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Optimized experimental design for the inhibition of calcium oxalate using a turbidimetrical model.

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ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING
Asia-Pac. J. Chem. Eng. 2008; 3: 425–431
Published online 9 July 2008 in Wiley InterScience
(www.interscience.wiley.com) DOI:10.1002/apj.151
Research Article
Optimized experimental design for the inhibition of calcium
oxalate using a turbidimetrical model
Aouatef Driouch,1 Abdelkader Djelloul,1 Zohra Kaid-Omar,1 Ahmed Semmoud,2 Abdelmajid Rais3 * and
Ahmed Addou1
1
Laboratory of STEVA, Department of Chemistry, University of Mostaganem, Mostaganem, Algeria
Laboratory of Infrared and Raman Spectrochemistry, University of Sciences and Technology, Villeneuve d’Ascq, France
3
Laboratory of Materials Sciences, Department of Physics, University of Sidi-Bel-Abbes, Sidi-Bel-Abbes, Algeria
2
Received 26 December 2007; Revised 21 March 2008; Accepted 4 May 2008
ABSTRACT: In this work, we studied the individual and combined effect of inhibitors such as citrate ions and
magnesium ions on crystallization of calcium oxalate. It is the main constituent of more than 70% of urinary stones.
In order to optimize the number of experiments with the help of a suitable mathematical model, an experimental
design was developed. The crystallization of CaC2 O4 with and without inhibitors, at physiological concentrations, was
studied by turbidimetry at 37 ◦ C. The inhibition effect was evaluated through the induction time (nucleation) and the
turbidimetrical slope (crystalline growth). The experimental design enabled the investigation of the effect of citrate ions,
magnesium ions, and their combination on the inhibition rate. The obtained results showed that the inhibition power
increases with inhibitor concentration when it is tested alone. This inhibition also affected the delay on nucleation.
Thus, the induction time varied from 0.22 min without inhibitor to 4.73 min with citrate ions and 1.96 min with
magnesium ions. The two inhibitors were more effective on nucleation and on crystalline growth when they were used
in combination compared to one of them tested alone. The mathematical model fitted the experimental results well
with a minimum of trials.  2008 Curtin University of Technology and John Wiley & Sons, Ltd.
KEYWORDS: inhibition; turbidimetry; calcium oxalate urinary stone; citrate; magnesium; experimental design
INTRODUCTION
Urolithiasis is a major problem of public health. Lithiasic subjects show severe urolithiasis forms with multiple
recurrences such as an alteration in the functioning of
kidneys. Medical treatments are costly and not always
conclusive. According to the epidemiological data, calcium oxalate (CaOx) is the main component of urinary
stones as found in more than 70% cases. Calcium affects
the concentration of oxalate since it binds to oxalate to
form calcium oxalate monohydrate. In addition, oxalate
urinary concentration plays an important role in stone
formation.[1 – 3] Even a small increase in urinary oxalate
has a significant impact on calcium oxalate saturation.
Although primary hyperoxaluria is relatively uncommon, patients with calcium oxalate stones have some
degree of hyperoxaluria. So, reducing the oxalate concentration would be helpful to most patients with urinary stone.
*Correspondence to: Abdelmajid Rais, Laboratory of Materials
Sciences, Department of Physics, University of Sidi-Bel-Abbes, SidiBel-Abbes, 22000, Algeria. E-mail: amrais@yahoo.com
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
Formation of such concretion implies several physicochemical events such as nucleation, growth, agglomeration, and retention of crystalline particles in the
urinary tract. However, the mechanism of these processes remains speculative. Urinary supersaturation is
the major factor responsible for lithogenesis. Indeed,
a stone is generated if the urine is supersaturated by
lithogenic solute like calcium oxalate. Urinary inhibitors
can balance the action of these solutes. However, the
stone formation often takes place when there is an
absence or a deficiency of natural inhibitors. In this
respect, several substances were identified for their
capacity to inhibit the crystallization of calcium salts
(oxalate and phosphate).
Magnesium and citrate ions were quoted as inhibitors
of low molecular weights.[4 – 9] These two inhibitors
have always been tested individually. As a matter of
fact, various published works[7,10 – 16] suggested that it is
important to take into account the interaction that takes
place between molecules in the urinary medium. Urine
is a complex medium containing several substances, and
global inhibition activity results from the synergetical
interaction of several inhibitors. Using a seeding model,
the inhibition activity of a mixture of two inhibitors on
A. DRIOUCH ET AL.
under constant steering by remote control at 800 rotations per minute. The different kinetic parameters of
the reaction were determined from the turbidimetrical
curve, in particular, the induction time Ti corresponding to the nucleation phase and the turbidimetrical slope
enabling the calculation of the inhibition rate. For similar conditions, the experiment was repeated six times.
As such, the mean, standard deviation, and variation
coefficients (VCs) were calculated. All VCs are less
than 10%.
Crystallization without inhibitor
Solutions of calcium chloride (CaCl2 , 2H2 O) and
sodium oxalate (Na2 C2 O4 ) have been prepared in a
solution of sodium chloride to maintain the ionic
strength at 0.15 M. A solution of CaCl2 of 8 mM was
prepared from the original solution and a volume of
1.5 ml was transferred into a measurement container
having 1 cm of optical path, to which we added an
equal volume of sodium oxalate of 2 mM. Then, measurement was immediately performed. The final concentrations in this test were 4 and 1 mM, respectively.
These concentrations were chosen in order to avoid an
instant nucleation. All the chemical products utilized
were Merck products with analytical purity. The kinetic
curve obtained by turbidimetry representing the three
crystallization phases (nucleation, growth, and agglomeration) is shown in Fig. 1.
Crystallization with inhibitor
The inhibitor effect on the different crystallization
phases was studied in the same experimental conditions,
as above. Nevertheless, it is noteworthy to mention that
the inhibition substance was added to the oxalate solution before mixing it to calcium chloride. We tested
Abs
Agglomeration
op
e
calcium oxalate crystallization was studied by Werness
et al .[17]
The in vitro crystallization model proposed in this
work was simultaneously developed in Belgium by
Beau fays et al .[18] and in France by Hennequin et al .[7]
It is an original model without seeding which enables by
turbidimetrical kinetics, the study of low-volume solution in high-saturation condition at different crystallization steps. Moreover, it enables monitoring the action
mechanism of the present inhibitors on the kinetics of
the three crystallization phases (nucleation, growth, and
agglomeration) at physiological concentrations.
It is the characterization of the crystal dimensions
by turbidimetry, which may require kinetic as well
as thermodynamic studies. Our work does not focus
on the measurements of the sizes of crystals, which
may be linked using the relation T (lambda) <= >Ra,
but rather on the slowing down effects of inhibitors
on the nucleation, growth, and/or agglomeration of
crystals. The turbidimetrical curve giving the three
crystallization states has been plotted and used as a
model in the inhibition study. Moreover, in the study
of the effect of magnesium and citrate on the calcium
oxalate crystallization, the model used based on the
turbidimetrical measurement is a model of spontaneous
precipitation. It involves both nucleation and growth
and appears interesting because it brings to bear the
urinary phenomenon.
Given the high number of experiments necessary in
this kind of work with one inhibitor or with a combination of two, we applied the method of experiment planning (Experimental design). This allows the optimization of the experiment number by varying the inhibitor
concentrations. Among the plans, enabling the use of a
second-degree polynomial, we chose an orthogonal plan
of the second order.[19 – 22] For a multivariable system,
it is more appropriate to use statistical tools in order to
optimize the number of experiments to perform.
In this article, we study the inhibition effects of
magnesium and citrate ions, individually as well as
their combination, over the crystallization of calcium
oxalate (main component of urolithiasis). As much as
we are aware, the study involving the combination of
magnesium and citrate ions in the turbidimetrical model
at physiological concentrations is new. The present
work is part of a wider research group project that
includes in perspective in vivo experiments and clinical
field tests.
Asia-Pacific Journal of Chemical Engineering
Sl
426
EXPERIMENTAL METHODS
The crystallization of calcium oxalate and the effect of
the inhibitors on the crystallization kinetics were studied
by turbidimetry[7] at 620 nm, in aqueous solution with
the help of a JASCO V-530 computer-controlled spectrophotometer. The solution was thermostated at 37 ◦ C
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
Ti
Nucleation
Growth
Time (sec)
Figure 1. Kinetic curve with three crystallization
phases.
Asia-Pac. J. Chem. Eng. 2008; 3: 425–431
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
OPTIMIZED EXPERIMENTAL DESIGN FOR INHIBITION OF CALCIUM OXALATE
the citrate and magnesium ions at physiological concentrations as well as their combinations. The inhibition
percentage was calculated using the relation:
[I % = (1 − PAI /PSI )/100]
(1)
where PSI is the turbidimetrical slope without inhibitor
and PAI is the slope with inhibitor.
Experimental design and optimization of
parameters
The planning of experiments (experiment design)
enables the acquisition of a maximum of information
within a minimum of trials. For a plane of two factors, nine experiments would be necessary. The nucleus
plane noted α is equal to 1.[21] The experimental conditions required by this design are defined in Table 1.
Independent variables, experimental range, and levels
for the combinations citrate–magnesium ions are given
in Table 2. A second-order model is selected in order
to predict each response (I % CMcal ) in all experimental
regions:[19 – 22]
(2)
The results of the experimental design were studied
and interpreted using the statistical software Statistica
to estimate the response of the dependent variable
I % CMcal . The tests of Student and Fischer were used
to determine the significance of the parameters of the
regression equations.
RESULTS AND DISCUSSION
Crystallization without inhibitor
Under conditions close to those of urine (ionic concentration, temperature, and ionic strength), the turbidimetrical crystallization model without seeding enabled
Table 1. Planning matrix.
Run No.
1
2
3
4
5
6
7
8
9
Range and level
Independent
variable
Citrate ions
concentration CI
(mM)
Magnesium ions
concentration Mg
(mM)
−α
−1
0
1
α
0.1
0.1
0.55
1
1
2
2
3
4
4
the monitoring of the different crystallization steps and
the determination of the kinetic parameters, especially
the latent or induction time Ti and the turbidimetrical
slope. The latter is found to be 0.19032 Abs/min and
the induction time Ti is found to be 0.22 min (Fig. 2(a)).
Under our work conditions, we obtained the monohydrated calcium oxalate that was identified using the
FT-IR technique.
Crystallization with inhibitor
I % CMcal = a0 + a1 x1 + a2 x2 + a12 x1 x2
+ a11 x1 2 + a22 x2 2
Table 2. Experimental range and level of independent
variables for citrate–magnesium ions.
Factor 1
Factor 2
Y
1
1
−1
−1
α
−α
0
0
0
1
−1
−1
1
0
0
α
−α
0
y1
y2
y3
y4
y5
y6
y7
y8
y9
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
Citrate ions
The citrate ions were tested at physiological concentrations ranging from 0.1 to 2.5 mM. Figure 2 shows the
kinetic curves of crystallization of calcium oxalate in
the presence of citrate ions. The turbidimetrical model
shows an inhibition reaching a maximum of 93.86%
for a concentration of 2.5 mM and an induction time
ranging from 0.22 to 4.7 min.
Our experimental results are reported in Table 3. It
could be noted that the inhibition rate and the induction
time increase with increase in the concentration of
citrate ions.
Magnesium ions
The magnesium ions have been tested at physiological
concentration ranging from 2 to 7 mM. Figure 3 shows
the inhibition curves as a function of crystallization
time. We notice in this figure that the induction time is
short for curves (a) to (e), whereas it is long for curves
(f) and (g). This indicates that the inhibition effect on
the nucleation starts from concentrations above 5 mM.
This is interesting, since the nucleation does not occur at
all and hence the advantage of increasing the induction
time.
From the concentration of 5 mM, we found an inhibition rate greater than 50%. The induction time indicates
that the nucleation is delayed by magnesium ions from
0.22 to 1.96 min. Our experimental results are reported
in Table 4.
The magnesium ion remains the most studied
inhibitor[4 – 7] and is considered as chelated by oxalate
Asia-Pac. J. Chem. Eng. 2008; 3: 425–431
DOI: 10.1002/apj
427
428
A. DRIOUCH ET AL.
Asia-Pacific Journal of Chemical Engineering
Figure 2. Kinetic curves of the effect of citrate ions concentration
on the crystallization of calcium oxalate. Without inhibitor (a); with
inhibitor: (b) 0.1 mM, (c) 0.25 mM, (d) 0.5 mM, (e) 1 mM, (f) 1.5 mM,
(g) 2 mM, (h) 2.5 mM.
Table 3. The evolution of the inhibition rate and the induction time according to citrate ions concentration.
CI (mM)
Inhibition rate (%)
Induction time (min)
0.1
0.25
0.5
1
1.5
2
2.5
13.4
0.23
30.06
0.23
44.88
0.36
64.09
0.86
82.87
2.3
89.01
3.1
93.86
4.73
ions. It competes with calcium and forms soluble
complexes whose main effect is a decrease of the oversaturation of calcium oxalate.[23] The inhibition effect of
magnesium ions was studied in numerous works.[5,24 – 26]
They found that these ions act only on two phases of the
crystallization of calcium oxalate: nucleation and crystalline growth.[24 – 26] The results of our study show that
the maximum induction time is 1.96 min for an inhibition rate of 71.57%, meaning less effect of citrate ions
on the two crystalline phases.
Combination effect of citrate and magnesium
ions
The same protocol was applied to study the combination
of the two inhibitors. Calcium oxalate crystallization
in the presence of a combination of citrate ions and
Mg ions was tested at physiological concentrations
following the pre-established planning matrix. Table 5
compiles the results of the crystallization evolution.
The results show that whatever the concentrations
of the combined citrate and magnesium ions, the
inhibition obtained is greater than the one obtained
in presence of the same inhibitor alone. It must be
noted that the maximum inhibition rate was obtained
for low concentration with respect to the effect of
the inhibitor alone. That is why certain concentrations
were not tested. (Mg = 5, 6, and 7 mM; CI = 1.5,
2, and 2.5 mM). Figure 4 shows the kinetic curves
of one combination (citrate ions at 1 mM; Mg ions
concentration from 2, 3, and 4 mM). The observed
Figure 3. Kinetic curves of the effect of magnesium concentration
on the crystallization of calcium oxalate. Without inhibition (a); with
inhibitor: (b) 2 mM, (c) 3 mM, (d) 4 mM, (e) 5 mM, (f) 6 mM, (g) 7 mM.
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2008; 3: 425–431
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
OPTIMIZED EXPERIMENTAL DESIGN FOR INHIBITION OF CALCIUM OXALATE
large value of the Fisher-test (FStatistics = 257.18 >
Ftabulated = 9.01) indicates that most of the variation
in the response can be explained by the regression
model equation. The predicted values (using the model
Eqn (3)) were compared with the experimental results
and are shown in Table 5. Figure 5 presents the distribution of the calculated relative errors. For instance,
relative errors are always below 4.3% (with an average of 1.36%). When the analysis of the experiment
is complete, one must verify that the predictions are
good. These are called confirmations runs (see Table 5,
run No. 10–14).
Urinary inhibition remains a complex process despite
the numerous works on it. The study of the inhibition
of different substances under conditions close to those
in urine (concentration of calcium and oxalate, ionic
force, temperature) showed a nonlinear relationship
between inhibition and the molecular concentration
when tested alone. The citrate ions were also inhibitors
studied for years; they act on the nucleation, growth
and crystalline agglomeration.[7,27 – 31] The inhibition
effect is essentially due to the complexation of calcium
by citrate ions, which lowers the amount of calcium
inhibition is higher than the one obtained using the
inhibitors individually whatever the concentrations of
citrate and magnesium ions.
The coefficients of the quadratic model in the polynomial expression were then calculated by multiple
regression analysis using Statistica software. It must
be stressed that such coefficients represent the weight
of each variable by itself, the weight of the quadratic
effect, and the weight of the first-order interactions
between the variables. The regression coefficient, t
(Student-test) and P -value for all the linear (x1 , x2 ),
quadratic (x1 2 , x2 2 ), and interaction effect (x1 .x2 ) of the
parameters are given in Table 6. The regression equation for the inhibition rate with a high value of the
correlation coefficient (R 2 = 0.9986) is as follows:
I % CMcal = 72.023 + 20.293x1 + 9.355x2
− 2.955x1 x2 − 8.94x1 2 − 0.785x2 2 (3)
It was observed that the coefficients for the linear effect of citrate concentration (x1 ), magnesium
concentration (x2 ) (p = 0.00007 and 0.0007 respectively), and the quadratic effects of concentration of
citrate (x1 2 ) (p = 0.004) were highly significant. The
Table 6. Estimated regression coefficient and corresponding t- and P-value.
Table 4. The evolution of the inhibition rate and
the induction time according to magnesium ions
concentration.
Mg (mM)
2
3
4
5
6
7
Inhibition
rate (%)
Induction
time
(min)
14.48
30.90
37.41
55.10
67.73
71.57
0.5
0.53
0.73
0.96
1.86
1.96
Term
Ord.Orig
x1
x2
x1 2
x2 2
x1 .x2
Coefficient
Standard
deviation
t
P
a0 = 72.023
a1 = 20.293
a2 = 9.355
a11 = −8.940
a22 = −0.785
a12 = −2.955
1.174
0.643
0.643
1.114
0.788
1.114
61.78
31.55
14.54
−8.02
−3.75
−0.70
0.000009
0.000070
0.000700
0.004000
0.030000
0.500000
Table 5. Codified and experimental values and results of the experimental design.
Codified values
Run No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Experimental values
CI
Mg
CI (mM)
Mg (mM)
Induction
time (min)
1
1
−1
−1
α
−α
0
0
0
1
−1
−1
1
0
0
α
−α
0
1.00
1.00
0.10
0.10
1.00
0.10
0.55
0.55
0.55
0.50
0.50
0.50
0.25
0.25
4
2
2
4
3
3
4
2
3
2
3
4
3
4
2.50
2.16
0.60
0.83
2.46
0.64
1.73
1.22
1.53
0.83
1.66
1.94
0.71
0.95
Inhibition rate (%)
I % CMexp
I(%) CMcal
90.40
77.53
29.48
54.17
82.20
44.72
80.90
62.33
72.84
60.06
75.54
81.36
62.80
73.58
89.51
76.71
30.21
54.84
83.90
43.31
81.11
62.40
72.54
59.71
70.18
79.08
55.04
65.58
CI, citrate ions concentration; Mg, Mg2+ ions concentration; I % CMexp , experimental rate of inhibition; I % CMcal , rate of inhibition calculated
according to model of Eqn (3).
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2008; 3: 425–431
DOI: 10.1002/apj
429
A. DRIOUCH ET AL.
Asia-Pacific Journal of Chemical Engineering
Figure 4. Kinetic curves of the effect of mixing citric acid with magnesium
ions on the crystallization of calcium oxalate. (a) Without inhibitor;
(b) CI = 1 mM; (c) Run No. 2; (d) Run No. 5; (e) Run No. 1. This figure
is available in colour online at www.apjChemEng.com.
5
Relative Error [ %]
430
4.3
4
3
2
1.6
1.7
1.4
1.1
0.7
1
0.4
0.3
0.7
0
1
2
3
4
5
N° Run
6
7
8
9
Figure 5. Distribution of the calculated relative errors. This
figure is available in colour online at www.apjChemEng.com.
available to react with oxalate ions. Furthermore, other
studies proved that citrate ions are capable, at least
in vitro, of getting fixed to the crystal surface, to reduce
their size, and to modify their shape.[30,32 – 34]
According to Antinozzi et al .,[34] citrate ions are
capable of getting fixed to the crystal surface of
monohydrated calcium oxalate and to act as a real
surface inhibitor. On the basis of results obtained using
in vitro crystallization model, Kok et al .[35] studied both
the growth and the agglomeration of calcium oxalate
crystals. They concluded that citrate ions have a strong
activity against the agglomeration of crystals. These
results have been contested by Hess et al .[36] who
did not observe any significant turbidimetrical effect
due to citrate ions on this crystallization phase in a
turbidimetrical model specifically adapted to the study
of agglomeration.[36] Our results confirm the works
of Antinozzi et al . on the effect of citrate ions on
the nucleation phase and the crystalline growth, since
we recorded an induction time of 4.7 min instead of
0.22 min without inhibitor and a maximum inhibition
rate of 93.86%.
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
For a combination of citrate–magnesium ions (Run
No. 1; Table 5), the obtained inhibition rate of 90.4%
is clearly greater than the one due to the effect of
citrate ions alone (64.09% for CI = 1 mM) and the one
due to magnesium ions alone (37.41% for Mg2+ =
4 mM). If we vary the concentration of one inhibitor
and keep the other inhibitor concentration constant, the
inhibition effect is higher than when the inhibitor is
alone, e.g. Run No. 2 (I % CMexp = 77.53%), Run No.5
(I % CMexp = 82.2%), and Run No. 1 (I % CMexp =
90.4%) for Mg2+ = 2, 3 and 4 mM which was 14.48,
30.90, and 37.41%, respectively.
The combination of citrate ions with magnesium ions
at different concentrations showed that the induction
times were higher than the induction time of each
inhibitor alone. Thus, the citrate ions alone at a concentration of 1 mM gave a time of 0.86 min, whereas when
they are combined with magnesium ions the nucleation is delayed by 2.16 min; 2.46 min, and 2.5 min
for concentrations 2, 3, and 4 mM of magnesium ions
respectively.
Figure 6 shows the response surface modeling in
a three-dimensional representation of the inhibition
rate as a function of citrate and magnesium ions
concentration. Using Excel software, the total inhibition
rate (100%) has been obtained by extrapolation and the
corresponding concentration values are: CI = 0.65 mM
and Mg = 8.55 mM.
CONCLUSION
The study of the inhibition of calcium oxalate by citrate
and magnesium ions reveals the following:
1. The experimental turbidimetrical model adopted in
this work appears simple to manoeuvre, has a good
Asia-Pac. J. Chem. Eng. 2008; 3: 425–431
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
OPTIMIZED EXPERIMENTAL DESIGN FOR INHIBITION OF CALCIUM OXALATE
Inhibition rate
100
80
60
40
4.2
1.2
3.4
M
g
0.8
2.8
io
ns
0.4 Citrate ions
1.8
00
Figure 6. Response surface plot of the inhibition
rate (%) showing the interactive effect of citrate and
magnesium ions concentration.
reproducibility, and offers the possibility to follow
the crystallization process continuously.
2. The combination of inhibitors in comparison with
the inhibitors used alone leads to a delay in the
nucleation and a higher inhibition rate.
3. The use of experiments planning enabled to develop
a mathematical model consistent with the experimental results with a minimum of trials.
4. The combination of inhibitors and the use of an
experimental design allowed determining the best
citrate and magnesium concentrations for a maximum inhibition.
Acknowledgements
This work has been supported by CMEP program TASSILI # 03MD595 in a joint Franco-Algerian research
project.
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 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2008; 3: 425–431
DOI: 10.1002/apj
431
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