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Passive mechanical stimulation induced by laminar and pulsatile shear stress

Organ on a chip (OOC) technology has paved the way for investigating the impact of mechanical strain in cell biology research by reproducing key aspects of an in vivo cellular microenvironment1. Combining microfluidics and microfabrication enables one to reproduce mechanical forces experienced by living tissues at the cell scale. Biomechanical stimulations experienced by cells fall into two categories:

  • Active mechanical stimulations as a direct consequence of the function of the organ. Organs like lung, muscle, intestine are in active motion. Cells in those organs are mainly subjected to compression and stretching.
  • Passive or indirect mechanical stimulation. Cells similar to conjunctive tissues or endothelial cells are passively exposed to the shear stress of blood or interstitial fluid. However, the effect is still substantial on cell growth, phenotype and genetic expression.

passive mechanical stimulation

Indirect mechanical forces – are those that mainly originate from hydrodynamic phenomena – and subsequent strain and shear stress are integral parts of the cellular microenvironment. Mechanical forces applied at the cell surface are translated into biochemical signals in cells. This phenomenon called mechanotransduction has been extensively described in the literature. It modulates cell proliferation, migration, phenotype, and/or differentiation1 and plays a critical role in tissue morphogenesis, homeostasis, and wound healing2–4. As a consequence, reproducing these mechanical forces and subsequent shear stress and strain is critical in order to fully capture the physiology of living tissues. Organs on chips are the perfect tools to implement shear stress as one or several fluids can be perfused within the chip. Liquid flow usually induces shear stress on cells or tissues cultured on the device and is called shear flow1. Three types of flows encountered in vivo are typically generated for producing shear stress in organ on a chip devices: laminar, pulsatile, or interstitial flow.

Shear flow in organ on a chip systems

shear from constant laminar flow

Laminar flow is predominant in tissues and organs and consequently in organ on a chip devices. The Reynolds number (for a tube Re  = ρud / µ , with ρ the fluid density, u the flow velocity, and d the tube diameter) helps to predict flow patterns in different fluid flow situations. At low Reynolds number (typically Re < 1000), the flow is laminar: fluid flows in parallel layers, with no disruption between them, as opposed to turbulent flow. As the dimensions are in micrometer scale in most tissues and organs (e. g., capillaries are about 8 to 10 microns in diameter), the Reynolds number is low (typically Re < 10). Flows are thus mainly laminar, with a characteristic velocity flow profile (figure 1). The shear stress is directly related to the flow velocity (more information is provided in the next section). As a consequence, laminar flow is a prerequisite in most organ on a chip research, and particular care should be addressed on flow control.

scheme of laminar and turbulent flow

Figure 1: Scheme of (a) laminar and (b) turbulent flow

D. Kamm et al. developed an in-vitro model of the human microvasculature to study the effect of luminal flow (typically laminar) on the migration of tumoral cells, allowing for a better understanding of the process of metastatic cascade (extravasation and subsequent interstitial migration). Particularly, they showed that luminal flow significantly promoted the extravasation potential of tumor cells compared to static conditions, with an average intravascular speed of tumor cells of ~ 12.5 μm/h under flow, compared to ~ 9.4 μm/h under static conditions. This result shows the important role of fluid flow during metastatic extravasation and invasion5.

For implementing flows, the type of perfusion system is critical. Peristaltic pumps are widely used but deliver a highly pulsatile flow that oscillates around the set flow rate value, which is not representative of any physiologic condition in the body and can damage cells. Conversely, a pressure-based system can deliver constant flow. We demonstrated the importance of flow stability in vascular models by perfusing endothelial cells seeded in microfluidic chips either using a peristaltic pump or pressure-based flow controllers.

Shear from pulsatile (laminar) flow

Pulsatile flow is mainly observed in arteries. Pulsations are smoothed by the muscle of the arterial walls. Pulsations are a direct consequence of heartbeats. The heart acts as a reciprocating pump that drives blood directly into the aorta. At each stroke, the flow reaches a peak (systole), then diminishing to a low (diastole) until the next stroke6. This produces pulsatile flow at each stroke instead of a continuous flow. Although pulsatile, flow remains laminar, the velocity flow profile varies as a function of time6. In fact, a typical flow rate curve of the artery for one heartbeat cycle displays two local maxima and a minimum, with positive and negative flow rate values (figure 2 a)7. As a consequence, the flow direction and the amplitude of the velocity flow profile will vary as a function of time (figure 2 b). This, of course, has an impact on the shear stress (or shear flow), as it is derived from flow velocity. More information on flow velocity patterns and subsequent shear flow can be found in the literature6. Pulsatile flow is usually performed in blood vessel-on-chip models to simulate the actual pulsatile blood flow in human circulation8.

Flow rate as a function of time during a single heart beat

Figure 2: a) Flow rate as a function of time during a single heart beat cycle

Example of an oscillatory velocity profiles in a rigid tube

Figure 2: b) Example of an oscillatory velocity profiles in a rigid tube6. Note that this is a mathematical simplification of oscillatory blood flow

As an example, microchannels mimicking human arteries and blood vessels were developed to investigate the influence of glucose and shear stress on endothelial cell apoptosis, a hallmark of vascular complications due to diabetes8. The authors performed the experiments under pulsatile and static flow conditions. They observed that under static conditions, glucose-treated cells induced 5.5-fold less apoptosis than when using pulsatile flow. This observation demonstrates the critical role of flow-induced shear stress in driving hyperglycemia-induced EC death.

Interstitial flow

Interstitial fluid flow is the movement of fluid through the extracellular matrix of tissues, where cells such as fibroblasts, immune tissue cells, and adipocytes can be found1,9. Fluid flow carries large proteins through the interstitium and mechanically stimulates interstitial cells. Several studies have demonstrated that shear flow induced by interstitial fluid was crucial for cellular activities, as such flows induced physiological responses from cells10–14, such as cell differentiation. Interstitial fluid typically flows at a lower velocity compared to blood flow within vessels because of the high flow resistance of the extracellular matrix. Flow velocity profile and subsequent shear flow is also more difficult to define due to the complex architecture of the extracellular matrix and as the fluid moves around the cell-matrix interface in all directions. Some studies have analyzed in-depth the shear stress with such architectures using numerical simulations.

A 3D cell culture microfluidic device was developed to provide new insight on how interstitial flow affects breast cancer cell invasion15. Specifically, the authors found that compared to static flow conditions, interstitial flow increased the number of migratory cells, as well as their migratory speed. These observations demonstrate how important it is to consider interstitial flows in tumor models, as they affect tumor cell invasion and invasion direction.

Flow shear stress calculation in a microfluidic device

As explained in the above paragraphs, shear stress has a strong impact on cell behavior. The shear flow applied on adherent cells when performing organ on a chip experiments can be determined using fluid dynamics equations, and more specifically, the continuity and Navier-Stokes equations. We present here the flow velocity profiles and shear stress equations for two common microfluidic channel geometries: circular and rectangular channels.

Circular chanel

circular cross section of diameter d, 3d representation

For a circular cross-section of diameter d, the fully developed velocity profile in cylindrical coordinates (r,θ,z) follows the equation16:

equation of velocity profile in cylindrical coordinates
velocity profile of laminar flow, 2d representation

With Q the flow rate, and r the radial distance from the centerline of the channel (see figure). The distribution of flow velocities follows a parabolic profile, and the maximum velocity is for r = 0, at the center of the channel. It is of interest to determine the shear stress distribution at the channel wall (r = d/2), as this is where cells are located in the chip. To do so, the strain rate should be calculated by differentiating the flow velocity with respect to r. We get:

strain rate equation for flow shear stress calculation in a microfluidic circular chanel

With µ the dynamic viscosity, Q the flow rate. This indicates that the shear stress remains constant along the channel walls and is a function of the viscosity, flow rate, and channel diameter. At constant channel diameter and viscosity, the higher the flow rate, the higher the shear stress.

Rectangular channel

In microfluidic devices with rectangular channels, the flow velocity profile and subsequent shear stress are more complex. Wall shear stress is not constant and varies across the top, bottom, and side walls of the channel. Detailed analysis can be found in the literature16. However, in some studies, the geometry is simplified by considering two infinite parallel plates instead of closed channels. Under this assumption, the shear stress follows the equation:

Shear stress equation for rectangular chanel

With Q the flow rate, µ the dynamic viscosity, w, and h the channel width and height, respectively.

scheme of a rectangular chanel


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