies across the laser beam; furthermore, the material thickness is not uniform. When the material is thicker, more laser pulses are needed to create an aperture. Respectively, in the center and slope positions, apertures appear with 1200 pulses; however, on the slope, the aperture is smaller [Figs. 15(a) and 15(e)]. For the corner position, an aperture appears with 1500 pulses [Fig. 15(c)]. Comparing the cases “corner” and “slope,” they suggest that although the thickness of the material is almost the same, making through-holes on the flat slope requires less pulses than on the corner when two slopes meet.

Comparing these top side ablation cases with the cases ablated to form the back side of the NOA81 foil, the creation of an aperture starts for the center and corner ablation already at a lower number of pulses, i.e., 900 and 1200 pulses, respectively [Figs. 16(a) and 16(c)]. It is not that obvious for the ablation on the slope [Fig. 16(e)], where the number of pulses before opening remains 1200 [Fig. 16(f)]. Compared to drilling from the top side, openings produced from the back side have a more uniform, circular appearance and are smaller in size, when superimposed with the pyramidal shape. A lower number of pulses can be explained by the fact that, in these cases, the distance between the laser and the substrate is closer to the focal distance of the laser. Moreover, the error margin on the measured diameters ablating from the top side is larger than when ablating from the back side, since focusing on a flat substrate surface is easier and more reproducible. There is also another difference. Comparing Figs. 15 and 16 shows that ablating from the top side will also create much debris, which can be interpreted in cell culture experiments as a kind of roughness or nanotopography on the surface of the cavity around the through-hole. This might potentially influence the neural cell processes more than the actual stress distribution, due to the geometry being realized in super-positioning the resulting shapes from replica molding of inverted pyramids and with conical laser ablated through-holes, as estimated by our numerical model. These features are clearer to see in the SEM images of the sample, when the substrate is tilted (Fig. 17).

Overall, by manually focusing our tool, there is robust control over the placement of through-holes to open the cavity in a particular location, namely, in the center, corner, or slope.

Here, we aim to control the geometry of the 3D pores by deploying different strategies in the laser ablation process. Therefore, we must have an understanding about the dimensions of the final features added to the inverted pyramidal cavities. Since the critical dimension is the aperture hindering a single cell from escaping the 3D micropore via the through-holes used to gently perform flow across the microsieve, the aperture size needs to be characterized. An aperture of 2–4 μm is desirable in this process. Using the particle analysis feature of imagej software, we calculated the area of the opening from the micrographs. Figure 18 compares the effective diameters of the aperture produced from the top side [Fig. 18(a)] and the back side [Fig. 18(b)], respectively, for the center, slope, and corner ablation cases, as an averaging of the three measurements taken from three micropores within one chip (n = 3).

From Fig. 16, we observe that the opening sizes, in the cases where the laser is focused in the center, are larger than the other two cases, whereas the apertures resulting at a corner ablation are the smallest. Moreover, the variation of the aperture size is also higher in the corner and slope ablations than in the center ablation position. Most likely, the variation in material thickness within the ablation region causes these differences. One reason is that the tool is not equipped with a microscope having a high-resolution objective; therefore, aiming on the desired spots could potentially have errors, and this error is higher in these two cases.

In addition to the difference in sizes of the openings, the location of the aperture against the laser entrance opening has shifted in some cases. By default, it is expected that the center of the laser entrance opening appears in the center of the aperture. However, our result shows that the centers of the entrance openings and their apertures show an offset for the top side ablation case [Figs. 19(a) and 19(b)] and not for the back side ablation case [Figs. 19(c) and 19(d)]. In the top side ablation, for both cases, slope [Fig. 19(a)] and corner [Fig. 19(b)], the center point of the aperture has shifted toward the center of the pyramidal cavity.

The 3D micropores were created with a combination of through-holes. In Sec. II C 4, we identify a back side ablation with two corner openings [Figs. 20(a) and 20(b)], two slope openings [Figs. 20(c) and 20(d)], and two slope openings with a corner opening in between, i.e., three-hole micropores (Fig. 21) as the most interesting configurations for this initial study.

The micrographs show the top view and back view images, respectively. For the two-hole cases, the number of pulses started from 900 until 1800. Notably, one opening seems to be larger than the other, especially in the slope case [Figs. 20(c) and 20(d)]. The larger opening is, in fact, the second fabricated hole; therefore, the order of ablations also plays a role in the geometry of the openings. This phenomenon is more visible when ablation on the slope takes place, where the holes are closer to each other and, therefore, the resulting conical shapes of the second laser drilling process are already adjacent to a hole rather than a solid material. Figure 20(c) shows that opening a second hole on an adjacent slope could already be created at 900 pulses, which is less than the required number of pulses for a single hole.

In a three-hole configuration (Fig. 21), apertures already appear on an even lower number of pulses per drilling position, i.e., at 600 pulses.

Figure 22 shows the result of three ablation cases at a 30° tilt angle, where two holes ablated with 1500 pulses each can be seen on the corners according to the CAD model depicted in Fig. 14(f) in Fig. 22(a). Figure 22(b) presents the two-hole configuration [Fig. 14(b)] realized at opposite sides of a single corner with 1500 pulses, and in Fig. 22(c), a three-hole configuration with two holes at opposite sides of a single corner, and a third hole is positioned and drilled on the corner, a bit above these two first holes [Fig. 14(c)]. In the ablation case with three holes, all holes are made by 1200 pulses. The latter setting shows not three separated apertures, but a larger hole, which might not be desired for the application.

In summary, we have investigated the microfabrication process of a micropore with predefined micromechanical cue geometry. It is not yet possible to demonstrate all configurations as depicted in the Siemens NX CAD model. On the other hand, the CAD models were required to determine input into our numerical modeling of the mechanical stress distribution in a cell when interacting with such shapes in three dimensions. Fabricating a set of these uniquely shaped micromechanical cues, i.e., a 3D topography, inside of a micropore, become technically feasible thanks to a micromachining process that combines replica molding using a UV curable optical adhesive; here, NOA81 and well-established laser micromachining. The direct-write laser ablation approach is one of the photon beam processes, which allows us to adjust process parameters locally and, hence, facilitates to yield different geometries and shapes inside a micropore in a unique fashion, which is important for future biological studies. Starting from the replicated shape of a pyramidal microcavity, we produced a set of through-holes that subsequently yield the geometry preselected by our numerical model. For a one-hole configuration, we found a simple relation of the required number of pulses with making through-holes at the center, slope, or corner, depending on the actual thickness of the material in these positions. However, for two-hole and three-hole configurations ablation, it is not straightforward anymore, and to define the best pulse number per hole that is sequentially made in one and the same pore, it has to be validated by an experiment. Our results demonstrated that the pulse number depends on the order of ablation, position, and focal distance. In conclusion, our research reported in this paper contributes by providing a fabrication process that yields unique culture substrates and facilitates biological research. The latter will enhance our understanding of how such cues and their resulting mechanical stress distribution can be explored further and, subsequently, mechanically modeled in a cell a priori.

This work has received funding from the European Union’s Horizon 2020 Research and Innovation Programme H2020-FETPROACT-2018-01 under Grant Agreement No. 824070 and Eurostars MINDMAP project under Grant Agreement No. E113501. We thank Bart Schurink for the fabrication of the original Silicon μSEA, which was used as the master mold for replica molding. Moreover, we thank the members of the Microfab/lab at the Eindhoven University of Technology for their experimental support.

The authors have no conflicts to disclose.

Rahman Sabahi-Kaviani: Conceptualization (equal); Data curation (supporting); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (supporting). Daan van Boekel: Data curation (supporting); Formal analysis (equal); Methodology (equal); Software (lead); Validation (supporting); Visualization (equal); Writing – original draft (supporting); Writing – review & editing (supporting). Regina Luttge: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – original draft (supporting); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.