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Bioreactor cultivation modes

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1 Cours BCM 6013 – Techniques en instrumentation Module 1 – Cellular experimentation Université de Montréal, May 2-6, 2011 Bioreactors and cultivation modes Presenter: Robert Voyer, B. Ing., M. Sc. A. My academic background Bachelor degree in Chemical Engineering, École Polytechnique de Mtl, 1989 Microbial fermenter: production of a biopolymer Applied cultivation modes: batch and chemostat Master in Applied Sciences, École Polytechnique de Mtl, 1993 Extraction and purification of biopolymers produced by microbial fermentation Applied cultivation mode: fed-batch at the 40 L and 750 L scales
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Page 1: Bioreactor cultivation modes

1

Cours BCM 6013 – Techniques en instrumentationModule 1 – Cellular experimentation

Université de Montréal, May 2-6, 2011

Bioreactors and cultivation modes

Presenter:

Robert Voyer, B. Ing., M. Sc. A.

My academic background

� Bachelor degree in Chemical Engineering, École Polytechnique de Mtl, 1989� Microbial fermenter: production of a biopolymer� Applied cultivation modes: batch and chemostat

� Master in Applied Sciences, École Polytechnique de Mtl, 1993� Extraction and purification of biopolymers produced by microbial

fermentation� Applied cultivation mode: fed-batch at the 40 L and 750 L scales

Page 2: Bioreactor cultivation modes

2

My Work Experience

� Employee of the Biotechnology Research Institute of the National Research Council (NRC) since 1994� Design, configuration and implementation of a control and monitoring

system to support bioreactors operation (3L to 500L scales).

� Operation of animal cell culture bioreactors (insect, mammalian and human cells).

� Design, and set-up of laboratories dedicated to mammalian cell culture in bioreactors.

� Project Leader: In charge of bioreactor scale-up infrastructure for animal cell culture and Large Scale Biosafety (Containment) Level 2 facilities.

� Project Manager with industrial partner for the production and the purification of an oncolytic virus.

� Active member of the Biosafety Committee.

Objectives of this session

1. Initiation to the operation of bioreactors and familiarization with their components and accessories, including the required steps to its preparation for cell cultivation and its operation.

2. Learn the different cultivation modes used for animal cell culture in bioreactors.

Page 3: Bioreactor cultivation modes

3

What is a bioreactor?

� General definition: A bioreactor is a vessel used to achieve a biochemical process involving organisms or active components derived from these organisms.

� Specifically, a bioreactor allows the control of the cultivation conditions to support the yield optimization of a bioproduct.

Usefulness of bioreactors

� R & D: Though often more complex to operate than a shaker flask in an incubator, the bench scale bioreactor allows for more accurate control of the cell cultivation conditions (aeration, monitoring, sampling).

Recent trends:

Miniaturization of bioreactorsAdvantages:� High throughput screening

� Small working volume allows for evaluation of expensive culture media� Allows to evaluate more clones that may not be the best producers but may happen

to be more robust and better suited to more stressful bioreactor cultivation condition

� Simplifies scale-up

Limitations:� Gas supply mode � Control strategies� Cultivation mode � Batch� Sampling volume � Kinetic studies

Page 4: Bioreactor cultivation modes

4

Examples of mini-bioreactors

www.applikon-bio.com µ-24 Bioreactor

Commercially available:� Working Volume: 10 mL � Controls: pH, temperature and pO2

Szita et al. Lab Chip, 2005, 5, 819 - 826

Prototype:� Working Volume: 150 µL � Controls: pH, temperature,pO2,

agitation rate� Monitoring of optical density

Usefulness of bioreactors

� Production: Bioreactors allow and facilitate the scale-

up of biochemical production process up to thousands of liters (~ 20,000 L for cell culture process and above 100,000 L for microbial fermenters).

Scale-up capability of a process is generally a critical step towards the commercialization of a product

Page 5: Bioreactor cultivation modes

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Which bioreactor design for my process?

� The choice of bioreactor design will vary based on the cell line and the targeted volumetric scale:� Adherent cells or cells adapted for free suspension culture

(with or without serum)?� Cell tolerance to hydrodynamic stress (sparging and mixing)?� Maximum targeted cell density to support?� Required sensors to monitor and control the process?

Types and sizes of bioreactors configured

for animal cell culture

� Stirred Tank Bioreactors (most broadly used)� Working volume range: 10 mL to 20,000 L

� Suspension cell culture, including micro carriers

� Autoclave sterilization: generally volume < 20L (typically glass vessels)

� in situ sterilization: volume > ~ 3L (Stainless Steel vessels)

� Mini-bioreactors: volume < 50 mL (high-throughput screening)

� Single-use bioreactors: volumes up to …

2000 L!!!

Page 6: Bioreactor cultivation modes

6

Types and sizes of bioreactors configured

for animal cell culture

� Single-use stirred tank bioreactors� Available working volume range: 50 L to 2000 L

� Sterile gamma-irradiated bags� Optical or traditional sensors with aseptic insertion device� Built-in elements for mixing and sparging

http://www.xcellerex.com/platform-xdr-single-use-bioreactors.htm

http://www.hyclone.com/bpc/sub_info.php

Types and sizes of bioreactors configured

for animal cell culture

� Wave Bioreactor� Available working volume (100 mL to 500L)

� Uses custom gamma-irradiated bags equipped with single-use sensors.

� Increasing use in biopharmaceutical manufacturing for the production of small clinical lots and as a cell expansion vessel.

� Not a preferred tool for R & D due to control and monitoring limitations and scalability.

www.wavebiotech.com Système 20/50

Page 7: Bioreactor cultivation modes

7

Other types of bioreactors

� ‘Air-lift’ or bubble column bioreactors� HL/DT limit its scalability� Cell death due to bubbles bursting at

the gas-liquid interface� Foaming issues depending on

selected culture medium

http://electrolab.co.uk FerMac Air Lift Bioreactor

Other types of bioreactors

� Single-use ‘Air-lift’ bioreactor

http://www.cellexusbiosystems.com CellMaker LiteTM

Page 8: Bioreactor cultivation modes

8

� Fixed-bed bioreactors� Used for adherent cell lines where

the product of interest is secreted� Typically used in perfusion mode� Difficult to assess the cell density

and viability as well as available dissolved oxygen within the bed

Other types of bioreactors

www.nbsc.com Celligen Plus®

www.corning.com E-CubeTM culture system

www.biovest.com/BiovestInstruments.htm

� Bioreactors for micro carrier based processes� Micro carriers allow cultivation of

adherent cells in traditional stirred tank bioreactors with design adjustments to hydrodynamic stress tolerances

� Cell density can be estimated through traditional sampling

� Limitation: diffusion of gas and nutrients through multilayers of cells

Other types of bioreactors

www.hyclone.com HyQ® Sphere™

Page 9: Bioreactor cultivation modes

9

Stirred tank bioreactor designed for

animal cell cultivation

� Typical internal configuration:

HL / DT = 1.0 to 1.5

Di / DT = 0.4 to 0.6

Sparging = 0.002 to 0.02 vvm

Number of mixers : scale dependent!

pO2(l)

DT

HL

Di

Process scale-up in STB

125 mL 500 mL 2000 mL

20 L

100 L500 L2000 L

4x – 8x

1 mL 10 mL

Dilution ratio 1/4 – 1/510000 L

Page 10: Bioreactor cultivation modes

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Main elements and accessories of an STBIn situ Sterilization STB

NRC – Biotechnology Research Institute

Exhaust gas – Filter and condenser

Inlet gas filter(s)

Heating/Cooling Jacket

Sensors

Sampling device

Harvest valve

Transfer bottle and tubingInjection ports

Control unit

Drive coupling

Main elements and accessories of an STBAutoclavable STB

http://www.nbsc.com/bf110_cc.aspx

Page 11: Bioreactor cultivation modes

11

Main elements and accessories of an STB

NRC – Biotechnology Research Institute

Helical ribbon impellerPitched blade impeller

NRC – Biotechnology Research Institute

Gas sparger

� Utilities� Cooling water supply (optional for autoclavable STB)� Autoclave (sterilization) or steam supply for in situ sterilization (steam

quality to be considered!)

� Process and instrumentation (dryness) compressed air supplies� Process gas (O2, CO2, N2 distributed from tanks)� Continuous power supply (emergency power and UPS)!!!� Drains (effluent segregation: sanitary and contaminated)

Other peripherals required for the

operation of a STB

Page 12: Bioreactor cultivation modes

12

Control of basic environmental parametersin STB for mammalian cell culture

� Temperature Control� Typical value:

� 37.0°C ± 0.1°C� T°shift strategy

� Sensing device: � Pt-100 probe (variation of electrical resistance proportional to

temperature; 100 Ohms at 0°C)

� Control operation strategy:� Cooling: Addition of cold water to a water circulation loop

within a jacket surrounding the vessel or in a submerged coil� Heating: Electrical heater or steam addition within the

circulation loop or electrical heating blanket surrounding the vessel

www.endress.com RTD model TH17

Control of basic environmental parametersin STB for mammalian cell culture

� pH Control� Typical value :

� 7.0 – 7.2

� Sensing device: � Gel pH electrode

http://us.mt.com DPA model

Reference electrode

Compares the external surface potential with that of the internal reference electrode using Nernst Equation:

E = E1 + (2.3RT/nF) log (unknown[H+]/internal[H+])

E: Change in potential n: number of electrons

E1: Reference electrode potential F: Faraday Constant

R: Perfect gas constant [H+]: Hydrogen ions concentrationT: Temperature (°K)

Page 13: Bioreactor cultivation modes

13

Control of basic environmental parametersin STB for mammalian cell culture

� pH Control (cont.)� Control strategy

� Increase of CO2 gas fraction in supplied gas mixture to acidify the culture

� Addition of a base solution of bicarbonate (NaHCO3 7.5%) to basify the culture (mixture of 9%NaHCO3/4%NaOH used to increase pH buffering capacity)

� Use a dead band = no controller action

CO2(g)

CO2(l) HCO3-

H+

CO2(g) CO2(l) pCO2 = He[CO2](l) ; f(T, N, P)

CO2(l) + H2O HCO3- + H+

Henry’s Law

Control of basic environmental parametersin STB for mammalian cell culture

� pH control exampleProduction virale - Régulation du pH

0

5

10

15

20

25

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00

Temps de culture (h)

YC

O2

(%),

cel

lule

s vi

able

s (E

6 ce

llule

s/m

L)

et p

H

0

40

80

120

160

200

Tem

ps

cum

ulé

d'a

dd

itio

n d

e b

ase

(min

)

pHYCO2XvNaHCO3

Infection

NRC – Biotechnology Research Institute

Page 14: Bioreactor cultivation modes

14

Control of basic environmental parametersin STB for mammalian cell culture

� Agitation rate control� Typical value at small scale with PBI:

� 90 – 150 revolution/min (rpm)� Scale-up:

� Impeller size ���� � Agitation rate � � � � (~30 rpm @ 500L)

� Measuring device: � Tachometer

� Control strategy:� Impellers mounted on an internal shaft that is driven by an

external motor using an aseptic coupling seal (mechanical, magnetic)

� Rocking platform (Wave Bioreactor)

Control of basic environmental parametersin STB for mammalian cell culture

� Dissolved oxygen control (pO2)� Typical value:

� 20 – 60% of air saturation

� Sensing device: � Polarographic electrode (‘Clark cell’)

� Control devices:� Rotameter, solenoid valve, Mass Flow Controller

http://us.mt.com InPro model

www.emersonprocess.com/brooks www.burkert.ca 6013 model www.emersonprocess.com/brooks

Page 15: Bioreactor cultivation modes

15

Control of basic environmental parametersin STB for mammalian cell culture

� Polarographic electrode� ∆ V applied between anode and cathode� Electrolyte: KCl Solution

Membrane

Anode (Ag)

Electrolyte Insulation

Cathode (Pt)

Anode reaction: Ag + Cl- AgCl + e-

Cathode reaction : ½O2 + H2O + 2e- 2OH-Pt

� Electron motion generate a small current (nA) proportional to dissolved O2 molecules

Control of basic environmental parametersin STB for mammalian cell culture

� Dissolved oxygen control strategy will vary based on cell line tolerance to stress

� Vessel overlay aeration� Air supplemented with oxygen (pO2(g))� Baffles at the gas-liquid interface to increase

the oxygen transfer into the liquid phase

� Gas sparging� Ring or L-shaped perforated SS tube� Porous diffuser� Silicone tubes (bubble-free)

� Agitation (manual)� Pressure

pO2(g)

pO2(l)

Page 16: Bioreactor cultivation modes

16

Control of basic environmental parametersin STB for mammalian cell culture

� Dissolved oxygen control exampleTransfection transitoire à l'échelle de 45L

0

20

40

60

80

100

120

140

0.00 50.00 100.00 150.00 200.00 250.00

Temps de culture (h)

Ag

itat

ion

(rp

m),

pO

2 (%

), t

emp

érat

ure

(°C

), p

H*1

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

QO

2 (L

/min

)

TEMP (°C)

Agitation (rpm)

DO2 (%)

pH*10

QO2 (L/min)

Aération en têtede bioréacteur

Aération submergée

NRC – Biotechnology Research Institute

� Cell density quantification (viable and total)� Microscope (manual or automated cell counts)� Particle counter (Coulter counter; total cells only)� Absorbance/turbidity (external or in situ; total cells only)� Capacitance (in situ; viable cells’ biovolume)

� Substrates and metabolites quantification� Glucose, lactate, glutamine, glutamate and ammonia

(Enzymatic) or NH4+ (electrode)� Amino acids (HPLC)� Osmolality (freezing point, vapor pressure)� Increasingly used in manufacturing: BioProfile (Nova Biomedical)

� Combines up to 10 measurements with a single sample injection…$$$

� Products� Western Blot, SDS-Page, ELISA, FACS, HPLC, Electrophoresis

(2-D, 3-D), etc

Additional off-line and on-line monitoring

tools for mammalian cell culture

Page 17: Bioreactor cultivation modes

17

Typical steps for the preparation and operation ofa bioreactor for animal cell cultivation

1. Cleaning of all parts coming in contact with the culture with an alkaline detergent (manual at small scale and automated at larger scale), including proper rinsing (PBS, RO)

2. Calibration of pH sensor with adequate buffers and test response of pO2 sensor (change electrolyte if need be)

3. Vessel set-up: assembly of internal components (agitating shaft, impellers, gas sparger, others), insertion of sensors (side-wall or lid), visual inspection of seals (replace if needed), lid assembly and installation of external components (filter, condenser, ports and plugs)

4. Pressure test (only for in situ sterilization bioreactor).

Typical steps for the preparation and operation ofa bioreactor for animal cell cultivation

5. Autoclave sterilization of addition lines and bottles, including base solution, and of gas inlet filter/s (autoclavable vessels are sterilized with these items already installed)

6. Bioreactor sterilization (121°C, 30-40 minutes*)7. Connection of inlet gas filter and addition lines during

post-sterilization cool-down phase (only for in situsterilization bioreactor) followed with air supplied to overlay to maintain positive pressure for final cool-down phase

8. Calibration of pO2 sensor after at least 6 hours to allow for polarization (0% can be set during sterilization at 121°C or post-sterilization with pure N2; 100% is calibrated in air)

Page 18: Bioreactor cultivation modes

18

Typical steps for the preparation and operation ofa bioreactor for animal cell cultivation

9. Withdrawal of sterile water and aseptic addition of medium (when prepared from powder, medium is filtered through a 0.22 µm; when practical, pre-heat medium to cultivation temperature before addition)

10. Start control and monitoring system to establish environmental conditions to desired set points

11. Bioreactor seeding12. Sampling during growth and production13. Harvest once set criteria is reached (duration, viability,

others) and transfer to DSP team for product recovery14. Vessel inactivation (typical: 60°C for 1 hr)15. Cleaning, rinsing, disassembly and dry storage

Then it’s ready to start over again!

Bioreactor cultivation modes

Batch Fed-Batch

Fresh Medium

Spent medium + cells

Chemostat

Filtrate = spent medium

with product

Perfusion

Ht=0

Hfinal

Fresh Medium Fresh Medium

Substrate boost

Page 19: Bioreactor cultivation modes

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Bioreactor cultivation modes

� Cultivation modes comparison:

Chemostat

Fed-Batch

Batch

Perfusion

Cultivation Time

Via

ble

Cel

ls

� Batch cultivation mode operation� I: Lag phase� II: Accelerating growth phase� III: Exponential growth phase� IV:Decelerating growth phase� V: Stationary phase� VI: Death phase

I II III IV V VI

Cultivation Time

X (biomass)

S (limiting substrate)

Product – non growth associated

(secondary metabolites)

Product – growth associated

Bioreactor cultivation modes

Page 20: Bioreactor cultivation modes

20

Specific growth rate estimation in batch cultivation mode

� Mass balanceHypotheses:

• no environmental limitations

• stable biomass composition

VL p

xvs

VL

S

Xv

P

: Bioreactor working volume

: Substrate concentration at time t

: Viable cell density at time t

: Product concentration at time t

VLdxv

dt=

VL µxv

µ: specific growth rate

dxv

dt=

µxv

� Fed-Batch cultivation mode operation� Started as a batch culture except for a lower starting working

volume. Once the limiting substrate is identified, a concentrated boost solution can be added to alleviate this growth limitation.

Cultivation Time

X, S, P Batch

X, S, P Fed-Batch

Initiation of feeding

Fresh medium

Bioreactor cultivation modes

Substrate boost

Page 21: Bioreactor cultivation modes

21

VL p

xvs

VL

s

xv

p

Fi

si

: Bioreactor working volume

: Substrate concentration at time t

: Viable cell density at time t

: Product concentration at time t

: Feed flow rate at time t

: Substrate concentration in feed

dxv

dt=

(µ- F/V)⋅xv

Fi, si

d(Xv)

dt= µXv

where Xv: number of total viable cells at time t.

For a constant feed flow rate, replacing Xv with V⋅xv,

in above equation gives :

xv = x0⋅(V0/V)⋅ eµtExponential:

Specific growth rate estimation in fed-batch cultivation mode

Mass balanceHypotheses:

• no environmental limitations

• stable biomass composition

� Medium or batch replacement cultivation mode operation (non growth associated product)

� Culture starts as a standard batch culture� Prior to substrate limitation, the whole or partial volume of the culture

broth is aseptically centrifuged and concentrated cells are returned to the vessel with fresh medium.

� Production medium could be different than growth medium� Limiting substrate could also be different� Production triggered by new component

X

S

P

Bioreactor cultivation modes

Cultivation Time

Page 22: Bioreactor cultivation modes

22

� Perfusion cultivation mode operation� The fed-batch cultivation mode eventually reach a limitation due to the

accumulation of inhibitors (inhibitory concentration of a specific by-product or due to inhibitory osmolality). The perfusion cultivation mode preventssuch inhibitors accumulation since the spent medium is continuously filtered and removed from the cultivation vessel while cells are kept or returned to the bioreactor. The total number of viable cells in the bioreactor eventually reaches a plateau that is dictated by the flow of fresh medium fed combined with the capacity of the filtration system.

Fed-Batch

Perfusion

Via

ble

cel

ls

Fresh medium

Bioreactor cultivation modes

Cultivation Time

Spent medium

with product

� Perfusion cultivation mode operation (cont.)� Here again, the culture is initiated in batch cultivation mode. The difference with

the fed-batch is that the working volume remains constant throughout the culture. After a few days of batch culture, fresh medium perfusion is initiated (generally of the same recipe as the starting medium). The filtration system is started and spent medium is removed at the same rate as the fresh medium feed rate: the perfusion rate (expressed as volume perfused/culture working volume/day [vvd])

� Once the viable cell density is in equilibrium with the limiting substrate, viable cells reach a plateau. The product titer also reaches a plateau a few days later. Total cell density keeps increasing and eventually reach a plateau as well.

Xv

P

S

Xt

Bioreactor cultivation modes

Cultivation Time

Page 23: Bioreactor cultivation modes

23

VLp

xvs

xv,0

F0

: Viable cell density in the spent medium

leaving the system at time t

: Flow of spent medium leaving the

system at time t

Fi, si

Where kd is the specific cell death rate. Dividing each side

of the equation by the volume:Fo, s, xv,o, p

Vd(xv)

dt= V⋅µ⋅xv - V⋅kd⋅xv - Fo⋅xv,o

d(xv)

dt= (µ - kd)⋅xv - D⋅xv,o

Plateau: dxv/dt = 0 µ ≈ kd for xv>>>xv,o

Beginning: kd and xv,o ≈ 0 d(xv)/dt = µ⋅xv

Specific growth rate estimation in perfusion cultivation mode

Mass BalanceHypothesis:

• External loop volume is much smaller than the

culture operating working volume

Cultivation mode performance comparisonBatch Fed-Batch Perfusion

Maximum cell density

2–8 E6 cells/mL 10- 20 E6 cells/mL 20 - 35 E6 cells/mL

Duration 4 - 6 days 8 - 12 days 100 – 180 days

Specific productivity

20 pg/cell/d 20 pg/cell/d 20 pg/cell/d

Volumetric productivity

14 mg/L/d 36 mg/L/d 600 mg/L/d

Bioreactor cultivation modes

Page 24: Bioreactor cultivation modes

24

� Pros and Cons of different cultivation mode:

Bioreactor cultivation modes

Batch Medium (batch) replacement

Fed-Batch Perfusion

Pros �Simple�Fast

�Optimal medium composition for production ≠≠≠≠ optimal growth medium�Rapid removal of undesirable metabolites

�High cell density�Larger volumetric productivity vs. batch mode�Fairly simple to implement

�Increased productivity over a long period�Significant reduction in required scale ($)�Reduction in cleaning frequency

Cons �Sub-Optimal�Manpower requirement�Scale needed

� Aseptic medium replacement operation and time for its completion limits scale-up

�Accumulation of inhibitors and increase in osmolality�Working volume limitations

�Complex�Risk for contamination�Drift of sensors and other measuring devices

Cultivation strategy examples

Example 1: Insect cells fed-batch culture

0

10

20

30

40

50

60

0 24 48 72 96 120 144 168 192 216 240 264

Time h

Cel

l den

sity

xE

6 ce

lls/m

L

200

300

400

500

600

Osm

ola

lity

(mO

sm)

total cells

viable cells

Osmolality

NRC – Biotechnology Research Institute

Page 25: Bioreactor cultivation modes

25

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20 25 30 35 40

Time (d)

On

-lin

e G

FP

flu

ore

sce

nce

(R

FU

)

0

5

10

15

20

25

30

35

40

To

tal

an

d v

iab

le c

ell

s

(10

6/m

L)

GFP Viable cells Total cells

Cultivation strategy example

Example 2: Insect cells perfusion culture

NRC – Biotechnology Research Institute

Addendum: Specific rate calculations for batch and fed-batch cultivation modes

Addendum

Page 26: Bioreactor cultivation modes

26

� ExampleÉvolution de la densité cellulaire viable

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 20 40 60 80 100 120 140

Temps (h)

Xv

(Mc

ellu

les

/mL)

Slope = dxv/dt

dxv

dt=

µxv

Estimation of specific growth rate in batch cultivation mode

Évolution du taux de croissance cellulaire

-5.00E-03

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

3.00E-02

3.50E-02

0 20 40 60 80 100 120 140

Temps (h)

µ (

1/h

)

µ = dxv/dt ⋅ 1/xv

� Example (cont.)

Estimation of specific growth rate in batch cultivation mode

Page 27: Bioreactor cultivation modes

27

� Exponential growth phase: µ = constant

dxv =µ⋅dt

xv

xv = x0⋅eµt

Évolution du taux de croissance

-5.00E-03

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

3.00E-02

3.50E-02

0 20 40 60 80 100 120 140

Tiemps (h)

µ (

1/h)

Estimation par lissage de courbe

Estimation du taux de croissance exponentiel

Estimation of specific growth rate in batch cultivation mode

� Exponential growth phase: µ = constant

xv = 2x0 = x0⋅eµt

Évolution du taux de croissance

-5.00E-03

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

3.00E-02

3.50E-02

0 20 40 60 80 100 120 140

Tiemps (h)

µ (

1/h)

Estimation par lissage de courbe

Estimation du taux de croissance exponentiel

Estimation of specific growth rate in batch cultivation mode

td = 2/ln(µ)

Page 28: Bioreactor cultivation modes

28

ds

dt=

-qs⋅xv As for µ, qs can be estimated

from the slope of s vs t.

qs = -ds/dt ⋅ 1/xv

� YieldYx/s = -dxv/ds

Yield can be obtained from the graph of

xv vs s.

Estimation of substrate consumption rate and yield in batch cultivation mode

dp

dt=

qp⋅xv As for µ and qs , qp value can be estimated

from the slope of p vs t.

qp = dp/dt ⋅ 1/xv

Estimation of the specific production rate in batch cultivation mode

Page 29: Bioreactor cultivation modes

29

ds

dt=

qs⋅xv + (si – s)⋅F/V

� Specific growth rate:

� Substrate specific consumption rate:

dp

dt=

qp⋅xv – (F/V)⋅p

Estimation of specific growth, consumption and production rates in fed-batch cultivation mode

� Specific production rate:

dxv

dt=

(µ- F/V)⋅xv


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