Microfluidic Cell Transport with Piezoelectric Micro Diaphragm Pumps

The automated transport of cells can enable far-reaching cell culture research. However, to date, such automated transport has been achieved with large pump systems that often come with long fluidic connections and a large power consumption. Improvement is possible with space- and energy-efficient piezoelectric micro diaphragm pumps, though a precondition for a successful use is to enable transport with little to no mechanical stress on the cell suspension. This study evaluates the impact of the microfluidic transport of cells with the piezoelectric micro diaphragm pump developed by our group. It includes the investigation of different actuation signals. Therewith, we aim to achieve optimal fluidic performance while maximizing the cell viability. The investigation of fluidic properties proves a similar performance with a hybrid actuation signal that is a rectangular waveform with sinusoidal flanks, compared to the fluidically optimal rectangular actuation. The comparison of the cell transport with three actuation signals, sinusoidal, rectangular, and hybrid actuation shows that the hybrid actuation causes less damage than the rectangular actuation. With a 5% reduction of the cell viability it causes similar strain to the transport with sinusoidal actuation. Piezoelectric micro diaphragm pumps with the fluidically efficient hybrid signal actuation are therefore an interesting option for integrable microfluidic workflows.


Introduction
The detailed experimental analysis of biological systems on a microscale is a common subject of current research. Within the last 30 years, micro fluidic systems developed rapidly and already offer solutions for various experimental setups [1,2]. Today, analysis on aggressively scaled devices is possible. However, the sample transport either relies on passive capillary forces or requires systems with bulky external pumps for active transport that often have a high power consumption and are connected with long tubing, which leads to a high dead volume [3][4][5][6]. The active transport in space-restricted situations, such as in clinical environments, is even more challenging. The integration of micropumps can offer a cost as well as an energy efficient on-chip solution for active sample transport.
Micropumps are not only of interest for the active transport in microfluidic setups, but can also offer a possibility to improve three-dimensional (3D) bioprinting. This technique enables the generation of complex structures that are of interest in pharmaceutical research, regenerative medicine, or the food industry [7,8]. For instance, the advantages of 3D-cultures compared to 2D-cultures for pharmaceutical research are demonstrated in

Piezoelectric Micro Diaphragm Pumps
A detailed evaluation of the pump type used in this work is given by Bußmann, Durasiewicz et al. [25]. The devices have a diameter of 20 mm and a height of 1.5 mm. The pumps consist of a stainless-steel pump body and a glued on piezoelectric disc actuator (PIC 151, diameter of 16 mm; thickness of 200 µm). The pump body includes two passive spring valves and the actuator diaphragm. All components are laser welded to the base plate. The pump chamber has a diameter of 18 mm and a height of approximately 100 µm to 150 µm, depending on the mechanical stress generated during the welding process and the electric tension applied during the mounting process of the piezoceramic actuator. The valves of the pump are 5 mm apart.
Fluid transport bases on the indirect piezoelectric effect (Figure 1). The exposure of the piezoelectric ceramic to an alternating high voltage signal leads to an oscillatory diaphragm movement. The resulting periodic expansion and reduction of the chamber volume in combination with the flow restriction of the passive spring valves leads to a directed fluid transport. The passive flap valves limit backflow and enable a high backpressure capability as well as high bubble tolerance. Therefore, they are indispensable for the fluidic performance of the micropump.

Materials and Methods
The pumps used for cell transport in this work are Fraunhofer EMFT's stainless steel pumps. A fluidic characterisation of the samples is conducted before and after the cell transport experiments.

Piezoelectric Micro Diaphragm Pumps
A detailed evaluation of the pump type used in this work is given by Bußmann, Durasiewicz et al. [25]. The devices have a diameter of 20 mm and a height of 1.5 mm. The pumps consist of a stainless-steel pump body and a glued on piezoelectric disc actuator (PIC 151, diameter of 16 mm; thickness of 200 µ m). The pump body includes two passive spring valves and the actuator diaphragm. All components are laser welded to the base plate. The pump chamber has a diameter of 18 mm and a height of approximately 100 µ m to 150 µ m, depending on the mechanical stress generated during the welding process and the electric tension applied during the mounting process of the piezoceramic actuator. The valves of the pump are 5 mm apart.
Fluid transport bases on the indirect piezoelectric effect (Figure 1). The exposure of the piezoelectric ceramic to an alternating high voltage signal leads to an oscillatory diaphragm movement. The resulting periodic expansion and reduction of the chamber volume in combination with the flow restriction of the passive spring valves leads to a directed fluid transport. The passive flap valves limit backflow and enable a high backpressure capability as well as high bubble tolerance. Therefore, they are indispensable for the fluidic performance of the micropump. Section of the pump's inlet valve including the spring valve and the valve seat that form the valve gap that is approximately 300 µ m long and in the open state of the valve 50 µ m high.

Actuator Stroke Measurements
The actuator stroke is an important metric for micro membrane pumps. It is measured optically using a white light profilometer (Fries Research and Technology, Bergisch Gladbach, Germany, sensor range: 3 mm, sensitivity: 30 nm). A voltage sweep is executed ranging from 0.4 kV/mm to 2 kV/mm (amplifier SVR 500−3, piezosystem jena GmbH, Jena, Germany) and the respecting actor positions are detected. The sweep is repeated multiple times. Repetitive tests of the same pump show a measurement accuracy of 2 µ m.

Fluidic Characterisation
The pumps are characterized with both air as well as deionised (DI) water at room temperature. The actuation signal for these measurements is a sinusoidal alternating voltage from −0.4 kV/mm to 1.5 kV/mm, which equals −80 V to 300 V for the 200 µ m thick actuator. Water flow is measured with Coriflow sensors (Bronkhorst, Kamen, Germany ML120V00: range 0.8 μL/min to 500 μL/min, accuracy: ±0.2% and Bronkhorst MINI CORI-FLOW M14: range 0.5 mL/min to 167 mL/min, accuracy: ±0.2%). The backpressure for both

Actuator Stroke Measurements
The actuator stroke is an important metric for micro membrane pumps. It is measured optically using a white light profilometer (Fries Research and Technology, Bergisch Gladbach, Germany, sensor range: 3 mm, sensitivity: 30 nm). A voltage sweep is executed ranging from 0.4 kV/mm to 2 kV/mm (amplifier SVR 500−3, piezosystem jena GmbH, Jena, Germany) and the respecting actor positions are detected. The sweep is repeated multiple times. Repetitive tests of the same pump show a measurement accuracy of 2 µm.

Fluidic Characterisation
The pumps are characterized with both air as well as deionised (DI) water at room temperature. The actuation signal for these measurements is a sinusoidal alternating voltage from −0.4 kV/mm to 1.5 kV/mm, which equals −80 V to 300 V for the 200 µm thick actuator. Water flow is measured with Coriflow sensors (Bronkhorst, Kamen, Germany ML120V00: range 0.8 µL/min to 500 µL/min, accuracy: ±0.2% and Bronkhorst MINI CORI-FLOW M14: range 0.5 mL/min to 167 mL/min, accuracy: ±0.2%). The backpressure for both water and air characterisation is set with a pressure controller (Mensor, San Marcos, TX, USA CPC3000: range −50 kPa to 200 kPa, accuracy: ±0.05 kPa). During water measurements, the differential pressure over the pumps is measured with two piezoresistive pressure sensors (TDK Electronics, Munich, Germany, EPCOS Gauge pressure transducers AKR 1.000 C40: range 0.0 kPa-10o kPa, accuracy: ±0.6 kPa).
When transporting liquid media, it is always possible that small bubbles occur and the pump needs to be able to transport them through the chamber. We therefore test the pump's backpressure capability with air at actuation frequencies for liquid transport (30 and 60 Hz). The pressure is increased by 2.5 kPa until the flow reaches zero.
Water characterisation of the pumps includes the frequency dependant flow at a constant pressure of 14 kPa in the range from 1 Hz to 50 Hz, the pressure dependant flow in the range from 0 kPa to 50 kPa, and pressure dependant leakage in the range from 5 kPa to 50 kPa.

Single Stroke Characterisation
We evaluate the pump's single stroke volume with DI water in a gravimetric measurement depicted in Figure 2. It is based on a setup introduced by Thalhofer et al. [26]. The inlet reservoir is placed on a precision scale (Sartorius, Göttingen, Germany, MC410S, resolution 100 µg) with the inlet tube immersed free-hanging in the liquid at all times. The pump, which is placed next to the balance, transports liquid from the inlet reservoir to the outlet. The actuation signal is triggered using an automated protocol. The single stroke signal is amplified with the SVR 500−3 (piezosystem jena GmbH, Jena, Germany). The fluid reservoirs are covered with Nitto SWT 10+R to minimize drift caused by condensation or evaporation. water and air characterisation is set with a pressure controller (Mensor, San Marcos, TX, USA CPC3000: range −50 kPa to 200 kPa, accuracy: ±0.05 kPa). During water measurements, the differential pressure over the pumps is measured with two piezoresistive pressure sensors (TDK Electronics, Munich, Germany, EPCOS Gauge pressure transducers AKR 1.000 C40: range 0.0 kPa-10o kPa, accuracy: ±0.6 kPa). When transporting liquid media, it is always possible that small bubbles occur and the pump needs to be able to transport them through the chamber. We therefore test the pump's backpressure capability with air at actuation frequencies for liquid transport (30 and 60 Hz). The pressure is increased by 2.5 kPa until the flow reaches zero.
Water characterisation of the pumps includes the frequency dependant flow at a constant pressure of 14 kPa in the range from 1 Hz to 50 Hz, the pressure dependant flow in the range from 0 kPa to 50 kPa, and pressure dependant leakage in the range from 5 kPa to 50 kPa.

Single Stroke Characterisation
We evaluate the pump's single stroke volume with DI water in a gravimetric measurement depicted in Figure 2. It is based on a setup introduced by Thalhofer et al. [26]. The inlet reservoir is placed on a precision scale (Sartorius, Göttingen, Germany, MC410S, resolution 100 µ g) with the inlet tube immersed free-hanging in the liquid at all times. The pump, which is placed next to the balance, transports liquid from the inlet reservoir to the outlet. The actuation signal is triggered using an automated protocol. The single stroke signal is amplified with the SVR 500−3 (piezosystem jena GmbH, Jena, Germany). The fluid reservoirs are covered with Nitto SWT 10+R to minimize drift caused by condensation or evaporation.  Figure A1 in Appendix A.
The weight of the outlet reservoir is detected before and after the dosage of one single stroke in order to calculate the dosed single stroke volume from the weight difference. The sampling frequency is 1 Hz and does not affect the measurement, since we detect the total weight of a single stroke and do not depict the time dependant weight change during the stroke. To account for the drift of the balance, we perform five scale measurements before a single pump stroke is performed with defined waveform and frequency.  Figure A1 in Appendix A.
The weight of the outlet reservoir is detected before and after the dosage of one single stroke in order to calculate the dosed single stroke volume from the weight difference. The sampling frequency is 1 Hz and does not affect the measurement, since we detect the total weight of a single stroke and do not depict the time dependant weight change during the stroke. To account for the drift of the balance, we perform five scale measurements before a single pump stroke is performed with defined waveform and frequency. After an eight seconds break, another five post-trigger scale measurements are recorded. The weight difference before and after the pump stroke is evaluated and corrected for the average drift that is calculated based on the five consecutive measurements before and after the trigger.
For the transport experiments, harvested cells are washed and aliquoted in buffer (autoMACS Running Buffer; Miltenyi Biotec B.V. & Co. KG; Bergisch Gladbach, Germany) to approximately 6 × 10 4 cells/mL. Individual samples of 500 µL each are prepared in reaction vessels. One sample of each culture bottle is set aside and not transported for the negative control. Another sample is set aside as positive control and, before staining, is treated with Triton TM X-100 (Merck KGaA, Darmstadt, Germany), which disrupts the cells' membrane. Cells are transported with five different actuation settings as indicated in Table 1. Three individual samples are transported per setting and pump, leading to a total of 15 samples per setting. Results are averaged over all transported samples for each setting. The experimental setup for the cell transport is depicted in Figure 2b. The pump's inlet and outlet are connected with the inlet and outlet reservoir using flexible tubing with 4 cm length and 1.4 mm inner diameter. The inlet reservoir contains 500 µL of cell solution. To assure sufficient resuspension of cells, each reservoir is agitated carefully prior to transport that is completed in less than ten seconds. The cells are transported with the desired setting and collected in a reaction vessel. The solution is pumped one single time and not circulated or transported repeatedly. For cleaning, we passively flush the pumps with 20 mL buffer (autoMACS Running Buffer; Miltenyi Biotec B.V. & Co. KG; Bergisch Gladbach, Germany) between samples with different actuation signals. After flushing, 500 µL of rinsing solution are collected and analysed for the number of cells to assure that the following sample is not influenced by remaining cells in the pump. The collected data are gated for single cells using the height versus forward scatter area. The samples for a given actuation signal are averaged over all five pumps. For comparison of two sample groups that include 15 individual samples with approximately 30,000 cells each, we use a two-tailed t-test with a p-value of 0.02.

Results and Discussion
Cell transport with very limited available space is a challenging task. Both damage on the cells caused by the pump as well as pump degradation due to cell transport are possible. With a detailed experimental consideration, we intend to clarify possible influences and provide the basis for further improvements.

Pump Characterisation
Micro diaphragm pump characterisation includes the evaluation of the general properties of the pump as well as an investigation of the single stroke with different actuation mechanisms. The later generates information on the fluidic efficiency of each actuation and allows us to adapt the actuation signal to a fluidically optimal transport with less influence on the cells.

General Micro Diaphragm Pump Characterisation
To estimate the impact of cell transport on the diaphragm pump itself, all devices are characterized prior to and after the cell transport. It is possible for cells to accumulate in the pump chamber as well as in the dead volume around the valves and therefore lead to a pump degradation. A change in stroke or passive as well as active flow characteristics allows for better understanding of failure mechanisms.
The exact movement of the diaphragm is a crucial part of the pump's functionality. A typical stroke measurement is shown in Figure 3a, with the clear piezoelectric hysteresis. The stroke height determines the stroke volume and therefore the achievable flow rate of the system. The stroke measurement allows to detect mechanical constraints to the actuator's movement. The average total stroke after cell transport is 81.7 ± 3.9 µm and not significantly changed compared to the initial average stroke of 82.4 ± 3.4 µm (Figure 3b). These findings indicate that cells do not agglomerate in the chamber and block the actuator movement. Figure 3 shows the frequency dependant flow rate of the used steel micropumps. The flow increases linearly with the frequency until dynamic damping effects in the chamber become dominant and the curve plateaus. In the non-linear regime, the flow strongly depends on the fluidic periphery [29]. Therefore, a performance comparison should take place in the linear regime. The flow prior to cell transport experiments matches the expectation based on former pump batches [25]. After cell transport, the average flow up to 10 Hz is equal to the flow before the exposure to cell solution. The ability to achieve the same flow at low frequencies indicates no significant change in the behaviour of the passive flap valves. Low frequencies with sinusoidal actuation lead to a slow actuator movement and therefore low pressure gradients. The valves are opened and closed comparatively slowly with low force. A bad valve quality is therefore often visible in the low frequency range. The assumption of constant valve performance before and after the cell transport is substantiated by the leakage rates, which only changed for one out of six pumps. The leakage rate at 50 kPa differential pressure of the pumps before cell transport is below 30 µL/min for all samples. After transport, it remains unchanged for all but one pump that shows a drastically increased leakage rate of 260 µL/min. This increase is potentially caused by fibres caught in the passive flap valves that were visible in the optical inspection and probably transported into the pump during use outside of the clean room environment. The leakage measurement always detects the leakage over both, the inlet as well as the outlet valve. If only one valve is sufficiently tight, the overall leakage is small. Significant backflow in active pump mode is still possible, if the other valve is leaking.  For higher frequencies, the average flow decreases and the end of the linear region is lower. A volume change in the chamber, due to agglomeration of cells or particles, is a possible explanation for the detected change in the fluidic performance. Furthermore, increased leakage through the passive flap valves can change the flow behaviour. However, as described above, increased leakage has a large influence on the flow at small frequencies and would be visible in the linear range.
The decrease in flow for higher frequencies after cell transport compared to the initial performance is also visible in the backpressure measurements of the pumps. With 30 Hz, sinusoidal actuation, the flow at 0 kPa is approximately 3 mL/min lower after the cell transport. The extrapolated blocking pressure however remains unchanged with approximately 70 kPa before and after cell transport. This indicates the same stiffness of the actuator and therefore nor degradation of the ceramic itself or the adhesive connection during the experiments. For higher frequencies, the average flow decreases and the end of the linear region is lower. A volume change in the chamber, due to agglomeration of cells or particles, is a possible explanation for the detected change in the fluidic performance. Furthermore, increased leakage through the passive flap valves can change the flow behaviour. However, as described above, increased leakage has a large influence on the flow at small frequencies and would be visible in the linear range.
The decrease in flow for higher frequencies after cell transport compared to the initial performance is also visible in the backpressure measurements of the pumps. With 30 Hz, sinusoidal actuation, the flow at 0 kPa is approximately 3 mL/min lower after the cell transport. The extrapolated blocking pressure however remains unchanged with approximately 70 kPa before and after cell transport. This indicates the same stiffness of the actuator and therefore nor degradation of the ceramic itself or the adhesive connection during the experiments.

Single Stroke Characterisation
The single stroke measurement with varying actuation signals allows to estimate the fluidic efficiency of the transport. A single actuator stroke requires approximately 2 mJ and single stroke power consumption of the pump itself (without driving electronics) is independent of the waveform and frequency [25]. From the energy required for one pump stroke and the volume transported per stroke, we can calculate the power consumption per dosed volume. Since the energy per stroke is constant, it depends on the single stroke volume that again depends on the actuation signal.
A perfectly rectangular actuation generates the fastest actuator movement and therefore the fastest pressure built-up. Consequently, the actuation of the passive flap valves is rapid and backflow through insufficiently closed valves is minimized [30]. A lower flank steepness, as is the case for sinusoidal actuation, leads to a slower pressure built-up and slow opening and closing of the passive valves. It therefore allows a portion of the transported fluid to move backwards through the valves [30]. A steeper flank therefore leads to a higher stroke volume. However, the fast actuator movement also increases the strain on both, the pump as well as the dosed medium, since it leads to high mechanical stress in the piezoelectric actuator and increases the fluidic shear stress.
A trade-off between fluidic efficiency and strain on pump and medium can be a hybrid actuation based on a rectangular waveform with sinusoidal flanks. Figure 4a shows the resulting waveform in comparison to other waveforms: the hybrid signal is a mix between a rectangular signal with a given frequency and a sinusoidal signal of a higher frequency. In order to evaluate which flank is appropriate, we determined the single stroke volume for several actuation frequencies with varying flanks. A frequency dependence of the single stroke volume is expected due to fluidic damping in the chamber at higher frequencies and flow rates. Figure 4b depicts the dependence of the single stroke volume on the actuation frequency and flank steepness. The single stroke volume is reduced for 50 Hz actuation frequency compared to slower actuation, whereas it is independent of the actuation frequency up to 20 Hz.

Single Stroke Characterisation
The single stroke measurement with varying actuation signals allows to estimate the fluidic efficiency of the transport. A single actuator stroke requires approximately 2 mJ and single stroke power consumption of the pump itself (without driving electronics) is independent of the waveform and frequency [25]. From the energy required for one pump stroke and the volume transported per stroke, we can calculate the power consumption per dosed volume. Since the energy per stroke is constant, it depends on the single stroke volume that again depends on the actuation signal.
A perfectly rectangular actuation generates the fastest actuator movement and therefore the fastest pressure built-up. Consequently, the actuation of the passive flap valves is rapid and backflow through insufficiently closed valves is minimized [30]. A lower flank steepness, as is the case for sinusoidal actuation, leads to a slower pressure built-up and slow opening and closing of the passive valves. It therefore allows a portion of the transported fluid to move backwards through the valves [30]. A steeper flank therefore leads to a higher stroke volume. However, the fast actuator movement also increases the strain on both, the pump as well as the dosed medium, since it leads to high mechanical stress in the piezoelectric actuator and increases the fluidic shear stress A trade-off between fluidic efficiency and strain on pump and medium can be a hybrid actuation based on a rectangular waveform with sinusoidal flanks. Figure 4a shows the resulting waveform in comparison to other waveforms: the hybrid signal is a mix between a rectangular signal with a given frequency and a sinusoidal signal of a higher frequency. In order to evaluate which flank is appropriate, we determined the single stroke volume for several actuation frequencies with varying flanks. A frequency dependence of the single stroke volume is expected due to fluidic damping in the chamber at higher frequencies and flow rates. Figure 4b depicts the dependence of the single stroke volume on the actuation frequency and flank steepness. The single stroke volume is reduced for 50 Hz actuation frequency compared to slower actuation, whereas it is independent of the actuation frequency up to 20 Hz.  For all tested frequencies, the single stroke volume plateaus for sufficiently steep flanks. The required flank steepness depends on the actuation frequency. While for actuation with 1 to 20 Hz, a flank steepness of approximately 60 Hz is sufficient, the single stroke volume at 50 Hz only plateaus at steeper flanks of approximately 90 Hz. The results are reproducible for all four evaluated pumps. These results indicate that the fluid transport is as efficient with sufficiently steep flanks as it is with rectangular actuation, however, the flank steepness needs to be comparatively high for higher actuation frequencies. The resulting flow rate for specific waveforms is verified with the measurement of the frequency dependant flow rate. Up to 25 Hz actuation frequency, the hybrid signal achieves the same flow rate as the rectangular signal. The experimental results are presented in Figure A2 in the Appendix B. Based on these findings, a 15 Hz hybrid signal with 60 Hz sinusoidal flank is chosen as one of the signals used for cell transport. This allows to compare the impact when the pump is actuated with sinusoidal, rectangular, or the hybrid signal.

Cell Transport
Viable cells are sensitive to their environment, and transport with a micro diaphragm pump can damage them in different ways. A first important indicator to assess the feasibility of cell transport with micro diaphragm pumps is the recovery rate of cells after transport. Neither the total cell concentration nor the percentages of cells within the gate deviate significantly between the negative control sample and the transported samples. Cells therefore do not accumulate within the pump, which corresponds well to the results of the electromechanical and fluidic characterisation of the pumps presented above.

Consideration of Effects Influencing the Cell Viability
Pumping can have a mechanical impact on the transported cells due to moving parts in the flow path. For instance, cells can get caught in between the valve and its seat. However, this scenario is unlikely: one pump stroke, and therefore one opening and closing motion of the valves, transports approximately 10 µL of fluid. The total fluid volume between the valve and its seat when the valve starts closing is calculated based on the valve geometry: the surface of the valve seat of 0.23 mm 2 and a valve opening of maximal 50 µm. It is approximately 0.01 µL for each valve. Therefore, if we assume that the cells are uniformly distributed and that all cells that are between the valve and its seat when the valve starts closing get caught in the valve, this would only affect 0.2% of the transported cells. We thus assume that the damage caused by hard-hard touch squeezing is neglectable.
It is also imaginable that cells become damaged when they come into contact with sharp edges. In particular, the etched valve structure or the drilled inlet and outlet access constitute such sharp edges. However, fluid flow around the cells causes fluidic drag thus their fluidic resistance is high and the cells move towards the middle of the flow path. Hence, the cells likely flow around the edges without contact. The effect is already shown by Ozbey et al. [31] who observe cells moving towards the centre of the channel in laminar flow.
A likely influence on the cell viability is the experienced fluidic shear stress. Studies discuss the impact of shear on non-adherent cells and indicate that the size as well as the deformability of a cell have an influence on its behaviour when subjected to shear stress [31][32][33].
To generate a first understanding of the shear force the cells are subjected to when passing through the pump, we consider the analytic description of a strongly simplified model. We aim to compare the influence of specific geometries in the pump, e.g., chamber and valves, as well as different actuation signals. We do not intend to give a quantitative analysis of shear forces.
The valve as well as the pump chamber have a high aspect ratio: The valve seat is 300 µm long and the valve opens 50 µm; the pump chamber is approximately 100 µm to 150 µm high (in the upwards position of the actuator) and we consider the distance of 5000 µm between the two valve openings as the gap length. We assume laminar gap flow in these geometries. Furthermore, for simplicity, we only consider the liquid medium itself and do not specifically calculate the velocity of the cells in this flow. This strong simplification allows a first comparison of geometries and actuation signals.
The shear stress of the laminar flow is given by with the viscosity of the liquid η and the flow velocity v x . Furthermore, the velocity profile of the laminar gap flow is parabolic and depends on the pressure difference ∆p, the gap length L gap , the gap height h gap , and the viscosity of the liquid η. When the pump is active, the movement of the actuator diaphragm generates the pressure difference ∆p that drives the fluid through the gap and therewith generates the fluidic shear forces. The maximal pressure that the bending actuator can achieve is its blocking pressure. This pressure is generated when the actuator is subjected to a rectangular actuation and the movement is extremely fast. Since the maximal pressure occurs during this fast actuator displacement, the pressure peak is independent of the actuation frequency for rectangular actuation. The maximal pressure difference depends on the bending actuator's geometry and used material and can be calculated with the analytical model presented by Herz et al. [34]. For sinusoidal actuation, the voltage change and therewith the actuator movement is considerably slower than for rectangular actuation. The time constant of the actuator movement and the fluid movement through the passive valves therefore converge and the maximal pressure peak decreases. Since the speed of actuator movement depends on the actuation frequency for sinusoidal actuation, the generated pressure difference is also a function of the actuation frequency. Similarly, for the hybrid signal, the maximal pressure depends on the speed of the actuator's movement and therefore on the sinusoidal flank steepness of the signal. Based on the model by Herz et al. [34] the analytic description of the pressure peak of the sinusoidal actuation can be derived. However, the equation cannot be solved analytically and a numerical description will be part of future work. However, the analytical model allows for a qualitative comparison that shows that the shear force is maximal for rectangular actuation and minimal for sinusoidal actuation with a small frequency. Due to the relation between the maximal pressure and the flank steepness, the pressure difference and therewith the shear forces in this model are equal for sinusoidal actuation with 60 Hz and the hybrid signal with 60 Hz sinusoidal flanks.
To identify the most relevant pump geometries, the shear stress in the valve and the chamber are compared for rectangular actuation. For the simplified model, we assume gap flow in the valve as well as in the pump chamber as described above. Furthermore, we assume that the maximal pressure difference applies to both the chamber and the valve, even if in reality the pressure is split.
Based on Equation (4) and the geometry of the flow path (the valve seat length L valve = 300 µm and valve opening h valve = 50 µm, as well as pump chamber length L chamber = 5000 µm and pump chamber height h chamber = 100 to 150 µm), the ratio of shear in the chamber and the valve can be estimated with and is approximately 0.12 to 0.18. As can be seen from Formula (5), the ratio is independent of the pressure difference. The estimation shows that the shear stress at the valve unit is larger compared to the shear stress in the pump chamber. To further reduce the impact of the pump on cells, it is thus necessary to adapt the valve geometry to reduce the occurring shear stress in this area.

Viability of K-562 and Jurkat Cells after Transport
In this preliminary study, we only detect the immediate influence of the pump on the cells, since we measure the percentage of intact cells compared to the negative control. The influence of the transport on the long-term viability of the cells are not yet examined and will be part of future studies.
Both cell types are impacted by the pumping process. For K-562 cells, the non-pumped (negative) control samples contains 89.9 ± 2.6% intact cells; for Jurkat cells it contains 88.6 ± 5.2% intact cells. Figure 5 shows the change of the percentage of intact cells due to transport with the micro diaphragm pump with different actuation signals. The mean percentage of intact cells is slightly lower for all transported samples compared to the non-pumped control and the decrease is significant with p ≤ 0.02. The impact of the pump on Jurkat cells is more pronounced. The diameter of the two cell lines is similar, though the deformability is different. Since the deformability determines the path of the cell in the fluidic channel [32], the increased impact on Jurkat cells can among others be caused by a difference in the experienced fluidic shear stress. The largest decrease of intact cells occurs after transport with a rectangular actuation of 60 Hz, which is the most stressful actuation. It generates the fastest actuator movement, highest pressure peak and the highest overall flow. On average, 65.6 ± 10.3% of cells stay intact after this transport, nearly one quarter of cells less than the control. A similar large impact (no significant difference, p ≥ 0.05) is caused by rectangular actuation with only 15 Hz (68.0 ± 8.0%). As described above, the maximal pressure peak and therefore the maximal fluidic shear stress caused by the pressure peak that pushes fluid through the valve channel, do not depend on the applied frequency for rectangular actuation. The similar reduction of viable cells for 15 Hz and 60 Hz rectangular actuation indicates that this maximal shear stress has a significant influence on the transported cells. For both actuation frequencies, sinusoidal actuation causes less damage with 81.3 ± 7.6% intact cells for 15 Hz actuation and 72.3 ± 10.3% for 60 Hz. However, the sinusoidal actuation with a frequency of 60 Hz still stresses the cells and the impact is not significantly different to rectangular actuation (p ≥ 0.05). The influence of the transport with hybrid actuation (15 Hz rectangular actuation with 60 Hz sinusoidal flanks) on the cells is very similar to the 15 Hz sinusoidal actuation and the difference is not significant with p ≥ 0.05. According to the analytical model described above, the generated pressure peak and imposed shear are the same for the hybrid actuation and 60 Hz sinusoidal actuation, since the flank steepness of the two sig-  15 Hz, which is the smoothest actuation. The mean percentage of intact cells is 85.4 ± 4.6% and therefore only 4.5 percentage points lower than the non-pumped control. The smaller impact can be due to the overall lower flow rate and thus reduced shear force. Furthermore, the maximal speed of the diaphragm and therewith the maximal pressure difference is decreased and evokes a smaller maximal pressure gradient. The average damage caused by a rectangular actuation with 15 Hz shows, that the faster actuator movement causes more damage. However, the difference is only significant with p ≤ 0.05. As described above, for rectangular actuation, the maximal pressure difference does not depend on the actuation frequency. Therefore, the analytical model cannot explain the different impact of 60 Hz and 15 Hz rectangular actuation on the transported cells. However, the average overall flow rate and thus average shear in the pump and periphery are larger for 60 Hz actuation. The transport with the hybrid signal (15 Hz rectangular signal with 60 Hz sinusoidal flanks: srs_15) imposes a slower actuator movement compared to 15 Hz rectangular actuation while maintaining the fluidic performance. The impact on the cells is also slightly reduced, but the difference is not significant.
The impact of the pump on Jurkat cells is more pronounced. The diameter of the two cell lines is similar, though the deformability is different. Since the deformability determines the path of the cell in the fluidic channel [32], the increased impact on Jurkat cells can among others be caused by a difference in the experienced fluidic shear stress. The largest decrease of intact cells occurs after transport with a rectangular actuation of 60 Hz, which is the most stressful actuation. It generates the fastest actuator movement, highest pressure peak and the highest overall flow. On average, 65.6 ± 10.3% of cells stay intact after this transport, nearly one quarter of cells less than the control. A similar large impact (no significant difference, p ≥ 0.05) is caused by rectangular actuation with only 15 Hz (68.0 ± 8.0%). As described above, the maximal pressure peak and therefore the maximal fluidic shear stress caused by the pressure peak that pushes fluid through the valve channel, do not depend on the applied frequency for rectangular actuation. The similar reduction of viable cells for 15 Hz and 60 Hz rectangular actuation indicates that this maximal shear stress has a significant influence on the transported cells. For both actuation frequencies, sinusoidal actuation causes less damage with 81.3 ± 7.6% intact cells for 15 Hz actuation and 72.3 ± 10.3% for 60 Hz. However, the sinusoidal actuation with a frequency of 60 Hz still stresses the cells and the impact is not significantly different to rectangular actuation (p ≥ 0.05). The influence of the transport with hybrid actuation (15 Hz rectangular actuation with 60 Hz sinusoidal flanks) on the cells is very similar to the 15 Hz sinusoidal actuation and the difference is not significant with p ≥ 0.05. According to the analytical model described above, the generated pressure peak and imposed shear are the same for the hybrid actuation and 60 Hz sinusoidal actuation, since the flank steepness of the two signals is equal. The different impact of the hybrid actuation and 60 Hz sinusoidal actuation indicate that not only the maximal experienced shear, but also the average overall flow rate impact the cells. The average flow is higher for the 60 Hz sinusoidal actuation than for the hybrid signal ( Figure A2, Appendix B).
Overall, the transport with 15 Hz hybrid signal has a similar impact on the cells as the transport with sinusoidal actuation ( Figure 5) while maintaining the fluidic performance of rectangular actuation as shown by the comparison of the single stroke volume as well as the flow characterisation presented in Figure A2, Appendix B. The hybrid actuation therefore offers the possibility of efficient cell transport while minimizing the damage. However, for both cell types, the impact is still significant with approximately 7.3 and 4.6 percentage points less intact cells compared to the control sample for Jurkat and K-562 cells respectively. It is thus necessary to further optimize the pump systems with respect to the exact valve geometry, the pump chamber, as well as the inlet and outlet channel.

Conclusions
Overall, the standard characterisation of the pumps before and after cell transport shows a small degradation but no complete loss of functionality. It is important to notice that during the transportation experiments the pumps were not used in a cleanroom environment and therefore not only exposed to cell solution but also to contamination such as fibres. The optical examination of the valves did show fibres in several pumps. Hence, it is not possible to distinguish degradation caused by cells from other influences and further evaluations are necessary to assess possible pump degradation. In preliminary experiments we plan to evaluate the particle resistance of the micro diaphragm pumps with the transport of polystyrene particles, before we evaluate the influence of cells.
Furthermore, a more detailed investigation of the pump's impact on the cells is necessary. In this preliminary experiment, we only evaluated immediate damage to the cells by staining. However, a long-term effect, e.g., reduced activity, is very likely. We will therefore conduct further evaluation including cell activity assays and long-term evaluation.
Overall, the results on pump performance as well as the impact on the cells are very promising. The impact on the cells can be further minimized with the optimization of the pump's geometry. The analytical estimation of shear forces in the pump shows higher shear forces in the valve gap compared to the chamber. To reduce this shear stress, an optimisation towards larger valve opening can be envisaged by a reduction of the stiffness of the flap valve. Furthermore, shear stress can be reduced by adapting the channel size of the inlet and outlet as well as the pump chamber geometry in terms of structure or height. With those measures we expect to further limit the damage caused by the pump and enable the development of improved and miniaturized transport systems. Acknowledgments: Special thanks to Alfred Michelfelder for his work in maintaining the cell cultures.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Experimental Setup for Cell Transport and Gravimetric Measurement
The setup for cell transport experiments ( Figure A1a) is simple with the pump being connected with flexible tubing with the inlet and outlet reservoir. The gravimetric setup was evaluated in a preliminary setup as shown in Figure A1b. In this setup, the pump transports liquid from the inlet reservoir on the balance towards an outlet next to it. The actuation signal of the pump is verified with an oscilloscope. This setup was improved for the experiments in this work as shown in Figure 2.

Flow Characterisation with Different Actuation Waveforms
The mean frequency dependant flow rate of five pumps shows an influence of the