Scaling-Up Vertical-Wheel Bioreactors Based on Cell Aggregate Exposure to Shear Stress and Energy Dissipation Rate

This study demonstrates that trajectory-based exposure to energy dissipation rate, rather than volume-averaged metrics or shear stress, provides a superior basis for scaling up vertical-wheel bioreactors for human pluripotent stem cell culture.

The Gist

Imagine you are a tiny, fragile seed (a stem cell) trying to grow into a massive forest (a billion cells needed for heart repair). To do this, you can't just sit in a pot on a windowsill; you need to be in a giant, swirling whirlpool that keeps you fed and oxygenated. This whirlpool is called a Vertical Wheel Bioreactor (VWBR).

However, there's a catch: if the water spins too gently, you don't get enough food. If it spins too wildly, the current might tear you apart or smash you into your neighbors. The goal of this research was to figure out exactly how to spin this whirlpool so that millions of seeds grow happily, no matter how big the whirlpool is.

Here is the story of their discovery, broken down into simple concepts:

1. The Problem: The "Average" Lie

For years, scientists tried to scale up these bioreactors (making them bigger, from a coffee cup size to a bucket size) by looking at the average speed of the water. They thought, "If the average speed is the same in a small cup and a big bucket, the cells will be happy in both."

The Analogy: Imagine you are driving a car. If you tell a passenger, "The average speed of our trip was 60 mph," that sounds safe. But what if the car sped up to 120 mph for 10 seconds and then stopped for 10 seconds? That "average" hides the dangerous spikes.

The researchers found that cells are like that passenger. They don't experience the "average" water speed. They get tossed around. Sometimes they are in a calm zone, and sometimes they get slammed into a high-speed current near the spinning wheel. Using the "average" to design big bioreactors was like planning a road trip based on an average speed and ignoring the potholes and speed traps.

2. The New Approach: The "Trajectory" Map

Instead of looking at the water as a whole, the researchers used a computer to track individual cell clumps (aggregates) as they moved through the bioreactor.

The Analogy: Think of a leaf floating down a river.

• The Old Way: Measuring the average speed of the whole river.
• The New Way: Following the leaf with a drone. The leaf might get caught in a fast eddy, then drift into a slow backwater, then get spun around a rock. The leaf's history of where it went and how hard it was pushed is what matters, not the river's average speed.

They tracked these "leaves" (cell clumps) of different sizes (from tiny specks to large marbles) and recorded every time they got hit by a strong current (Shear Stress) or a violent energy burst (Energy Dissipation Rate).

3. The Big Discovery: Size Matters

They found that the size of the cell clump changes everything.

• Tiny clumps are light and get swept along with the water, mostly staying in the calmer upper parts of the tank.
• Big clumps are heavy. Gravity pulls them down, and they crash into the spinning wheel at the bottom, where the water is moving fastest and most violently.

The Metaphor: Imagine a dance floor.

• Small dancers (tiny cells) can easily glide across the floor and avoid the DJ booth (the spinning wheel).
• Large dancers (big clumps) are heavy and clumsy. They get dragged straight into the DJ booth and get bumped around hard.

If you just look at the "average" dance floor energy, you miss the fact that the heavy dancers are getting bruised while the light ones are having a great time.

4. The Results: What Actually Hurts the Cells?

The team mixed their computer tracking with real-life experiments using human stem cells. They discovered two main things:

1. Energy is the Real Boss: The thing that actually determines if the cells grow well or get damaged is the Energy Dissipation Rate (EDR). This is basically how much "punch" the water delivers to the cell. If the cell gets hit by too much energy too often, it stops growing or breaks apart.
2. Shear Stress is Overrated: Scientists used to worry a lot about "Shear Stress" (the friction of water sliding past the cell). This study found that, for these specific cells, shear stress wasn't the main villain. It was the energy of the collisions that mattered more.

5. The Solution: A Dynamic Dance

The paper suggests that we shouldn't just set the bioreactor to one speed and leave it. Because the cells grow bigger every day, they need different conditions.

The Strategy:

• Day 1 (Tiny cells): Spin slowly. The cells are light and need to gently stick together to form clumps.
• Day 6 (Big clumps): Spin faster. Now the clumps are heavy and need more energy to stay suspended and get enough food, but not so fast that they break.

Why This Matters

This research is like upgrading the GPS for growing stem cells. Instead of guessing based on "average" conditions, we now have a map that tells us exactly how the cells move and what they feel.

This is crucial for heart disease. To fix a damaged heart, doctors need about one billion stem cells. To make that many, we need to scale up from small lab cups to giant industrial tanks. This paper gives us the rules to do that without crushing the precious cells in the process. It ensures that when we move from a 100mL cup to a 500mL bucket, the cells get the same personal experience, not just the same average environment.

Technical Summary

1. Problem Statement

The clinical translation of human pluripotent stem cell (hPSC)-derived therapies, particularly for cardiovascular disease, requires the large-scale manufacturing of billions of cells. While suspension cultures in bioreactors offer a solution for high-yield production, the hydrodynamic environment (fluid flow) significantly impacts cell viability, aggregation, and proliferation.

Current scale-up strategies for bioreactors typically rely on Eulerian-based metrics, such as keeping the Volume-Averaged (VA) Energy Dissipation Rate (EDR), shear stress, or impeller tip speed constant across different bioreactor sizes. However, these methods fail to account for:

• The specific trajectories of cell aggregates as they move through the fluid.
• The fact that aggregates of different sizes experience different local forces due to drag, lift, gravity, and buoyancy.
• The discrepancy between the "average" environment of the fluid and the actual "history" of mechanical exposure experienced by the cells.

This paper addresses the gap in understanding how cell aggregates actually experience mechanical stimuli in Vertical Wheel Bioreactors (VWBRs) and proposes a more accurate basis for scale-up.

2. Methodology

The study employed a combined In Silico (Computational Fluid Dynamics) and In Vitro (Experimental) approach.

A. In Silico: CFD Simulations

• Geometry: Transient, 3D turbulent flow simulations were conducted for two VWBR sizes: 100 mL and 500 mL.
• Flow Modeling: Used the Realizable $k-\epsilon$ turbulence model with a free air-liquid interface (Level Set method) to simulate partially filled bioreactors.
• Particle Tracking (Lagrangian Approach):
  • Cell aggregates were modeled as spherical particles with diameters ranging from 200 µm to 1,000 µm.
  • Particle motion was governed by Newton's second law, accounting for drag, lift, gravitational, pressure-gradient, and virtual mass forces.
  • Trajectories were tracked for 30 seconds (covering 10–30 wheel revolutions) after the flow reached a steady periodic state.
• Exposure Metrics: Along these trajectories, the history of Shear Stress ($\tau$) and Energy Dissipation Rate (EDR) was recorded. These were compared against traditional Volume-Averaged (VA) and Maximum values.

B. In Vitro: Cell Culture Experiments

• Cell Line: Undifferentiated ESI-017 human pluripotent stem cells (hPSCs).
• Conditions: Cultured in 100 mL and 500 mL VWBRs at agitation rates of 30, 40, and 60 rpm for 6 days.
• Measurements:
  • Aggregation Efficiency: Percentage of seeded cells that formed aggregates by Day 1.
  • Proliferation: Daily fold ratios and total fold expansion (Final Day / Day 0).
  • Aggregate Size: Distribution of aggregate diameters at the end of the culture.

3. Key Contributions

1. Lagrangian vs. Eulerian Analysis: The study demonstrates that Lagrangian-based exposure histories (tracking the actual path of aggregates) provide a fundamentally different and more accurate picture of the mechanical environment than Eulerian volume-averaged metrics.
2. Size-Dependent Exposure: It establishes that cell aggregate size significantly alters trajectories. Larger aggregates are more influenced by gravity and centrifugal forces, causing them to spend more time in high-shear regions near the impeller, whereas smaller aggregates circulate more in the upper, low-shear domains.
3. EDR as a Primary Driver: The research identifies Energy Dissipation Rate (EDR) as a more critical factor than shear stress for hPSC aggregation and proliferation in VWBRs.
4. Scale-Up Discrepancy: It reveals that matching Volume-Averaged EDR between different bioreactor sizes (e.g., 100 mL at 40 rpm vs. 500 mL at 30 rpm) does not result in equivalent biological outcomes because the distribution of exposure experienced by the cells differs significantly.

4. Key Results

Hydrodynamic Findings

• Trajectory Differences: Larger aggregates (e.g., 1,000 µm) travel faster and follow more direct downward paths, spending more time near the high-energy impeller. Smaller aggregates (e.g., 200 µm) follow the fluid streamlines more closely, often circulating in the upper domain where EDR is lower.
• Exposure Mismatch:
  • No tracked aggregate encountered the maximum fluid domain shear stress or EDR values.
  • The Volume-Averaged (VA) values were poor predictors of actual exposure. In many cases, the median exposure experienced by aggregates was significantly higher than the VA value.
  • Two conditions with identical VA EDR (100 mL @ 60 rpm vs. 500 mL @ 30 rpm) resulted in vastly different exposure distributions for the aggregates (e.g., 25% vs. 75% of time spent outside recommended ranges).

Biological Findings

• Optimal Agitation: In the 100 mL bioreactor, 40 rpm yielded the highest final cell counts and the lowest variance in aggregate size.
• Scale-Up Failure: Scaling the 100 mL (40 rpm) condition to the 500 mL bioreactor using VA shear stress (suggesting 30 rpm) resulted in significantly lower final cell counts and different aggregate size distributions, despite the "theoretical" equivalence of the fluid environment.
• Impact of EDR:
  • Aggregation Efficiency: Highly sensitive to EDR. Lower EDR (< $2.0 \times 10^{-4} m^2/s^3$) correlated with higher aggregation efficiency.
  • Proliferation: While daily fold ratios showed mild sensitivity to EDR, the total fold ratio showed a significant cumulative effect. Higher EDR ranges (associated with 60 rpm) led to higher daily fold ratios but lower initial aggregation efficiency.
• Shear Stress: Shear stress had a less pronounced effect on proliferation and aggregation compared to EDR under the tested conditions.

5. Significance and Conclusion

This paper fundamentally challenges the traditional "constant VA parameter" approach to bioreactor scale-up. The authors conclude that:

• Volume-averaged metrics are insufficient for predicting cell behavior in VWBRs because they ignore the trajectory-dependent exposure of cell aggregates.
• Lagrangian-based analysis (considering the history of EDR and shear stress exposure along particle paths) is a superior basis for scale-up, especially when cell aggregate sizes change over time.
• Dynamic Protocols are Recommended: Since optimal EDR for aggregation (early stage) differs from that for proliferation (later stage), the authors suggest variable-speed protocols (e.g., starting at 30 rpm for aggregation, then ramping to 40–60 rpm for expansion) to optimize both yield and quality.
• Future Implications: This approach is critical for scaling up to larger, geometrically dissimilar bioreactors and for culturing larger structures (like organoids) where gravitational settling becomes a dominant factor.

The study provides a robust framework for optimizing stem cell manufacturing by aligning hydrodynamic simulations with biological outcomes, moving beyond simple geometric scaling to a physics-based understanding of cell-mechanics interactions.