Data Reconciliation of Concentration Estimates from Mid-Infrared and Dielectric
Spectral Measurements for Improved On-Line Monitoring of Bioprocesses
Michal Dabros
Laboratory of Chemical and Biological Engineering, Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale
de Lausanne, CH-1015 Lausanne, Switzerland
Michael Amrhein and Dominique Bonvin
Automatic Control Laboratory, School of Engineering, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
Ian W. Marison
School of Biotechnology, Dublin City University, Dublin 9, Ireland
Urs von Stockar
Laboratory of Chemical and Biological Engineering, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
DOI 10.1021/bp.143
Published online March 30, 2009 in Wiley InterScience (www.interscience.wiley.com).
Real-time data reconciliation of concentration estimates of process analytes and biomass
in microbial fermentations is investigated. A Fourier-transform mid-infrared spectrometer
predicting the concentrations of process metabolites is used in parallel with a dielectric
spectrometer predicting the biomass concentration during a batch fermentation of the yeast
Saccharomyces cerevisiae. Calibration models developed off-line for both spectrometers suffer from poor predictive capability due to instrumental and process drifts unseen during calibration. To address this problem, the predicted metabolite and biomass concentrations,
along with off-gas analysis and base addition measurements, are reconciled in real-time
based on the closure of mass and elemental balances. A statistical test is used to confirm the
integrity of the balances, and a non-negativity constraint is used to guide the data reconciliation algorithm toward positive concentrations. It is verified experimentally that the
proposed approach reduces the standard error of prediction without the need for additional
C 2009 American Institute of Chemical Engineers Biotechnol. Prog., 25:
off-line analysis. V
578–588, 2009
Keywords: in situ bioprocess monitoring, FTIR spectroscopy, dielectric spectroscopy,
continuous elemental balances, on-line data reconciliation
Introduction
The field of biotechnology has witnessed over the past
decade an increasing demand for real-time process automation, monitoring, control, and optimization.1–4 These process
enhancement techniques require analyzers that provide reliable real-time information about the system. On-line spectrometers are such devices, which, in addition, have the
advantage of small sampling times, straightforward in-situ
installation, low-maintenance requirements, inherent sterility,
noninvasiveness, and nondestructiveness.3,5–7 Near-infrared
(NIR) and Fourier transform mid-infrared (FTIR) spectrometers, in particular, have been used successfully as on-line
analyzers of medium metabolites. Meanwhile, capacitance
(dielectric) spectrometers are gaining the status of a workhorse for in situ monitoring of biomass.
However, the spread and implementation of spectroscopic
sensors is still limited in the industrial setting due to the lack
Current address of Michal Dabros: School of Biotechnology, Dublin
City University, Dublin 9, Ireland.
Correspondence concerning this article should be addressed to U. von
Stockar at urs.vonstockar@epfl.ch.
578
of real-time and long-term reliability of calibration models.
Instruments calibrated off-line often perform poorly in online conditions due to instrumental and process drifts unseen
during calibration.8–13 Various signal and model adaptation
methods exist, but most of them require off-line sample analysis to obtain the necessary reference or transfer standards.3,14 Data reconciliation is a key method for correcting
concentration estimates from spectroscopic measurements
without sacrificing the on-line applicability of analyzers.
Data reconciliation, sometimes called data confrontation
or rectification, is a statistical technique that evaluates the
consistency of measurements and attempts to reduce errors
in measured variables by taking into account a defined set of
physical equalities (or inequalities15) such as balances.16–21
The corresponding algorithm is typically formulated as an
optimization problem, where the physical equalities are formulated as constraints and the cost function is the weighted
distance between reconciled and measured values. Data reconciliation has mainly been applied for reconciling flow rate
and concentration measurements in flow circuits.
In contrast to flow circuits, mass balance equations cannot
be easily established in bioprocess applications because of
C 2009 American Institute of Chemical Engineers
V
Biotechnol. Prog., 2009, Vol. 25, No. 2
difficulties in identifying the presence of all relevant species
and the lack of complete measurements. Nevertheless, data
reconciliation has been applied successfully to obtain
improved estimates of conversion rates and yield coefficients
using macroscopic elemental and/or energy balances based
on measurements from various process analyzers such as online gas sensors, mass-flow controllers, or reaction calorimeters.6,16,21–24 In the field of spectroscopy, Kornmann et al.6
used data reconciliation to correct concentration estimates of
medium analytes from FTIR data during batch fermentations
of bacteria and used the reconciled measurements to recalibrate the instrument model on-line. Two constraints were
used: carbon and degree of reduction balances. It was shown
experimentally that the technique can lead to a significant
reduction in the number of standards required for off-line
calibration though, due to the lack of an appropriate on-line
analyzer, biomass could not be monitored and was omitted
in the algorithm. This omission was justified by the low-biomass yield of the bacterial strain used. However, the unmodeled biomass led to a bias in the reconciled concentration
estimates.
In this work, data reconciliation is extended to cases with
a non-negligible biomass yield. The concentrations of medium metabolites and biomass are estimated simultaneously
using, respectively, FTIR and dielectric (capacitance) spectrometers. Both instruments are calibrated off-line using calibration standards and reference data from a first batch
fermentation of Saccharomyces cerevisiae. During a second
fermentation, the predicted concentrations of all analytes are
reconciled on-line by imposing the verification of four elemental balances (carbon, nitrogen, degree of reduction and
charge) and an additional hard constraint that limits the reconciled concentrations to non-negative values. The elemental
balances require, besides the predicted concentrations of medium metabolites and biomass, on-line measurements of offgas composition and of the amount of base added for pH
control. The balances are checked for gross errors using a
statistical test before being used as individual or concurrent
constraints by the reconciliation algorithm. The performance
of the proposed algorithm is assessed by evaluating the
standard error of prediction for each analyte.
The article is organized as follows: The balance equations,
the data reconciliation algorithm, and the constraints are presented first. Details pertaining to the culture, the experimental
setup, the spectrometers, and the reference analysis methods
used in the work are then described. There follow the results of
the study, a discussion and some concluding remarks.
Problem Formulation
Mass balances
The mass balances serve to calculate, based on the available measurements, the number of moles, n, of each substrate and product that has been either consumed or
produced from the start of the experiment up to the observation time t.24
Assumptions and Conventions. The following general
assumptions are made in the balance equations:
• The levels of dissolved O2 and CO2 are negligible. In
similar conditions, Schenk et al.25 reports O2 and CO2 levels
of 7 and 12 mg/L, respectively;
• Stripping of any medium species other than ethanol (the
most volatile) is negligible; and
579
• The elemental composition of biomass is known and
constant.
The balance notation adopted in this study is that the number of moles of each substance j (nj) is positive if the species
is produced and negative if it is consumed from the start of
the experiment.
Mass Balances of O2 and CO2 Measured by Gas Analyzer. Oxygen and carbon dioxide levels in the off-gas are
measured on-line by a gas analyzer. The measurements provided by the gas analyzer are in molar fraction. The following mass balance equations are used to convert the molar
fraction values into the number of moles of CO2 and O2 that
have evolved from the beginning of the process up to time t:
Zt
nCO2 ðtÞ ¼
yCO2 ðtÞGout ðtÞ yCO2 ;in Gin dt
(1)
0
Zt
nO2 ðtÞ ¼
yO2 ðtÞGout ðtÞ yO2 ;in Gin dt
(2)
0
The constants yCO2,in and yO2,in are the levels of carbon
dioxide and oxygen in the inlet air, respectively. The inlet
and outlet gas flow rates Gin and Gout are expressed in moles
per hour. The inlet flow rate is set constant by a mass flow
controller, whereas the outlet flow rate is calculated by performing a mass balance of the inert nitrogen gas:26
Gout ðtÞ ¼ Gin
1 yO2 ;in yCO2 ;in
1 yO2 ðtÞ yCO2 ðtÞ yw
(3)
The constant yw is the fraction of moisture in the outlet
gas determined on the basis of an oxygen balance around the
reactor before inoculation:
yw ¼
yO2 ;in yO2 ;wet
yO2 ;in
(4)
The constant yO2,wet represents the oxygen level that is
measured in the ‘‘wet’’ outlet gas that passes through the reactor filled with the reaction medium before inoculation.
Mass Balance of Base. The mass of KOH added into the
reaction for pH control is continuously monitored by a laboratory balance, and the molar flux of base up to time t is calculated using the density and the molarity of the base:
Zt mKOH
nKOH ðtÞ ¼
MKOH dt
qKOH
(5)
0
where m, q, and M stand for mass, density, and molarity,
respectively.
Mass Balances of Medium Analytes Measured by Infrared
Spectroscopy. The concentrations of the chemical components present in the medium Cj(t) (in terms of grams per litre
of medium) are estimated on-line using a FTIR spectrometer
and a calibration model. Knowing the initial mass concentration of all the medium species at the beginning of the experiment Cj(0), the molar flux of species j up to time t is
calculated using the following mass balance equation for
batch applications:
580
Biotechnol. Prog., 2009, Vol. 25, No. 2
Cj ðtÞVR ðtÞ Cj ð0ÞVR ð0Þ þ
P
a
nj ðtÞ ¼
MWj
Cj ðaÞVa
;
(6)
where VR(L) is the reactor volume, Va(L) is the volume of
each successive sample withdrawn from the reactor, and
Cj(g/L) is the mass concentration of species j in that sample.
The molecular weight of species j is represented by the constant MWj(g/mol). The reactor volume at time t is computed
by knowing the initial volume, VR(0), and keeping a continuous inventory of all liquid volumes entering and leaving the
reactor.
In the case of ethanol, an additional term is added to Eq.
6 to account for the amount of this component stripped by
the gas passing through the reactor. The ethanol mole fraction in the outlet gas can be estimated using a partition coefficient determined experimentally by Duboc and von Stockar
for reactions at 30 C and aeration rates between 0.63 and
1.3 vvm:26
yEtOH ¼ 0:532xEtOH
(7)
where xEtOH is the liquid mole fraction of ethanol in the medium. This empirical coefficient not only includes the volatility of ethanol (Henry’s law) but also the effects of mass
transfer. The amount of ethanol stripped up to measurement
time t can thus be calculated by integration over time and
added to Eq. 6, which takes on the following form for
ethanol:
nEtOH ðtÞ ¼
CEtOH ðtÞVR ðtÞ þ
Rt
yEtOH ðtÞGout ðtÞdt þ
P
CEtOH ðaÞVa
a
0
ð8Þ
MWEtOH
Note that the initial term, CEtOH(0)VR(0), is omitted
because there was no ethanol in the medium before
inoculation.
Mass Balance of the Biomass Measured by a Biomass
Monitor. The concentration of biomass CX(t) is estimated
on-line using a dielectric (capacitance) spectrometer, also
known as the biomass monitor (BM), and a calibration
model. The mass balance equation used to calculate the
molar flux of biomass up to time t is very similar to Eq. 6:
CX ðtÞVR ðtÞ CX ðinÞVin þ
nX ðtÞ ¼
P
a
MWX
CX ðaÞVa
(9)
Here, the initial biomass concentration comes from the
amount Cx(in)Vin used to inoculate the reactor. The constant
MWX represents the molecular weight of a C-mole of biomass including the ash, i.e., the amount of dry biomass containing 12.01 g of carbon.
Elemental Carbon Balance. Six species are involved in
the carbon balance: glucose, ethanol, glycerol, acetic acid,
biomass, and carbon dioxide. The matrix of element fractions is equal to the carbon content of 1 mole of each of
these six compounds:
XC ¼ ½ 6
2
3 2
1
1
(10)
Hence, the carbon balance takes on the following form:
eC ¼ 6nGluc þ 2nEtOH þ 3nGlyc þ 2nHAc þ nX þ nCO2 (11)
The term eC contains the balance error (in mol) resulting
from measurement inaccuracies.
Elemental Nitrogen Balance. Only two species are present in the nitrogen balance: ammonium and biomass. The
matrix of element fractions is equal to the nitrogen content
of 1 mole of these species:
XN ¼ ½1
eN;X ;
(12)
where eN,X represents the stoichiometric coefficient of nitrogen in biomass to be determined by elemental analysis. The
nitrogen balance can be written as follows:
eN ¼ nNHþ4 þ eN;X nX
(13)
Elemental Degree of Reduction Balance. The degree of
reduction (c) of a substance is defined as the number of electrons required for the oxidation of 1 mole of that substance.
Thus, a degree of reduction balance is essentially an account
of the available electrons in the system. It is more convenient to use this balance in microbial cultures because it
removes the necessity to account for water in the system.
The exact inventory of water is difficult to maintain, thus
making oxygen and hydrogen balances impractical. However, because water has a degree of reduction of zero, it disappears altogether from the balance without affecting the
total number of degrees of freedom.
The degree of reduction for 1 mole of substance j of
elemental formula CeC,j HeH,j OeO,j NeN,j is calculated in the
following manner:17
ci ¼ 4eC;j þ eH;j 2eO;j 3eN;j
(14)
Note that in this way the degree of reduction of H2O,
CO2, and NH3 is equal to zero.
Six species are considered in the degree of reduction balance: glucose, ethanol, glycerol, acetic acid, biomass, and
oxygen. The matrix of element fractions is equal to the
degree of reduction of each of these compounds:
Xc ¼ ½ 24
12
14:01
8 cX
4 (15)
The value of cX will depend on the elemental composition
of biomass, which needs to be determined. The degree of
reduction balance takes on the following form:
Elemental balances
ec ¼ 24nGluc þ 12nEtOH þ 14:01nGlyc þ 8nHAc
þ cX nX 4nO2
The elemental balances describe the conservation of the
four elements considered in this work: carbon, nitrogen,
degree of reduction, and charge. They take on the form of
e ¼ Xn, where e is the balance error and X contains the specific balance fractions for each variable in n.23,24
Elemental Charge Balance. The charge balance in the
system is attained through the maintenance of a constant pH
throughout the culture. During growth, biomass uptakes ammonia (NH3) from ammonium (NHþ
4 ), liberating a hydrogen
ð16Þ
Biotechnol. Prog., 2009, Vol. 25, No. 2
581
ion (Hþ) for each mole of ammonium consumed. In addition, the cells produce acetic acid that dissociates into aceþ
tate giving (C2H3O
2 þ H ) per mole of acetic acid. The
free hydrogen ions in the medium are neutralized by OH
ions coming from the added base, forming water and maintaining a constant pH.
Thus, three species are present in the charge balance:
NHþ
4 , acetic acid, and OH , which gives the following matrix of element fractions:
XCharge ¼ ½ 1
1 1 ;
(17)
and the charge balance can be written as follows:
eCharge ¼ nNHþ4 þ nHAc nOH
(18)
Combined Balance. The combined balance includes the
four elemental balances described earlier and considers all
nine species arranged in the following order: glucose, ethanol, ammonium, glycerol, acetate, biomass, CO2, O2, and
base. Thus, the matrix of element fractions X becomes a
4 9 matrix and the elemental balances can be written as:
e ¼ Xn ¼
2
6
6 0
6
6
4 24
0
2
2
0
3
2
1
1
0
0
1
0
0
eN;X
0
0
12
0
0
1
14:01
0
8
1
cX
0
0
0
4
0
nGluc
3
6n
7
6 EtOH 7
6
7
nNHþ4 7
36
6
7
0 6
7
n
6
Glyc 7
6
7
0 7
76
76 nHAc 7
7
0 56
7
6 nX 7
6
7
1 6
7
6 nCO2 7
6
7
4 nO2 5
nOH
ð19Þ
Combined balances are considerably more difficult to
close and reconcile simultaneously, but they offer the potential of more robust results because the closest solution is less
prone to chance.24
Statistical test
A statistical test can be applied to each of the balances to
determine whether the balance errors fall inside a normally
distributed range of acceptable values. A standard way of
performing such a test is to calculate a statistical function h
based on the measurement variance–covariance matrix, W,
and to check whether h falls below an upper control limit
defined by a v2-distribution.16,21,24 The statistical function is
given by the following formula:
1
h ¼ eT XWXT e
(20)
The computation of the upper control limit involves the
number of degrees of freedom for the system under consideration. The number of degrees of freedom, F, is defined as
the number of unknown variables, N, minus the number of
variables available either through measurements, M, or bal-
ances, K. A positive value of F indicates that some of the
variables can be chosen freely to satisfy certain criteria (e.g.,
in optimization). In contrast, a negative value of F indicates
the level of redundancy that is available to tackle the effect
of measurement noise. The yeast fermentation under consideration has F ¼ N M K ¼ 4, with:
N ¼ 9, unknowns: glucose, ethanol, ammonium, glycerol,
acetic acid, biomass, CO2, O2, and base;
M ¼ 9, measured or estimated concentration changes: glucose, ethanol, ammonium, glycerol, acetic acid, biomass,
CO2, O2, and base; and
K ¼ 4, balances: carbon, nitrogen, degree of reduction,
and charge.
Using the same approach, it can be shown that the individual balances (carbon, nitrogen, degree of reduction, and
charge) have a number of degrees of freedom of negative
one. For a significance level of 95%, the upper control limit
(UCL) is 9.49 for F ¼ 4 and 3.84 for F ¼ 1.
The statistical test will be useful in the analysis of the
results. As data reconciliation does not handle systematic
gross errors, it could perform poorer in areas where the statistical function h exceeds the upper control limit.
Data reconciliation algorithm
The data reconciliation algorithm used in this work is governed by the following minimization problem subject to two
constraints, evaluated at time t:
minðnr ðtÞ nm ðtÞÞT WðtÞ1 ðnr ðtÞ nm ðtÞÞ
nr
etol Xnr etol
such that
nr ðtÞ þ n0 0
ð21Þ
The cost function describes the distance between the
measured values, nm, and the reconciled values, nr, whereas
the covariance matrix W acts as a weighting factor such that
a higher penalty is imposed on adjusting those variables that
are expected to be more accurate. The first constraint contains the elemental balance equations whose residuals are to
be kept within some tolerance levels for each measurement
time t. The tolerance levels, etol, introduce a certain flexibility into the balances to account for potential inaccuracies in
the balances equations. The values of etol are chosen based
on the typical errors obtained for balances performed using
off-line reference measurements in earlier runs and are as
follows: 0.06 mol for the carbon balance, 0.015 mol for the
nitrogen balance, 0.3 mol for the degree of reduction balance, and 0.02 for the charge balance. The second, ‘‘nonnegativity’’ constraint guarantees that the concentrations,
computed as nr(t) þ n0, of all the species are positive, where
n0 contains the initial molar concentrations of the components present in the culture medium. Figure 1 illustrates how
the nearest solution satisfying both constraints can be found.
Assuming that the measurement errors are independent of
each other, W can be considered diagonal.16 The diagonal
elements of W are computed as:
2
wj ¼ nj;max ej ;
(22)
where nj,max is the largest expected molar flux of species j
and ej the corresponding measurement error.
The measurement errors for the metabolites and biomass
are set to 15%, which represents the typical prediction errors
582
Biotechnol. Prog., 2009, Vol. 25, No. 2
to have a continuous estimate of the reactor volume throughout the experiment.
The maximum molar fluxes (nj,max) expected in this culture, based on previous experiments, were set to 0.3 mol of
glucose, 0.4 mol of ethanol, 0.2 mol of ammonium, 0.03
mol of glycerol, 0.02 mol of acetic acid, 0.7 C-mol of biomass, 0.8 mol for CO2, 0.6 mol for O2, and 0.1 mol of
KOH.
Analytical methods
Figure 1. Solution of the data reconciliation algorithm.
The point labeled nr,A is the closest solution to the measurement nm lying in the solution space described by etol Xnr
etol in Eq. 21. However, it does not satisfy the non-negativity
constraint; the corresponding feasible region is represented by
the white domain of the solution space. Thus, the measurement
will be reconciled to nr,B, the nearest solution that satisfies all
constraints of Eq. 21.
for the two spectrometers. The gas analyzer measurement
error is set to 3% and the base balance error to 1%.
Materials and Methods
Organism and culture conditions
Two aerobic batch fermentation runs were performed
using a wild-type strain of the crab tree-positive bakers’
yeast Saccharomyces cerevisiae. The strain (CBS 8066) was
obtained from the Centraalbureau voor Schimmelcultures
(Utrecht, NL). The first batch served to collect data for the
off-line, in situ calibration of the biomass monitor before the
study. The second batch was used for the main data reconciliation experiment.
Source cells were stored at 80 C in 1.8 mL aliquots. For
each batch, the reaction inoculum was obtained by adding
one aliquot into a 1-L Erlenmeyer flask containing 100 mL
of a sterile complex preculture medium (10 g/L yeast extract
OXOID, 10 g/L peptone BACTO, and 20 g/L glucose) and
incubating it for 24 h at 30 C and 200 rpm. The defined culture medium was sterilized by filtration and contained, per liter: 20 g glucose, 5 g (NH4)2SO4, 3 g KH2PO4, 0.5 g
MgSO47H2O, as well as trace elements and vitamins
(adapted from Verduyn et al.27 and Cannizzaro et al.28). The
medium was supplemented with 0.5 ml/L of a standard antifoam agent to prevent foaming. The initial biomass concentration, following inoculation was 0.25 g/L.
The cultures were grown in a 3.6-L laboratory bioreactor
from Bioengineering (Wald, Switzerland), with a working
volume of 2.6 L, equipped with a rushton-type agitator, baffles, temperature and pH probes and control mechanisms,
gas inlet and outlet ports, a base inlet port, and a sampling
port. Outlet gas passed through a condenser to minimize liquid loss by evaporation. The reactor was sterilized in situ at
121 C for 20 min. The cultures were grown at 30 C with an
agitation speed of 800 rpm and an inlet air flow rate of 3.35
L/min (1.3 vvm). A solution of 2 M KOH (density, 1.12 g/
cm3) was used to maintain the pH at 5; no acid control was
necessary. A detailed account of volumes entering the reactor (i.e., base added) and leaving it (i.e., samples) was kept
For validation purposes, reference samples of about 12 mL
were collected at intervals of 1 h using an in-house developed
automated sampling robot, BioSampler 2002.7 The robot was
equipped with a refrigeration system storing the samples at
4 C before treatment.
A portion of each sample was stored frozen at 20 C
before elemental analysis. Concentrations of ethanol,
glycerol, and acetic acid were quantified by HPLC (HewlettPackard 1100 Series, Agilant, Palo Alto, CA). Concentrations of glucose and ammonium were determined with an
automated enzymatic analyzer (Cobas Mira, Roche, Basel,
CH) using commercially available enzymatic kits (R-Biopharm AG, Darmstadt, D). Both analyzers were calibrated
using 4–5 synthetic standards for each of the monitored
analytes.
Biomass dry cell weight (DCW) was determined by putting 8 mL of the culture medium through a preweighed 0.22
lm pore filter, drying the filter, and subsequently reweighing
it. Optical density measurements were performed as a
backup method at 600 nm using the Spectronic Helios-Epsilon spectrophotometer from Thermo (Waltham, MA, USA).
Elemental analysis of the biomass harvested at the end of
the culture and freeze-dried provided the stoichiometric coefficients of carbon, hydrogen, oxygen, and nitrogen in 1 Cmole of biomass, giving the formula CH2.15O0.49N0.18 þ
ashes. The molecular mass is 26.39 g/C-mol and the degree
of reduction is 4.62 (Eq. 14).
Oxygen and carbon dioxide levels in the outlet gas were
analyzed using an infrared gas analyzer (Dr. Marino Müller
AG, Esslingen, CH). A two-point linear calibration is performed for each gas before the experiment using the
following:
–.for CO2 calibration, N2 as 0% and a calibration-grade
gas mixture as 5% CO2;
–.for O2 calibration, N2 as 0% and pure air as 20.946%.
FTIR spectrometer
Concentration levels of glucose, ethanol, ammonium,
phosphates, glycerol, and acetic acid were monitored using a
single-beam ReactIRTM 4000 FTIR from Mettler Toledo
(Greifensee, Switzerland). The instrument was equipped with
a MCT detector and an Attenuated Total Reflection (ATR)
diamond probe (DiCompTM, ASI Applied Systems, Millerville, MD). Dry air was continuously supplied as purge gas
into the spectrometer housing, the optical conduct, and the
probe shaft. The probe was built into a thermostatically
controlled 5 mL flow cell (StreamlineTM, Mettler Toledo),
sterilized in situ together with the reactor. During the experiment, the culture medium was pumped continuously through
the flow-through cell via a sterile recirculation loop with a
residence time inside the loop of less than 20 s. Spectra
Biotechnol. Prog., 2009, Vol. 25, No. 2
583
Table 1. Characteristics of the Calibration Model Used for the FTIR
Analyte
Concentration Range (g/L)
Spectral Range (cm1)
PLS Factors
SEC (g/L)
Glucose
Ethanol
Ammonium
Phosphate
Glycerol
Acetic acid
0–25
0–10
0–2
0–4
0–2
0–2
1,200-950
1,150-950
1,500-1,400 & 1,200-1,000
1,200-1,000
1,200-1,000
1,500-950
7
10
4
5
8
10
0.47
0.10
0.04
0.11
0.10
0.03
were collected at an interval of 2 min from the averaged
values of 64 scans. The spectral range spanned wavenumbers between 4,000 and 650 cm1 with an approximate resolution of 4 cm1. Spectra were saved in binary format by
the instrument’s custom software, ReactIRTM 2.1 (ASI
Applied Systems, Millerville, MD) and subsequently
imported into and analyzed in Matlab (The MathWorks,
Inc., Natick, MA).
The instrument was calibrated off-line, before the experiment, using partial least squares (PLS). The PLS model was
developed using 49 synthetically prepared standards and a
seven-level multivariate design.29 The choice of the number
of PLS factors was based on predicted residual error sum of
squares (PRESS) plots of leave-one-out cross-validation.30
Distinct spectral ranges were selected for each analyte to
account for the different frequencies of the vibration modes
of each component. Spectra of demineralized water were collected in parallel to each standard during the calibration procedure and used as background. Mean-centering was applied
to the calibration sets. Table 1 summarizes the concentration
range, spectral range, and the corresponding standard error
of calibration (SEC) for each analyte.
During the experiment, absorbance spectra for each measurement were calculated from the ratio of the corresponding
intensity spectrum to the single spectrum of demineralized
water taken immediately before the run. The standard error
of prediction (SEP) was calculated based on 16 reference
samples collected during the experiment and analyzed by
HPLC/enzymatic analyzer. The equations used for calculating the values of SEC and SEP for a particular analyte are
given below:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
uP
u nc
y y i Þ2
u ð^
ti¼1 i
SEC ¼
;
nc
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
uP
n
u p
y y i Þ2
u ð^
ti¼1 i
SEP ¼
np
(23)
where y^i and yi are the predicted/reconciled and true (reference) concentration values of the analyte in sample i, nc is
the number of samples in the calibration set and np is the
number of samples in the prediction set.
Biomass monitor
Concentration levels of biomass were measured with the
dielectric spectrometer Biomass Monitor 210 from Aber
Instruments (Aberystwyth, UK). The BM was equipped with
a 12 mm probe containing four annular electrodes. This configuration is particularly favourable, as four-terminal probes
(as opposed to two-terminal probes) reduce electrode polarization.31,32 The probe was introduced directly into the reactor and sterilized in situ. During the cultures, 25 excitation
frequencies from 0.1 MHz to 20 MHz were scanned every
15 s and the capacitance as well as the conductivity of the
cell suspension was registered at each frequency. A program
developed in-house using LabView (National Instruments,
Austin, TX) was used to collect and store the measured data.
The instrument was calibrated off-line, before the experiment during the first batch culture. A simple linear correlation model was established between biomass dry cell weight
and dual-frequency capacitance values obtained by measuring the difference in capacitance readings at 500 kHz and
10 MHz (DC ¼ C500 C10,000). To eliminate noise in the
signal, a low-pass filter with a frequency of 60 s was
applied. All data were mean-centered before modeling. The
standard error of calibration was 0.36 g/L for a biomass concentration range of 0–7 g/L. The standard error of prediction
(SEP) was calculated based on 17 reference samples collected during the experiment and analyzed as described
earlier.
Experimental setup
The basic experimental setup is illustrated in Figure 2.
The BM probe was installed directly in the reactor, whereas
the FTIR probe was nested inside a flow cell. Temperature,
pH, and dissolved oxygen probes are not shown. Inlets into
the reactor included air (flow rate measured by a mass flow
controller) and base. The flow rate of the base was measured
by continuously monitoring the scale on which the base flask
was placed and dividing the result by the density of the
base. Outlets included off-gas (flow rate calculated according
to Eq. 3) and the samples. The volume of the samples was
registered manually. The volume of the reactor was verified
at the end of the experiment to confirm its agreement with
the estimated final value of VR. During the experiment, the
prediction of metabolite and biomass concentrations, the
individual and combined balances and the data reconciliation
routine were performed in real-time at an interval of 2 min,
corresponding to the measurement interval of the slowest
instrument in the setup, the FTIR.
The general flow of tasks can be summarized as follows:
(a). Off-line tasks before the experiment:
–.Calibrate the FTIR spectrometer using synthetic
standards;
–.Calibrate the biomass monitor using standards from
the first batch fermentation run; and
–.Calibrate the gas analyzer using calibration gases.
(b). On-line tasks during the experiment (second batch fermentation run):
–.Predict the concentrations of the medium metabolites
and biomass using measurements from the FTIR
spectrometer and biomass monitor, respectively;
–.Measure the off-gas composition and inlet and outlet
gas flow rates;
–.Measure the amount of base added;
–.Check for gross errors of the individual and combined elemental balances using a statistical test;
–.Apply the proposed reconciliation algorithm to
reconcile the predicted concentrations of medium
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Biotechnol. Prog., 2009, Vol. 25, No. 2
Figure 2. Experimental setup.
Figure 3. Predicted (line) versus reference (dots) concentration profiles obtained with the original FTIR and BM calibration models.
metabolites, biomass, off-gas composition, and
amount of base added; and
–. Collect reference samples for off-line validation;
measure VR and Va.
(c). Off-line tasks after the experiment:
–. Analyze the reference samples to validate the reconciliation algorithm by calculating the errors of the
original and reconciled concentration estimates of
medium metabolites and biomass.
Results and Discussion
Results with original FTIR and BM calibration models
Figure 3 shows the concentration profiles of the species
considered in this study, predicted using the original FTIR
and BM calibration models and compared with their reference values. Qualitatively, the results show the major trends
in the culture (note the diauxic growth of the crabtree-positive yeast strain). However, significant prediction errors due
to instrumental and process shifts can be observed. The
standard errors of prediction (SEP) for all the species
involved are as follows: 2.29 g/L for glucose, 0.60 g/L for
ethanol, 0.23 g/L for ammonium, 0.36 g/L for glycerol, 0.54
g/L for acetic acid, and 0.62 g/L for biomass (see Column 2
in Table 2).
Data reconciliation results obtained with
the various balances
Carbon Balance. The statistical test of the carbon balance is shown in Figure 4. The values of the test function h
(Eq. 20) remain below the upper control limit of 3.84 for the
duration of the culture. Hence, the carbon balance can be
considered reliable.
Using the carbon balance for reconciliation, significant
improvement is achieved, in particular for glucose (Figure
5), where the SEP is reduced to 0.22 g/L. The ethanol profile
is also adjusted and its SEP value reduced to 0.39 g/L. The
corrections in the profiles of glycerol and acetic acid amount
to a simple flattening of the negative values (see Column 4
Biotechnol. Prog., 2009, Vol. 25, No. 2
585
Table 2. Comparison of the Values of the Standard Error of Prediction Obtained With the Original Calibration Models, the ‘‘Zeroing’’ Method,
and Data Reconciliation Using Individual and Combined Elemental Balance
Analyte
SEP (g/L)
Original
SEP (g/L)
‘‘Zeroing’’
SEP (g/L)
C Balance
SEP (g/L)
N Balance
SEP (g/L)
c Balance
SEP (g/L)
Charge Balance
SEP (g/L)
Combined Balance
Glucose
Ethanol
Ammonium
Glycerol
Acetic acid
Biomass
2.29
0.60
0.23
0.36
0.54
0.62
0.84
0.39
0.23
0.33
0.07
0.61
0.22
0.39
–
0.33
0.07
0.60
–
–
0.12
–
–
0.40
0.47
0.38
–
0.33
0.07
0.58
–
–
0.13
–
0.11
–
0.32
0.35
0.12
0.33
0.08
0.39
Figure 4. Statistical test values obtained for the carbon
balance.
The solid line shows the upper control limit.
Figure 5. Glucose profile reconciled with the carbon balance
(solid line) compared with the original FTIR profile
(dotted line) and the reference measurements (dots).
Figure 7. Ammonium profile reconciled with the nitrogen balance (solid line) compared with the original FTIR
profile (dotted line), and the reference measurements
(dots).
Figure 8. Statistical test values obtained for the degree of
reduction balance.
The solid line shows the upper control limit.
Figure 6. Statistical test values obtained for the nitrogen
balance.
The solid line shows the upper control limit.
Figure 9. Statistical test values obtained for the charge
balance.
The solid line shows the upper control limit.
in Table 2). However, this was expected considering that the
concentration ranges of these two species are around the
limit of detection of the FTIR. Surprisingly, the prediction
error for biomass is only slightly reduced to 0.60 g/L.
Nitrogen Balance. Figure 6 shows the results of the statistical test for the nitrogen balance. Because of the relatively large errors in the prediction of ammonium (see
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Biotechnol. Prog., 2009, Vol. 25, No. 2
Figure 3), the upper control limit is slightly exceeded toward
the end of the experiment. The results obtained after the culture time of 14 h could, therefore, be less reliable.
Overall, the nitrogen balance is fairly effective for data
reconciliation, and the prediction error is reduced to 0.12 g/L
for ammonium and 0.40 g/L for biomass (Column 5 in Table
2). In agreement with the statistical test, the reconciliation
performance seems to worsen after the culture time of 14 h
(Figure 7).
Degree of Reduction Balance. The result of the statistical
test for the degree of reduction balance is shown in Figure 8.
The statistical test values are very similar to those
obtained with the carbon balance. The results of using the
degree of reduction balance in the reconciliation algorithm
are also comparable with those achieved with the carbon balance (see Columns 4 and 6 in Table 2).
Charge Balance. Figure 9 shows the outcome of the statistical test for the charge balance. The large errors in both
ammonium and acetic acid at the beginning and toward the
end of the culture contribute to a large statistical test value.
During the first 3 h of the experiment and after the culture
time of 14 h, the value of h exceeds the upper control limit.
Consequently, the results obtained during this period could
be less reliable.
Using the charge balance, the standard prediction error
decreases to 0.13 g/L for ammonium and to 0.11 g/L for
acetic acid. It should be noted that the result for ammonium
obtained with the charge balance is very similar to that
obtained with the nitrogen balance (compare Columns 5 and
7 in Table 2). As the concentration of acetic acid remains
very low throughout the culture, the correlation between
base uptake and biomass formation is quite strong.
Combined Balance. The statistical test results for the
combined balance are shown in Figure 10. Because of the
significant errors in the estimates of several species during
the initial states of the culture, the test value exceeds the
upper control limit of 9.49. However, after culture time of
2.5 h, the value of h falls and remains below the upper control limit and hence, the combined balance can be considered
fairly reliable.
Reconciling the concentration estimates using the combined balance improves the prediction profiles of all six species (see Column 8 in Table 2 and Figure 11). In particular,
the errors for ethanol, ammonium, and biomass are reduced
even more than with any of the individual balances, suggesting that combining balances may in some cases help find
solutions closer to the optimum.
As expected with the low measurement errors assigned to
the gas analyzer and base balance measurements (Data Reconciliation Algorithm Section), the average absolute percentage changes to nCO2, nO2, and nOH are low, respectively,
1.564%, 0.003%, and 0.016%. By comparison, the average
absolute percentage changes for the six analytes vary
between 11.5% for glucose to 83.9% for ammonium.
Comparison of data reconciliation with ‘‘zeroing’’ of
negative results
Figure 10. Statistical test values obtained for the combined
(carbon, nitrogen, degree of reduction, charge)
balance.
The solid line shows the upper control limit.
As an alternative to the proposed data reconciliation
approach, the standard error of prediction can also be
reduced by zeroing the negative concentrations—an on-line
postprocessing technique commonly used. Applying this
method, the SEP values are reduced significantly for some of
the analytes, but not as effectively as with data reconciliation
using the combined balance. In general, data reconciliation
outperforms the ‘‘zeroing’’ method because it also corrects
Figure 11. Predicted (line) versus reference (dots) concentration profiles obtained after reconciling the FTIR and BM results with the
combined (carbon, nitrogen, degree of reduction, charge) balances.
Biotechnol. Prog., 2009, Vol. 25, No. 2
the positive values in the profiles. It is also a more systematic approach, because the reconciled results are checked for
consistency of all balances. Table 2 compares the results
obtained with the original calibration models, the ‘‘zeroing’’
method, the individual elemental balances and the combined
balance.
Concluding Remarks
Signal drifts in on-line spectrometers can lead to significant
inaccuracies in the prediction of low-concentration metabolites. In this work, data reconciliation based on continuous
elemental balances involving spectroscopic measurements,
off-gas analysis, and measurements of base addition has been
presented as a method for correcting the on-line concentration
estimates of both medium components and biomass without
additional off-line sample analysis. One of the main advantages of the proposed approach is that it can easily be coded
into the prediction routine for on-line spectrometers.
The particular challenge in implementing data reconciliation for bioprocesses arises from the necessity to accurately
formulate elemental balances for the system. Elemental balances are often difficult to close because species that were
not seen during the modeling step may unexpectedly appear
and vary in concentration at various stages of the process.
On the other hand, the presence of unseen species can be
easily detected using statistical tests. Therefore, data reconciliation also serves as a tool to gain insight into the process
and to check for the validity of the balances. This feature
may prove valuable in longer fermentations, where instrument drift becomes a significant issue or where, for instance,
cell clumping or swelling affect the reliability of biomass
measurements. Finally, difficulties may arise in cultures
grown on complex media. However, because the concentration variations of many of the ill-defined compounds in complex media tend to be very small, their influence can be
neglected when monitoring by FTIR spectroscopy.
Note also that performance may be improved by eliminating gross errors, for example, through offset removal14 or
on-line drift correction,33 before reconciling the estimated
concentrations.
Acknowledgments
The Swiss National Science Foundation is greatly acknowledged for financial support of this work. Special thanks to Jonas
Schenk for help with the data acquisition systems and to Paman
Gujral for help with the implementation of the data reconciliation algorithm.
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Manuscript received July 28, 2008, and revision received Oct. 23, 2008.