Table of Contents
- Introduction
- Oxygen supply - Aeration
- Oxygen mass transfer
- Some methods for determining kLA
- Key variables that impact kLA
- Conclusion
Introduction
Bioreactors are used for development and production of many high value products, such as biopharmaceuticals (we've written a blog post on that topic already, so make sure to check that one out). In order to produce them efficiently on industrial level, cell culture conditions need to be optimized and maintained, since cells are very sensitive to any changes in their environment.
Oxygen is one of the most critical nutrients for cultivating aerobic organisms. It is needed in order for cell metabolism to operate efficiently and allow the cells to grow. However, oxygen has a low solubility in liquid phase. This leads to one of the main problems in cell culture, which is the transfer of sufficient oxygen into the medium.
In this blog importance of sufficient aeration for optimal cell growth will be discussed. As well as, how to control oxygen supply by manipulating bioreactor parameters.
Oxygen supply - Aeration
Aeration is used to describe a process of continuous delivery of oxygen to the cells in the culture. Cells uptake oxygen in a form of dissolved oxygen (DO).
DO can be supplied to the culture medium in 2 ways:
1. Oxygen can diffuse from the head-space of the reactor through the cell culture medium interface.
2. Oxygen is supplied through spargers and with agitation dissolved in the medium via convection.
Initially the demand for oxygen in the cell culture is low, since the cell density is low. Over time cell mass increases and consequently the demand for oxygen supply increases. At a certain point O2 solubility becomes limiting for cell growth, as oxygen transfer rate into the bulk liquid is not rapid enough for the cell metabolism. In cell culturing the latter wants to be avoided, as it leads to cell death and consequently lower yield and lower quality product.
Oxygen mass transfer
Oxygen mass transfer occurs in 2 phases in a typical bioreactor:
1. Just below the surface and around the bubble, there is a stagnant layer of liquid that is not mixed. Oxygen has to diffuse through a stagnant layer around the gas bubble in order to pass through the gas-liquid interface and from gas to the culture medium. This is called the oxygen transfer rate (OTR).
2. Next, oxygen has to overcome liquid-cell interface in order to be available for cell uptake. This is called the oxygen uptake rate (OUR).
Even though the stagnant layer is very thin, it is thick enough to cause problems with oxygen transfer.
In order to avoid cell death, the rate of oxygen transfer has to be carefully planned and controlled. Oxygen transfer rate (OTR) is mainly influenced by 2 factors:
Mass transfer coefficient - kLA
is the mass transfer coefficient from the gas bubble to liquid phase (culture medium), given in s‑1. can be represented by the following equation:
kLA = kL * A
Where, is oxygen mass transfer coefficient (m.s-1) and A is specific surface area gas-liquid interface (m2m-3).
Available area for oxygen transfer
The efficiency of mass transfer increases with increasing surface area available for transfer. Thus, agitation is used to disperse oxygen bubbles, making their surface area smaller and therefore promoting the oxygen transfer rate.
The specific surface area in a bubble column is given by:
Where, is rise velocity of the bubbles (m.s-1), D is reactor diameter (m), F is gas flow (m3.s-1) is bubble diameter (m).
Calculating oxygen transfer rate (OTR) and oxygen uptake rate (OUR)
The oxygen transfer rate through an interface is calculated by using the following equation:
OTR = kL * A * (C*ol - Col)
Where kL is the oxygen transfer coefficient (m.s-1), A is the specific surface area (m2.m-3) and C*ol - Col describes the gradient of concentrations and is also named “the driving force”. The driving force is the difference between C*ol, that is oxygen concentration at the top layer of the medium that is in equilibrium with gas phase (mol.m-3) and Col that is oxygen concentration in the bulk of the medium (mol.m-3). The latter one is a setpoint of DO, where cells grow optimally and is cell line dependent.
All cells in a large-scale bioreactor need to be supplied with a sufficient amount of oxygen. This means that the cells need to be supplied with at least the same amount of oxygen that they will take up. Oxygen uptake rate (OUR) is cell-line dependent.
OUR can be calculated by using the following equation:
OUR = qo * Cv
Where is the specific oxygen consumption rate per cell (mol.cell-1.s-1) and Cv is viable cell concentration (cells.m-3).
The oxygen transfer should balance the consumption of the cells. This can be expressed as follows:
OTR = OUR
kL * A * (C*ol - Col) = qo * Cv
The OTR and OUR rates are correlated by the oxygen mass transfer coefficient, kLA. OTR based on its correlation with determines theoretical maximum cell density that can be achieved in cell culture.
Some methods for determining kLA
In real systems, determining specific surface area gas-liquid interface (A) is very difficult, as it depends on the number and size of the gas bubbles, which is further dependent on media composition, mixing and air flow rate. Therefore, exact value of the specific surface area is difficult to determine as is the value for the transfer coefficient. However, the combined value, the kLA can be easily measured.
Dynamic method – gassing out
The often-used method for empirically determining kLA is the dynamic method. With the dynamic method concentration of oxygen in the bioreactor changes over time. During the experiment, the oxygen concentration is brought to zero by degassing with nitrogen gas. This is followed by replacing nitrogen with air and measuring the rise in oxygen concentration over time. The rate of change of DO concentration is measured.
There are many variations and improvements of the dynamic method, which are not discussed in this post.
Steady-state method
This method is used when the oxygen concentration during the process in the bioreactor is constant. Oxygen concentration is measured in the airflow going into the bioreactor and in the airflow going out of the bioreactor. The difference between the two measured concentrations equals the oxygen transfer rate from gas to liquid.
Key variables that impact kLA
Changes in running the bioreactor will have an impact on kLA. Therefore, the effects of changes should be assessed in bioprocess design with computational simulations and modelling.
The key variables that can affect kLA values are:
Gas bubble size
Gas bubbles can vary in sizes and are mainly determined by the sparger. Sparger with small diameter holes generates smaller bubbles than a single orifice sparger.
If the gas bubbles are smaller, that means in decreased surface area leading to increased gas residency time. Gas bubbles stay in the culture media for longer allowing oxygen more time to pass through the stagnant layer around bubbles and diffuse into the cell culture medium.
Agitation
Agitation in a bioreactor is used to eliminate gradients of concentration (gas, temperature, nutrients) in the culture. In addition, gas bubble size highly depends on impeller type and speed.
In a process where there is no agitation the cells are oxygen limited, due to slow OTR.
kLA values increase as agitation speed increases. If agitation rate is increased the kLA consequently increases and results in a higher OTR. Therefore, cell concentration increases due to enough oxygen in the culture. However, at a certain moment cell increase stops, due to another component in the medium being limited (glucose/glutamine).
However, higher agitation can lead to higher shear forces and consequently cell death. Different impeller positions and agitation speed need to be taken into account and tested when designing a bioreactor to achieve target kLA values with minimal shear forces.
Airflow rate
Higher oxygen availability drives kLA to increase. Increasing oxygen supply to a bioreactor drives this availability and can be controlled by modifying oxygen enrichment in air concentration. By increasing the oxygen concentration in the head space of the bioreactor the driving force is increased, leading to a higher kLA. Lowering the set point of oxygen concentration in the culture media results in the same effect.
Although high kLA values are preferred, it is important to consider the implications to cell viability and associated process costs. In addition, high airflow rates can also cause shear forces and lead to cell damage and death.
Coalescing properties of the medium
When the liquid has coalescing tendencies it results in small gas bubbles colliding and forming larger bubbles, which decreases A and subsequently decreasing kLA. Mass transfer is enhanced when there is continuous bubble breakup in the media.
In some operation modes, such as batch (to get to know more about the different modes of operation, read this blog), the viscosity and coalescence properties of the fluid change during the fermentation, due to changing cell, substrate, and product concentrations. Consequently in such case, the kLA is variable.
Temperature
Temperature affects oxygen solubility. Increasing temperatures result in a lower oxygen solubility leading to a smaller driving force and to a lower OTR. However, the diffusion rate of oxygen increases with increasing temperatures, while the liquid viscosity and surface tension decrease.
These effects in turn result in an increased kLA value. The positive effects of the increase in temperature on kLA might offset the smaller driving force caused by lower oxygen solubility.
Height of the bioreactor
Death rate of the cells can be reduced by increasing the height of the bioreactor. The reason for this is similar as with the size of the bubbles. If the bioreactor is higher that leads to longer gas residency time, increasing the time of oxygen to pass through the stagnant layer around bubbles and diffuse into the cell culture medium.
Conclusion
A complete understanding of bioreactors and parameters that influence its functioning is essential when designing a bioprocess or scaling up a process. Making informed decisions about the physical design, mixing and sparging options will lead to a properly oxygenated culture and higher productivities.
