1 Introduction

Hepatocytes, parenchymal cells of the liver, are cultured in vitro for different target applications such as bioartificial livers, tissue engineering, and drug testing. In order for these applications to be successful, the cells should behave as closely as possible to those in vivo in regards to functionality, morphology, and metabolism. Microfluidics and microfabrication technologies allow better control of the culture parameters (Kim et al. 2007; Andersson and van den Berg 2004; Khademhosseini et al. 2006), which leads to better artificial conditions, specifically since they can provide a controlled 3D microenvironment (Toh et al. 2007), co-culture capabilities (Ostrovidov et al. 2004), a high surface per volume ratio, perfusion conditions (Leclerc et al. 2004a), a better cell/medium volume ratio, and a low cell number and medium amount (an asset for drug testing applications).

One of the critical problems in in vitro culture is the effect of cellular density on various functions of cells or tissues. Most studies dealing with how cell density affects cellular growth and differentiation (Ichihara 1991), metabolic activity, and the function and morphology of cells (Dvir-Ginzberg et al. 2003) are done with a rather lower density than that found in vivo. The studies employing densities ≥108cells/mL are usually concerning bioartificial livers and always involve a large scaffold volume (5 mL for Hongo et al. (2005), 400mL for Kawada et al. (1998)), with the exception of Lee et al. (2007) who did a culture of hepatocytes in an artificial liver sinusoid at a density of 2 × 108 cells/mL.

Oxygen has an important influence on hepatocyte attachment and spreading (Rotem et al. 1994), especially at the early stages of culture. Moreover, at very high cell density, oxygen demand is expected to be high, and even if a gradient of oxygen concentration can be advantageous to mimic the zonation of hepatocyte rows in a hepatic lobule (Allen et al. 2005), hypoxic conditions should be avoided. Despite the importance of the O2 metabolism of hepatocytes at a high cell density (≥108 cells/mL), experimental data on oxygen consumption rates under these conditions have been rarely reported so far, and are needed a fortiori at the microscale level.

In our previous work (Provin et al. 2008), we have proposed a method to generate a scaffold with an ordered 3D microstructure supporting hepatocyte cells at a high cell density (5 × 107 cells/mL), together with a numerical model to determine the flow characteristics and the oxygen metabolism inside for various flow rates during perfusion culture. In this study, we have used this method to design and to fabricate a scaffold with a possibility for cells to attach at the very high density of 108 cells/mL. We have also measured the oxygen consumption rate (OCR) of HepG2 cells cultured in geometrically optimized scaffolds at various flow rates. The measured oxygen metabolism was analyzed utilizing our previous model, with revision, to explain the mechanism of oxygen transport in a high cell density culture.

2 Materials and methods

2.1 Scaffold details

2.1.1 Geometry of the scaffold

The 3D scaffold (Fig. 1a and b) possesses an ordered microstructure composed of tens of thousand of square columns (pillars) (Fig. 1c) whose geometry has been optimized to offer a surface per volume ratio sufficient for 108 cells/cm3 to attach. The designing method was already reported elsewhere (Provin et al 2008), but is briefly repeated here; by assuming a capped scaffold with, a, the side length of one pillar, 2b, the distance between two pillars (width of the fluids channel), h, the height of a pillar, and A cell, the area occupied by each attached cell, the cell density n can be defined as

$$n = \frac{{2\left\{ {\left( {a + 2b} \right)^2 - a^2 \} } \right\} + 4ah}}{{h\left( {a + 2b} \right)^2 A_{{\text{cell}}} }}.$$
(1)
Fig. 1
figure 1

(a) Schematic of the scaffold: top view; (b) schematic of the scaffold: top view; (c) schematic of the scaffold: ordered microstructure. Each pillar has a side length equal to a, is separated from others by channels whose width is 2b, and has a height equal to h

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Partial differentiation of n by pillar size a (which maximizes n) leads to the optimum a, a opt, as a function of b and h:

$$a_{{\text{opt}}} = \frac{{2bh}}{{2b + h}}{\text{ at }}\frac{{\partial n_{{\text{opt}}} }}{{\partial a}} = 0.$$
(2)

The height of the scaffold, h, can be derived from the following equation when the optimum cell density, n opt, channel width 2b, and the adherent area of single cell, A cell, are given.

$$n_{{\text{opt}}} = \frac{{\left( {2b + h} \right)^2 }}{{2A_{{\text{cell}}} hb\left( {b + h} \right)}}$$
(3)
$$h = \frac{{4b - 2A_{{\text{cell}}} b^2 n_{{\text{opt}}} + \sqrt 2 \sqrt {A_{{\text{cell}}} } b^{{\raise0.7ex\hbox{$3$} \!\mathord{\left/ {\vphantom {3 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}} \sqrt {n_{{\text{opt}}} } \sqrt {8 + 2A_{{\text{cell}}} bn_{{\text{opt}}} } }}{{2\left( { - 1 + 2A_{{\text{cell}}} bn_{{\text{opt}}} } \right)}}$$
(4)

Substituting h in Eq. 2 with Eq. 4 gives the side length as a function of the channel width 2b.

$$a = \frac{{4\sqrt {\text{b}} - 2A_{{\text{cell}}} b^{{\raise0.7ex\hbox{$3$} \!\mathord{\left/ {\vphantom {3 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}} n_{{\text{opt}}} + 2\sqrt {A_{{\text{cell}}} } b\sqrt {n_{{\text{opt}}} } \sqrt {4 + A_{{\text{cell}}} bn_{{\text{opt}}} } }}{{3A_{{\text{cell}}} \sqrt b n_{{\text{opt}}} + \sqrt {A_{{\text{cell}}} } \sqrt {n_{{\text{opt}}} } \sqrt {4 + A_{{\text{cell}}} bn_{{\text{opt}}} } }}$$
(5)

a was arbitrarily chosen as the optimizing variable.

Values assumed in Eqs. 1, 2, 3, 4, and 5 are as follows:

  • The adherent area of single cell (~23 μm in diameter), A cell, was taken as 415 μm2.

  • n opt was arbitrarily chosen as 108 cells/mL.

  • The area of the base of the entire scaffold (the part including pillars) was 20.49 mm × 35.73 mm.

All numerical calculations in this paragraph were performed by Mathematica 5.1 software (Wolfram Research, IL, USA).

2.1.2 Fabrication of the scaffold

The chosen scaffold material was polydimethylsiloxane (PDMS) because it offers biocompatibility, transparency, moldability, and is widely used for microfluidics applications (Sia and Whitesides 2003). A more complete description of the process employed here can be found elsewhere (Leclerc et al. 2003). Briefly, uncured PDMS (Silpot 184, Dow Corning, MI, USA) was mixed with its catalyst (10:2 w/w) and poured onto a mold made by a photopatterned SU-8 resin (SU-8 2075, Microchem, MA, USA) on a silicon wafer. After curing in an oven at 100°C for 45 min, the PDMS was peeled off and permanently bonded on the unmolded side to a glass slide using an O2 plasma (Fig. 2).

Fig. 2
figure 2

Photograph of the PDMS scaffold bonded on a glass plate

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2.2 Cell culture

2.2.1 Preparation of scaffolds for cell culture

PDMS scaffolds were coated covalently with collagen (Cellmatrix type I-P, Nitta Gelatin, Japan) following protocol by Nishikawa et al. (2008). Sterilization was done during the UV exposure step of this protocol. Briefly, PDMS scaffolds were exposed to O2 plasma for 10 s in a Reactive Ion Etching equipment (RIE-10NR, Samco, Japan) followed by 10 s of deep UV irradiation provided by an Eximer lamp (UVS-1000SMn, Ushio, Japan). Scaffolds were immediately recovered with aqueous solution containing 1% v/v of KBE903 (Shinetsu Silicone, Japan) and 0.5% v/v of acetic acid (Wako, Japan) for 45 min at room temperature, and then for 1 h at 80°C for coupling with aminosilane. After cooling down to room temperature, the solution was removed and the scaffolds were washed twice with sterilized water and twice with HEPES (Ultrol Grade, Calbiochem, USA) buffer at 200 mM. Scaffolds were put in contact with a photoreactive crosslinker SAND (Pierce, P-C21549, Rockford, IL) in HEPES 200mM and put over a bed of ice before exposure to UV for 1 min, twice, under a mask aligner (Union, Japan). This UV exposure step also ensured the sterilization of the scaffolds. The scaffolds were then washed with iced HEPES at 200 mM twice, then with ice sterilized water, and were coated with collagen type I solution overnight. They were then washed twice with phosphate buffer sodium (PBS) solution and stored in PBS prior to use.

2.2.2 Cell culture protocols

Human hepatoma cells (HepG2) (Health Science Research Resources Bank, Japan) were inoculated at a density of 107 cells/mL on the PDMS scaffolds, which were laid in Tissue Culture-PolyStyrene dishes (Grenier, Canada), and were cultivated with Dulbecco’s Modified Eagle’s Medium (Gibco, Invitrogen Corporation) supplemented with 10% fetal bovine serum (Gibco, Invitrogen Corporation)—0.5% antibiotic-antimycotic solution (Sigma, Japan) under 5% CO2 at 37°C in an incubator. The medium was changed 24 h after cell seeding and every 2 days thereafter.

When cells became confluent (usually after a week of culture), the scaffold was covered with a glass plate, on which inlet and outlet silicon tubes were connected to supply the medium. The tight sealing of the scaffold was ensured mechanically by using a metallic holder around the glass plate. The whole scaffold was installed in an acrylic container with an inside heater (Fig. 3) to keep the temperature at 37.0 ± 0.1°C. The perfusion line to the scaffold was connected to a peristaltic pump and a culture medium tank heated at 40.0 ± 0.1°C to lower gas solubility and diminish the generation of bubbles in the scaffold. The gas outlet from a conventional incubator was connected to the medium tank to provide humidified air and CO2.

Fig. 3
figure 3

Photograph of the perfusion setup. Inset shows the homemade incubator with the PDMS scaffold inside

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2.3 Oxygen measurement set-up and protocols

In order to perform the O2 measurement experiments, an electrochemical O2 meter (S.I. 782, Strathkelvin Instruments, UK) was used (resolution 0.1 μmol/L). An electrode was assembled into a flowing cell, which was connected to the perfusion circuit system at the outlet of the scaffold and was kept at 37.0 ± 0.1°C in a thermostatic bath (Fig. 4). The O2 meter was calibrated at the zero oxygen level and at the air-saturated level of the culture medium (214.4 μmol/L of O2). For the calibration at the zero oxygen level, the electrode was immersed in a 5%/w Na2SO3 solution before the installation of the O2 meter into the perfusion circuit. The calibration at the air-saturated level was performed before every single measurement at every flow rate, by using a by-path perfusion circuit providing an air-saturated medium to the O2 meter at the same flow rate as the measurement.

Fig. 4
figure 4

Schematic of the experimental setup for perfusion and oxygen metabolism measurement. Blue lines (with empty triangles) show the perfusion circuit without oxygen measurement, and red ones (with black triangles) show the circuit for oxygen measurement. For the calibration, the flow goes through the by-pass and avoids the scaffold (color figures can be seen in the online version of this article)

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The measurement of oxygen concentration was performed in the following way: the flow rate, Q v , was increased in a stepwise manner, and at each step, the oxygen concentration at the outlet was noted once it had reached a steady state. The difference in the oxygen concentration between the inlet (considered constant at 214.4 μmol/L) and the outlet, ΔO 2, multiplied by the flow rate Q v corresponds to the oxygen consumption of the scaffold (in mol/m3).

2.3.1 Cell counting

At the end of the O2 measurement experiments, all the cells in the scaffold were removed using trypsin-EDTA (Gibco, Invitrogen Corporation) and counted with a particle counter (Sysmex CDA-500, Japan) to get the final number of cells, N. Prior to the oxygen measurement, the initial number of cells was also evaluated by measuring the glucose consumption rate of the cells (Yoshida et al. 2008). For calibration of this method, the amount of glucose in the culture medium of confluent HepG2 cells in a 25 cm2 flask was measured every hour with a Gluco-card Diam-meter α (Arkray Co. GT-1661, resolution 0.1 mg/dL), followed by counting the number of cells with a particle counter for 12 samples (S.E. 12.3%). The glucose consumption, ΔG (g/L), as a function of time, ΔT (hour), gave a linear relationship whose slope was proportional to the initial number of cells, N i , and the volume of medium in L, V; this lead to Eq. 6, which was used to determine the initial number of cells in our device.

$$N_{\text{i}} = 8.912 \cdot \frac{{\Delta G \cdot V}}{{\Delta T}}$$
(6)

The initial and final numbers of cells were on the same order. The final number of cells, N, was used to define the averaged cellular oxygen consumption rate (OCR, in mol/s/cell) as follows.

$${\text{OCR}} = \frac{{\Delta O_2 \cdot Q_{\text{v}} }}{N}$$
(7)

2.4 Model analysis for flow characteristics and oxygen consumption rate in the scaffold

The flow characteristics and the oxygen consumption rate in the scaffold were calculated by the reported numerical simulation model. The simulation model was explained in detail elsewhere by the authors (Provin et al. 2008) and consequently only general explanations and equations that have been modified will be presented here. Briefly, two sets of equations for steady flow were used to calculate the oxygen consumption rate. The first set of equations is based on cree** flow equations to accurately determine the velocities around the pillars, the shear stress on all the walls in the scaffold, and the attachability of cells with regards to shear stress; the second set uses Darcy flow equations solved for the whole scaffold (considering that the flow in such a scaffold with an aligned microstructure can be renormalized as Darcy flow). The Darcy coefficient was calculated from the pressure gradient and the averaged velocity given by the first set of equations. The results of this calculation provided the distribution of velocities and attached cell ratios for the whole scaffold, which were used to perform the calculation of oxygen consumption rate. FlexPDE 5.0 software (PDE Solutions Inc, CA, USA) was used for the CFD analysis.

2.4.1 Cellular adherence with regards to shear stress

Since adherent cells are detached from the surface when the shear stress upon them is too high, we used the calculated shear stress to determine the attached cell ratio. We have considered a linear relationship between cell detachment and applied shear stress. Considering it is difficult to get the parameters corresponding to our exact conditions, the local attached cell ratio (number of attached cells/number of seeded cells), ϕ, was arbitrarily assumed as follows:

$$\phi = \left\{ {\matrix 1 \hfill {;\bar \tau \leqslant \bar \tau _1 Pa} \hfill \\ { - \frac{{\bar \tau - \bar \tau _2 }}{{\bar \tau _2 - \bar \tau _1 }}} \hfill {;\bar \tau _1 Pa \leqslant \bar \tau \leqslant \bar \tau _2 Pa} \hfill \\ 0 \hfill {;\bar \tau _2 Pa \leqslant \bar \tau } \hfill \ } \right.$$
(8)

with \(\bar \tau _1 \) as the shear stress above which the cells start to peel off, and \(\bar \tau _2 \) as the shear stress above which they are totally removed. The integration of ϕ on the surface of the unit scaffold defines Φ, the attached cell ratio in a scaffold unit.

2.4.2 Oxygen consumption rate (OCR)

The steady flow distribution, \(\bar U\), \(\bar V\), and the attached cell ratio, Φ, in the scaffold were used to calculate the mass transfer of oxygen. The mass transfer of oxygen considering cellular oxygen consumption is shown in Eq. 9.

$$\bar U \cdot \frac{{\partial C_{O_2 } }}{{\partial x}} + \bar V \cdot \frac{{\partial C_{O_2 } }}{{\partial y}} = D{}_{O_2 } \cdot \nabla ^2 C_{O_2 } - \Phi \cdot n \cdot M{}_{O_2 }$$
(9)

\(C_{{\text{O}}_2 } \) is the concentration of oxygen in the medium (taken as 214.4 μmol/L at 37°C), D oxygen is the diffusion coefficient of oxygen (1.473 × 10−9 m2/s at 37°C, given by the Stokes-Einstein equation), and \(M_{{\text{O}}_2 } \) (in mol s−1 cell−1) is the oxygen metabolism of a single cell. \(M_{{\text{O}}_2 } \) is described as in the Michaelis–Menten equation in Eq. 10.

$$M_{{\text{O}}_2 } = \frac{{{\text{SOCR}} \cdot C_{{\text{O}}_2 } }}{{K_{\text{m}} + C_{{\text{O}}_2 } }} = \frac{{{\text{2}}{\text{.2}} \times {\text{10}}^{ - {\text{16}}} C_{{\text{O}}_{\text{2}} } }}{{3.3 \times {\text{10}}^{ - {\text{3}}} + C_{{\text{O}}_{\text{2}} } }}$$
(10)

The saturated oxygen consumption rate (SOCR) is 2.2 × 10−16 (mol s−1 cell−1). This value was obtained in our group for a low density of HepG2 cultured on a flat plate (Yoshida et al. 2007). The half concentration constant (K m) is 3.3 × 10−3 mol s−1 cell−1, i.e. the oxygen concentration that leads to a value of \(M_{{\text{O}}_2 } \) equal to half of the SOCR. This is the maximum value measured by Foy et al. (1994) for a monolayer of rat hepatocytes. The maximum value was chosen since our system supports a high density of cells, which usually corresponds to higher values of the half concentration constant (Hay et al. 2001).

Apoptosis by hypoxia

The cells in the scaffold might encounter a long duration of hypoxic conditions during the O2 measurement experiments, especially during the long stabilization time at a low flow rate. For this reason, we simulated hypoxic deleterious effects by introducing a simple “dead or alive” criterion of oxygen concentration in our model. If the oxygen concentration is below a certain value at some place in the scaffold, cells are considered to be dead in that region. The response of cells to hypoxia is a complex process (Hochachka et al. 1996), and the only goal of this criterion is an attempt to reproduce some experimental conditions with our steady-state model. The percentage of living cells with regards to apoptosis by hypoxia is defined as ζ, and the concentration limit for the death of the cells is arbitrary chosen as K m/2 or K m/4. Considering this hypoxic effect, Eq. 9 was modified as follows.

$$\bar U \cdot \frac{{\partial C_{{\text{O}}_{\text{2}} } }}{{\partial x}} + \bar V \cdot \frac{{\partial C_{{\text{O}}_2 } }}{{\partial y}} = D{}_{{\text{O}}_{\text{2}} } \cdot \nabla ^2 C_{{\text{O}}_2 } - \Phi \cdot n \cdot \zeta \cdot M{}_{{\text{O}}_2 }$$
(11)

Boundary layer

Since the oxygen concentration in the culture medium is very low, its mass transfer is limited by the boundary resistance (Schneider 1995). We modified Eq. 11 considering the mass transfer coefficient of oxygen, \(h_{{\text{O}}_2 } \), and the concentration at the surface of the cells, \(C_{{\text{O}}_2 {\text{Surf}}} \).

$$\bar U \cdot \frac{{\partial C_{{\text{O}}_{\text{2}} } }}{{\partial x}} + \bar V \cdot \frac{{\partial C_{{\text{O}}_2 } }}{{\partial y}} = D{}_{{\text{O}}_{\text{2}} } \cdot \nabla ^2 C_{{\text{O}}_2 } - \Phi \cdot n \cdot \zeta \cdot h{}_{{\text{O}}_2 } \cdot A_{{\text{cell}}} \cdot \left( {C_{O_2 } - C_{{\text{O}}_{\text{2}} {\text{Surf}}} } \right)$$
(12)

In a steady state, Eqs. 11 and 12 are equivalent, which leads to Eq. 13.

$$A_{{\text{cell}}} \cdot h_{{\text{O}}_2 } \cdot \left( {C_{{\text{O}}_2 } - C_{{\text{O}}_{\text{2}} {\text{Surf}}} } \right) = M_{{\text{O}}_{\text{2}} } $$
(13)

Replacing \(M_{{\text{O}}_2 } \) by Eq. 10, \(C_{{\text{O}}_2 {\text{Surf}}} \) can be solved as Eq. 14.

$$C_{{\text{O}}_{\text{2}} {\text{Surf}}} = - \frac{{ - C_{{\text{O}}_2 } \cdot h_{{\text{O}}_{\text{2}} } \cdot A_{{\text{cell}}} + h_{{\text{O}}_2 } \cdot K_{\text{m}} \cdot A_{{\text{cell}}} - \sqrt {4 \cdot C_{{\text{O}}_2 } \cdot h_{{\text{O}}_{\text{2}} }^{\text{2}} \cdot K_{\text{m}} \cdot A_{{\text{cell}}}^2 + \left( {C_{{\text{O}}_2 } \cdot h_{{\text{O}}_{\text{2}} } \cdot A_{{\text{cell}}} - h_{{\text{O}}_2 } \cdot K_{\text{m}} \cdot A_{{\text{cell}}} - {\text{SOCR}}} \right)^2 } + {\text{SOCR}}}}{{2 \cdot h_{{\text{O}}_2 } \cdot A_{{\text{cell}}} }}$$
(14)

Substituting \(C_{{\text{O}}_2 {\text{Surf}}} \) in Eq. 12 with Eq. 14, a final ruling equation of oxygen transfer gives Eq. 15.

$$\begin{aligned} \bar U \cdot \frac{{\partial C_{{\text{O}}_{\text{2}} } }}{{\partial x}} + \bar V \cdot \frac{{\partial C_{{\text{O}}_2 } }}{{\partial y}} = D{}_{{\text{O}}_2 } \cdot \nabla ^2 C_{{\text{O}}_2 } \\ - \Phi \cdot n \cdot \zeta \cdot h{}_{{\text{O}}_{\text{2}} } \cdot A_{{\text{cell}}} \cdot \left( {C_{{\text{O}}_2 } + \frac{{ - C_{{\text{O}}_{\text{2}} } \cdot h_{{\text{O}}_2 } \cdot A_{{\text{cell}}} + h_{{\text{O}}_2 } \cdot K_{\text{m}} \cdot A_{{\text{cell}}} - \sqrt {4 \cdot C_{{\text{O}}_2 } \cdot h_{{\text{O}}_2 }^2 \cdot K_{\text{m}} \cdot A_{{\text{cell}}}^{\text{2}} + \left( {C_{{\text{O}}_2 } \cdot h_{{\text{O}}_2 } \cdot A_{{\text{cell}}} - h_{{\text{O}}_2 } \cdot K_{\text{m}} \cdot A_{{\text{cell}}} - {\text{SOCR}}} \right)^2 } + {\text{SOCR}}}}{{2 \cdot h_{{\text{O}}_{\text{2}} } \cdot A_{{\text{cell}}} }}} \right) \\ \end{aligned} $$
(15)

Two values of \(h_{{\text{O}}_2 } \) were tested: 2 × 10−5 m2/s, as given by Schneider (1995) for mammalian cells, and 10−6 m2/s, obtained by calculation using Eq. 16 for forced convection in a laminar flow on a plane surface (i.e. a pillar where the cells adhere);

$$h_{{\text{O}}_{\text{2}} } = \frac{{{\text{Sh}} \cdot D_{{\text{O}}_2 } }}{a},$$
(16)

with Sh, Sherwood number, representing the ratio of convective to diffusive mass transport.

3 Results and discussion

3.1 Scaffold

Different combinations of optimized height, side length and width can be used to reach the possible theoretical attachment of a density of 108 cells/mL. However, considering the fabrication process limitations and the size of HepG2 cells, values chosen were a side length a of 26.6 μm, a channel width 2b of 34 μm and height h of 138 μm. The subsequent fabricated mold and scaffolds used for the experiments had an actual size of (average of 10 scaffolds) a = 26.7 ± 0.5 μm, 2b = 33.1 ± 5 μm, and h = 109.6 ± 10.7 μm.

3.1.1 Cellular adherence and cells density

The HepG2 cells showed a good spreading (Fig. 5a) and attachment on the scaffold surface, even on the sidewalls and top of the pillars (Fig. 5b). This confirms the assumption made in the design of the scaffold concerning vertical sidewalls as usable surfaces for the cells. The covalent bonding of collagen used for the coating of the scaffold was an asset to obtain such results, since a conventional coating of collagen obtained by overnight contact between a collagen solution and a PDMS surface (Leclerc et al. 2004a,b) was not sufficient to keep the cells attached over a few days of culture (data not shown). The final number of cells varied from 8 × 106 cells to 1.6 × 107 cells per scaffold, which corresponds to an attached density of 108 to 2 × 108 cells/mL (average 1.7 × 108 cells/mL), which is very high and above the designed density. Indeed, we have assumed an attached monolayer of cells for the optimization of the geometry of the scaffold, but it seems the cells have also grown to compose aggregates or multilayers to bridge the gap between pillars due to the small distance between them (Yang et al. 2005). Moreover, as the cells were counted at the end of experiments, once a high flow rate had peeled off some cells from the scaffold, the number of cells that had grown is probably slightly higher than the figures stated above.

Fig. 5
figure 5

(a) HepG2 cells uniformly spread on the PDMS scaffold surface after 5 days of culture (×4 magnification). (b) HepG2 cells efficiently attached on the entire available surface offered by the pillars after 7 days of culture

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3.1.2 Oxygen consumption rate

Figure 6 displays an example of the experimental data. The oxygen concentration drops slowly as the perfusion circuit is switched from by-pass to scaffold, and reaches a steady state (when the consumed oxygen concentration value was noted) after only a few hours.

Fig. 6
figure 6

Example of experimental data of the oxygen measurement at Q v = 0.42 mL/min. Black line corresponds to the oxygen concentration at the inlet of the scaffold (considered constant at the saturated value of 214.4 μmol/L). Gray line is the measured oxygen concentration at the outlet of the scaffold. The arrows point to the moment the perfusion circuit was switched from by-pass to scaffold

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Experimental results for the average OCR per cell is shown in Fig. 7a (black diamond shaped dots) as a function of volume flow rate. First, the average OCR increases as the available quantity of oxygen rises with increasing Q v, until it reaches an average maximal value of 3.4 × 10−17 mol s−1 cell−1 for the average Q v of 1.6 mL/min, and finally it decreases with the very high flow rates, which may be caused by the detachment of cells.

Fig. 7
figure 7

(a) Average measured oxygen consumption rate per cell (on eight different scaffolds, SD = 0.4∼2.0 × 10−17, in mol s−1 cell−1) as a function of flow rate (mL/min). (b) Simulated oxygen consumption rate per scaffold as a function of volume flow rate (mL/min) for different conditions: A hypoxia criterion \({{K_{\text{m}} } \mathord{\left/ {\vphantom {{K_{\text{m}} } {2,\,h_{O_2 } = 2 \times 10^{ - 5} {{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}}}} \right. \kern-\nulldelimiterspace} {2,\,h_{O_2 } = 2 \times 10^{ - 5} {{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}}},\bar \tau _1 - \bar \tau _2 = 1 - 20\;{\text{Pa}}\) (empty circles); B hypoxia criterion \({{K_{\text{m}} } \mathord{\left/ {\vphantom {{K_{\text{m}} } 2}} \right. \kern-\nulldelimiterspace} 2},\,h_{{\text{O}}_{\text{2}} } = \,1 \times 10^{ - 5} {{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}},\,\bar \tau _1 - \bar \tau _2 = 1 - 20\;{\text{Pa}}\) (empty squares); C hypoxia criterion \({{K_{\text{m}} } \mathord{\left/ {\vphantom {{K_{\text{m}} } 2}} \right. \kern-\nulldelimiterspace} 2},\,h_{{\text{O}}_2 } = 1 \times 10^{ - 6} {{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}},\,\bar \tau _1 - \bar \tau _2 = 1 - 4\;{\text{Pa}}\) (empty diamonds), D hypoxia criterion \({{K_{\text{m}} } \mathord{\left/ {\vphantom {{K_{\text{m}} } {4,\,h_{{\text{O}}_2 } = 1 \times 10^{ - 6} \,{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}},\,\bar \tau _1 - \bar \tau _2 = 1 - 4\;{\text{Pa}}}}} \right. \kern-\nulldelimiterspace} {4,\,h_{{\text{O}}_2 } = 1 \times 10^{ - 6} \,{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}},\,\bar \tau _1 - \bar \tau _2 = 1 - 4\;{\text{Pa}}}}\) (empty triangles). The average measured oxygen consumption rate per scaffold (on eight different scaffolds, \({\text{SD}} = 0.2 \sim 1.3 \times 10^{ - 10} \), in mol/s) is represented by black diamond symbols

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This value of the oxygen consumption rate is one order lower than the OCR found in the literature for porcine and rat hepatocytes and human carcinoma hepatocytes, including results obtained from our group (Table 1).

Table 1 Hepatocyte OCRs found in literature
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Several hypotheses may be suggested to explain the low oxygen consumption rate.

  1. 1.

    Diffusion resistance (oxygen transport phenomena): The cell density used in the present study is 2 to 3 order higher than the ones summarized in Table 1. Hay et al. (2001) have mentioned that the SOCR should be lower at a higher cell density because of the reduction in diffusive flux, which limits the oxygen-dependent metabolism. Additionally, the scaffold geometry may affect the oxygen delivery to the cells. In this study, cells are attached on a PDMS surface with a 3D microstructure, unlike the other studies done either with a suspension of cells (Jones and Mason 1978; Guarino et al. 2004) or with a monolayer of cells on a flat surface (Balis et al. 1999; Yoshida et al. 2007).

  2. 2.

    Hypoxia: Measurements were started with a very low flow rate, inducing severe hypoxic conditions in the downstream part of the scaffold, which may lead to the death of cells in that region and therefore to a decrease in the number of living cells in the scaffold from the initial number.

We have used a numerical model to better understand the observed behavior and to evaluate hypotheses 1 and 2. Results for the OCR per scaffold calculated by the numerical simulation model are displayed in Fig. 7b (lines), together with the experimental data (diamond symbols). First we have evaluated the effect of the mass transfer coefficient. With a \(h_{{\text{O}}_2 } \) of 2 × 10−5 m2/s (Fig. 7b, curve A), the effect of the diffusion layer is almost negligible. 85% of the cells are alive and contribute to obtain a maximal OCR about five times higher than the experimental one. This result is close to the behavior of our model without a boundary layer (data not shown), which is not comparable to the experimental observations. In contrast, with a \(h_{{\text{O}}_2 } \) of 1 × 10−6 m2/s (Fig. 7b, curve B), only 36% are alive because of the low oxygen concentration at the surface of cells. The given maximal OCR is then about half of the experimental result. It is also important to note that at lower flow rates with low % \(h_{{\text{O}}_2 } \), the oxygen is not totally consumed at the outlet of the scaffold (Fig. 8), which is similar to what was observed experimentally (Fig. 6). This supports our hypothesis 1, implying that the mass transfer coefficient plays a critical role in oxygen metabolism.

Fig. 8
figure 8

Distribution of oxygen concentration (mol/m3) in the scaffold given by simulation (hypoxia criterion \({{K_{\text{m}} } \mathord{\left/ {\vphantom {{K_{\text{m}} } {2,\,h_{{\text{O}}_2 } = 1 \times 10^{ - 6} {{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}}}} \right. \kern-\nulldelimiterspace} {2,\,h_{{\text{O}}_2 } = 1 \times 10^{ - 6} {{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}}},\bar \tau _1 - \bar \tau _2 = 1 - 20\;{\text{Pa}}\)) for a volume flow rate Q v of 0.49 mL/min. The inlet is located in the left boundary, and the outlet in the right one. Cell number for the CFD calculation is 512

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Moreover, the behavior of the calculated OCR with regards to high flow rates does not show a decrease as the experimental one does, which is thought to result from the detachment of cells. We subsequently changed the range of detaching shear stress τ 1–τ 2 from 1–20 Pa (given by Powers et al. (1997) for hepatocyte cells on a low concentration Matrigel coating) to τ 1–τ 2 values of 1–4 Pa (Fig. 7b, curve C). Those latter values were taken arbitrarily to match the observed behavior of high cell attachment at a flow rate under 1 mL/min and sudden peel-off of the cells above 2 mL/min. Following this change of parameters, the calculated OCR behavior becomes closer to the measured one (Fig. 7b, curve C). The descent of OCR is nevertheless gentler than that of the experimental data. Further changes of the range of detaching shear stress did not permit any better matching of the observed behavior (not shown), which suggests a non-linear relationship or a more sudden decrease of the cellular adhesion ratio with the shear stress.

Finally, we’ve evaluated the hypoxia criterion by changing the value (arbitrarily chosen) of K m/2 to K m/4 (while kee** 1–4 Pa values for τ 1–τ 2). It resulted in an increase from 37% to 100% of living cells (with regards to hypoxia) in the scaffold, and a maximal OCR slightly higher than the measured one (Fig. 7b, curve D). Curves C and D are then delimiting the experimental data. In conclusion, hypotheses 1 and 2 are mainly explaining the low observed OCR, with a low mass transfer coefficient preventing the cells from accessing the surrounding oxygen, and a possible lower number of alive cells in the scaffold due to apoptosis by hypoxia. This emphasizes the limitation of the optimization of the scaffold design and flow rate to sustain cells with enough oxygen. In order to avoid hypoxic conditions and maximize hepatocyte viability and functionality, it is necessary to use other delivery means for the oxygen (Mareels et al. 2006) in order to increase its availability to cells. For cell culture at a large scale, this may include the use of O2 permeable materials for the scaffold (Leclerc et al. 2004b), dissolved oxygen carriers in the medium (Nieuwoudt et al. 2005), higher O2 partial pressure, or a combination of the aforementioned methods (Mareels et al. 2006). In the case of culture at a high cell density, we have shown that one of the main limitations comes from the oxygen mass transfer coefficient itself. Reducing the oxygen diffusion resistance on the surface of adhered cells is necessary to enhance the oxygen mass transport to the cells. The most efficient way to overcome this limitation is probably to use dissolved oxygen carriers in the extracellular matrix (Nahmias et al. 2006), by which oxygen can be in direct contact with the cell membrane, or to use mixing devices that can control the flow near the cells, resulting in a reduction of the oxygen diffusion resistance.

4 Conclusion

The use of an optimized geometry of 3D PDMS scaffold had made possible the attachment of a high density of cells (up to 2 × 108 cells/mL experimentally) at the microscale. Oxygen consumption rates have been measured for various flow rates, and the results were one order lower than the reported values for a density two orders lower. Using a numerical model, we have shown that main possible explanations are the low mass transfer coefficient of oxygen, and the death of some cells due to hypoxic conditions.