Two‐ and three‐dimensional in vitro nucleus pulposus cultures: An in silico analysis of local nutrient microenvironments

Abstract Background It is well established that the unique biochemical microenvironment of the intervertebral disc plays a predominant role in cell viability and biosynthesis. However, unless the effect of microenvironmental conditions is primary to a study objective, in vitro culture parameters that are critical for reproducibility are both varied and not routinely reported. Aims This work aims to investigate the local microenvironments of commonly used culture configurations, highlighting physiological relevance, potential discrepancies, and elucidating possible heterogeneity across the research field. Materials and Methods This work uses nutrient‐transport in silico models to reflect on the effect of often underappreciated parameters, such as culture geometry and diffusional distance (vessel, media volume, construct size), seeding density, and external boundary conditions on the local microenvironment of two‐dimensional (2D) and three‐dimensional (3D) in vitro culture systems. Results We elucidate important discrepancies between the external boundary conditions such as the incubator level or media concentrations and the actual local cellular concentrations. Oxygen concentration and cell seeding density were found to be highly influential parameters and require utmost consideration when utilizing 3D culture systems. Discussion This work highlights that large variations in the local nutrient microenvironment can easily be established without consideration of several key parameters. Without careful deliberation of the microenvironment within each specific and unique system, there is the potential to confound in vitro results leading to heterogeneous results across the research field in terms of biosynthesis and matrix composition. Conclusion Overall, this calls for a greater appreciation of key parameters when designing in vitro experiments. Better harmony and standardization of physiologically relevant local microenvironments are needed to push toward reproducibility and successful translation of findings across the research field.


| INTRODUCTION
It is well established that the unique biochemical microenvironment of the intervertebral disc (IVD) has a predominant role in degeneration and the success of potential regenerative strategies. [1][2][3] Due to the IVD being avascular, nutrients, and metabolites must be transported to and from the cells through the extracellular matrix (ECM), giving rise to gradients throughout the tissue. 4 The viability and biosynthesis of a sparse population of central nucleus pulposus (NP) cells are critical to the maintenance of a highly specific ECM composition required for the inherent biomechanical function of the IVD. As a result, the effect of nutrient concentrations and pH on native NP cells, [5][6][7][8][9][10][11][12][13][14] and potential cell therapies has been extensively investigated. [15][16][17][18][19] Key findings suggest that glucose is the nutrient critical for maintaining viability, with bovine NP cell death occurring when glucose falls below $0.5 mM for more than 3 days, while cells have remained viable up to 13 days in the absence of oxygen. 6,7 However, oxygen level appears to play a dominant role in maintaining the NP phenotype and controlling the synthesis of key water-binding proteoglycan (PG) molecules of the ECM. 20,21 Meanwhile low pH due to the accumulation of lactic acid, has long been connected with induced cell death and hampered PG synthesis, 5,7,8,22 but more recently it has also been associated with the upregulation of proinflammatory cytokines and pain-related neurogenic factors. 23 As a result, it is evident that for repeatable and clinically translatable in vitro results, experiments need to be performed at consistent and physiologically relevant levels of nutrition.
Our recent study sought to consolidate the current knowledge of the IVD nutrient microenvironment and re-evaluate the concentrations in the context of different stages of degeneration. 24 This work suggests that at a stage of degeneration when cell-based regeneration remains a viable treatment option, the central NP microenvironment consists of glucose concentrations of approximately 1-3.5 mM, an average oxygen level of 6-8 %O 2 , and a median pH of 7. Therefore, when investigating the response of potential cell therapies in vitro, we need to tailor the biochemical microenvironments to these values to ensure that results are more physiologically relevant and clinically translatable. This concept has recently been deliberated for more advanced ex vivo disc organ culture systems, 25 while it is often considered that in less complex in vitro cell culture, these conditions can be simply implemented through culturing cells in low oxygen, reduced glucose and/or serum and increased acidity. However, aside from studies which specifically study the effect of microenvironmental conditions, the majority of disc cell culture across the research field do not adjust the pH of the culture media. Glucose concentration of the culture media and the incubator oxygen levels are more commonly regarded as controllable in vitro boundary conditions. Despite this, only 32 (58.2%) of 55 reviewed papers reported on the glucose concentration and only 23 (41.78%) reported on incubator oxygen level two-dimensional (2D) cell expansion. Figure 1A shows that among the studies that reported on the boundary nutrient concentrations 62.5% used high glucose (HG: 25 mM or 4.5 g/L) and 37.5% used low glucose (LG: 5.5 mM or 1 g/L), while 44.8% used "normoxia" (NX: 20-21 %O 2 ), 34.5% used "physioxia" (PX: $5 %O 2 ), and 20.7% used "hypoxia" (HX: $2 %O 2 ). Taking note that of the 23 studies reporting oxygen values, 6 studies investigated more than one oxygen level.
This not only highlights large variation across the field but also that parameters that are critical for reproducibility are not routinely being reported. There is an urgency for this to be addressed, particularly with a recent push toward harmonization within disc research and the increased attention to the reproducibility of research findings across all scientific fields. 26 Furthermore, a disconnect often occurs between the external incubator or media concentrations and the actual local cellular concentrations. [27][28][29][30] There is an underappreciation for the effects of parameters such as diffusion rate, media volume and cell density on the true nutrient microenvironment of cell culture systems. A number of studies use soft scaffolds such as hydrogels to mimic the native disc tissue and maintain cells in their three-dimensional (3D) phenotype.
However, potential nutrient gradients through these systems will not only affect cell viability and differentiation but also regulate gene expression and metabolism, creating distinct regions of ECM deposition. Therefore, it is critical that we carefully consider the combined effects key culture parameters may have on the microenvironment of in vitro systems and the downstream confounding influence on heterogenous matrix synthesis. This work aims to characterize the local nutrient microenvironment of 2D cell monolayers and commonly used 3D in vitro culture systems, to highlight the effect of culturing parameters and to place "standard practice" culturing conditions into context in terms of physiological relevance.

| METHODS
Long-term leaders in disc cell culture were identified through the ORS Spine subgroup involved in standardization and harmonization of cell isolation and culture methods. As a result, we looked at studies over the last $15 years from 20 prominent disc groups from across 14 different universities/medical centers. A list of the reviewed literature with a summary of key parameters can be found in Table S1. 2.1 | Two-dimensional cell culture models

| Metabolic rates and proliferation kinetics
Several studies have reported oxygen consumption rates (OCR), [8][9][10]12 glucose consumption rates (GCR), and lactate production rates (LPR) for NP cells from animals and humans under varying nutrient conditions. 8,10,13,14,17,34,35 Tabulated rates from these studies can be found in Table S2-S4. For this work the literature has been compiled based on the external boundary conditions of glucose (LG or HG) and oxygen (NX, PX, or HX), as shown in Figure 1C. Significantly higher oxygen consumption has been reported for degenerated human cells (aged 43-62 years, Thompson Grade III or IV), 12 as a result OCRs can be separated into a "lower" rate group comprising of values reported for animal and healthy human cells (aged 21-65 years, Thompson Grade I or II) and a "higher" rate group for a degenerated phenotype. However, similar categorizing of glycolytic rates does not appear to be possible with the literature available and average GCR and LPR values will be used regardless of species/ degeneration stage. As previously demonstrated together with successful ex vivo validation, 25 OCR (μM/h) is modeled as being dependent on local pH and oxygen by employing Michaelis-Menten equations. 8,9,36,37 where t is the time (h), C O2 is the local oxygen concentration (μM), pH is the local pH level, and ρ cell is the cell density (million cell/ml). V max is the maximum consumption rate (nmol/million cells/h) and K m is the rate limiting Michaelis-Menten constant (μM).
GCR was more explicitly modeled using a maximum GCR based on the external glucose boundary conditions (as no clear and obvious difference exists between 5.5 and 25 mM in Figure 1C) but becomes rate limited at $2 mM, by curve fitting Michaelis-Menten kinetics to experimental measurements at lower glucose concentrations (<5 mM). 14,17 where t is the time (hr), C gluc is the local glucose concentration (mM), ρ cell is the cell density (million cell/ml). V max is the maximum consumption rate (nmol/million cells/h) and K m is the rate limiting Michaelis-Menten constant (μM).
In order to capture rate limited glycolysis, LPR was implicitly modeled based on the ratio of lac:gluc molecules which is typically 2:1. 8,9,36,37 However, considering the compiled experimental literature this ratio appears to vary as a function of oxygen. Furthermore, when the pH drops below 6.7 in certain culture configurations, LPR was modeled explicitly to capture experimental observations of rates dropping from $200 nmol/million cells/h at pH 7.4 to $150 nmol/million cells/h at pH 6.7 and to $50 nmol/million cells/ h at pH 6.2. 8 The finalized metabolic parameters used in the models, based on the media glucose and external oxygen levels are presented in Table 1.
Cell proliferation was modeled using first order kinetics based on our observed population doubling time (the time for the doubling of a single cell under mitosis). Based on our experience of culturing NP derived porcine cells and assuming an initial seeding density of 5 Â 10 3 cells/cm 2 and an upper limit of 5 Â 10 6 from a T-175 after 5-6 days (i.e., $ 28 571 cells/cm 2 at 80% confluency), an exponential growth rate (k) of 0.348 [1/d] can be calculated using the population doubling time.
where k is the frequency of cell cycles per unit time, N t is cell number at time t, N 0 is the initial cell number, and t is the culture time in days.
Given that it is common practice to perform a media exchange twice a week and given the assumption of 5-6 days to $80% confluency, the transient 2D analysis was modeled for 7 days, incorporating a media exchange at the midway point. Although other studies may report different growth rates, the culture time is arbitrary; whether cells reach 80% confluency at 5-6 days or 12-15 days, 38 the results at 80% confluency will be the same regardless of the time frame. An example of different proliferation kinetics can be found in Figure S1A-C.
Diffusion through culture media was the same as for the 2D models.
However, as an idealized model, diffusion was not modelled through the base of the construct which was in contact with the tissue culture plastic.
Hydrogel geometry, cell seeding densities, culture vessel type and media volume, external boundary concentrations, and metabolic rates all play a role in establishing the local cell nutrient microenvironment.
The most utilized configurations for alginate beads, cylindrical constructs, and pellet cultures are presented in Figure 1F-

| External boundary concentrations: Glucose and oxygen
As mentioned previously, culture media is typically either LG (5.5 mM) or HG (25 mM) and both concentrations will be investigated for all culture configurations except pellet culture, as all pellet literature report the use of HG only. However, in terms of oxygen the volume/ volume ratio of oxygen to other gases in an incubator is decreased compared with dry room air (21.2 kPa or 159 mmHg at sea level), Figure 2A. As a result, the relative gas concentration in a NX, PX, or HX incubator, with the addition of 5% CO 2 (38 mmHg) and 75% humidity (47 mmHg), is lower than the conventional concentrations typically cited. 50 Furthermore, for modeling through COMSOL, the partial pressure of incubator oxygen must be converted into the concentration of dissolved oxygen by using Henry's law (oxygen solubility coefficient of 1.3 μM/mmHg in culture media at 37 C). 29,50 The resulting oxygen concentration of the culture media equilibrated within each oxygen incubator is shown in Figure 2B.

| RESULTS
2D results are presented as a transient analysis to capture the effect of cell proliferation and media exchange over a 7-day period.  Figure 2D shows the average glucose concentration of both LG and HG culture media at $80% confluency (day 5-6), following a standard media exchange of twice weekly, while Figure 2E shows the corresponding pH level of the media. As expected, glucose and pH are predicted highest in the culture vessel with the lowest cell yield (6-well) and lowest in the culture vessel with the greatest cell yield (T-175). Additionally, no significant difference was seen in glucose between the different oxygen incubators in 2D due to a surplus of glucose, while pH reduces slightly more under HX due to increased glycolytic rates.  at 8 million cells/ml oxygen drops to 11.1 %O 2 . As expected, the reduction in oxygen within beads cultured in HG is less due to the slightly lower OCR under these conditions. However, even at NX conditions, cells with very high rates of oxygen metabolism ( Figure 3B), predict minimum oxygen levels of 11.3 %O 2 , 5.9 %O 2 , and 1.4 %O 2 within beads with 2, 4, and 8 million cells/ml, respectively. In concentrations for the different seeding densities and external boundary conditions. Glucose appears in excess at HG and even at LG conditions with 8 million cells/ml, glucose does not fall critically low between media exchanges. Nonetheless, under HG conditions glycolysis is not rate limited by low glucose (<5 mM) and as a result pH is predicted to drop lower within the beads cultured at HG compared with LG ( Figure 4C). This is most apparent in Figure 4D under HX conditions, where glycolytic rates are modeled to be highest. A bead with 8 million cells/ml is predicted to have a minimum pH of $7.0 under LG conditions compared with $6.9 under HG conditions, just prior to media exchange.  Figure 5A presents the glucose gradient through the center of beads just prior to a media exchange.
Concentrations were observed to drop substantially lower in the well containing 10 beads at both LG and HG. In Figure 5B we see the beginning of a plateauing effect of glucose limited glycolysis in LG but not HG. Figure 5C presents the corresponding pH gradient through the alginate beads. As expected, we see significantly lower pH levels within one of the 10 beads under HX conditions and HG media. Again, in Figure 5D we see the strong effect of glycolysis not being rate limited by glucose under HG culture.  Figure 6B compares the axial profile through the center of the cylindrical hydrogel.    Figure 8A presents the gradients of metabolites in the midplane through the culture system on day 3, just prior to a standard media exchange. Figure 8B  Looking first at 2D cell culture, the majority of NP cell culture work report 6-well plates, followed by T-25 flasks. This appears to be more typical in studies working with species such as rat and The greatest effect is the total cell number within the culture vessel, providing a microenvironment which changes with time due to proliferation kinetics. As the cells multiply, the rate at which glucose reduces and lactate accumulates increase. Despite this, standard media volumes together with twice weekly media exchanges are predicted to be sufficient, with glucose exhaustion and lactate acid build-up of no significant concern, even at high levels of confluency.
However, the drop in glucose and increase in pH between media exchanges will be dependent on how metabolically active the cells are and their specific glycolytic rates. This is highlighted in the case of oxygen, by comparing the "lower" animal and healthy human rates to the "higher" degenerated human rates of OCR available from the literature. While there is no major difference in the oxygen at the cell surface over time for cells with a lower OCR rate, the local cellular oxygen concentration does change over time for cells with higher rates of respiration and may need to be considered in highly oxygen dependent studies.
Oxygen is a key parameter in cell culture, as its diffusion and delivery to cells in vitro is very different to hemoglobin transportation in vivo. 26,28,29,50,54 The level experienced by the cells reflects a balance of oxygen diffusion through the media from the surrounding incubator oxygen and OCR together with the total number of cells.
While this reduction in oxygen may not be significant at NX levels,  onstrates that cell numbers must be considered very carefully and that it is challenging to compare between samples with varying cell densities without considering that the local microenvironments will be different. When culturing a single bead in a well, we predicted that there remains a surplus of glucose between feeds, thus questioning the use of supraphysiological HG media, something which has already been experimentally examined at the larger scale of ex vivo disc organ culture. 25 In addition, research groups have reported culturing multiple beads in a single well. 67,69,70 In this scenario, we predict that more frequent media exchanges may be necessary to replenish glucose (particularly in the case of 10 beads in LG) and to circumvent the detrimental accumulation of lactate and subsequent drop in pH. The effect of refreshing the media daily is presented in Figure S2A-D and demonstrates that doing this can maintain a relatively constant level of glucose and pH throughout the culture period.
The second most popular 3D culture system are cylindrical hydrogel constructs, with the majority of studies using bovine, 71,72 porcine, 17,73-75 and goat cells. 76 As a result, only the "lower" animal metabolic rates were modeled. In terms of the geometry, construct diameters are typically 4 or 5 mm, while the thickness appears to range from 1.5 to 3 mm. 71,72,74,76,77 The results showed that reducing In order to provide confidence in the in silico construct models we can look toward a recent cartilage study that measured oxygen levels of 3.0-7.6 %O 2 (depending on cell type) in the center of hydrogel constructs (diameter = 5 mm, thickness = 3 mm, and 20 million cell/ml) cultured at external NX conditions. 79  The results of this study suggest that high cell density constructs may be best suited to culturing at external NX conditions, while lower or more native cell densities require "PX" incubator levels in the disc field to be raised from $5 to $10 %O 2 to create more physiologically relevant oxygen niches, in an attempt to reduce the heterogeneity across studies in terms of the oxygen environment.
Like the alginate bead, the cylindrical hydrogels also bring into question the physiological relevance of culturing in HG, particularly when assessing the suitability or effectiveness of cells as a therapy for IVD regeneration. Not only is the glucose supraphysiological for both low and high cell densities, but the models predict greater acidity in the HG constructs (particularly the 20 million cells/ml constructs).
Although we did explicitly implement a significant reduction in LPR, based on experimental measurements as pH reduces below 6.7, 8  Based on the current study we recommend utilizing physiologically relevant LG media for 3D disc culture. Although this is contrary to previous findings which measured glucose concentration in "spent" HG media revealing significant drops in glucose from $25 to $5 mM within 3 days, 89 it is important to note that these constructs had half This study is an idealized representation of culture microenvironments and thus is not definitive or without limitations. For example, proliferation kinetics were not considered within the 3D models. The rational for this is that the local microenvironment itself will influence The large range in rates of disc cells reported may reflect differences in isolation procedures, expansion, measurement configuration and the difficulty of obtaining reproducible interlaboratory measurements. 57 This large variability between studies, in addition to limited availability of literature resulted in averaged or idealized glycolytic rates (GCR + LPR) being used within the in silico models based on the external boundary conditions, rather than modeling each specific cell type. However, it has been reported that notochordal IVD cells are more metabolically active and more sensitive to nutrient deprivation. 10 In some studies, high oxygen has been observed to reduce the rate of glycolysis which is known as a positive Pasteur effect. 20,94 However, a number of other studies have shown a negative Pasteur or no effect for NP cells. 8,14 Despite IVD cells preferring a more prevalent glycolytic pathway for energy in its harsh microenvironmental conditions, the reasons for differences in observed phenomenon under varying nutrient concentrations remain unclear. When explicitly modeling the averaged glycolytic rates (Table 1), it is apparent that a positive Pasteur is not captured throughout the compiled literature, with PX conditions appearing to have the lowest rates and thus predict the highest concentrations of glucose and pH within the 3D models.
To address these potential limitations, we performed a sensitivity analysis of the lowest and highest metabolic rates (Appendix S1).
Taken together, this work highlights the importance of considering the metabolic demands of the specific cell type being

| CONCLUSION
Predominantly, the models in this work seek to illustrate the effect that parameters such as external boundary conditions and cell seeding densities have on the local nutrient microenvironment. It highlights that large variation and gradients in metabolite concentrations are easily established without careful consideration of these key parameters and that this diversity currently exists across the disc research field. As a result, we call for greater attention to the specific local microenvironment when trying to understand heterogeneity in results between studies. While one external concentration may be suitable for one culture configuration, they may not be appropriate for another. External conditions need to be tailored to the specific cells and culture system to establish homogeneous and physiologically relevant microenvironments. We believe that with more deliberate con-