What is microfluidic vortex shedding?

Microfluidic vortex shedding (µVS) has been shown to enable the efficient delivery of various constructs like mRNA, plasmid DNA and Cas9 RNPs (CRISPR) to primary human T cells [1]. But, what is µVS? And, how does µVS enable intracellular delivery of constructs to primary cells like activated T cells?

In this blog post, we provide some background on vortex shedding and use single-phase simulation to explain what happens to cells during µVS. We also discuss how µVS enables intracellular delivery.

Vortex shedding and the related Kármán vortex street are not novel. These phenomena can be found in rivers or streams as they flow past boulders, and even in the clouds as they move past mountains or islands. Vortex shedding has also been used to precisely mix fluids on the microscale [2].

 

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Image of a Kármán vortex street created by vortex shedding

The gist of it is, vortex shedding has been well-studied and for a while [3]. The team at Indee Labs, however, is the first to apply microfluidic vortex shedding (µVS) to gene delivery and has received a number of granted patents as a result.

During µVS, cells are mixed in suspension with the desired construct then exposed to hydrodynamic conditions or fluid forces sufficient to temporarily porate the cell membrane -- this allows for constructs like Cas9 ribonucleoproteins (Cas9-RNPs) to enter the cell cytoplasm. Our current µVS prototypes can quickly process tens of million of cells while preserving native cell states [1]. This is measured by T cell activation, exhaustion, cytokine profiling and transcriptome-wide sequencing. Serendipitously, these are the ideal characteristics of an intracellular delivery technology for gene-modified cell therapies like chimeric antigen receptor T cells or CAR-T.

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Plots of the cytokine profiles for µVS relative to handling, media and activation controls

So, what exactly is vortex shedding? Vortex shedding occurs in the near wake of a bluff body due to instability created at the right flow conditions. Put simply, if you flow a fluid like air or water past a bluff body such as a post, boulder or mountain at the right conditions you create fluctuating flow fields along with drag and lift forces acting on the bluff body. This results in vortex shedding where a Kármán vortex street can frequently be observed.

For a cylindrical post, the onset of vortex shedding occurs at an object Reynolds number of about 40 (Reo > 40)  [4]. These vortex shedding patterns become more complicated with an increasing object Reynolds number or with increasing numbers of bluff bodies and their proximity.

blue-black-profile

Overview of different vortex shedding regimes.

Now, you are probably wondering, “what is a Reynolds number?” In fluid dynamics, Reynolds number is the non-dimensional ratio of inertial forces to viscous forces. This means vortex shedding typically occurs when the inertial forces of a fluid flow around a bluff body are at least 40 times greater than the viscous forces acting on the fluid. For Reo > 40, we should see downstream flow instability and resultant vortices. Herein, the Reynold number for flow past a bluff body is denoted as the object Reynolds number (Reo)

For the team at Indee Labs, understanding the intricacies of vortex shedding is essential. This knowledge allows us to engineer vortex shedding such that our µVS devices and protocols result in optimal yield or the percentage of recovered, viable and modified T cells.

In more detail, a numerical study of detailed wake patterns of laminar flow past microarrays platform is briefly presented here. Our standard µVS device geometry for activated T cells is used for this simulation. This array consists of 16 circular cylinders in side-by-side arrangements with total 6 columns in parallel positioned as shown below. The flow condition is considered laminar due to low flow cell (Refc), channel (Rec) and gap (Reg) Reynolds numbers.

Not all Reynolds numbers are alike and there are different Reynolds numbers for the flow cell, individual channels, gap and posts. Under typical µVS processing conditions for activated T cells, we see Reynolds numbers according to the table below.

 

Reynolds Number Value
Flow cell, Refc 271
Channel, Rec 180
Gap, Reg 291
Object, Reo 146


Flow in the device flow cell and channels is definitively laminar. When considering flow through a flow cell and channels, laminar flow occurs between
1 < Re < 2,100 [4]. Thus, we know the vortices shown in the simulation below are likely a result of vortex shedding since the object Reynolds numbers estimated to be 146 or much greater than 40 while all other Reynolds numbers are much less than 2,100.


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Contour plot of instantaneous velocity for a transient simulated flow field. Units are in m s-1

Vortex shedding as a result of flow past a single bluff body is one thing. Vortex shedding as a result of flow through a post array is an additional field of research. We are not the first to study flow over multiple cylinders, and a lot of the prior work has been focused on dual cylinders due to simple configuration [5-7]. Others have studied the effects of vortex shedding on more complex post arrays, however, this is to minimize vortices for high-fidelity cell separation and the opposite of our intent [8]. Select prior work concluded that flow could be summarized into two major regimes with a complex transition region between the two [9-12].

For two cylindrical posts in close proximity, the flow is periodic and the wake is a single Kármán vortex street as if the flow past a single bluff body. When the same two cylinders are further, coupled and synchronized vortex streets in the wake has been observed. Lastly, intermediate spacing leads to a very complex transitional patterns such as bi-stable biased gap flow as observed by Kim and Durbin [13].

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Plots of instantaneous vorticity contours (left) and streamlines (right) for these wake patterns:  (a) unsteady antiphase-synchronized, (b) unsteady in-phase-synchronized, (c) unsteady flip-flopping, (d) steady single bluff-body, (e) steady deflected and (f) steady pattern [14].

Sangmo has performed two-dimensional numerical studies on various dual cylinders arrangements at a range of low Reynolds number 40 < Reo < 160 and a gap ratio (gap width / cylinder diameter) of less than 5 [14]. Sangmo’s numerical results have identified a total of six different kinds of wake patterns in the flow field. These wake patterns are named and categorized as the following, more detail of these patterns can be found from his paper:

  1. Unsteady anti-phased synchronized pattern
  2. Unsteady in-phased synchronized pattern
  3. Unsteady flip-flopping pattern
  4. Steady single bluff-body pattern
  5. Steady deflected pattern
  6. Steady pattern

Typically, the flow characteristics significantly depend both on the object Reynolds number and relative gap spacing [14].

By now you are asking, what does this have to do with intracellular or gene delivery? Well, at Indee Labs, we need to fine tune each µVS device geometry such that we create the optimal vortex shedding for intracellular delivery. As a starting point, we examined what happens in our standard µVS device when a single-phase flow is simulated at standard conditions.


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Contour plot and graph of pressure in a µVS device under typical processing conditions.

As you can see from above, suspended cells flow through the post array and are pulsed with an approximately 1.4 ATM (20 psig) pressure drop followed by a 0.4 ATM (6 psig) pressure increase. If we use the results of the simulation described above to estimate flow speeds for approximate time scales, then the pressure drop occurs over about 2 µs and the pressure increase occurs over about 40 µs. And, while between post arrays, the cells and surrounding constructs are subject to a high degree of vorticity or ‘mixing.’ This is thought to enhance cell-construct interactions while the cell membrane remains permeable. Cumulatively, intracellular delivery is likely caused by the superposition or combination of both pressure changes and vorticity or ‘mixing.’ More specifically, the combination of these hydrodynamic fluid forces sufficiently permeabilizes the cell membrane to allow various constructs to enter the cell prior to modifying or engineering each cell.

Single-phase simulation is a great starting point, however, all simulations need to be verified experimentally. Plus, these single-phase simulations assume suspended cells have negligible effect on the fluid dynamics. Developing and verifying more accurate simulations will be no easy feat. This will require imaging objects with a diameter of 1/10 to 1/100 the thickness of a human hair while they are traveling at speeds as high as 20 m s-1 (45 mph).

We are working on a multi-phase computational model in order to expedite µVS device development for both T cells and other cell types. Verifying that model will involve imaging cell and particle trajectories at frame rates exceed 500,000 frames per second. Technical jargon aside, success with that project will allow us to more readily develop chips for alternative cell types and different processing media. This will accelerate development timelines as we move outside of just primary human T cells.

For more information on other cell contenders in the CAR field please check out our other blog posts here and here then stay tuned for more updates on µVS for intracellular delivery.

About the Author

Picture1Fong L. Pan,  B.Sci M.Sci
earned his BS and MS degrees in Aeronautics and Astronautics Engineering from Purdue University with 15 years of extensive experience in applied fluid mechanics and computational fluid dynamics. His past working experience spans various industries including Temasek Laboratories, Rolls-Royce, Navistar, United Technologies Research Center, Caterpillar and Honda R&D America. He has served in many positions including associate aerothermal engineer, senior CFD engineer, research acoustics engineer, fluid system technical team lead and product management. He is the author of 8 published technical papers and was awarded 4 US patents. He serves as a technical paper reviewer for SAE conference publication in aerodynamics, thermal management and aeroacoustics sessions. He was awarded Research Symposium Series Best Presentations Award for outstanding technical communication and excellent in research achievement and Magoon Teaching Award received from the School of Aeronautics and Astronautics at Purdue University in 2003 and 2004. 

References

[1]  Jarrell, Justin A., et al. "Intracellular delivery of mRNA to human primary T cells with microfluidic vortex shedding." Scientific reports 9.1 (2019): 3214.

[2]  Renfer, Adrian, et al. "Vortex shedding from confined micropin arrays." Microfluidics and nanofluidics 15.2 (2013): 231-242.

[3]  Bearman, Peter W. "Vortex shedding from oscillating bluff bodies." Annual review of fluid mechanics 16.1 (1984): 195-222.

[4]  Gerhart, Philip M., Andrew L. Gerhart, and John I. Hochstein. Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version. John Wiley & Sons, 2016

[5]  Deng Jian, Ren An-lu, and Zou Jian-Feng, “Three-dimensional flow around two tandem circular cylinders with various spacing at Re=220”, Journal of Hydrodynamics, Ser. B, 2006, 18(1): 48-54.

[6]  Sun Ren, Chwang Allen T., “Interaction of a floating elliptic cylinder with a vibrating circular cylinder”, Journal of Hydrodynamics, Ser. B, 2006, 18(4): 481-491.

[7]  Sumner D., Wong S. S., and Price S. J. et al, “Fluid behavior of side-by-side circular cylinders in steady cross-flow”, Journal of Fluids and Structures, 1999, 13(3): 309-338.

[8]  Dincau, Brian M., et al. "Deterministic lateral displacement (DLD) in the high Reynolds number regime: high-throughput and dynamic separation characteristics." Microfluidics and Nanofluidics 22.6 (2018): 59.

[9]  Bearman P. W., Wadcock A. J., “The interaction between a pair of circular cylinders normal to a stream”, Journal of Fluid Mechanics, 1973, 61: 499-511.

[10]  Kiya M., Arie M., and Tamura H. et al, “Vortex shedding from two circular cylinders in staggered arrangements”, ASME Journal of Fluids Engineering, 1980, 102(2): 166-173.

[11]  Zdravkovich M. M. “Flow induced oscillations of two interfering circular cylinders”, Journal of Sound and Vibration, 1985, 101(4): 511-521.

[12]  Williamson C. H. K., “Evolution of a single wake behind a pair of bluff bodies”, Journal of Fluid Mechanics, 1985, 159: 1-18.

[13]  Kim H. J., Durbin P. A., “Investigation of the flow between a pair of circular cylinders in the flopping regime”, Journal of Fluid Mechanics, 1988, 196: 431-448.

[14]  Sangmo K., “Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds number”, Physics of Fluids 15, 2486 (2003).