Characterization of the Microflow Through 3D Synthetic Niche Microenvironments Hosted in a Millifluidic Bioreactor

Background: Development of new medicines is a lengthy process with high risk of failure since drug efficacy measured in vitro is difficult to confirm in vivo. Intended to add a new tool aiding drug discovery, the MOAB-NICHOID device was developed: a miniaturized optically accessible bioreactor (MOAB) housing the 3D engineered scaffold NICHOID. The aim of our study was to characterize the microflow through the 3D nichoid microenvironment hosted in the MOAB-NICHOID device. Methods: We used computational fluid dynamics (CFD) simulations to compute the flow field inside a very fine grid resembling the scaffold microenvironment. Results: The microflow inside the multi-array of nichoid blocks is fed and locally influenced by the mainstream flow developed in the perfusion chamber of the device. Here we have revealed a low velocity, complex flow field with secondary, backward, or local recirculation micro-flows induced by the intricate architecture of the nichoid scaffold. Conclusion: Knowledge of the microenvironment inside the 3D nichoids allows planning of cell experiments, to regulate the transport of cells towards the scaffold substrate during seeding or the spatial delivery of nutrients and oxygen which affects cell growth and viability.


1
Validation of the pressure losses in the MOAB flow system

Experimental measurement of the pressure inside the MOAB circuit
We measured experimentally the pressured drop over the MOAB flow system. As shown in Figure 4 in the main text, the experimental flow system is composed of a syringe pump (Pump 11, Harvard Apparatus, Holliston, MA) that circulates water at 24°C in a silicone rubber tubing circuit in which a pressure transducer (MP150 Biopac Systems, Goleta, CA) and the MOAB device are included. For a flow rate of 2.295 mL/min, the experimentally measured pressure drop was 11.86 mmHg.

Generation of MOAB flow circuit mesh
A detailed model of the MOAB flow circuit was generated using a CAD program (FreeCAD, https://www.freecadweb.org/). As show in Figure 4B in the main text, starting from right to left, this model consists of the inlet luer, of diameter 2.6 mm and length 30 mm, then a small part of length 1 mm and 4mm diameter, from which the microbore tubing of length 33 mm and diameter 0.5 mm starts. Then the fluid enters the scaffold chamber, and after the chamber the fluid is exiting the system through the outflow microbore tube that ends with a luer of length 10 and diameter 4 mm. The entire fluid path surface was exported in stereolithography (STL) file format and then was sub-divided into separate parts representing the patches used in CFD simulations like inlet, outlet, and walls, as shown in Supplemental Figure 1.
Supplemental Figure 1. STL model of the MOAB flow system. The fluid path was divided into 18 parts that will be individual entities for the boundary conditions of CFD analysis.
The computational grid of the MOAB flow circuit was generated with the snappyHexMesh preprocessor of the OpenFOAM CFD toolbox (OpenCFD Ltd, 2020). A fine mesh composed of more than 5.7 million cells was generated, as detailed in Supplemental Figure 2.

CFD simulation of the MOAB flow system
Steady simulations were run using the solver simpleFoam solver of OpenFOAM suite (OpenCFD Ltd, 2020). The fluid considered was the same used in experimental measurements of pressure, i.e., was water at 24°C, for which we assumed density (ρ) equal to 0.9973 g·cm -3 and dynamic viscosity (µ) equal to 0.0091 g·cm -1 ·s -1 . Newtonian rheology model was assumed. As boundary conditions, we set a constant volumetric flow rate at the inlet equal to that of the infusion pump used in the experimental setting, which was 2.295 mL/min. On the outlet a zero-pressure condition was set, and no-slip condition was set on all system walls.

Numerical simulation results
The numerical simulations resolve for the pressure and velocity fields within the MOAB flow system circuit.

IN OUT
As shown in Supplemental Figure 3, the highest-pressure gradients take place in the inflow and outflow microbore tubes, where the diameter is minimum (0.5 mm). For the flow rate used in the experimental setting (e.g., 2.295 mL/min, water at 24°C), the pressure drop (calculated as P1 -P2 as shown in Supplemental Figure 3A) was 11.67 mmHg, while the pressure drop only in the flow chamber (calculated as P1FP -P2FP as shown in Supplemental Figure 3A) was 1.34 mmHg. Since the experimentally measured pressure drop was 11.86 mmHg, we concluded that the numerical simulations may well predict the pressure losses over the MOAB flow system.
To derive the characteristic flow-pressure curve of the whole circuit, as well as of the scaffold chamber alone, we have run steady simulations with a set of volumetric flow rates and medium commonly used in in vitro experiments on cells using the MOAB device. For the medium for cells at 37°C we assumed density (ρ) is 0.99 g·cm -3 and dynamic viscosity (µ) is 0.0076 g·cm -1 ·s -1 (Franzoni et al., 2016). We therefore derived characteristic pressure vs. flow rate curves of the MOAB system as well as of the scaffold chamber for both fluids, as shown in Supplemental  2 Meshing study for one nichoid block

Introduction
The CAD surface (in STL format) of a basic nichoid block is shown in Figure 3 in the main text. The entire block is 450x450 m wide and 33 m height. We decided to perform a preliminary meshing study for one basic nichoid block before proceeding to the final grid generation.

Grid generation testing
Initially, the STL file was rescaled such as to match 434 m width as we found in the dimensional analysis described in the main text. Then, a parallelepiped of dimensions 454x454x40 (WxLxH) m was chosen as overall 3D domain, in such a way as to contain the nichoid block on the bottom and aligned in the middle. For mesh generation we tested both snappyHexMesh and cfMesh preprocessors of OpenFOAM v2012 suite.
Some attempts were made with snappyHexMesh to generate accurate grids of the scaffold block, which revealed that meshing the nichoid is a challenging task. Several meshes of 2.4 and 2.6 million cells were generated, for which, even though at macroscopic examination the mesh seemed good, when observed in detail, it had distorted or even missing cells, as exemplified in Supplemental Figure 5.
Supplemental Figure 5. Computational grid generated with snappyHexMesh. View of mesh surface and details showing common meshing errors at rods intersection.
The grid errors shown in Supplemental Figure 5, like distorted or missing cells for vertical rods, indicate that the mesh must be further refined to obtain a numerical grid as close as possible to the geometry of nichoid structure. We performed further refinements by increasing the number of cells, especially near the rods since the obtainment of the best mesh with snappyHexMesh composed of more than 5.5 million cells.
Similarly, several tries were made with cfMesh to generate the computational grid for one nichoid block, until the correct parameters were set. A final, best mesh composed of more than 5.4 million cells was thus obtained with cfMesh pre-processor. The quality of best meshes obtained with these two different mesh generators was assessed by means of checkMesh utility (OpenCFD Ltd, 2020) and the output is presented in Supplemental Table 1. mesh has less cells, we decided to keep as best mesh that generated with cfMesh, which is shown in Supplemental Figure 6.