Microfiltration Device For Circulating Tumor Cells Isolation (MEMS)-(CTCS)

Introduction: The article is the product of the research “Design and simulation of a microfiltration device for the isolation of circulating tumor cells developed at the Universidad


INTRODUCTION
The migration of circulating tumor cells (CTCs) in the bloodstream to other organisms occurs when the cancer cell detaches from the primary tumor, filters into the blood vessels (intravasation), and migrates in the bloodstream to other organisms in the body (extravasation). This process is one of the deadly characteristics of cancer also known as metastasis [1], [2], [3], [4], [5].
The computed tomography method [6] is a detection method that can determine the size of the tumor and determine its growth through follow-up images. The treatment takes months between each shot and it is not always possible to know if the tumor is proliferating or sleeping. With the established cell models, we design the filtration device by a variation of the flow and geometry, and the best hydrodynamic condition generated is selected.
For the favorable behavior of cell classification, in the first stage, CTCs with a diameter between D = 12 -18 μm are filtered, in the second output, white cells are captured with a diameter between D = 14 μm along with red blood cells (RBCs).
For the simulations, the mesh is generated in two dimensions using quadrilateral elements structured in a transient model and using the volume fraction VOF method with the COUPLED algorithm using the ANSYS FLUENT solver.
For the capture efficiency, the percentage of CTCs captured in the outlet is determined, established by their separation, concerning the total number evaluated.
The purity percentage measures the purity of the captured sample, determined by the volume percentage of white cells and red cells that are not filtered.
Finally, the efficiency and purity data are compared with the designs available in the literature, the data is plotted and the model is validated, demonstrating superior capture efficiency by achieving a higher processing volume.

SIZE AND DEFORMABILITY OF CANCER CELLS
Cancer cells are larger compared to erythrocytes, but can be similar in size to white blood cells with variable sizes depending on the type of leukocyte (monocyte, granulocyte). In examinations of tissue samples, epithelial cells (solid tumor cells) are always larger than all blood cells including leukocytes based on primary tumor tissue biopsies [7].
Cancer cells can be variable and present a challenge in modeling them. One of the reasons is that the surface tension can be found in a range from 0.001 mNm -1 to 1000 times this value. Some cells behave as a liquid drop within the fluid, so they present a characteristic surface tension; the ''cortical tension'' or "the area expansion modulus" with unit of measure in (pN/μm). On the other hand, the deformations of the lipid membrane require much larger tensions, which can also be expressed in the following equivalent units (1 nN/μm = 1 mN/m = 1 dyne/cm); the latter is the most common form when measuring the surface tension of cell membranes [8].
On the other hand, in the work developed by [9], they determined the critical pressure necessary to generate the passage of a CTC through a microfilter, in which viscosities of less than 1 Pa•s were conveniently selected. In order to validate the results with theoretical models of critical, viscous and superficial pressure, for the design purposes of this project, the data of viscosities greater than 10 Pa•s are selected The affectation of conditions such as the hematocrit level was evaluated in [10], along with: the channel size and flow velocity on the behavior of a CTC in blood fluid, the flow of red cells with hematocrit between Ht(0.1 -0.3) in a straight channel with a length of L = 47 μm and channel diameters between D(10 -20 μm). After evaluating the lateral migration of the CTC in the channel, it was determined that high levels of hematocrit (Ht>0.3) prevent adhesion cells of the CTC to the wall. For a lower hematocrit (Ht<0.1, Ht<0.2), the CTC adheres to the wall in a time of approximately (t=0.2s), concluding that for hematocrit levels lower than (Ht<0.1 ) the cell adhesion of the CTC is greater, with a rapid response of adhesion of the CTC to the walls as shown in Figure   1. In the investigation, two channels with diameter size D (15-20μm) were evaluated.

Source: Own work
Another important factor is the relative resistance to flow; with the increase in the diameter of the channel, the relative resistance to flow is lower for CTC cells. In the simulations, they found that for a specific flow rate (g = 17.72s -1 ), the CTC detaches from the wall due to the increasing lifting force, but after a short time, the red blood cells flowing towards the center of the vessel expel the CTC from the red blood cell e-ISSN 2357-6014 / Vol. 19, no. 1 / january-april 2023 / Bogotá D.C., Colombia Universidad Cooperativa de Colombia center and further initiate adhesion of the CTC to the vessel wall, concluding that at high flow rates, for microchannel diameters greater than the diameter of the cancer cell and due to the effect of red blood cell aggregation in the center of the channel, cancer cells move towards the walls. It is finally concluded that with low levels of hematocrit (Ht<0.1), channel diameters much larger than the size of cancer cells (CTCs), and for high flow rates, they produce migration of the CTC towards the walls.

LEUKOCYTES (WHITE BLOOD CELLS).
Unlike erythrocytes (Red blood cells), leukocytes (White blood cells), WBC for its acronym, are part of the immune system. They protect the body from diseases or external agents and have the ability to travel to the tissues through the walls, by adhesion, to reach the infection. After subjecting neutrophils to a micropipette study with pressure differences from (ΔP = 98 -882 Pa), using pipettes with a diameter of (D=8-10μm), a study [13] showed that the white cell cytoplasmic viscosity is dependent on the applied suction pressure, specifically dependent on the shear rate of the fluid. The study found that as the suction pressure increases, the average cytoplasmic viscosity decreases in an exponential decreasing, being initially a viscosity of (μ=500Pa.s) for a pressure of (P=98Pa) and average viscosity of (μ=55Pa.s) for a suction of (P=882Pa), these data indicate that the cytoplasm in the neutrophil is a non-Newtonian fluid. Finally, the study concludes that the mechanical behavior of the neutrophil can be approximated as a power-law fluid. Research [14] carried out on the radial distribution of white blood cells in microtubes, was aimed at measuring the radial distribution of white blood cells (WBC) in blood flow in a channel of length L=3.5cm and diameter (D=69μm). The exit position was evaluated for an interval of wall shear stress (τ=0.1-2.0 Pa). The results obtained concluded that for an increase in the flow, the wall shear stress leads to a displacement between (30-50%) of the cells towards the center of the channel, while the minimum distance of the cells to the wall at high and low shear stress becomes a cell free layer of approximately 5.8μm.

ERYTHROCYTES (RED CELLS)
Erythrocytes are cells without a nucleus inside and their function is to transport the hemoglobin protein for oxygen transport, made up of iron in its structure, (red blood cell) (RBC) for its acronym, red in color and biconcave discoid shape, are characterized by their high deformability and can move between capillaries with diameters smaller than (D<3μm). The red cell is differentiated by its characteristic of having a membrane with a high modulus of deformation, which defines it as almost incompressible, therefore, it has a higher surface tension, low viscosity that allows the red cell to maintain the mass surface area, and high plasticity due to low viscosity. Erythrocytes have an average diameter between (D=6-8.5μm) [15].
Fahraeus and Lindqvist [16] reported a change in blood composition (and consequent change in blood viscosity) when blood flows through a capillary tube with diameter less than D<0.3 mm, which is also known as the Fahraeus effect. They explain that the blood cells are transported in the fast axial flow while the plasma moves in a slow marginal current or cell free layer, see Figure 2. Then the average speed of the blood cells is greater than the plasma particles. Cécile [17] found that lateral confinement or channel flow induces another phenomenon also associated with particle deformability: the migration of red blood cells away from the wall. The associated lift force is enough to make an isolated RBC go to the center in the D=30μm wide channel, see Figure 3. The strong lateral confinement in the D=30μm wide channel has a tremendous impact on the formation and stability of the structure; the fluid velocities were between v(0.0008 -0.004 m/s) for a straight channel with a length of (L=6000μm).
For low hematocrit and a channel width of D=30μm, regular and stable bands are formed since the effect of the lateral wall is felt throughout the width of the channel. As shown in Figure 3, for hematocrit between (2 and 4%), a single band of centered red cells is formed; for hematocrit between (5% and 9%), more bands of blood cells begin to be generated in the channel, preserving a cell free layer of Cfl = 10μm.  Research [18] has been carried out for the development of a microfilter device for the separation of blood plasma from red cells, reaching high efficiency e>80% and high purity. During development, they determined the effect produced by the application of an obstruction in the width of the critical stream by placing it right in the place of the bifurcation for the capture of the plasma. Using two-dimensional simulations with ANSYS-Fluent software, it was determined that an obstruction with an inclination reduces the width of the critical current and the shape of the ramp promotes the formation of recirculation zones (vortices), which increases resistance to the passage of red blood cells through the lateral channels.  Knowing that the volume flow can be established as Q v = A X ν, where A is the cross-sectional area and ν is the linear velocity of the flow, we have. [19], [20], [21].

(3)
Additionally, ΔP contraction -expansion is caused by rapid contraction at the filter inlet and rapid expansion at the filter outlet, which can be calculated using the following relationship.

(4)
Where U 1 and U 2 are the flow velocities at the inlet and outlet of the filtration chamber, K 1 and K 2 are the constriction and expansion coefficients, respectively.
These coefficients are set as 0.5 and 1 respectively. The viscous pressure is finally expressed as: The pressure generated by the surface tension ally, ΔP surface tension , can be determined using the Young-Laplace equation. If the flow in a microfilter is very low, the aspiration process of the cell in the filtration chamber can be approximated by a quasi-static process. Assuming that the aspirated part and the part not staked have circular shapes, then the surface pressure has the following expression.

(6)
Where σ is the surface tension, ally, r ch is the radius of the aspiration chamber and r cell is the radius of the cell of the non-aspirated part during deformation [22].     , the motion of two immiscible interfaces of different densities and viscosity is described using a discrete function.

CELL MODEL DESCRIPTION
The geometry of the filter is shown in Figure 5,

Source: Own work
In the strain-based microfilter, the white cell and the CTC are displaced through the filtration channel by the pressure imposed at the microfilter inlet called the system pressure, and its variation for time is called the pressure profile. System pressure is used to overcome resistance in the microfilter which is at maximum when the cell begins to enter the filtration channel. The maximum pressure of the system is generally called the critical pressure (P cr ).

MICROFILTER DESIGN
The geometry of the channels of the filtration device is defined taking into account the effect (Fahraeus-Lindqvist) is effective in channels of size between S = 40μm -300μm and the effects are pronounced for smaller size channels. As shown in Figure   6, in the first stage, the separation of cancer cells from erythrocytes and leukocytes is performed, and the definition of the geometry or domain is performed by defining a fluid input water as the discrete phase and oil as the continuous phase. Oil is supplied from the same source with an inlet flow rate (ν i ). We use individual droplets to simulate cancer cells, white and red cells.
The channel with the (Droplets) has a width of (P f ) and a length of (l). This distance generates the effect of migration of the erythrocytes towards the center of the flow and the effect of diffusion that drives the more rigid bodies present in the blood such as the cancer cell (CTC) to move towards the wall of the channel [25], [26].

RESULTS
In the first place, simulations are carried out to determine the critical pressure for

CONCLUSION
Cell characterization for the white cell shows its low resistance to deformation, and the ability to remain in the main current of the fluid, being affected by drag. The method (Power-law) reflects the real behavior of a white cell, which presents viscosities lower than the nominal viscosity of 130Pa.s and a high rate of deformation at high shear speeds. The cancer cells were taken as Newtonian because they had high viscosity and high rigidity. By increasing the viscosity, the critical pressure increased proportionally, reflecting that for higher the viscosities, the critical pressure is mainly due to the viscous pressure in the cell.
The designed microfilter device was carried out by studying the dynamic analy-