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Uncertainty Analysis of Penicillin VProduction Using Monte Carlo Simulation
Arno Biwer,1 Steve Griffith,1,2 Charles Cooney1
1Department of Chemical Engineering, Massachusetts Institute of Technology,Massachusetts 02139; telephone: 617-253-3108; fax: 617-258-6876;e-mail: [email protected] Pharma, Cambridge, Massachusetts 02139
Received 8 July 2004; accepted 1 October 2004
Published online 28 February 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/bit.20359
Abstract: Uncertainty and variability affect economic andenvironmental performance in the production of biotech-nology and pharmaceutical products. However, commer-cial process simulation software typically provides analysisthat assumes deterministic rather than stochastic processparameters and thus is not capable of dealing with thecomplexities created by variance that arise in the decision-making process. Using the production of penicillin V as acase study, this article shows how uncertainty can bequantified and evaluated. The first step is construction ofa process model, as well as analysis of its cost structureand environmental impact. The second step is identifica-tion of uncertain variables and determination of their proba-bility distributions based on available process and literaturedata. Finally, Monte Carlo simulations are run to see howthese uncertainties propagate through the model and af-fect key economic and environmental outcomes. Thus, theoverall variation of these objective functions are quantified,the technical, supply chain, and market parameters thatcontribute most to the existing variance are identified andthe differences between economic and ecological eval-uation are analyzed. In our case study analysis, we showthat final penicillin and biomass concentrations in the fer-menter have the highest contribution to variance for bothunit production cost and environmental impact. The pen-icillin selling price dominates return on investment vari-ance as well as the variance for other revenue-dependentparameters. B 2004 Wiley Periodicals, Inc.
Keywords: Monte Carlo simulation; uncertainty; vari-ability; penicillin; economic assessment; environmentalassessment
INTRODUCTION
Commercial process simulation software usually provides
analysis that assumes deterministic process parameters.
The software does not consider existing variations of tech-
nical, supply chain, and market parameters that can sig-
nificantly alter operating decisions and batch-to-batch
expectations. However, an understanding of these param-
eters and their uncertainty is essential for the economic
success of a process design and the analysis of existing
processes. Thus, a methodology is needed that combines
standard process simulation software with uncertainty anal-
ysis. In this article, we use a well-characterized process, the
production of penicillin, to illustrate how this goal might
be accomplished.
Penicillins produced by Penicillium chrysogenum are
still among the most important antibiotics. Penicillins be-
long to a family of hydrophobic h-lactams. Each contains
a different acyl side chain attached by an amide link-
age to the amino group of the penicillin nucleus, the
6-aminopenicillanic acid. Penicillin G and penicillin V
are the main commercial penicillins. Most of the pen-
icillin V (phenoxymethylpenicillin) is converted to 6-
aminopenicillanic acid (6-APA), which in turn is used
to make amoxicillin and ampicillin (McCoy, 2000). In
addition, penicillin V is used directly as an antibiotic
(f1,600 tons per year) (Van Nistelrooij et al., 1998)
and ranks among the 100 top prescribed drugs in the
United States (American Druggist, http://www.rxlist.com/
top200a.htm, May 2004).
h-Lactam antibiotics amount to about 60% of the
worldwide antibiotics market; this was approximately
$5 billion per year in sales in 1999 (Demain and Elander,
1999). The global demand for h-lactams grows by around
2% annually, mainly because of rising demand in countries
such as China and India (Milmo, 2003). Lowe (2001)
estimates that the world production of penicillin was
65,000 tons in 2001. As a result of large overcapacity
in the market, penicillin prices have been under continu-
ous pressure for several years. Prices have fallen signifi-
cantly during the last several years from $20/billion units
(BU) during the mid-1990s to $12/BU in 1997 to $9/BU
in 2000 (McCoy, 2000). As of 2003, the price of peni-
cillin G was approximately $11/BU, which is $17–18/kg
(Milmo, 2003).
Improvements in the penicillin production process result
primarily from genetic-based strain improvements, while
the process flowsheet has changed very little (Van
Nistelrooij et al., 1998). Although some improvement has
been realized from refinement in operating conditions,
B 2004 Wiley Periodicals, Inc.
Correspondence to: C. Cooney
This article includes supplementary material available via the Internet at
http://www.interscience.wiley.com/jpages/0006-3592/suppmat.
these changes are often difficult to observe because vari-
ance in the overall process masks small improvements in
production. As such, it takes many more experiments or
production runs to statistically verify the impact of a par-
ticular process change. In the present work, we assess how
variance in strain and process parameters affects key eco-
nomic and environmental impact metrics. Because environ-
mental concerns have become increasingly important, we
include an environmental evaluation in our analysis.
Using a process model for penicillin V, Monte Carlo sim-
ulations are performed to investigate the effect of param-
eter uncertainty on overall process performance. Thereby,
we use a new approach that provides a general method-
ology for combining process simulation software and
spreadsheet modeling to conduct high-leverage uncertainty
analysis. This offers a fundamental basis for decision
making in the design and analysis of bioprocesses.
MATERIALS AND METHODS
The process model for penicillin V production was built
using the process simulator SuperPro Designer version 5.1
(Intelligen, Scotch Plain, NJ), which provides the material
balance and key economic parameters of the process. To
perform the Monte Carlo simulations, key parts of the
model were transferred to Microsoft Excel and analyzed
via Monte Carlo simulation, using Crystal Ball 2000
(Decisioneering, Denver, CO). Crystal Ball is an ‘‘Add-in’’
for MS Excel that enables the definition of the probabil-
ity distributions of stochastic variables, generates random
numbers based on these distributions, and stores the re-
sults of MS Excel calculations for each trial. Monte Carlo
simulations with 100,000 trials take around 20 min (PC:
Pentium III processor, 512 MB RAM). Each run requires
around 5 MB disc space. We note, however, that a good
estimate of the sampling distribution of the mean for
primary forecast variables can often be achieved with the
default Crystal Ball setting of 1,000 trials.
All SuperPro model parts that are affected by the
uncertain parameters were transferred to MS Excel. Since
most computations in SuperPro can also be done in spread-
sheet calculations, this transfer is possible, but it is the
most time consuming part and has a certain risk of tran-
scription errors. Therefore, it is currently necessary to vali-
date the constructed base case spreadsheet model against
SuperPro results to ensure that all inputs are correct.
Further work is necessary to develop a direct linkage be-
tween the simulation software and the Monte Carlo simu-
lation tool.
For the environmental assessment, a method developed
by Biwer and Heinzle (2004) is used. In this method, a
weighting factor is calculated for every input and output
component representing the environmental relevance of the
compound. These environmental factors (EF) are multi-
plied by the amount of the compound in the mass balance
to obtain the environmental index (EI). The sum of all
input, respectively, output components gives the EIs of the
process. These indices, like the economic indicators, rep-
resent one of several possible indicators to describe the
environmental performance of a process. For the economic
evaluation, generally accepted indicators are used and their
definitions can be found in appropriate textbooks (e.g.,
Peters et al., 2003).
MODELING BASE CASE
Fermentation Model
In commercial processes, penicillin V is produced as a
fed-batch fermentation (Ohno et al., 2002). Regardless of
whether a penicillin producer uses its own unique strain or
one acquired from a common club, fermentation conditions
and downstream steps are established that are optimal for
the producer’s strain and fit within the context of a par-
ticular facility. However, most processes follow a similar
structure and variance is introduced from operating con-
ditions. A typical medium is composed of glucose, corn
steep liquor, or another complex source (for other possi-
ble sources, see Lowe, 2001), mineral salts, and phenoxy-
acetic acid as a precursor for penicillin V (Demain and
Elander, 1999; Van Nistelrooij et al., 1998; Perry et al.,
1997). P. chrysogenum has difficulty synthesizing the phe-
nolic side chain for penicillin and phenoxyacetic acid is
added continuously to the culture medium.
Penicillins are secondary metabolites, generally pro-
duced at low growth rates (Strohl, 1999). Penicillin synthe-
sis starts from three activated amino acids, involves several
enzymes and isopenicillin N as a major intermediate
(Strohl, 1999). More details about the penicillin synthesis
can be found in Paradkar et al. (1997) and Strohl (1997).
Key operating parameters requiring optimization are tem-
perature, pH, dissolved oxygen, and assimilable nitrogen,
precursor, reducing sugars, and biomass concentrations
(Van Nistelrooij et al., 1998).
In the present study, we use a simplified fermentation
model to describe the dependence of final product and
biomass concentrations on the cell yield and maintenance
coefficient and the specific product formation rate and yield
coefficient. The values for the model parameters (Table I)
are derived from a combination of literature and process
data. Two fermentation stages (growth and production
phase) are assumed, although in some of today’s highly
productive fermentations, such a separation no longer exists
(Lowe, 2001). The first (primary) phase lasts about 50 h,
and during this time mainly biomass is produced in a batch
culture. After the biomass formation slows down, penicillin
V is produced in the secondary phase (106 h). During the
production phase, glucose is fed continuously.
Process Model
The production process model for penicillin V is based on
the available literature (Ohno et al., 2002; Perry et al.,
168 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 90, NO. 2, APRIL 20, 2005
1997; Lowe, 2001; Van Nistelrooij et al., 1998). Aspen
Batch Plus and Intelligen’s SuperPro Designer were the
software packages considered for the implementation of the
process model. Although both packages are robust simu-
lation tools, SuperPro Designer was chosen based on the
intuitive relationship between its process representation
and the spreadsheet model that was constructed for
Monte Carlo analysis.
Figure 1 shows the process flow diagram created with
the software SuperPro Designer. Fermenters with a total
capacity of 40–200 m3 are used for production (Ohno et al.,
2002; Lowe, 2001; Falbe and Regnitz, 1999; Perry et al.,
1997). We chose a facility with 11 fermenters, each with a
volume of 100 m3, optimizing the usage of the downstream
equipment. Penicillin V sodium salt is the final product.
The media components (pharmamedia, trace metals,
phenoxyacetate; S-102 to S-104) are blended in tank P-1
and sterilized in the continuous heat sterilizer P-4. The glu-
cose solution is prepared in tank P-2. Medium and glucose
solution are fed to the fermenter P-7 (glucose solution is
fed continuously only during the production phase). The air
(S-113) is compressed (P-5) and filter sterilized (P-6). The
exhaust air, containing mainly carbon dioxide, is filtered
(P-8) to prevent release of by-products to the environment.
Figure 1. Process flow diagram of the penicillin V production model (SuperPro Designer, version 5.1).
Table I. Parameter values of the fermentation model of penicillin V production.
Parameter Value Yield coefficients Value
texp (time of exponential growth) (h) 50 YX/pharmamedia (g/g) 2.14
tprod (time of production) (h) 106 YX/gluc. (g/g) 0.45
Xf (biomass concentration at texp) (g/L) 30 Ypen./gluc. (g/g) 0.81
Xnl (final biomass concentration) (g/L) 45 Ypen./phenoxyacetic acid (g/g) 2.00
Vin (initial volume) (L) 55,000 YX/O2 (g/g) 1.56
Vfinal (final volume) (L) 75,000 mgluc. (maintenance coefficient)
(g glu./g dcw h)
0.022
Pfinal (final product concentration) (g/L) 63.3 mO2 (maintenance coefficient)
(g/g dcw h)
0.023
BIWER ET AL.: UNCERTAINTY ANALYSIS PENICILLIN PRODUCTION 169
In the agitated fermenter, biomass and penicillin V are pro-
duced consuming the carbon sources, the precursor, and the
mineral salts.
After the fermentation, the fermenter content is fed to a
harvest tank (P-9).
A typical downstream process is divided into the
following unit processes: biomass removal, extraction, re-
extraction, and crystallization, filtration and crystal washing
and drying (Van Nistelrooij et al., 1998). The fermenta-
tion broth flows to the rotary vacuum filter P-20, where
wash water (S-150) is used to recover product for the re-
tained biomass. The retained fungal biomass is discharged
(S-151).
Before extraction, the cell-free broth is acidified to a
pH of f3 in P-22, using sulfuric acid (S-154) and cooled
to minimize degradation during acid extraction. In the
centrifugal extraction step (P-23), the penicillin is trans-
ferred into the organic phase (butyl acetate, S-157). The
remaining aqueous solution is discharged and neutralized in
P-24 with sodium hydroxide (10% w/w, S-159). The
penicillin is re-extracted (P-25) into acetone/water (S-162),
where sodium acetate is added (S-163). The sodium salt
of penicillin V then precipitates. The crystals (S-165) are
separated and washed in the basket centrifugation (P-26)
and conveyed to the fluid bed dryer (P-31). The remaining
washing solution is discharged (S-173). The solution sep-
arated in the centrifuge (S-168) is lead to P-27, where
most of the butyl acetate is split off in a recycling step
(not shown in detail). The rest is discharged and neu-
tralized in P-28 (NaOH, 10% w/w; S-170). The butyl
acetate is reused in the extraction. In P-29, fresh butyl
acetate is added (S-156). In the dryer (P-31), the penicillin
is dried with air (S-175) and the final product stored in
tank P-32.
EVALUATION BASE CASE
A process simulation was run as a base case to establish
a reference point for both economic and environmental
assessment.
Base Case Analysis
The average production rate from the facility is approx-
imately 263 kg penicillin V sodium salt per hour. This
results in an annual production of 2,090 tons with the as-
sumption of 330 operating days. The initial fermenter
volume is 55 m3 and 20 m3 are added as nutrient and
precursor feeds (36%). The volume added in the model is
within the range given by Lowe (2001). Annual production
is 546 batches and it is assumed that 16 fail (3%). The
overall yield of the fermentation is 0.21 g penicillin/g
glucose. The yield across downstream recovery is 90%.
The carbon balance shows that around 25% of the C-atoms
are converted to penicillin, 17% to biomass, and 60% to
carbon dioxide.
Table II presents the summary material balance for the
base case process. Altogether, 7,880 kg/h raw materials
are needed, which is 30 kg per kg final product (kg/kg P).
The input includes a number of materials that are typical
for fermentation processes: a high amount of water, glu-
cose as carbon source, oxygen, media, and trace metals.
Specific to the penicillin production is the demand for
phenoxyacetic acid. Furthermore, relevant amounts of the
solvents butyl acetate and acetone are needed for extrac-
tion, and a smaller amount of sodium acetate that forms
the final product with the penicillin is needed in the crys-
tallization step.
Besides the product, the fermentation output consists of
large amounts of carbon dioxide and biomass. Further-
more, significant amounts of unused raw materials and
unrecovered product leave the process. This model assumes
an 80% recycling of butyl acetate (see also Chang et al.,
2002). Acetone (S-167, S-173) is also recycled (70%) (not
shown in Fig. 1).
The process consumes 41 GWh electrical power
(20 kWh/kg P); 4,400 tons steam (2.1 kg/kg P); 6.4 million
m3 chilled water (3.1 m3/kg P), and 3 million m3 cooling
water (1.4 m3/kg P). The compressor and the fermenter
consume 90% of the electrical energy required. The ster-
ilization process (P-4) is the main consumer of steam,
although some steam is also required for drying. Chilled
water is used mainly in the fermenter and the steriliza-
tion step; additional cooling water is used in the com-
pressor P-5. In the extraction step, freon is used as heat
transfer agent. The energy demand for the recycling of
the freon is added to the electricity demand. The results
of the energy analysis are consistent with Ohno et al.
(2002), who state the energy requirement per kg product
Table II. Material balance of the model of the penicillin V production.*
Component Input [kg/kg P] Output [kg/kg P]
Acetic acid — 0.16
Acetone 0.12 0.12
Biomass (dcw) — 0.86
Butyl acetate 0.28 0.28
Carbon dioxide — 5.31
Glucose 4.95 0.10
Oxygen 2.5 —
Penicillin V (loss) — 0.10
Penicillin V sodium salt — 1.00
Pharmamedia 0.46 0.06
Phenoxyacetic acid 0.58 0.01
Sodium acetate 0.23 0.01
Sulfuric acid 0.05 0.05
Trace metals 0.67 0.09
Sodium hydroxide 0.12 0.12
Water 20.0 21.8
Total 30.0 30.0
*The recycling of butyl acetate and acetone is already considered. From
the amount of air transported through the fermenter, only the amount of
oxygen consumed is compiled in (kg/kg P) = kg component per kg final
product; final product = penicillin V sodium salt; dcw = dry cell weight.
170 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 90, NO. 2, APRIL 20, 2005
to be 108 MJ (30 kWh) electrical energy, 40 kg steam
and 9 m3 cooling water. However, the demand of steam
is only 5% of that amount. In Ohno et al. (2002), most
of the steam is needed for batch sterilization. In our mod-
el, continuous sterilization is used, and it requires much
less steam.
Economic Assessment
The base case model provides an estimate of the costs
involved in penicillin manufacture. Combined with the
current market price of penicillin, these estimates allow us
to calculate a number of financial measures that indicate
the economic value of an investment in penicillin manu-
facture. Although in a rigorous capital budgeting process,
we would seek to determine the net present value of the
estimated investment, we use the basic financial metrics of
earnings before interest and taxes (EBIT), earnings before
interest, taxes, depreciation, and amortization (EBITDA),
and return on investment (ROI) in the analyses that follow.
The justification for the use of these metrics is that our
primary objective is illustration of uncertainty analysis
rather than project valuation.
In the model, the total purchased equipment costs is
$9.1 million. Based on data from Peters et al. (2003), it
was assumed that the purchased equipment cost is 27.5%
of fixed capital investment (FCI) leading to a FCI of
$44.1 million and a total capital investment (TCI) of
$51.4 million. The fermenters with $5.5 million dominate
the purchase costs. All other equipment costs less than
$1 million; thus, the fermenters and related equipment dom-
inate the equipment costs, in agreement with the analysis
of Swartz (1979).
The total operating costs are $33.8 million per year. The
raw material costs, mainly glucose, phenoxyacetic acid and
butyl acetate (including recycling costs), have the biggest
share (37%); this is consistent with results from Lowe
(2001). They are followed by equipment-dependent costs
(24%) (mainly depreciation and maintenance) and the labor
costs (14%). Utility costs (11%, mainly electricity) and
plant overhead cost (11%) also play an important role,
while laboratory/QC/QA, waste treatment, and consum-
ables (altogether 3%) have only a small impact. Seven
single operating cost parameters capture each by them-
selves more than 2% of the global operating costs. The
fermenter-related costs of glucose (6.3%), phenoxyacetic
acid (12.9%), and electricity for fermenter (2.0%) and
compressor (3.0%) constitute 25% of the total operating
costs. Furthermore, basic labor cost (11.5%), butyl acetate
(9.1%, including recycling cost), and chilled water demand
(3.1%) contribute considerably to the operating cost. Here
we note that the price of glucose and assumed hourly labor
rates play an important role. This explains why today most
penicillin producing plants are located in countries where
sugar and labor costs are low but are capable of supplying a
stable source of energy given the high energy requirements
of the process.
Based on an annual production of 2,090 tons, the unit
production costs in the model are $16.2/kg final prod-
uct, which equals $10.3/BU. The selling price is set to be
$17.3/kg (Milmo, 2003). Hence, the annual revenue is
$36 million. Since the cost of operations is $32 million per
year, this results in EBITDA of $4.0 million. Including
depreciation leads to negative EBIT of �$350,000 and
the ROI is negative (�0.5%). Note that the ROI number
assumes a 35% tax rate and no financial leverage for the
project (i.e., no interest payments).
Environmental Assessment
Environmental aspects have become increasingly important
in pharmaceutical production and should be considered
together with the economic assessment (DeSimone and
Popoff, 1997). The method used, which was recently
developed by Biwer and Heinzle (2004), aggregates the
whole range of possible environmental impacts to two per-
formance figures that enable an appropriate comparison
with the economic key figures and the examination of
how uncertainty affects the environmental impact. They
are therefore more suitable for this purpose than complex
methods such as the life cycle assessment.
Wastewater is discharged mainly from the extraction
step (remaining broth after penicillin removal) and after the
separation of the crystals in the basket centrifugation,
where a mixture of butyl acetate, acetone, water and some
impurities are discharged. After a partial removal of the
butyl acetate (P-27) and acetone (not shown), both waste
streams (S-171, S-173) are assumed to pass to a biological
wastewater treatment plant. Solid waste is produced in the
biomass removal. The only relevant emission is the exhaust
air of the fermenter, which includes a large amount of
carbon dioxide (S-117). We have not attempted to assess
fugitive emissions from the process.
Figure 2 shows the EI of the input and output
compounds. On the input side, the media components
Figure 2. Environmental indices (EI) of the input and output
components of the penicillin V production model. [IP/kg P] = index
points per kg final product.
BIWER ET AL.: UNCERTAINTY ANALYSIS PENICILLIN PRODUCTION 171
(mainly ammonium sulfate), the precursor phenoxyacetic
acid, butyl acetate (extraction), and acids and bases (used
for pH control of the extraction and neutralization of
waste streams) have the highest indices. Although glu-
cose and pharmamedia are used in large amounts, they
are not relevant in any of the input impact categories
(for further details, see Biwer and Heinzle, 2004). Hence,
their environmental factor is EFIn = 0, and they do not
appear in the evaluation of the input. The output EIs
are strongly dominated by the carbon dioxide produced
during the fermentation. Furthermore, the biomass, the
butyl acetate used in the extraction, acids + bases and
the acetic acid formed in the re-extraction step (P-25) have
some impact.
The overall EI, which describes the environmental
performance of the process, for the input is EIIn =
0.45 Index Points/kg P (= IP/kg P), for the output EIOut =
0.72 IP/kg P. Thus, from an environmental point of
view, the output has a higher relevance than the input. In
addition to the material balance, the energy consumption
also contributes significantly to the environmental impact
of a process (Castells et al., 1994). The supply of energy
affects the input side by consuming fossil energy sources
and the output side by generating air pollution (e.g., carbon
dioxide, sulfur dioxide).
OBJECTIVE FUNCTIONS, VARIABLES, ANDPROBABILITY DISTRIBUTIONS
One of the inherent problems in fermentation process de-
velopment is the variability associated with both the biol-
ogy and the process itself. We set out to understand how
variance in key biological and process parameters would
impact the final result. Using the process model as the basis
for a Monte Carlo simulation (MCS), we can explore how
variance propagates through the entire process to impact
both economic and environmental results. A crucial step in
this analysis is selecting the objective functions, the input
variables, and their probability distributions.
Several output parameters are useful as economic
objective functions. These include the unit production
costs (UPC); the EBIT; the EBITDA; and the ROI. Also
relevant is the input and output EI of the process. In our
analysis, the investment cost and the plant overhead cost
are kept constant to represent an existing facility.
From the process model, a number of technical, supply
chain, and market parameters routinely exhibit uncertain-
ty. Table III summarizes these parameters and their prob-
ability distribution. The probability distributions shown
there are derived from experimental data and are assumed
to reflect the expected uncertainty in a process. For a more
detailed discussion of these terms, see Vose (2003). For
simplification, all variables chosen are assumed inde-
pendent. This assumption is true for most parameters.
For those parameters, where a known correlation exists,
e.g., biomass concentration and agitator power, the im-
pact on the objective functions is small and so Crystal
Ball’s correlation capability was not used in the Monte
Carlo simulations.
Technical Parameters
Technical parameters are all process parameters that affect
the fermentation and the downstream steps on a batch-
to-batch basis. In our analysis of technical parameter
variability, we take the perspective of product development
and assume that the true mean of each parameter is
unknown but described by a distribution. This allows us to
calculate economic parameters, such as ROI, for each
Monte Carlo trial in a meaningful way. We recognize,
however, that the penicillin process is quite well charac-
terized, so we could have performed technical parameter
uncertainty analysis with regard to process capabilities,
which are defined by operating specifications, means, and
standard deviations.
In this work, variability is described for values that
determine the biomass and product formation. For all such
parameters (see Table III) we have assumed a normal
distribution and their mean values and coefficients of
variation are derived from experimental data. Additionally,
minimum and, for some parameters, maximum values as
well, are defined, since in reality many distributions that
are normal within a few standard deviations of the mean
never assume values that are many standard deviations
from the mean and so should not be sampled during
simulation. The mean value of the final product concen-
tration is based on the work of Demain and Elander (1999)
and Van Nistelrooij et al. (1998). Fermentation time and
initial and final broth volumes are assumed to be deter-
ministic. Fermentation conditions do vary, as represented in
the MCS by the aeration rate and the power consumption of
the stirrer.
In the base case, the overall yield of the separation and
purification section is 90%. In the MCS, the variation in
overall recovery is achieved by varying the yield of indi-
vidual steps (P-20, P-25, P-26, P-31) and the partition co-
efficient (KPen) of the extraction step (P-23). For these
parameters, a set of probability distributions is assumed
that results in variability of the overall purification yield
equal to the variability usually observed in actual processes.
For the yield parameters, a normal distribution is assumed,
while for the partition coefficient, a uniform distribution is
chosen (see Table III). Depending on minor variations of
pH value, the KPen varies between the two values defined.
Under environmental and economic aspect the recycling of
butyl acetate and acetone is crucial. Mean values and stan-
dard deviations are defined based on yields and variability
usually occurring in the recycling of organic solvent.
Supply Chain and Market Parameters
The technical parameters are largely defined by the process
and are under the control of the manufacturer (e.g., strain
172 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 90, NO. 2, APRIL 20, 2005
used, fermentation or purification conditions). Supply chain
and market parameters are not influenced by the process
conditions and display variance that affects the economics
of the process over an extended period.
The raw material costs account for a large part of the unit
production costs. They are dominated by the costs for
glucose and phenoxyacetic acid. Therefore, the prices of
these materials are considered in the MCS. The mean
glucose price was calculated from monthly average prices
on the world market from 1996 to 2001. Using the ‘‘batch
fit’’ function of Crystal Ball, a h distribution was identified
as the best fit (values see Table III). h distributions are
often used to describe empirical data. For phenoxyacetic
acid, an average price is chosen that is realistic for the
annual demand of 1,600 tons.
The energy costs are dominated by the costs for
electricity. Mean value and probability distribution for this
parameter are derived from monthly average prices for the
United States from 1995 to 2003. (Weibull distribution,
values see Table III).
The price for penicillin V and penicillin in general has
varied dramatically over the last few years as noted earlier.
As the mean value, the current price stated by Milmo (2003)
is used, and a coefficient of variation of 10% is assumed.
Best-Case and Worst-Case Scenario
Based on the parameters chosen, a best-case and a worst-
case scenario are calculated. For those parameters where a
standard deviation is defined, 2 times the standard devi-
Table III. Parameters used for Monte Carlo simulation and their variation and probability distribution chosen.*
Parameter
Base case
value Source
Probability
distribution Variation data Source
1. Technical Parameters
Yield biomass on
glucose (g/g)
0.45 Internal estimate, based
on fermentation data
Normal V = 17.5%; min: 0.2 Industry data
Maintenance coefficient
(mg glucose/g dcw h)
22 Internal estimate, based
on fermentation data
Normal V = 17.5%; min: 10 Industry data
Precursor utilization
efficiency (%)
92 De Tilly et al., 1982 Normal V = 15.0; 70–100 (min, max) Industry data
Final biomass
concentration (g/L)
45.0 Internal estimate, based
on fermentation data
Normal V = 17.5%; min: 25 Industry data
Final product
concentration (g/L)
63.6 Demain and Elander,
1999; Van Nistelrooij
et al., 1998
Normal V = 10%; 20–100 (min, max) Industry data
Aeration rate (vvm) 0.8 Perry et al., 1997;
Lowe, 2001
Normal V = 10%; 0.5–1.0 (min, max) Perry et al., 1997;
internal estimate
Agitator power (kW/m3) 2.5 Perry et al., 1997;
Lowe, 2001
Normal V = 20%; 1.5–3.5 (min, max) Perry et al., 1997;
internal estimate
Yield downstream recovery (%) 90 Lowe, 2001;
Van Nistelrooij
et al., 1998
Normal Calculated for single step yields
Yield biomass removal (%) 97 Internal estimate Normal F2 (SD)
Industry data
(overall yield)
Kj extraction 60 McCabe et al., 2001 Uniform 60–80
Yield crystallization (%) 97 Internal estimate Normal F2 (SD)
Yield basket centrifuge (%) 99 Internal estimate Normal F1 (SD)
Yield fluid bed dryer (%) 99 Internal estimate Normal F1 (SD)
Yield butyl acetate
recycling (%)
80 Internal estimate Normal F5 (SD) Internal estimate
Yield acetone recycling (%) 70 Internal estimate Normal F5 (SD) Internal estimate
2. Supply chain parameters
Price glucose [$/kg] 0.216 USDA Foreign
Agricultural Service,
2001a
h a = 3.49; h = 1.2;
scale = 29.1 (for a normal
distribution: V = 25%)
USDA Foreign
Agricultural Service, 2001a
Price phenoxyacetic
acid ($/kg)
3.80 Internal estimate;
supplier data
Normal V = F10% Internal estimate
Electricity cost ($/kWh) 0.0468 U.S. Energy Information
Administration, 2004b;
Peters et al., 2003
Weibull Loc: 4.13; Scale: 0.61;
Shape: 1.96
(for a normal distr.: V = 6%)
U.S. Energy Information
Administration, 2004b
3. Market parameters
Selling price final
product ($/kg)
17.30 Milmo, 2003 Normal V = F10% Internal estimate
*SD, Standard deviation; V, coefficient of variance.aForeign Agricultural Service. 2001. World and U.S. raw and defined sugar prices. Available at U.S. Department of Agriculture, Foreign Agricultural
Services: http://www.fas.usda.gov/htp/sugar/2000/November/prices.pdf.bU.S. Energy Information Administration. 2004. February 2004 Monthly Energy Review. Available at http://www.eia.doe.gov.
BIWER ET AL.: UNCERTAINTY ANALYSIS PENICILLIN PRODUCTION 173
ation is used to increase and respectively decrease the
base case value. When the values are higher than the
highest possible value, the highest possible value is used
(e.g., recovery yield basket centrifuge: 100%). When a
certain range is defined for a parameter, the maximum and
minimum values set the worst-case and best-case values.
For instance, the lowest and highest prices in the real data
for glucose and electricity are used.
Table IV shows the values of the objective functions for
the three cases. These values define, based on variation
known today, the range over which the objective function
will vary in the future. However, they do not give any
information about the probability distribution of the values
within this range.
RESULTS AND DISCUSSION:MONTE CARLO SIMULATIONS
To enable the Monte Carlo simulations, the process model
has to be transferred from SuperPro Designer to MS Excel.
The software Crystal Ball 2000 is used as the random
number generator to perform the MCS. For a large number
of trials (or iterations), random numbers are generated
for the set of uncertain input parameters based on the
probability distribution for these parameters (see Table III).
The entire model is recalculated for each trial, and the
resulting values of the objective functions are saved.
In the first MCS, only the technical parameters are varied
(MCS-TP), followed by a variation of the supply chain and
market parameters (MCS-S/MP). In the next step, Monte
Carlo simulations are done for all parameters defined in
Table III (MCS-AP). In these simulations, the final peni-
cillin concentration of the fermentation is identified as
the dominant technical parameter (see following sections).
To examine the influence of final penicillin concentra-
tion and other technical parameters on objective func-
tions, additional MCS are run, one simulation varying the
technical parameters without the final penicillin concen-
tration (MCS-TPW) and another only varying the final
penicillin concentration (MCS-Pen). For all parameter
sets, 100,000 trials are run to ensure a low mean standard
error for all objective functions (<1%). A detailed docu-
mentation of the MCS results is given in the online sup-
plementary material.
Unit Production Cost
Figure 3 shows as an example of the probability distribu-
tion of the UPC on a batch-to-batch basis for the MCS-TP.
All UPC distribution curves are more or less normally
distributed. Since the supply chain variables have distribu-
tions balanced around their mean (mean = base case)
values, the mean value of the MCS-SC/MP is equal to the
UPC of the base case. The mean values of the MCS-TP,
MCS-TPW, and MCS-Pen are significantly higher than the
base UPC. For several technical parameters, a minimum or
maximum value is defined resulting in an unbalanced
distribution, e.g., the downstream yield and the precursor
utilization efficiency are truncated at 100%. The average
of these parameters in the MCS is therefore less then
their base case values. This leads to a higher mean UPC
in the MCS. Since the supply chain parameters do not
have such an effect, the MCS-AP also shows a higher mean
UPC of $16.7/kg.
As expected, all values lie within the range defined by the
worst/best case scenarios. The supply chain parameters
cover a much smaller range of values than the technical
parameters. The same tendency is shown by the standard
deviation. The MCS-TP has a standard deviation of
$1.6/kg, equal to a coefficient of variation (V) of 9.5%.
The coefficient of variation of the MCS-S/MP is more than
four times lower with V = 2%. Thus, the variance of the
MCS-AP is dominated by the technical parameters and its
coefficient of variation (10%) is almost identical to the
value of the MCS-TP. In the MCS-AP, the UPC is less than
$18.8/kg with a probability of 90% and less than $17.4/kg
with a probability of 70%.
Figure 4 shows the parameters that drive the variance
of the UPC. The final penicillin concentration dominates
the variation in MCS-TP. The concentration defines the
amount of final product per batch and thus the percentage
of raw materials converted to biomass and carbon dioxide.
Furthermore, the relative amount (and cost) of butyl acetate
necessary in the extraction stage decreases as product
concentration increases (as long as the solvent/broth ratio
remains unchanged). The second driver is the final biomass
Figure 3. Probability distribution of the unit production costs (UPC) in
the MCS-TP, defined in Table III (100,000 trials, 100 groups in the graph).
Table IV. Objective functions in the base case, worst-case, and best-
case scenario.
Objective function Worst case Base case Best case
UPC ($/kg) 28.0 16.0 10.5
EBITDA ($ million) –18 4.0 31
EBIT ($ million) –22 –0.35 26
ROI (%) –32 –0.5 39
EI input (IP/kg P) 0.69 0.45 0.32
EI output (IP/kg P) 1.65 0.72 0.36
174 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 90, NO. 2, APRIL 20, 2005
concentration. Higher biomass concentration increases the
diversion of C-atoms to cell growth and respiration (i.e.,
CO2) and increases the raw materials requirements to pro-
duce a specific amount of penicillin. Besides these factors,
the different recovery yields in the downstream process play
an important role since they determine the amount of final
product that is ultimately recovered. Finally, the precursor
utilization efficiency affects the phenoxyacetic acid demand.
In the MCS-S/MP, the variance is mostly caused by the
variation of the glucose and phenoxyacetic acid prices.
With the probability distribution used in the MCS, the im-
pact of the electricity cost is small.
The sensitivity chart explains why the additional MCS-
TPW and MCS-Pen simulations were performed. The high
impact of the final penicillin concentration is reaffirmed
in the MCS-Pen. The penicillin concentration alone causes
a variation of V = 8.5%, while all other technical param-
eters (MCS-TPW) result in a coefficient of variation of
V = 5%.
Figure 5 compares the different probability distributions
for the UPC. The MCS-S/MP shows the smallest variation
and has a coefficient of variation of only 2%. As one might
expect, the MCS-AP displays the broadest variation. The
MCS-Pen, which includes substantial variation contributed
by penicillin concentration, is only slightly smaller; the
MCS-TPW distribution lies between those of MCS-S/MP
and MCS-Pen.
ROI, EBITDA, and EBIT
To look at the ROI, EBIT, and EBITDA of a process
retrospectively, only the mean values of the process
parameters are relevant, since batch-to-batch variations
should center on the mean in the long run. However, if one
wants to predict future performance when process param-
eters with uncertain means propagate through the process,
the variation of the process variables influences long-term
economic objective functions.
In the MCS-S/MP and the MCS-Pen, all input variables
have symmetrical distributions. Hence, these MCS show
the same mean ROI as the base case ROI. For the same
reason discussed earlier, in the section UPC, the other MCS
have a lower mean ROI of �1.5%. For all five parameter
sets, the distribution curves of the ROI are symmetrical
(skewness c0) and show the peakedness of a normal
distribution (kurtosis c3.0). Including all input variables,
the values of MCS-AP vary between a minimum of ROI =
�28% and a maximum of ROI = +29%. Thus, they cover a
range of 57%. As expected, the other MCS show a smaller
range width. In contrast, the worst/best case scenario ranges
from �32% to +39% and has a range width of 71%. Thus,
both lie outside the feasible range for the base case and so
actually have a zero probability of occurrence. This shows
the limited value of worst/best case scenarios, if their actual
probabilities are not taken into account.
While the UPC is only defined by the process costs, the
ROI is also affected by the revenues. Therefore, the selling
price of the final product plays a crucial role for the ROI
and causes 50% of the variation in the MCS-AP, while the
penicillin concentration contributes only 35%. Addition-
ally, the biomass concentration, the crystallization yield,
Figure 5. Probability distribution of the unit production costs in MCS-
AP, MCS-TPW, MCS-Pen, and MCS-S/MP (100,000 trials, 100 groups in
each graph). The curve of MCS-TP is very similar to the curve of MCS-AP
(not shown). The area under curves is always the same.
Figure 4. Contribution of the parameters to the variance of the unit pro-
duction costs in the MCS-TP (a), MCS-S/MP (b), and MCS-AP (c). Only
parameters with more than 1% contribution to the variance are shown.
BIWER ET AL.: UNCERTAINTY ANALYSIS PENICILLIN PRODUCTION 175
the yield of the biomass removal, and the prices for glucose
and phenoxyacetic acid contribute to a certain extent.
Compared with the UPC, the additional impact of the
selling price to the ROI changes the standard deviations and
the probability distributions of the different parameter
sets (see Fig. 6). The MCS-TPW is not affected by the two
most sensitive parameters (penicillin concentration, selling
prices) and therefore has the smallest standard deviation
(2.3%). The MCS-AP includes both penicillin concentra-
tion and selling prices and thus exhibits the largest standard
deviation (6.5%). The other curves lie in between these two
extremes. Here, the MCS-S/MP with the most sensible
penicillin selling price has a larger variance (SD = 5.2%)
than the MCS-TP with the second most sensible parameter
(SD = 4.8%). As expected, the MCS-Pen lies between the
MCS-TP, which it dominates, and the MCS-TPW.
The EBIT and the EBITDA are influenced by the input
variables in the same way as the ROI. For the MCS-AP the
mean EBITDA is $3.3 million, with a standard deviation of
$4.8 million. Thus, the EBITDA is not positive for all
possible scenarios. It is positive with a probability of 75%
and above $2 million with a probability of 60%. In the
MCS-AP the mean EBIT is �$1 million. This means that
when depreciation and today’s selling price are accounted
for, the process is not capable of realizing a profit on
average. Besides the existing overcapacity in the market,
this explains why new penicillin production facilities have
not been built in recent years. However, with an existing
and already completely depreciated plant, profitability can
be achieved.
For those indicators that are affected by market con-
ditions (ROI, EBIT, EBITDA), the selling price drives the
uncertainty and this allows us to understand the difficult
situation faced by many penicillin manufacturer faced
with a volatile penicillin market. Beside the selling price,
the most relevant parameter for the uncertainty of the
economic indicators is the penicillin concentration. Hence,
key to process control is the ability to achieve a high
penicillin concentration quickly and reproducibility. This is
one of the most promising means of cost reduction and
improved profitability.
Environmental Index Input and Output
The variation of the EIs is determined only by the technical
parameters. Hence, the results of the MCS-TP and MCS-AP
are identical. Figure 7 shows the probability distribution of
the EI input and the EI output. It is clearly shown that even
considering the existing uncertainty the EI input is sig-
nificantly lower than the EI output. This means the output
components are environmentally more relevant than the
input components. The mean values are for all parameter
sets only slightly higher than in the base case. The EI varies
between 0.34 and 0.68 IP/kg P, the EI output between
0.42 and 1.55 IP/kg P. Thus, in contrast to the ROI, they
show almost exactly the same range as the worst/best-case
scenarios. The specific amount of carbon dioxide, environ-
mentally the most relevant output component, varies more
than the specific amount of phenoxyacetic acid, the most
relevant input component.
Figure 8b shows the contribution of the technical param-
eters to the variance of the EI input (MCS-AP). The media,
butyl acetate, acetone, and phenoxyacetic acid have the
highest EFs and input EIs, and this influences the variance.
The final biomass concentration has the highest impact.
It determines the amount of media that must be added to the
fermenter. In contrast to the UPC, the penicillin concen-
tration is only the second relevant factor. It defines the total
amount of final product and the specific consumption of
raw materials and solvents. Furthermore, the butyl acetate
recycling rate, and to a smaller extent the acetone recycling,
contribute to the variation by defining the amount of butyl
acetate, respectively acetone in the waste. However, they do
not contribute significantly to the economic uncertainty.
Similar to the UPC, the precursor (phenoxyacetic acid)
utilization efficiency and the recovery yields (amount of
final product) contribute substantially to the EI variance.
Figure 8a shows the contribution of the parameters to
the variance of the EI output. Carbon dioxide, biomass, and
butyl acetate have the highest output EIs, which again in-
fluences the EI variance. The final biomass concentra-
tion defines the amount of biomass in the waste and by
association the amount of CO2 formed. The maintenance
coefficient for glucose and the yield coefficient of bio-
Figure 7. Probability distribution of the environmental index input
(V = 8%) and Output (V = 15%) in the MCS-TP as defined in Table III
(100,000 trials, 100 groups in each graph). The area under the curves is the
same. [IP/kg P] = index points/kg final product.
Figure 6. Probability distributions of the return on investment (ROI) for
the five different sets of parameters (100,000 trials, 100 groups in each
graph). The area under the curves is always the same.
176 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 90, NO. 2, APRIL 20, 2005
mass on glucose also affect the amount of carbon dioxide.
Both parameters have no significant impact on the eco-
nomic uncertainty.
The reduced impact of the final penicillin concentration
compared with the economic objective function is clearly
shown in Figure 9 by a smaller variance of the MCS-Pen
curve. The MCS-TPW is wider and lies nearer to the MCS-
AP distribution curve.
These results show that the relevant parameters and how
strongly they contribute to the uncertainty differ to some
extent between the economic and environmental indica-
tors. However, the direction of change is the same for all
relevant parameters. The contributions of the variables to
the overall uncertainty indicate the sensitivity of the pro-
cess to these variables. Thus, there are parameters that can
be changed to improve the economic performance without
affecting the environmental performance. While for other
parameters, an economic improvement leads directly to an
environmental improvement. This represents an economic
and environmental (eco-efficiency) win-win scenario that is
contrary to the use of end-of-pipe technologies for en-
vironmental pollution control that lead to additional costs.
Sensitivity Analysis for Final Penicillin Concentration
The final penicillin concentration is the most important
technical parameter in the model. Therefore, it is inter-
esting to see how the objective function changes when
either the mean or the coefficient of variation of the peni-
cillin concentration changes.
In general, it can be expected that the higher the coef-
ficient of variation of penicillin concentration, the higher is
the variation of the objective function since each draw of the
MCS will assess a different long-run mean concentration.
Figure 10a shows the probability distribution of the UPC at
different coefficients of variation of the penicillin concen-
tration. The strong impact of this variable on the UPC
Figure 9. Probability distribution of the environmental index output
in the MCS-AP, MCS-TPW, and the MCS-Pen (100,000 trials, 100 groups
in each graph). The variation of each parameter is defined in Table III.
[IP/kg P] = index points/kg final product.
Figure 10. Probability distribution of the unit production costs (UPC) (a)
and the EI input (b) at different coefficients of variance of the final
penicillin concentration (100,000 trials).
Figure 8. Contribution of the technical parameters to the variance of (a)
the environmental index input (EI input), and (b) the environmental index
output (EI output) in the MCS-AP (as defined in Table III).
BIWER ET AL.: UNCERTAINTY ANALYSIS PENICILLIN PRODUCTION 177
results in significant change of the curve shape and a higher
standard deviation. Figure 10b shows the EI Input for the
same sets of different coefficients of variation. Here, the
variation of the penicillin concentration also leads to a
broader variance of the EI input. However, the effect is
much smaller than for the UPC, based on the smaller impact
of the penicillin concentration shown in Figure 8.
The differences described are illustrated by the relation
of the coefficients of variation of the objective functions to
an increasing coefficient of variation of the penicillin
concentration (VPen). The values at VPen = 0% are identical
to an MCS of all parameters without the penicillin con-
centration. From these base lines, the coefficients of the
objective function increase with increasing VPen. The
coefficient of the EI input increases relatively slowly and
stays clearly smaller than the coefficient of the penicillin
concentration. The EI output starts at a higher coefficient
(broader variance in MCS-TPW). It also increases rela-
tively slowly and runs from VPen = 15% upward in parallel
with the increasing VPen. The UPC increases more quickly
and reaches at about 8% the value of VPen. For the range
VPen = 8–20% the coefficient of the UPC is more or less
identical to the coefficient of the penicillin concentration.
At lower values, the other input variables contribute to the
variation of the UPC to a greater extent. These results
illustrate the fact that an exact definition of the probability
distribution of the main uncertainty drivers is crucial to
obtaining realistic results.
Final penicillin concentration was varied between 40 g/L
and 70 g/L with a constant coefficient of variation to further
explore the impact of uncertain long-run strain performance
that is confined to specific ranges. Figure 11 shows the
change of the UPC probability distribution. The mean
moves to the right with decreasing penicillin concentration.
The constant coefficient of variation of the penicillin
concentration propagates through the model resulting in a
more or less constant coefficient for UPC. Since the UPC
increases with decreasing penicillin concentration, the
standard deviation must also increase and leads to the
broader shape of the distribution curves that is observed.
The distributions of the other objective functions look
similar. The parameters that drive the uncertainty remain
the same. Thus, the results derived are applicable to all
penicillin processes independent from the penicillin con-
centration that is reached.
Figure 12 shows EBITDA as a function of different
penicillin concentration. The penicillin concentration for
which EBITDA = 0 can be graphically identified (56 g/L); a
positive EBITDA is reached at higher concentrations. A
MCS was run with the identified concentration. From the
resulting EBITDA standard deviation at this concentration,
the standard deviation for the penicillin concentration
EBITDA = 0 can also be derived graphically (see Fig. 12).
The obtained standard deviation is 9.5 g/L, documenting
a relative high uncertainty. The variation of the mean
penicillin concentration shows its importance for the eco-
nomic success of the process when assessed from a devel-
opment perspective.
CONCLUSIONS
The development of the base model and the use of Monte
Carlo simulations have led to a better understanding of
penicillin V production and the impact of both technical
and market variance. As such, the most relevant stochastic
variables are identified and proposed as parameters that are
critical to an efficient process control strategy, as well as
starting points for potential process improvements.
From a computational perspective, this work demon-
strates a general methodology for decision analysis that
allows one to understand the impact of uncertainty on
key process metrics. This is of significant value, since it
allows decision makers to more clearly understand process
and economic risks. The construction of a spreadsheet
model that allows for such stochastic analysis is fairly
straightforward, since most bioprocess material and energy
balances have analytical solutions that are amenable to
spreadsheet formulation, and the results of such formula-
tions are readily verified using a simulation tool such as
SuperPro Designer.
Final penicillin and biomass concentrations in the fer-
menter have the highest contribution to the uncertainty
Figure 11. Probability distribution of the unit production costs (UPC)
at different final penicillin concentrations (100,000 trials, 100 groups in
each graph).
Figure 12. Earnings before interest, taxes, depreciation, and amortiza-
tion (EBITDA) at different penicillin concentrations and graphical
derivation of the standard deviation of the penicillin concentration for
which EBITDA = 0.
178 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 90, NO. 2, APRIL 20, 2005
of UPC and EI. Fermentation parameters such as yield,
maintenance coefficient, and precursor utilization also
have a high impact on the variance of the environmental
impact, as well as the recycling rate of the organic sol-
vents. The production costs are significantly affected by
downstream yield and raw material costs. The selling
price dominates the variation of ROI and other revenue-
dependent parameters.
The additional use of an environmental assessment
method that aggregates the environmental performance of
the process to two indicators allows one to understand
how the uncertainty of the input variables affects not only
economic performance, but also impact on the environ-
ment and the differences between these two metrics. This
approach has been used infrequently so far in the evalua-
tion of chemical and pharmaceutical processes.
The sensitivity analysis shows how important it is to
define exactly the variance of key input parameters. The
threshold for positive EBITDA has been graphically
derived and used to show that decreasing selling prices
over the past few years have drastically increased the
pressure for further strain improvements and cost reduction.
We note, however, that the case presented is limited by the
fact that the base model is a generalized model of the
penicillin V product process. Depending on the location,
the cost structure of a manufacturer might vary.
This article presents the penicillin V production as a case
study. It proves that combining calculation-based modeling
with Monte Carlo simulations can be used as a general
methodology for multi-parameter uncertainty analysis.
Thus, it goes beyond the usual case of economic assessment
based on average value analysis that is standard practice
in process development using commercial simulation soft-
ware. The methodology presented is generally applicable
to the analysis of any process where stochastic variables
influence both within-batch and between-batch process
capability and the long-run economic performance upon
which development decisions are based.
The authors thank Intelligen, Inc., for their support and helpful
discussions. This work was supported by a fellowship within the
Postdoctorate Program of the German Academic Exchange Service
(DAAD).
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