Stress effect on 3D culturing of MC3T3-E1 cells on microporous bovine bone slices

2.1 Bone slices

Microporous bone slices were used to provide a 3D living environment for cells. To obtain suitable bone slices, the metaphyses of fresh bovine femurs were cut using an electric saw, during which uneven areas such as soft tissues and growth plates were removed, obtaining approximate cuboid bone blocks. Subsequently, the bone blocks were cut with a precise cutter into pieces of 40 × 10 × 1.2 mm³. To eliminate the grease in the bone slices, they were immersed in the 30% hydrogen peroxide solution (Beijing Chemical Works, China) and placed in an ultrasonic cleaner. After 3–5 days, they were taken out and rinsed under distilled water. This whole procedure was repeated until the solution became clear and the voids of the bone slices were evident, as shown in Figure 1. The bone slices were then washed 5 times with 1× PBS and sterilized in 4× AB/AM (antibiotic/antimycotic) solution (Genview, USA) diluted with distilled water for 2 days with the AB/AM changed once. Subsequently, the bone slices were incubated in DMEM (Gibco, USA) for 1 day, which was repeated two times until the medium color was stable. The treated bone slices were stored at −20°C for further use.

Figure 1

The configuration of the bone slice after degreasing.

The microstructure morphology of the bone slice was observed under a SEM (Scanning electron microscope). The results showed that it had complex microporous structures with high porosity. The pore size was approximately between 100 and 900 µm, as shown in Figure 2.

Figure 2

The microstructure morphology of the bone slice under SEM and the structures are divided into three typical structures.

2.2 Loading device

A custom-made four-point bending device was designed to create a stress environment in the bone slices, which is shown in Figure 3. It consists of a customized cell culture dish made of Teflon and aluminum alloy indenters inside (Figure 3d). The lid and bottom of the culture dish are tightly connected to the upper and lower indenter, respectively (Figure 3b and c).

Figure 3

Schematic diagram of the four-point bending device: (a) schematic diagram of the loading process of the bone slice; (b and c) photograph of the complete four-point bending device; (d) photograph of the demounted four-point bending device.

After placing the bone slice with living cells into the device, weights were placed on the lid to create a bending moment in the bone slice. The part of the bone slice between the two fulcrums of the lower indenter was in a pure bending state. According to the theory of mechanics of materials, the maximum bending moment in the bone slice M _max is given by

where M max is maximum bending moment in the bone slice, m 0 is the quality of the lid and the upper indenter, m is the quality of weights, L is the distance between the two fulcrums of the lower indenter, L 0 is the distance between the two fulcrums of the upper indenter, and g is the gravitational acceleration. The key parameters of the loading device are as follows: m 0 = 22.64 g , m = 20 g , L = 32 mm , L 0 = 22 mm .

Cells on the bone slice were subjected to bending stress. If the bone slice was treated as a homogeneous material, the maximum bending stress can be expressed as

where σ is bending stress, b is the width of the bone slice, and h is the height of the bone slice.

It should be mentioned that equation (3) only provided a reference in the stage of determining the dimensions of the loading device, which could not calculate the true stress distribution in the bone slice.

2.3 Cell culture

Before the experiment, MC3T3-E1 cells were cultured in DMEM supplemented with 10% FBS (Fetal bovine serum) (Gibco, USA) in an incubator at 37°C with a humidified atmosphere of 95% air and 5% CO₂. After 80% confluence, cells were digested by 0.25% trypsin (Gibco, USA), centrifuged, and resuspended in DMEM at a concentration of 2.85 × 10⁶ cells/mL. 5.7 × 10⁵ cells in 200 µL cell suspension were dropped gently onto each bone slice, waiting for cell adhesion to add media till whole bone slices immersed and keep cultured for one day. Subsequently, the bone slices were divided into two groups: the stressed group and control group. Three bone slices in the stressed group were cultured in the designed loading device, and three bone slices in the control group were set at the same time. Each group was cultivated for up to 8 days. The medium was changed, collected, and stored at −80°C on day 2, 4, 6, and 8 for the later alkaline phosphatase (ALP) detection. At the end of the culture, all bone slices were harvested and stained.

2.4 Immunofluorescent observation

To make the cells visible for microscopic observation on the bone slices, cells were labeled with fluorescent dye. Each bone slice was fixed in 4% paraformaldehyde for 15 min at ambient temperature, then permeabilized with 0.1% Triton X-100 for 10 min, and blocked in 4% BSA for 30 min. The F-actin cytoskeleton of osteoblasts on bone slices was stained with TRITC Phalloidin (1:200) for 1 h, and then the cell nuclei were stained with DAPI (1:250) for 10 min. Each stained bone slice was observed under a CLSM (confocal laser scanning microscope) (Leica Microsystems, Wetzlar, Germany) at a magnification of 100-fold and the typical structures were photoed by lamellar scanning at 8 μm increments.

2.5 Cell density calculation

Due to the complexity of the microporous structures of the bone slices observed by the microscope, for better comparison, they were divided into three typical structures: the surface (S), the connection (C), and the pore wall (P), as shown in Figure 2. The surface is the surface of the bone slice, which is relatively flat; the connection is generally lower than the surface, which connects different parts of the bone slice; the pore wall consists of the wall of pores and most of the highly inclined slopes.

The photographs were then processed and classified, and typical structural images with cell distribution of all bone slices were obtained. Afterwards, Image J was used to obtain the cell density of each typical structural image, which is given by

where N is the number of cells on a certain structure, A is the area occupied by these cells, and ρ is the cell density on this structure.

Then the average cell density on each typical structure of the stressed and control groups was obtained, and the percentage difference η of average cell density between the two groups was expressed as

where ρ ¯ ′ , ρ ¯ are the average values of cell density of the stressed and control groups on a certain structure, respectively.

2.6 Quantitative assay of ALP activity

The viability of MC3T3-E1 cells in two groups was detected by the ALP activity in the collected medium using the colorimetric ALP detection assay kit (Mecenbio, China). First, each medium of 1 mL was freeze-dried for 24 h at a temperature of −60°C with a pressure of 0.01 mbar, and then redissolved into 160 µL of diluent (provided by the kit). Three parallel samples with a volume of 50 µL were taken from each redissolved medium and standard samples. Subsequently, the redissolved and standard samples were tested following kit instructions. Finally, the values of OD (optical density) of each sample were measured at a wavelength of 450 nm and the ALP content of each sample was obtained through OD values.

Then the average ALP content in the stressed and control groups on different days was obtained, The measured average ALP content represented the amount of ALP cell secreting within two days, which was the time interval of medium change.

2.7 Micromechanical environment analysis of the bone slice

As mentioned above, due to the complex microstructures of the bone slice, the stress state of the typical structures (S, C, and P) cells growing on was very complicated under bending moment and could not be accurately calculated. Therefore, finite element simulation was employed for the stress distribution analysis of typical structures (S, C, and P) to explore how much force was being exerted on the cells in the stressed group and provide stress data for the later model establishment.

The geometric model of the microstructures of the bone slice was created using micro-CT scanning with the accuracy of 18 µm. For further analysis, the model was improved using Geomagic Studio 2010 for smoothness. The partial model was then introduced into the Abaqus 6.13 for finite element simulation.

In Abaqus 6.13, the solid model was meshed by C3D10 elements with total grids number of 1,60,926, and a pure bending moment which was calculated according to equation (2) was applied to its cross section. The loading process was conducted using Abaqus/Standard.

2.8 Normalization of cell density in mathematical model

Due to the influence of the projection effect during the microscopic observation, cell density data were also related to structure. However, the cell density data required during the creation of the mathematical model of cell growth affected by stress must only be related to stress. Therefore the normalized technique was employed to exclude the projection effect. Since the slope structures (C and P) in the bone slices were recognized as horizontal planes under microscopic observation, the areas of these structures calculated were less than the actual areas, and the cell density values were relatively large. Therefore, the cell density values of the connection and pore wall should be normalized through dividing by a coefficient. In the control group, normalized cell density values should be the same on each structure. Therefore, the cell density values were normalized by

where ρ s , ρ c , ρ p are average values of cell density on the surface, connection, and pore wall in the control group, respectively. k 1 and k 2 are normalization coefficients of the connection and pore wall, respectively, and they can be calculated once ρ s , ρ c , ρ p are obtained from the experiment.

2.9 Statistical analysis

All values were expressed as mean ± standard deviation (SD). Statistical analysis was performed by repeated measurements analysis of variance and unpaired T test. (GraphPad Prism 8). The variance was thought to be significant when p < 0.05.

3.1 Statistics and analysis of cell density

Images of cell distribution on various typical structures for the stressed and control groups are shown in Figure 4. Average values of cell density in each group and each structure were obtained, as shown in Figure 5a. The results showed that on the surface, connection, and pore wall, the average values of cell density in the stressed group were 650, 947, and 1,949 cells/mm², respectively, while the values were 529, 618, and 1,245 cells/mm² in the control group, respectively.

Figure 4

Cells on different typical structures in the stressed and control groups. Synthetic images of nucleus and F-actin of cells on the surface (a and d); connection (b and e); pore wall (c and f); (a–c) stressed group; (d–f) control group.

Figure 5

Results of experimental data analysis: (a) average cell density on each typical structure in the stressed and control groups; (b) total ALP content in the stressed and control groups on different days. *p < 0.05.

The average values of cell density in the stressed group were mostly higher than those in the control group. The largest difference appeared at the pore wall, reaching a value of 56.55%, followed by the connection with a value of 53.24%, and the surface had the smallest difference with a value of 22.87%. In addition, the differences were significant in the connection and pore wall between the stressed group and their relative control group. The results showed that a higher degree of proliferation occurred in the stressed group, indicating that the stress has promoted the proliferation of cells.

3.2 ALP test

Total ALP content which represented ALP content secreted by cells from the beginning to the 2nd, 4th, 6th, and 8th days was acquired through accumulating the average ALP content on different days. As shown in Figure 5b, the total ALP content in the stressed group was always a little higher than it was in the control group. However, there were no significant differences between two groups, indicating that stress has no compelling effect on the activities of the cells. The combined results of cell density analysis and ALP test demonstrated that stress can promote the proliferation of cells while having no significant effect on the differentiation of them within the experiment duration of 8 days.

3.3 Stress of the typical structures

The distribution of Mises stress in the bone slice is demonstrated in Figure 6. Computational results showed that the micromechanical environment in the bone slice was very complicated and the stress maximum was about 84.64 kPa, while the range of stress values for the majority of the bone slice was 0.1–20 kPa. However, it was notable that diverse structures were experiencing different magnitudes of stress. For example, most high-stress areas were located on the pole wall. Therefore, to simplify the stress distribution, based on the typical structure division, average values of stress on each structure were calculated through 20 random points in each typical structure. The approximate average stress of the surface, connection structure, and pore wall was 2.14, 2.62, and 4.47 kPa, respectively. It can be seen that the average stress of the pore wall was the largest, followed by the connection structure, and the average stress of the surface was the smallest.

Figure 6

Mises stress distribution in the bone slice.

3.4 Mathematical model of cell growth affected by stress

It was significant to explore potential correlations between the stress on cells and corresponding cell density and construct a mathematical model. The first step was to obtain the correct data. It can be seen from the results of the finite element analysis that there were four stress levels in the bone slices in the experiment, which were zero of the unstressed bone slices and the average stress of the three typical structures of the stressed bone slices. According to equation (6), the normalization coefficients of the connection and pore wall were k 1 = 1.1682 and k 2 = 2.3535 , respectively. All cell density values on the connection and pore wall in the stressed group were then normalized, obtaining the cell density data only relevant to stress, which is shown in Figure 7.

Figure 7

Cell density relationships with stress in different bone structures. The cell density values corresponding to each stress level were expressed in terms of mean and standard deviation.

As shown in Figure 7, the cell density increased with the growth of stress in general, and the increasing trend gradually slowed down. This phenomenon was consistent with the theory of bone remodeling in equation (1). Therefore, based on the theory of bone remodeling, mathematical model of cell growth affected by stress was established, which was given by equation (7). The average stress was an independent variable and the normalized cell density corresponding to each stress was a dependent variable.

where a and b are constant coefficients, c is the density of normally growing cells without being affected by stress, s is stress, and ρ is the cell density value.

Weighted least squares estimation was used to fit unknown parameters in equation (7), because the variance of the error of each cell density value was different. Equation (7) can be expressed as

where i = 1 , 2 , 3 , … , 57 is the sequence number of all the cell density data obtained in the experiment, and ν i is the error of ρ i , which is assumed to satisfy a normal distribution with a mean of 0 and a variance of σ i 2 .

The covariance matrix of error ν i is

Equation (8) can be written in the form of a matrix as

where y = ρ 1 ⋮ ρ 57 , H = s 1 2 , s 1 , 1 ⋮ ⋮ ⋮ s 57 2 , s 57 , 1 , x = a b c , and ν = ν 1 ⋮ ν 57 .

x ˆ is the best estimate of x, the residual ε y is the difference between the measured value y and the vector H x ˆ , and J is the cost function, namely

The most likely value of x ˆ was obtained when it made equation (12) the smallest. J can be expressed as

x ˆ should satisfy

Therefore, x ˆ can be expressed as

The unknown parameters were calculated by substituting relevant data into equation (15), and the result was a = − 10.0307 , b = 116.2279 , c = 523.2098 . The mathematical model of cell growth affected by stress can be expressed as

As can be seen from the model, when there is no stress present, cells proliferate at a normal rate; at this point, s = 0, ρ = 523.2098 . Within the stress range of 0 < s < 11.59 kPa, cell density values were higher than those without stress, indicating that the proliferation of cells was promoted by stress. In addition, the effect of promotion first increased and then decreased as stress increased, reaching a peak at s = 5.79 kPa. However, stress greater than 11.59 kPa will inhibit the proliferation of cells until excessive stress causes cell apoptosis.