Cell adhesion in microchannel multiple constrictions – evidence of mass transport limitations

S.F. Neves (Methodology) (Investigation)<ce:contributor-role>Writing –original draft) (Writing review and editing) (Software) (Data curation) (Visualization), J. Ponmozhi (Investigation)<ce:contributor-role>Writing –original draft) (Data curation), F.J. Mergulhão (Conceptualization) (Resources) (Writing review and editing) (Methodology) (Supervision) (Funding acquisition), J.B.L.M. Campos (Resources) (Writing review and editing) (Supervision) (Project administration) (Funding acquisition), J.M. Miranda (Conceptualization) (Methodology) (Software) (Visualization)<ce:contributor-role>Writing –original draft) (Writing review and editing) (Supervision) (Project administration) (Funding acquisition)


Introduction
Biofouling consists of the accumulation of microorganisms over surfaces and its formation and development is a complex chain of events including initial cell adhesion, microcolonies formation, multi-layered clusters development, and detachment [1,2].

J o u r n a l P r e -p r o o f
In the last years, an effort to understand this complex interdependency at the microscale has been made, with particular emphasis on microfluidic devices [6][7][8][9][10][11][12], which are commonly used in biomedical instrumentation (catheters, syringes, biosensors among others). In these devices, the formation of a microbial biofilm can originate serious problems to the patient health (e.g. urinary and catheter-related bloodstream infections [13,14], implant failure [15]), beyond this, it can also compromise the lifespan of the device. The first stage, i.e., initial cell adhesion, has a huge impact on biofouling development, and therefore its understating is crucial and can lead to new and improved engineering solutions in the biomedical field.
Technological advances in biomedical instrumentation have conducted to increasingly efficient microdevices such as Cell Processing Systems, Micro-Electro-Mechanical Systems (MEMS), Lab on Chip Devices (LOC) and Point of Care Systems (POC), that often require complex geometries [16][17][18][19][20][21][22]. However, these complex geometries and the associated flow variations increase the probability and the available area for bacterial attachment. When this happens, the performance of the device can be at stake, particularly in geometries with narrow regions such as in cell trapping [18,19] and cell processing systems that are used in a continuous mode like cytometry systems [16].
Localized fouling in devices with constrictions is a topic of recent research [6,23].
When a device has headers that connect the microchannels, several behaviours are observed [5,23] including: i) high and uniform fouling in the headers; ii) low fouling in the microchannel, and; iii) high localized fouling at the microchannel entrance. In the headers and microchannels, fouling is inversely proportional to the wall shear stresses (WSS), since when WSS increases tangential and lift forces are high enough to remove cells from the surface [24]. However, in some cases, high fouling may occur at a region of high WSS. Several explanations have been proposed for this phenomenon, including clogging by fibbers or by the so-called bridge effect [25]. Another hypothesis is that cell transport is significantly affected by the Brownian motion of the cells [6,23,24]. Cell diffusion occurs due to the cell concentration gradient between the bulk liquid and the wall [5,24]. If it is assumed that cells arriving at the surface are instantaneously immobilized (perfect-sink model [24]), it is plausible that cell deposition/adhesion rates increase in regions with high local WSS, such as the microchannel entrance. In the literature, studies about the relation between the wall shear stresses and biofouling are scarce and only for simplified geometries (i.e. rectangle microchannels; [5,12]

Experimental set-up and procedures
The experimental set-up and the multi-constrictions microchannel design are shown in      Table 1.

Cell adhesion test
An Escherichia coli suspension was prepared (Section 2.  [5]. This strain was shown to have an adhesion behaviour similar to different clinical isolates including E. coli CECT 434 (ATCC 25922) [27] and has therefore been used in different works from our group where different biofilm platforms are used [28][29][30]. Furthermore, it has been demonstrated that E. coli can cause infections in the circulatory system [31] where the hydrodynamic conditions simulated in the present study can be found.
A starter culture was prepared as described by Teodosio et al. [32] and incubated overnight. A volume of 60 mL from this culture was centrifuged (for 10 min at 3202 × g) and the cells were washed twice with citrate buffer 0.05 M [33], pH 5.0. The pellet was then re-suspended and diluted in the same buffer to obtain a cell concentration of 7.6 × 10 7 cell mL −1 .

Flow conditions
The effect of microchannel constrictions on cell adhesion was studied at 37 ºC under an average wall shear stress of 0.2 Pa, to mimic the conditions found in the human body and medical devices such as in circulatory system and endotracheal tubes [30,34,35].  (1) is an approximation valid when w is significantly larger than h [36]. The wall shear stress defined to calculate the flow rate will be, from now on, referred as "nominal wall shear stress". More accurate values were obtained by CFD (Section 3.2).

J o u r n a l P r e -p r o o f
Due to the small dimensions of the microfluidic device, the flow regime is laminar with typical Reynolds numbers smaller than 1. For a square duct, the Reynolds number calculation is based on the fluid properties, flow rate and width and height of the microchannel: where ρ and  are the water density and the water kinematic viscosity (i.e. 993.36 kg·m -3 and 6.97  10 -7 m 2 ·s -1 at 37 ºC respectively). A Reynolds number of 0.57 was obtained through equation 2.

Model assumptions and equations
A numerical study was conducted considering the 3D geometry of the microchannel antechamber, the straight zones (i.e. upstream and downstream) and the constriction and expansion regions (Figure 1b; features in Table 1). The numerical domain neglects the sharper regions of the antechamber geometry (Supplementary data: Figure S1a). To model the cell transport, an Eulerian approach was used [4], which is often applied to simulate the transport of small particles in aqueous solutions. The following simplifications were assumed to model cell mass transport: i) colloidal forces were neglected; ii) no blocking; iii) detachment was assumed negligible; iv) no-slip between the cells and the fluid.
Hence, the following equation was used to simulate the cell transport by convection was considered at the antechamber inlet and at the bottom walls, the cell concentration was set to zero since it is assumed that all the cells that arrive at the wall stay instantaneously immobilized and therefore disappear from the dispersed phase. This is the so-called perfect sink model, and it is the most commonly used boundary condition at the collectors surface [24,39,40]. In these wall conditions (i.e. of null concentration and velocity), the cell flux (Jcell) was calculated by: This cell flux is usually expressed in terms of the Sherwood number, which represents the ratio of the convective mass transfer to the rate of diffusive mass transport and can be calculated by [24]: where km is the convective mass transfer coefficient (equation 9) and h the microchannel height. Along the constriction zones (filled circles; Figure 2), the adhesion is 3 times higher than in the upstream and downstream zones (square symbols, Figure 2) and it is 10 times higher than in the expansion zones (unfilled circles; Figure 2). The results obtained in the multiple constrictions region show a systematic oscillation between the results of each constriction zone (filled circles; Figure 2) and each expansion zone (unfilled circles; Figure 2). Figure 3 demonstrates that the typical cell density is higher in the constrictions. It is also observed, in the expansion zones, that the percentage of the area without adhered cells is significant when compared with the constriction zones.
{Insert Figure 3 around here}

Flow characterization: numerical
To understand the initial cell adhesion dependence on local flow patterns, Figure 4 shows the velocity field in the middle x,y plane (x, y, 0), the wall shear stress in the This is consistent with the significant rise of the local wall shear stress shown in Figure   4b.
{Insert Figure 5 around here}

Mass transport: numerical
The cell concentration in the vicinity of the bottom wall is shown in Figure 6. The concentration maps were obtained along the middle x,z-plane of the microchannel (x,0,z) in the upstream zone (Figure 6a), in the constrictions/expansions zone ( Figure   6b) and in the downstream zone (Figure 6c). At the antechamber, the concentration   (Table 1), and consequently, the fluid velocity increases significantly (i.e. ~6-fold increase in the maximum velocity; Figure 4a). Due to the increase of wall shear stress, which leads to the increase of drag and lift forces over the cells [41], cell adhesion would be expected to decrease, a phenomenon already observed in straight channels [31]. However, the results show an opposite tendency (unfilled circles; Figure 2 An interesting similarity between experimental and predicted local Sherwood data evolution along the microchannel is shown in Figure 7, particularly in the upstream and constriction zones. This promising behaviour is reinforced by the correlation between adhered cells and local Sherwood distribution demonstrated in Figure 8. This J o u r n a l P r e -p r o o f correlation suggests that local Sherwood numerical predictions may be a way to identify and correct possible blocking zones, even before the construction of the prototype. Nevertheless, quantitatively, the predicted Sherwood numbers are systematically higher than the experimental data (Figure 7), respectively, 1.2 and 3.5 times in the upstream and constriction zones (squares and filled circles). The comparison between predicted and experimental Sherwood data in the expansion zones (filled circles; Figure 7) shows that the physical model proposed to predict cell adhesion (equation 6) is not sufficiently accurate and additional factors need to be considered: colloidal forces, hydrodynamics forces [33] exerted on adhered cells, the presence of surface appendages (e.g. flagella and pili), expression of adhesins and other biological factors [5,42]. The perfect sink boundary condition would need to be modified to include phenomena associated to colloidal and hydrodynamic forces exerted on cells, such as blocking and detachment.

Conclusions
An experimental cell adhesion test was conducted for the first time in a microchannel with multiple constrictions, for operating conditions obtained in biomedical devices. An