Computational fluid dynamics enables predictable scale-up of perfusion bioreactors for microvessel production

Abstract

Scaling up microvessel culture systems is essential for producing clinically relevant vascularized tissues, yet conventional microphysiological platforms offer limited insight into how to maintain flow conditions during scale-up. Here, we present a computational—experimental framework using computational fluid dynamics (CFD) to guide the design and scaling of microvessel bioreactors. Interstitial flow (IF) distributions were predicted in two perfusion-based platforms—a permeable well-plate insert and a rhomboidal microfluidic chamber—across multiple scaling factors and hydrostatic pressures. CFD identified IF ranges conducive to microvessel network formation and quantified how geometry and pressure modulate the flow field. IF-preserving scale-up in permeable well-plate inserts generated microvessel networks with consistent morphology metrics across a more than 30-fold increase in culture volume. In microfluidic rhomboidal chambers, regions with distinct CFD-predicted IF velocity fields showed significant differences in average lumen diameter and total vessel length per area under otherwise matched experimental conditions, supporting an association between local IF environment and regional morphology. Together, these results show that CFD can predict and compare IF environments during scale-up, that preserving IF conditions during scale-up can result in similar morphology metrics, and that IF distributions inside a device can correlate with regional network morphology.

Significance statement.

Scaling up microvessel bioreactors is critical for engineering large prevascularized tissues. This study combines computational simulations and experimental data to demonstrate that computational fluid dynamics (CFD) can guide scale-up of bioreactors for microvessel production by predicting interstitial-flow conditions and associated flow-related microenvironments. Experiments across a more than 30-fold volume increase showed that maintaining CFD-predicted interstitial flow velocity during scale-up preserved experimentally measured microvessel network morphology under the tested conditions. Together, the computational and experimental results support a simulation-based design paradigm for bioreactor systems for microvessel production at scale, leveraging CFD to design systems with targeted interstitial flow conditions associated with reproducible network morphology.

Introduction

The vascular system enables the transport of oxygen and nutrients and the removal of waste products—functions essential for sustaining any living tissue (1). In engineered tissue constructs, vascularization is critical for recapitulating these functions, as oxygen and nutrient diffusion into tissues is limited to ∼200 µm; beyond this range, cells encounter hypoxia, lack of nutrients, and consequently undergo necrosis (2, 3). After an engineered tissue construct is transplanted, the host vasculature may penetrate into the transplanted tissue at rates as low as tens of microns per day (4), resulting in inadequate oxygen and nutrient supply. One strategy to overcome this limitation is to integrate vasculature into tissue constructs before transplantation, a process referred to as prevascularization (3, 5).

Engineered tissues are commonly prevascularized by co-culturing target tissue cells with endothelial cells (ECs) derived from pluripotent stem cells (PSCs) or isolated directly from tissue sources (6). Cocultures also include supporting cells, such as mesenchymal stem cells (MSCs), fibroblasts, or pericytes, which promote vascular stabilization and maturation by providing structural support and signaling to endothelial cells (6, 7). When these cocultures form microvessels, they can accelerate vascular integration after implantation through sprouting angiogenesis and anastomosis with the host vasculature, faster than approaches relying only on host-driven vessel ingrowth (3, 5, 8–10).

Beyond cellular composition, the local microphysiological environment regulates de novo vascular network formation in vivo and exposes endothelial cells to various biochemical and mechanical stimuli, such as shear stress, extracellular matrix (ECM) stiffness, pressure gradients, and growth factors (11, 12). To recapitulate these conditions, microphysiological systems (MPS) have been utilized to study and modify engineered microvascular networks (13, 14) and microlymphatic networks (15). For vasculogenesis applications, MPS must integrate media perfusion, enhancing nutrient and waste transport while introducing controllable flow-induced mechanical stimuli, which has been shown to be key for the alignment and organization of endothelial cells into functional, perfusable microvascular networks (13, 16–18). Commercially designed and customized platforms for vessel-on-chip applications have been developed in various configurations, such as idenTx, IFlowPlate, and customized open microfluidic devices (19–21).

A common design choice for vessel-on-chip applications is the use of one or several chambers containing cell-seeded fibrin or collagen gels, connected to two microfluidic channels running in parallel along the outline of interconnected chambers. The channels, operating at different pressures, induce flow through the chambers to provide nutrients and growth factors while removing waste. The chambers are often designed with hydrogel-retaining features, such as rhomboidal or saw-tooth layouts, to provide effective control and confinement of cell-embedded hydrogel. For example, gel-filled microfluidic platforms with hydrostatic pressure differences have been used to generate controlled interstitial flow through 3D hydrogel chambers for studies of angiogenesis, vascularization, and cell transport (22–24). A conceptually similar version of this platform featuring three interconnected rhomboidal chambers was used by Wang et al. (25), who reported microvessel formation throughout the chamber, with vessel diameters of ∼50 µm near the chamber inlet and outlet. In the rhomboidal geometries considered in this work, this configuration results in a nonuniform interstitial flow (IF) field with both streamwise and cross-streamwise velocity components, and with larger velocities near the midline of the chambers. In a related study using the same rhomboidal chamber geometry, Hsu et al. (23) achieved a total vessel length of ∼16 mm after 2 weeks of culture.

An alternative device design used to impose IF effects on endothelial cells uses permeable inserts on standard well plates, which facilitates vessel retrieval and offers design simplicity. Deng et al. (12) demonstrated the effectiveness of this platform by placing a 12 mm column of growth media on top of a well-plate insert filled with endothelial-seeded fibrin gel resting on top of a permeable membrane, resulting in microvessels with diameters ranging from 10.0 to 40.0 $\mu$m.

Despite high physiological relevance, current MPS platforms for microvessel production are limited in yield by small chamber volumes (0.2 and 25 mm³ for the rhomboid and permeable-insert platforms, respectively), and their scalability remains unproven for larger tissue constructs. As tissue engineering applications move from the bench to the clinic, yield requirements for target cell types increase significantly (26). It has been shown that engineered heart tissues can be generated using a combination of 70% cardiomyocytes, 15% cardiac fibroblasts, and 15% endothelial cells, requiring as few as 1.6×10⁴ cells for small constructs (27). Scaling these ratios to clinically relevant sizes involves millions of cells and larger bioreactor volumes. For instance, tubular engineered heart tissues have been successfully fabricated with an inner diameter of 6 mm, wall thickness of 1 mm, and length of 18 mm, using cardiomyocytes at a density of 18.0×10⁶ cells/mL (28), requiring ∼3.5×10⁶ endothelial cells. Generating microvessels from these endothelial cells would require sustaining target IF conditions in up to 20 permeable insert platforms (25 µL).

It is thus paramount to gain a thorough understanding of the scalability of these platform designs, the variations in flow-induced mechanical environment between different scaling strategies, and their effect on the yield, morphology, and functional characteristics of resulting microvessel networks. Computational fluid dynamics (CFD) simulations enable this understanding by predicting the IF field for any device and chamber shape or size. When combined with in vitro microvessel formation experiments, CFD can enable richer characterization, interpretation and cost-effective optimization of perfusion-based platforms. For instance, Wang et al. (22) demonstrated through CFD simulations that a microfluidic platform design ensured uniform interstitial flow (pressure drop of 5 mmH${ }_2$O, or 49 Pa) conducive to vasculogenesis and predictable cell flow paths. Hajal et al. (24) further explored the influence of flow conditions, both measuring (in vitro) and predicting (in silico) interstitial velocities between 0.08 and 2.14 µm∕s, with predicted shear stresses of 0.15–1.0 P, while elucidating the effect of luminal, transendothelial and interstitial flow conditions on tumor cell extravasation and migration.

In summary, CFD models validated with in vitro data can provide valuable insights for analysis and design of bioreactor platforms that create environments consistent with proliferation, differentiation, and maturation of endothelial cells and microvessel formation. In this article, we study the scalability of IF conditions across two distinct platform designs: Rhomboidal chambers and permeable insert setups. We investigate the feasibility of scaling up these designs while maintaining interstitial flow velocities within the physiological range of 0.1–11.0 $\mu$m/s (29), subject to constraints on the maximum height of a fluid column driving the perfusion flow. This size constraint effectively limits the maximum inlet pressure. To this end, we use CFD methods to predict, analyze and compare the IF fields within the culture chambers. Experiments conducted with these two platforms provide evidence regarding the ranges of IF that lead to successful formation of microvessel networks. In addition, comparative experiments with different platforms but similar average IF velocities support the use of the detailed IF field as an engineering descriptor for interpreting microvessel network outcomes, while recognizing that other biological and biochemical factors may also play an important role in microvessel network formation.

Materials and methods

Platform designs

Two platforms were analyzed in this work, a permeable insert platform (12) and a rhomboidal chamber platform (22), which will hereafter be referred to as platform A and platform B, respectively, shown in Fig. 1. For simulation purposes, computer-aided design (CAD) models of the platforms were created in SolidWorks and subsequently imported into the COMSOL simulation software.

Figure 1.

Microvessel network benchtop platforms. A) Permeable insert (platform A), including 3D and cross-sectional views, and the CFD simulation domain (right). Media flows through the porous gel and bottom membrane (8 µm pores) driven by the pressure exerted by a fluid column placed on top of the inlet. B) Rhomboid chambers (platform B), including 3D view and top views. Created in BioRender. Vatani, P. (2026) https://BioRender.com/3yb9gak. Created in BioRender. Vatani, P. (2026) https://BioRender.com/j4acddr.

Scaled versions of the platforms were created by modifying the CAD models to allow key dimensions to be scaled independently or in combination. For platform A, the gel chamber thickness (distance between inlet and outlet) and the chamber radius were the primary scaling parameters. For platform B, the length (across all three rhomboidal tissue chambers) and the width (distance between inlet and outlet channels) were used. For any of the platforms, geometrical parameters were first scaled by factors of 2, 5, 10, and 20, applied independently to each dimension. Secondly, the same scaling factors were applied simultaneously to all dimensions scaling the entire geometry while maintaining the aspect ratio.

Mathematical model and CFD simulations

The simulation models used in this work assume that the culture gel behaves as an isotropic, spatially homogeneous porous medium (22). Based on the pore dimension of the fibrin gel (30) and the average flow velocities through the gel under the conditions tested (∼5–20 $\mu$m/s) (22), the Reynolds number for this flow is $\mathrm{Re}\approx$ 8.45×10⁻⁶ to 3.38×10⁻⁵ ($\mathrm{Re}\ll 1$). Hence, we model the flow through the gel using Darcy’s Law for flow in porous media (31). The governing equation for interstitial flow is thus expressed as:

$$u=-\frac{\kappa }{\mu }(\mathrm{\nabla }p+\rho g),$$ (1)

where u is the fluid velocity [m/s], κ is the permeability [m${ }^2$], μ is the fluid viscosity [Pa·s], $\mathrm{\nabla }p$ is the pressure gradient [Pa/m], and $\rho g$ is the gravitational force per unit volume [N/m${ }^3$]. Darcy’s Law was solved together with the differential form of the Conservation of Mass principle, which for an incompressible porous medium is:

$$\frac{\mathrm{\partial }}{\mathrm{\partial }t}(\rho ϵ)+\mathrm{\nabla }\cdot (\rho \mathbf{u})=Q_m,$$ (2)

where $ϵ$ is the porosity, and $Q_m$ accounts for any mass source or sink (assumed zero in this work). The solution of these equations provides interstitial flow velocity profiles within the gel, defined as the total volumetric flow rate through the bulk gel divided by the cross-sectional area of the gel. Thus, IF is a measure of an average, equivalent flow speed through a conduit of the same cross-sectional area but without the porous media. The corresponding volumetric flow rate can be obtained as $Q=u{A}_{\perp }$, where $A_{\perp }$ is the cross-sectional area normal to the mean flow direction; equivalently, $Q[\mu {\text{L s}}^{-1}]={10}^{-3}\times u[\mu {\text{m s}}^{-1}]A_{\perp }[{\text{mm}}^2]$. Alternatively, the flow field inside the porous media can be expressed in terms of the average pore velocity, defined as:

$$u_{ϵ}=\frac{u}{ϵ},$$ (3)

which represents the average flow velocity that any cells located inside the porous media pores will be directly subjected to. In this work, results are expressed in terms of interstitial flow (IF) velocity to remain consistent with prior studies (32). However, the volume-averaged pore velocity ($u_{ϵ}$) may offer a more physically relevant quantity for defining the flow conditions that are favorable to microvessel formation.

Equations 1 to 3 indicate that permeability and porosity are two critical properties of the porous media that modulate interstitial flow. Based on previous experimental data (33) and image analysis on dextran flow experiments (described in Fig. S1), permeability and porosity values of 1.5×10⁻¹³ m² and 0.91, respectively, were used in this work to generate all results.

The equations were discretized using the finite element method in COMSOL Multiphysics. The simulations were performed in a 2D axisymmetric model for platform A and a 2D model for platform B. A stationary solver with an iterative method was used. The convergence threshold was set to a mass conservation residual of ${10}^{-15}$, starting from initial residuals in the range of ${10}^4$. The computational domain for both platforms was meshed with triangular elements, and a mesh independence study was conducted to ensure that the results were not influenced by further mesh refinement. No-slip boundary conditions were enforced at chamber walls on both platforms. For platform A, the pressure gradient was defined across the thickness of the gel. For platform B, the CFD model reproduced the experimental four-reservoir hydrostatic pressure configuration. Pressure boundary conditions corresponding to the reservoir liquid levels were prescribed at the four reservoir-connected channel ends (P1 $=$ 23 mmH${ }_2$O, P2 $=$ 8 mmH${ }_2$O, P3 $=$ 18 mmH${ }_2$O, and P4 $=$ 3 mmH${ }_2$O; Fig. S9). In this configuration, media flows through the microfluidic channels, creating a pressure gradient across the rhomboidal chambers, thus driving interstitial flow through the porous fibrin gel. Therefore, the pressure field is not symmetric, and symmetry boundary conditions were not used for platform B.

Microvessel network generation

Immortalized GFP-expressing human umbilical vein endothelial cells (HUVEC, passage 15–25, a gift from Dr. Roger Kamm, MIT (34)) were cultured in a completed VascuLife medium (LifeLine Technology) with only 25 % of the provided supplement volume of heparan sulfate. Normal human lung fibroblasts (NHLF, passage 5–6, Lonza) were cultured in DMEM (Gibco) supplemented with 20 % fetal bovine serum (heat inactivated, Wisent) and 1 % penicillin/streptomycin (Gibco). Human Brain Vascular Pericytes (HBVP, passage 4–6, ScienCell) were cultured in a completed Pericyte Medium (ScienCell).

The generation of a microvascular network in platform A was based on a previously established protocol (12). Briefly, cell-culture inserts (8 µm pore size) were modified with either a 2 mm-high PDMS ring (for 24-well sized insert) or PDMS film coating on the insert inner wall (for 6-well sized insert) to limit the hydrogel height and meniscus. All inserts were coated with poly-D-lysine (Gibco) to ensure hydrogel adherence to the insert. Dissociated HUVEC and stromal supporting cells (either NHLF or HBVP) were resuspended in a fibrinogen solution at 8–10 and 0.25–2 million cells/mL respectively, depending on specific experiments. With a prechilled pipette tip, cell-embedded fibrinogen solution was quickly mixed with thrombin in DPBS until the final mixture contained 10 mg/mL fibrinogen and 10 U/mL thrombin. The resulting hydrogel was immediately placed in the insert at room temperature. Because the thrombin concentration was 10 U/mL, polymerization was rapid, and the hydrogel changed from a liquid-like to a solid-like state within 10–15 s. During this initial gelation period, the insert was rotated upside down every 3–5 s to reduce directional cell settling. After further incubation at 37 °C for 30 min, the inside of the insert was filled with VascuLife at a higher medium level than the outside, resulting in a hydrostatic pressure difference of ∼16 mmH₂O and thus interstitial flow through the fibrin hydrogel. The medium was refilled every day for over a 1-week duration.

The generation of microvascular network in platform B was based on a previously established protocol (35). Briefly, dissociated HUVEC and NHLF were resuspended in a fibrinogen solution at 8 and 2 million cells/mL, respectively. With a pre-chilled pipette tip, 9 µL of cell-embedded fibrinogen solution was quickly mixed with 1 µL of 50 U/mL thrombin in DPBS, resulting in the final concentration of 10 mg/mL fibrinogen and 5 U/mL thrombin, before being injected in the gel-loading chamber of the microfluidic chip. After sealing both gel-loading ports, the chip was then incubated at 37 °C for 20 min. VascuLife was used in the co-culture and filled into each medium reservoir. On one medium channel, the inlet reservoir no. 1 was filled with 1,500 $\mu$L (equivalent to 23 mmH₂O) and the outlet reservoir no. 2 was filled with 500 µL (equivalent to 8 mmH₂O). On the other channel, the inlet reservoir no. 3 was filled with 1,000 $\mu$L (equivalent to 18 mmH₂O) and the outlet reservoir no. 4 was filled with 200 µL (equivalent to 3 mmH₂O). This medium-filling configuration ensures a hydrostatic flow along the medium channel (reservoir no. 1 $\to$ no. 2, and reservoir no. 3 $\to$ no. 4) as well as across the gel-loading chamber (reservoir no. 1 and 2 $\to$ nos. 3 and 4). All medium reservoirs were replenished to the initial level every day over a 1-week duration, where the medium level of each side channel was reversed (reservoir nos. 1 and 2 ↔ nos. 3 and 4) each day to prevent HUVEC from migrating preferentially toward one side channel.

Quantitative morphology analysis

For platform B regional morphology analysis, fluorescence images from seven independent platform B experiments acquired after 7 days of culture were analyzed using predefined central and lateral regions of interest (ROIs). Three central ROIs and two lateral ROIs were selected based on the chamber geometry. Within each ROI, vessel area, skeleton length, and apparent lumen diameter were quantified from segmented fluorescence images. The image-analysis workflow used to generate the segmented vessel mask, skeletonized vascular network, and apparent diameter map is shown in Fig. S2. For the main analysis, the three central ROIs and two lateral ROIs were aggregated into two groups. The same grouped ROI definitions were also used to extract CFD-predicted IF velocity distributions. Details of the segmentation workflow, ROI definitions, skeletonization, diameter extraction, supplementary disaggregated ROI analysis, and CFD-based regional IF extraction are provided in Sections S2–S4. Similar methods were applied for ROI analysis of vertical cross-sections of platform A, also included in the Supplementary material.

Results

Baseline platforms

Interstitial flow simulations were conducted under baseline pressure configurations for both platforms. Figure 2A shows that both platforms successfully generated IF velocities within the physiological range 0.1–11.0 $\mu$m/s (29). Platform A exhibits uniform IF velocities throughout its porous domain, attributed to its simple geometry, constant cross-section and unidirectional flow. In contrast, platform B shows spatial IF variability throughout each rhomboidal chamber. These results indicate that both platforms can achieve flow conditions suitable for vascular network formation, despite their differing geometries.

Figure 2.

Interstitial flow (IF) velocity profiles along vertical and horizontal midlines under baseline (16 mmH₂O) and increased (50 mmH₂O) pressure conditions. A) IF along vertical midline, baseline pressure. B) IF along horizontal midline at both baseline and increased pressures.

Controlling IF through pressure gradients

Scaling up platforms presents notable challenges, particularly the reduction in interstitial flow (IF) velocities when the pressure is kept constant. According to Darcy’s law, IF velocity is inversely proportional to the characteristic length, i.e. length measured along the main direction of the flow. As platforms are scaled up, this characteristic length might increase, leading to a natural decrease in IF velocities if the pressure difference driving the flow is kept constant. For a platform to remain viable during scaling, it must generate IF velocities above the physiological lower limit 0.1 $\mu$m/s, required for vascular network formation.

Figure 2B illustrates changes in IF velocity profile in both platforms under baseline pressure conditions (a hydrostatic pressure difference of 16 mmH₂O) and the maximum pressure gradient we imposed as a design constraint (50 mmH₂O). From these data, it is clear that pressure can be used to modulate IF magnitudes across the gel while preserving the underlying spatial flow pattern. This modulation is limited, however, by the mechanical integrity and compressibility of the gel and the susceptibility of endothelial and supporting cells to pressure stimuli.

Experimental validation of microvessel formation

Over 7 days of culture, HUVECs, as our model endothelial cells, gradually moved and connected to one another to form a microvascular network across the entire hydrogel. Platform B exhibited an interconnected network of lumens or hollow channels inside. This network was perfusable with Dextran Rhodamine solution without any leakage into the hydrogel space, indicating the patency of the microvessel. Similarly, platform A also showed the formation of microvascular network, though patency was not tested in this platform.

CFD simulations using the experimental hydrostatic pressure configurations were conducted to compare predicted IF fields with the observed vascular patterns (Fig. S9). The resulting IF field in Platform B showed a diverging-converging pattern of streamlines connecting inlet and outlet ports in the three chambers (Fig. S9A), with additional streamlines indicating flow between the central chamber (Fig. S9B) and the lateral chambers. The IF field in platform B is not symmetric, owing to the different reservoir pressures driving flow across each chamber. This spatial IF pattern was visually consistent with the vascularized region observed experimentally (Fig. S9C), suggesting vessel alignment along the direction of IF. This spatial correspondence provides evidence in support of the use of the CFD-predicted IF field as a design descriptor for evaluating whether a given geometry and perfusion condition is likely to support microvessel formation, and motivated the regional morphological analysis presented below. Accordingly, CFD simulations can support preliminary evaluation of candidate platform designs or scaled-up platforms by identifying whether their IF velocities fall within ranges associated with microvessel network formation under conditions tested here and reported in the literature.

Figure S9D shows the microvessel networks obtained in platform A. Unlike platform B, where imaging was performed in the same plane of the interstitial flow direction, images in platform A were acquired perpendicular to the IF direction. This precluded a direct spatial comparison between predicted streamlines and vascular alignment. To verify that microvessel network formation occurred throughout the full fibrin gel volume in platform A, tile-scan imaging was performed on a vertical cross-section of platform A samples. Microvascular structures were observed across the cross-sections in all replicates, providing evidence that network formation was not limited to the lower surface or bottom-view imaging plane (Fig. S10).

Quantitative morphology analysis

To quantitatively assess regional morphology in platform B, predefined ROIs were selected in central and lateral regions of the rhomboidal chamber (Fig. 3C) and analyzed using the morphology metrics described in the Materials and methods section. The disaggregated results for vessel diameter, vascular area fraction, and vessel length density across the five individual ROIs are shown in Figs. S3–S5. The predefined CFD ROIs and the grouped CFD-based IF velocity comparison are shown in Figs. S6 and S7, respectively. The same grouped ROI definitions were also applied to the CFD-predicted IF velocity field (Fig. 3J; see also Fig. S8 for individual ROI distributions), showing distinct IF velocity distributions between the central and lateral ROI groups. The central regions showed significantly larger average lumen diameter and lower total vessel length per area compared with the lateral regions, while vascular area was not significantly different (Fig. 3G–I). These results provide quantitative support for regional morphology differences within platform B. Because the central and lateral ROIs were analyzed for each experimental replicate, within the same device and thus under the same culture conditions, these regional morphology differences can be correlated with distinct CFD-predicted IF velocity distributions. These results suggest that local IF velocity plays an important role in regional variations in microvessel network morphology, although it does not establish IF as its sole determinant.

Figure 3.

Experimental microvessel formation, morphology, and CFD-predicted IF velocity field in platforms A and B. A, B) Microvessel formation in platform A using 25 and 800 $\mu$L gel volumes. Each panel shows the well insert image, whole-gel fluorescence image, and high-magnification view of GFP-HUVEC networks. C) Platform B microvascular network and central/lateral ROIs. D–F) Average lumen diameter, vascular area, and total vessel length per area for different sizes of platform A (25, 200, and 800 $\mu$L). G–I) Average lumen diameter, vascular area, and total vessel length per area for central and lateral ROIs in platform B. J) Central and lateral ROIs overlaid on the CFD-predicted IF velocity field in platform B, IF velocity distributions extracted from these regions. Bar plots show mean with SEM and individual samples, while the IF velocity boxplot represents CFD-predicted IF velocity in each ROI. Statistical significance is indicated as ns, not significant; **, $P<0.01$.

In contrast with platform B, predicted IF fields in platform A are uniform (Fig. 2). Furthermore, quantitative morphology analysis of vertical cross-sectional images of platform A (Fig. S11), and of horizontal cross-sections (Fig. 3A,B,D–F) showed no statistical differences in vascular area and lumen diameter between ROIs defined in the top, middle and bottom of the gel volume. Taken together, these experimental observations suggest that the IF velocity field contributes to microvessel network characteristics, while other biological and matrix-related factors may also play a role.

Scaling up platform A

The diameter and gel thickness of platform A were scaled, first independently and then jointly, to assess scale-up effects on IF patterns. Note that modifications of the diameter and/or thickness of the gel can be implemented using PDMS rings of different sizes, larger-diameter off-the-shelf permeable inserts, or by modifying the volume of gel added.

The full scaling results are summarized in Fig. 4. Figure 4A shows the results of scaling the diameter by factors of 2×, 5×, 10×, and 20× with respect to the baseline design, with corresponding volume increases by factors of 4×, 25×, 100×, and 400×, respectively. IF velocity remained constant regardless of the scaling factor when the applied pressure was unchanged. In contrast, Fig. 4B shows that increasing the gel thickness resulted in a significant decrease in IF velocity for each pressure condition. Figure 4D provides the pressure adjustments required to maintain constant IF velocity across various height scaling factors, offering practical guidance for preserving physiological flow conditions during scaling.

Figure 4.

Scaling for platform A: A) IF velocities under diameter scaling, showing no changes in velocity with increasing diameter under constant pressure. B) IF velocity under height (gel thickness) scaling, showing a significant decrease in velocity with increased height. C) IF velocity for whole geometry scaling highlighting dominant effect of gel thickness on IF. D) Required pressure adjustments (numbers above/below data markers) to maintain physiological IF velocity (colors) across various gel height scaling factors.

Additionally, the simultaneous scaling of both diameter and gel thickness was evaluated. As depicted in Fig. 4C, this scaling approach significantly reduces IF velocity across all pressure conditions, with gel height having the dominant influence. These findings provide guidance for dimension-specific scaling strategies, balancing IF control, increased yield, and experimental feasibility.

To validate these simulation results and demonstrate the feasibility of scaling up platform A, microvessel formation was compared in permeable insert devices with three different gel volumes: a 25 µL baseline geometry and two scaled-up geometries of 200 µL (results not shown) and 800 µL, following the same experimental protocol described above. The increase in volume was achieved by enlarging the insert membrane diameter. Fluorescence images and quantitative results, included in Fig. 3A, B, and D–F, respectively, show interconnected microvessel networks for different scale-ups of platform A. Statistical analysis was performed using the Shapiro–Wilk test for normality, followed by Brown-Forsythe and Welch ANOVA with Dunnett’s T3 multiple comparisons test to account for unequal variances. Across all groups ($n=3$ per group), no statistically significant differences were found in average vessel diameter, vascular area, or vessel length per unit area. This indicates that maintaining similar IF velocity across geometrically similar bioreactor sizes was associated with consistent measured network morphology.

Scaling up platform B

Unlike platform A, platform B does not exhibit uniform interstitial flow (IF) velocity throughout its domain. Due to spatially varying nature of IF in this platform, box-and-whisker plots were used to represent the IF distribution across different scaling strategies. Figure 5 presents an array of results for independent scaling of different dimensions of platform B (figure rows), namely length and width (distance between inlet and outlet of the chambers), under varying pressure conditions (figure columns). It can be observed that as the scaling factor increases, the overall range and interquartile range (IQR) of the IF distributions decreases with respect to the baseline geometry (1×). At larger scaling factors, the system creates a narrower range of IF velocities compared to the baseline geometry, particularly under lower pressure conditions (e.g. 12 mmH₂O). It can also be observed that across scales, a portion of the gel volume is exposed to IF outside the target range (shaded area in the plots), especially at larger pressures.

Figure 5.

Interstitial flow velocity distribution for scaling different dimensions of platform B (rows) under varying pressure conditions (columns). Shaded area in all figures indicates an IF range that resulted in microvessel networks in the literature. Baseline geometry corresponds to 1×.

The third row of plots in Fig. 5 presents the results of scaling the entire rhomboid geometry with a constant aspect ratio. Compared to scaling individual dimensions, scaling the entire geometry provides significant increases in chamber volume while still replicating the IF distribution of the baseline geometry. The results indicate that scaling the entire geometry up to 5× maintains interstitial flow (IF) velocities within the physiological range across the domain. Beyond this scale factor, the velocity distribution narrows compared to the baseline geometry. These findings suggest that whole-geometry scaling is effective up to moderate scale factors, but maintaining the IF distribution at larger scales requires adjustments in the applied pressure gradient.

Commonly used AIM Biotech and similar microfluidic vascularization platforms provide useful context for the IF ranges predicted here. Winkelman et al. (36) measured hydrostatic-pressure-driven dextran transport across cell-free fibrin gels in AIM Biotech chips and reported velocities of 1.73–5.73 $\mu$m/s for reservoir height differences of 0.375 mmH₂O to 1.5 mmH₂O, with a measured fibrin permeability of 4.35(23)×10⁻¹³ m². Using the Darcy-law scaling $u\propto \kappa \mathrm{\Delta }P$, their 1.5 mmH₂O condition corresponds to ∼66 $\mu$m/s when scaled to the permeability used in this study ($\kappa =$1.5×10⁻¹³ m²) and a 50 mmH₂O pressure difference. This order-of-magnitude estimate is consistent with the upper IF range predicted for platform B under the same driving pressure, although exact comparison would require matched geometry and boundary conditions. Hajal et al. (24) and Offeddu et al. (37) reported lower mean IF values in AIM Biotech and related microvascular platforms under trans-endothelial or transmural pressure conditions, where part of the applied pressure is resisted by the endothelial barrier before fluid enters the gel.

Geometry comparison under controlled volume and IF conditions

Platform A and platform B were compared to evaluate how their geometries influence IF velocity distribution under matched gel volume and average IF velocity conditions. IF velocities for the baseline design were extracted, and platform A was scaled to match the total gel volume of the baseline platform B. Pressure adjustments were applied to achieve the same average IF velocity in both platforms. Figure 6 illustrates the IF velocity distributions for the two platforms. Platform A generates a uniform IF velocity field across the gel, as indicated by the horizontal red line in the Fig. 6A (also the vertical red line in Fig. 6B). In contrast, platform B exhibits a wide range of IF velocities across different regions of the gel, as shown by the box-and-whisker and histogram plots. The variability in platform B highlights its ability to create localized flow profiles, while platform A maintains consistent flow throughout its domain. These IF distributions can be compared with literature-reported relationships between IF and microvessel morphology metrics such as lumen diameter or length per area, although such comparisons should be interpreted as design guidance rather than direct predictive mapping. Figures 6C and D show the vessel characteristics that were observed for different interstitial flow values by Zhang et al. (13).

Figure 6.

Interstitial flow (IF) velocity distributions for platform A and platform B under matched gel volume (1.1 mm³) and average IF velocity (2.2 µm/s) conditions. The shaded region represents the physiological IF range 0.1–11.0 $\mu$m/s. A) Boxplot of IF velocities, B) histogram of IF velocities, and C) and D) microvessel lengths and diameters obtained at different IF velocities by Zhang et al. (13).

Discussion

This study explored the scalability of platform A (permeable insert) and platform B (rhomboid chambers), focusing on interstitial flow (IF) velocities across various scale-up factors and pressure conditions. While both platforms demonstrated scalability potential, platform A exhibits greater ease of control and spatial uniformity in IF velocity regardless of scaling, with scaling options that do not require larger pressure gradients to sustain a target IF. In contrast, platform B exhibits a wide range of IF, and requires pressure adjustments to sustain a target IF under most scaling scenarios. Experimental validation results support IF as a key engineering variable associated with successful microvessel network formation and correlated with network morphology within the target IF range used in this work. However, these findings do not isolate IF as the sole or dominant determinant of network morphology. Microvessel formation is multifactorial, and variables such as endothelial and stromal cell density (6, 7), fibrin concentration, matrix stiffness, secreted biochemical factors (13, 17), and matrix remodeling (29, 30), may interact with IF to shape network outcomes. To consider one non-flow variable in platform A, we examined lumen diameter distributions across two pericyte densities at different timepoints in the culture (days 3, 5, and 7), shown in Fig. S12. The lumen diameter distributions changed over culture time, particularly showing differences in spread (IQR, range, variance) but near-constant median between pericyte-density conditions, supporting the interpretation that measured diameter distributions and heterogeneity can be influenced by cell-composition and time-dependent biological factors in addition to IF. Nevertheless, IF remains a controllable and experimentally actionable variable that can be used to compare platforms, guide scale-up, and define target flow environments for microvessel formation. While the direct mechanistic role of IF gradients on network formation was not isolated herein, it was shown by Staples et al. (38) that endothelial cells predominantly polarize against the direction of flow at high shear stresses (0.1 Pa), while up to 55% of endothelial cells polarize in the direction of the flow, or even orthogonally, at lower shear stress levels (0.08 Pa). Importantly, shear stress has also been shown to modulate intussusceptive angiogenesis (38) and angiogenic sprouting (39). The ROI-based platform B analysis provides quantitative support for a relationship between regional IF environment and microvessel morphology. The central and lateral regions, which corresponded to distinct CFD-predicted IF velocity distributions, showed significant differences in average lumen diameter and total vessel length per area, while vascular area was not significantly different (Fig. 3G–J). Because these ROIs were analyzed within the same device and culture condition, the observed morphology differences occurred under otherwise matched experimental conditions. These results suggest that local IF velocity plays a role in regional morphology, while still not establishing IF as the sole determinant of morphology. Soluble-factor transport, matrix remodeling, cell density, and device geometry may also contribute to the measured regional differences.

Comparative insights on scaling

The uniform IF velocity profile of platform A aligns with previous findings (12), which confirms its suitability for scaling scenarios where consistent flow conditions are essential. For platform B, scaling revealed significant variations in IF velocity across different areas of the geometry, including at relatively small scale factors. This spatial variability is supported by dextran perfusion experiments showing uneven gel saturation in platform B (Fig. S1), consistent with spatially varying transport through the chamber, and by the CFD-based ROI extraction showing distinct predicted IF velocity distributions between the central and lateral ROI groups (Fig. 3J). The spatial gradients of IF may more closely mimic physiological conditions leading to formation of vascular networks. Indeed, several studies reporting successful microvessel formation employed platforms that inherently exhibit spatial IF gradients due to their geometries or perfusion strategies (13, 18, 29, 35), leading to nonuniform vessel diameter distributions.

Recent evidence indicates that IF gradients (in both magnitude and direction) can modulate vascular network morphology. Controlled 3D models have demonstrated that mild IF levels (0.1–5 $\mu$m/s) promote greater vessel area, branch length, and average diameter compared with static cultures (36), with flow gradients on the order of 0.01–0.1 $\mu$m/s per 100 $\mu$m correlating with directional bias in sprouting (18). Convective transport also reshapes morphogen distributions, as low physiological IF (0.5–5 $\mu$m/s) can dissipate VEGF gradients, redirecting sprouting against the flow vector and reducing local branching density (29). Collectively, these findings suggest that moderate IF gradients (roughly 0.01–0.05 $\mu$m/s per 100 µm spatial scale) may be associated with more complex, branched vascular topologies, whereas steeper gradients may be associated with enlarged or more mature vessel structures, depending on the biochemical and matrix context. It is unclear, however, if IF gradients affect network morphology directly or, instead, indirectly through their effect on morphogen (e.g. VEGF) gradients. Beyond its mechanical role, IF can shape microvessel formation via morphogen redistribution (17, 29) and MMP-2 upregulation (13), so local morphology may reflect coupled transport, matrix-remodeling, and cellular mechanisms rather than local IF magnitude alone. Accordingly, the broader IF spectrum observed in platform B was associated with region-dependent measured morphology, while platform A’s more uniform IF field is consistent with the reproducible morphology observed across scaled conditions. These results support the use of CFD-predicted IF fields as design descriptors for identifying regions where different morphologies may emerge, while recognizing that the measured differences represent an association rather than a single-factor causal relationship.

An important distinction between the two platforms is their potential for post-formation luminal perfusion. Platform B may provide an advantage for studies requiring direct luminal perfusion because its side-channel architecture provides defined access points to the vascular network. In contrast, platform A was evaluated here primarily as a scalable interstitial-flow-guided formation platform. Cross-sectional imaging showed microvascular structures across the gel thickness (Fig. S10), but direct luminal openings at the upper gel surface and sustained postformation luminal perfusion were not systematically assessed. Purposeful engineering of gentle IF gradients, through graded permeability or tapered geometries, could therefore serve as a design strategy for exploring and potentially guiding microvascular morphology in scalable bioreactors.

In addition, results from platform B suggest the existence of an upper boundary for effective scaling, beyond which achieving both physiological IF velocities and a flow distribution conducive to microvessel formation becomes more challenging. Tailored scaling strategies aligned with specific experimental objectives are therefore essential to optimize scalability. For example, scaling the width of platform B proved less effective as a standalone strategy, requiring higher pressure adjustments to achieve target velocities. Scaling the entire geometry, however, demonstrated a better balance between volume increases and maintaining IF velocity, although a lower IQR of the IF distribution was observed at higher scaling factors, potentially impacting the diameter, length or connectivity distributions of the resulting microvessel networks, as was observed by Soon et al. (35).

Experimental validation in the scaled-up versions of platform A confirmed microvascular network formation under hydrostatic pressure-driven interstitial flow. Additionally, quantitative assessment of vessels formed within platform A across scaled-up diameters showed consistent vessel diameter distributions, vascular area, and vessel length per area across different gel volumes, despite a more than 30-fold increase in culture volume (Fig. 3D–F). This consistency, achieved while maintaining constant interstitial flow conditions, supports the importance of IF as an engineering variable associated with reproducible microvascular morphology under the tested conditions. Successful vessel formation under IF, along with quantitative morphological assessment, has also been demonstrated in platform B (35).

CFD-based scale-up

This study demonstrated the feasibility of scaling up platform A (permeable insert) and platform B (rhomboid) while maintaining IF within a target range using numerical simulation approaches. CFD simulations provided a detailed understanding of spatially varying IF profiles in the examined platforms, and elucidated how pressure adjustments can maintain functional flow conditions during scaling. Combining CFD and in vitro results, this work provides further evidence that IF is associated with microvessel formation and measured morphology under the tested conditions. Our scale-up results on platform A, where we imposed the same IF on multiple scales of the same geometry, showed remarkable uniformity. In contrast, platform B produced a spatially varying IF profile, and the ROI analysis supports the use of these predicted regional flow differences as design descriptors for interpreting where distinct microvessel morphologies may emerge. Broader IF-dependent distributions of microvessel diameters and lengths have also been reported in previous works (13, 17, 18).

As IF–morphology relationships are further quantified, IF distributions predicted with experimentally validated CFD models could be used to design bioreactors that generate prescribed IF distributions, which may help guide future efforts to bias vessel diameter or length distributions toward those that may be associated with better clinical outcomes.

Simulation-based design optimization as a computational proof-of-concept

To illustrate how the CFD framework could be used to redistribute IF within a platform, we formulated a simulation-based design optimization problem to modify the design of platform A. Specifically, we modified the insert geometry to have several cross-sections, similar to a set of vertically stacked cylinders with different heights and radii, joined by short transition sections shaped like inverted truncated cones, as shown in Fig. 7A. We defined as design parameters a) the height $H_i$ and radius $r_i$ of each vertical section, and the height $h_i$ of the transition sections. We conducted a dimensional optimization study in COMSOL, with the same simulation settings described in the Materials and methods section, and with an inlet pressure of 68.6 Pa (7.0 mmH₂O) applied on the top of the insert, with the goal of achieving a target distribution of interstitial flows inside the gel volume.

Figure 7.

Optimization of modified platform A for targeted IF distribution. A) Design variables, B) IF velocity field in the baseline design, corresponding to $x_0=(0.3500,0.6500,0.5000,1.8000,1.9500,2.0500,0.2500,0.2500)\times {10}^{-3}$ m, C) IF velocity field in the optimized design, corresponding to $x_{\mathrm{opt}}=(0.7468,0.4318,0.4139,1.1519,1.8052,1.9938,0.1545,0.2531)\times {10}^{-3}$ m. Maximum and minimum values in the color scales shown on the right of the figure, corresponding to IF velocity and the IF-based microvessel diameter estimate (Fig. 6D), have been clipped to facilitate the simultaneous depiction of IF and the estimated vessel diameter in the same figure.

Let $\mathbf{x}=[H_1,\dots ,H_N,r_1,\dots ,r_N,h_1,\dots ,h_{N-1}]$ be the vector of design parameters. Let $I=I_1,\dots ,I_N$ be a partition of the target IF range [0.1, 15] $\mu$m/s into N intervals,

$$I_i=[v_i^{min},v_i^{max}),i=1,2,\dots ,N,$$ (4)

where $v_1^{min}=0.1$, $v_N^{max}=15$, and $v_i^{max}=v_{i+1}^{min}$ for all i. For each IF interval $I_i$, we compute the fraction of the gel volume with IF in the corresponding range, $f_i(\mathbf{x})$, and we denote the target fraction for that interval as $f_i^t$. Then, the optimization problem is formulated as

$$\begin{array}{cc}{\mathbf{x}}_{\mathbf{o}\mathbf{p}\mathbf{t}}=\underset{\mathbf{x}}{\arg min}& \sum _{i=1}^N{(f_i(\mathbf{x})-f_i^{\mathrm{t}})}^2-\lambda {(1.0-\sum _i{f}_i)}^2\\ \text{subject to}& H_j^{min}\le H_j\le H_j^{max},j=1,\dots ,N\\ & r_j^{min}\le r_j\le r_j^{max},j=1,\dots ,N\\ & h_j^{min}\le h_j\le h_j^{max},j=1,\dots ,N-1\\ & \sum _i{H}_i=H_{\mathrm{tot}},\end{array}$$ (5)

where $H_{\mathrm{tot}}$ is the total height of the permeable insert. Note that the objective function is the sum of squared deviations from the targets and includes an additional term that seeks to minimize the fraction of the gel with IF velocities outside the target ranges.

For illustration purposes, let us define three target IF ranges, namely 0.1–1.0, 2.0–3.0, and 5.0–10.0 $\mu$m/s, corresponding to three vertical sections for the permeable insert. Table 1 shows the design parameter ranges and the rationale for our choices.

Table 1.

Design space for modified platform A.

Design variable	Baseline	Step	Min	Max	Rationale
Bottom radius $r_1$	1.80 mm	0.002	1.00 mm	2.15 mm	Maximum radius is baseline 2 mm + buffer, minimum radius keeps sizes reasonable.
Middle radius $r_2$	1.95 mm
Top radius $r_3$	2.05 mm
Bottom section height $H_1$	0.35 mm	0.001	0.30 mm	$\le 1.40{mm}^{*}$	Total height is baseline 2 mm, Maximum and minimum set to enforce 3 zones with 2 smaller, non-vanishing transitions.
Middle section height $H_2$	0.65 mm
Top section height $H_3$	0.50 mm
Bottom transition height $h_1$	0.25 mm	0.001	0.15 mm	0.30 mm
Middle transition height $h_2$	0.25 mm

Three gel zones are defined to meet a user-defined allocation of gel volume to target IF ranges. Design ranges for gel zone heights and radii are defined around a baseline, enforce a constant system height, and nonvanishing transition zones between the target gel regions. The section and transition heights satisfy $H_1+h_1+H_2+h_2+H_3=H_{\mathrm{tot}}=2.00\text{mm}$.

*The allowable value is also determined by the fixed total-height constraint in Eq. 5.

Figure 7 shows the results of this optimization study. Specifically, Fig. 7B and C depict the geometry and IF flow field of the initial and optimized designs, respectively. As expected, successive reductions of cross-sectional area cause the flow to accelerate, resulting in a spatially varying IF distribution. In addition, the changes in cross-section modify the direction of the flow, introducing radial velocity components, as shown by the flow streamlines and velocity vectors depicted in the Fig. S13.

Studies by Abe et al. (17) and Kim et al. (18) have shown that flow gradients and directionality can bias the orientation and extension of angiogenic sprouts, with angiogenesis often occurring opposite to the direction of flow. Therefore, CFD-based design of bioreactor geometry can be used to control the spatial distribution of IF magnitude, direction, and gradients, providing a framework for generating experimentally testable hypotheses about how platform geometry may influence microvessel topology and morphology. For instance, given a mapping correlating IF velocities with the geometrical and topological characteristics of the resulting microvessel networks, the optimization problem of Eq. 5 could be recast in terms of target distributions for vessel diameter, vessel length, total vessel area coverage, and/or average number of branching points (17). In this work, we used experimental results by Zhang et al. (13) that characterize the average vessel segment length and diameter as a function of the IF used during the culture period (Fig. 2 in the reference). Based on these data, and just for illustration purposes, we fitted a linear regression to map the IF fields depicted in Fig. 7B and C to fields of IF-based vessel diameter estimates, please refer to the rightmost colorbar in Fig. 7.

This study illustrates the value of CFD models for bioreactor design. As the effects of the mechanical and biochemical environment on microvessel formation and morphology are elucidated in the coming years, CFD models, potentially augmented with the inclusion of mathematical models for cell signaling networks (40), could support the design of scalable microvessel bioreactors with improved control over the flow environments that influence network characteristics.

Limitations and future studies

In this study, we assumed uniform, average permeability and porosity throughout the gel and treated these properties as static during culture. Thus, our CFD simulations may not capture spatial variability in manufactured gels or time-dependent changes in gel properties during vessel formation. Prior work has shown that angiogenesis involves ECM degradation by MMPs (41), and that effective matrix permeability can change during MVN formation due to cell-secreted ECM and matrix remodeling (13). Such changes could alter local IF velocity distributions by changing the local hydraulic resistance of the gel. Future research may incorporate detailed models derived from high-resolution image analysis, such as segmented z-stacks (e.g. Zhao et al. (42)). These models would enable more accurate predictions of local IF velocity. Specifically, predicting pore-scale velocity and shear stress would better describe the mechanical environment directly experienced by the cells. Combined with multiscale modeling (40), such approaches could predict spatio-temporal variations in IF, permeability, porosity, and microvessel formation. In addition, the present study primarily quantified vessel diameter, vascular area, and vessel length density; therefore, a more complete quantitative relationship between IF distributions and higher-order network features, such as branching, connectivity, and perfusability, will require region-specific and 3D network analyses.

Compressibility of the fibrin gel under pressure was not considered. This could potentially affect porosity and permeability, particularly under high pressure. However, our initial in silico tests indicate that accounting for gel compressibility did not impact IF predictions. Specifically, we observed $<0.1\mathrm{\%}$ change in predicted IF, at an inlet pressure of 127.5 Pa (13.0 mmH₂O), for a gel with elastic modulus of 0.9 kPa and Poisson’s ratio of 0.49. However, fibrin gel stiffness is known to modulate directional angiogenic bias (29), an effect not considered in our hydrodynamically focused study. Similarly, we did not consider potential effects of pressure stimuli on endothelial cell function, signaling, and gene expression (43).

Finally, this study focuses on IF velocity as the primary engineering descriptor, while shear stress (36, 39) and matrix evolution were not explicitly modeled. These factors may influence scalability because maintaining the same average IF during scale-up does not necessarily preserve local pore-scale shear, matrix remodeling, permeability evolution, nutrient transport, or secreted-factor distribution throughout the gel. Nutrient and secreted-factor transport is governed by both diffusion and advection, and only the advective component is directly driven by IF. In addition, shear stress depends on local velocity gradients at the pore scale, so conditions with similar pore-scale velocity may still produce different shear environments. Future work should expand this framework to include shear-related cues and dynamic remodeling effects, which may alter local flow and nutrient distribution and thereby impact vessel network characteristics across scales.

Conclusions

This study provides a comprehensive assessment of the scalability of two microvessel bioreactor platforms. CFD simulations combined with in vitro perfusion experiments characterized the interstitial flow (IF) conditions under which microvessels form and analyzed IF fields across scaled-up platform versions. Results demonstrated the feasibility of scaling while maintaining IF within physiological target ranges. Experimental validation of platform A scale-up showed that microvessel formation and measured morphology were maintained across a more than 30-fold increase in culture volume when IF conditions were preserved under the tested conditions. In platform B, regions with distinct CFD-predicted IF velocity distributions showed significant differences in average lumen diameter and vessel length density under otherwise matched experimental conditions, supporting an association between local IF environment and regional network morphology. Together, these results show that CFD can be used to define and compare IF environments during scale-up, that scale-up with matched IF can result in similar measured morphology, and that IF distributions inside a device can correlate with regional network morphology.

Scale-up results indicate that platform A provides uniform flow profiles with direct pressure-gradient control and produced microvessel networks with consistent measured vessel diameters across the tested scaled conditions when IF was maintained. For instance, scaling platform A diameter by 10× results in a 100-fold increase in volume while sustaining the same IF conditions as the baseline without requiring an increase in the pressure gradient. In contrast, platform B exhibits a spatially varying IF profile that more closely mimics the complex IF environments of native tissues and was associated with region-dependent differences in average lumen diameter and vessel length density.

By combining computational modeling with experimental validation, this study provides a framework for evaluating and scaling perfusion bioreactor systems based on interstitial flow dynamics.

Supplementary Material

Supplementary material is available at PNAS Nexus online.

Competing Interest

The authors declare no competing interests.

Funding

We acknowledge the support of the Government of Canada’s New Frontiers in Research Fund (NFRF) under grants NFRFT-2022-00447 and NFRFT-2020-00787, and the Natural Sciences and Engineering Research Council of Canada (NSERC) through its Discovery program.

Author Contributions

P.V. developed the CFD models, conducted the in silico scale-up studies, and participated in drafting the manuscript. K.S. performed the microvessel network formation experiments and participated in drafting the manuscript. Z.H. estimated the porosity and permeability values from experimental data and participated in drafting the manuscript. D.A.R. developed the CFD models, conducted the in silico scale-up studies, and participated in drafting and reviewing the manuscript. S.S.N. performed the microvessel network formation experiments and participated in drafting and reviewing the manuscript. C.H.A. developed the CFD models, conducted the in silico scale-up studies, and participated in drafting and reviewing the manuscript. All authors reviewed and approved the final manuscript.

Data Availability

The data and computer code underlying this article are available in the Zenodo open repository, with identifier DOI:10.5281/zenodo.21477564.