248 Vol. 63, No. 4

© 2015 The Pharmaceutical Society of Japan

Chem. Pharm. Bull. 63, 248–254 (2015)

Regular Article

Prediction of the Stability of Meropenem in Intravenous Mixtures

Yuko Takasu, Miyako Yoshida, Mio Tange, Keiichi Asahara, and Takahiro Uchida*School of Pharmaceutical Science, Mukogawa Women’s University; 11–68 Koshien 9-Bancho, Nishinomiya 663–8179, Japan.Received July 15, 2014; accepted February 2, 2015

The purpose of this study was to predict the stability of meropenem in a mixed infusion. The hydrolysis of meropenem in aqueous solution was found to be accelerated by pH, and by increasing concentrations of sodium bisulfite (SBS) and L-cysteine. Equations were derived for the degradation rate constants (kobs) of pH, SBS and L-cysteine, and fractional rate constants were estimated by the nonlinear least-squares method (quasi-Newton method using the solver in Microsoft Excel) at 25°C. The activation energy (Ea) and frequency factor (A) were calculated using the Arrhenius equation. The pH of the mixed infusion was estimated using the characteristic pH curve. From these results, an equation was derived giving the residual ratio (%) of meropenem at any time after mixing an infusion containing SBS and/or L-cysteine at any temperature, and in the pH range 4.0–10.0. A high correlation was shown to exist between the estimated and determined residual ratios (%).

Key words stability prediction; meropenem; pH; sodium bisulfite (SBS); L-cysteine; degradation rate constant

Carbapenems are the most potent β-lactam antibiotics and were  first  developed  in  the  1980s  to  enhance  resistance  to β-lactamases. The early carbapenems were not very hydro-lytically stable, however, limiting drug administration to con-trolled intravenous infusions. In the search for a more stable compound with better  toxicity profile,  the basic nuclear struc-ture was maintained and a dimethyl carbamoyl-pyrrolidinyl-thio group was added as a weakly basic C-2 side-chain. This resulted in a reduction of central toxicity and nephrotoxicity, while maintaining anti-pseudomonal activity. In addition, the improvement of stability (DHP-I stability) in vivo and the improvement of activity against Haemophilus influenzae, etc., were achieved by introducing 1-β-methyl group into the car-bapenem frame, resulting in the creation of meropenem. The improvement in nephrotoxicity was the key advance in allow-ing the global development of meropenem as a single agent.1)

Meropenem is a broad-spectrum carbapenem, active against several clinically relevant Gram-positive and Gram-negative aerobes, anaerobic bacteria and Pseudomonas aeruginosa. The bactericidal activity of meropenem results from the inhibition of cell wall synthesis through the inactivation of penicillin-binding proteins.Sodium  bisulfite  (SBS),  used  as  a  stabilizer  in  injectable 

preparations, is known to degrade various drugs including thiamine,2) epinephrine,3) gabexate mesilate,4) nafamostat me-silate,5) urokinase,6) morphine7)  and  fluorouracil.8) However, there are no reports of detailed kinetic studies on the degrada-tion of meropenem in the presence of SBS.

The prediction of the stability of a drug in an intravenous admixture (mixed infusion) is important for accurate and safe drug administration. Generally, the stability of a drug in  a mixed  infusion can be predicted  from  the pH profile  and Arrhenius equation of the degradation rate constants, if the temperature and pH of the test solution are known. Although meropenem is generally administered as an infusion in saline, in some cases it may be mixed with other substances, such as amino acids.9)

A method for predicting the pH of mixed infusions was developed in order to be able to evaluate the compatibility of

the components of a mixed infusion. Employing the charac-teristic pH curve (PHC curve; a kind of pH titration curve),10) a method for pH estimation has been reported by Hirouchi et al.11) based on computer simulations. However, the theoreti-cal equations described by Hirouchi et al. were derived from model preparations for  injection and did not  take  into account the  influence  of  dilution  with  titrant.  The  PHC  curve  of  a mixed  infusion  could  not  therefore  be  fitted  to  the  equations of Hirouchi et al., but must be derived from observed values, a painstaking and time-consuming exercise. In the present study, a simple, theoretical, pH estimation method for mixed infusions  was  derived,  using  a  fitted  PHC  curve  and  curve simulation by a computer (using Microsoft Excel).

In addition, we examined the degradation of meropenem due  to  catalytic  hydrolysis  by  SBS  and  L-cysteine. From the results, we derived an equation to predict the residual ratio (%) of meropenem at any time after mixing, on the basis of the simulated pH of the mixed infusion using the PHC curve, SBS and L-cysteine concentrations, and the temperature.

ExperimentalMaterials Meropenem was supplied by Wako Pure

Chemical  Industries,  Ltd., Osaka,  Japan.  SBS,  L-cysteine and other reagents were special grade commercial products. As buffer solutions, 0.05 M acetate buffer (pH 4.0–5.0), 0.05 M phosphate buffer (pH 6.0–8.0) and 0.05 M carbonate buffer (pH  9.0–10.0) were  adjusted  to  an  ionic  strength  of  0.15 with sodium chloride. Meropen® (Dainippon Sumitomo Pharma Co., Ltd., Osaka, Japan), AMINOLEBAN® Injection, Fructlact Injection,  and AMINOFLUID®  Injection  (Otsuka Pharmaceu-tical Factory, Inc., Tokushima, Japan), FULCALIQ® 2 and AMIGRAND® (Terumo Co., Ltd., Tokyo, Japan) were used as injectable preparations.

Determination of Meropenem Meropenem concentration was measured by high-performance liquid chromatography (HPLC). Meropenem concentrations were determined 0, 1, 2, 3 and 4 h after mixing with SBS or L-cysteine. Each degrada-tion rate constant (kobs) was calculated from the slope of the relationship between the log residual ratio of meropenem (%)

* To whom correspondence should be addressed.  e-mail: takahiro@mukogawa-u.ac.jp

Vol. 63, No. 4 (2015)  249Chem. Pharm. Bull.

and time after mixing.Equipment  A  Shimadzu  LC-10AT  VP  high-performance  liquid  chro-

matograph, a Shimadzu SPD-10A VP UV-VIS detector,  and a Shimadzu C-R7A plus chromate pack were used.

Measurement Conditions  Preliminary  studies  confirmed  that  optimized  chromato-

graphic conditions were as described in the Pharmacopoiea.12) Column, CAPCELL PAK C18 HPLC packed column type MG 5 µm (4.6 mm i.d.×150 mm);  flow  rate  1.0 mL/min;  column oven  set  at  40°C;  injection  volume  20 µL; detection wave-length 300 nm. The isocratic mobile phase was a mixture of 10 mM sodium phosphate buffer (pH 7.4) and acetonitrile (100 : 10, v/v).

Estimation of the pH of the Mixed Infusion Observed values from pH titration were used to plot the PHC curve of the  mixed  infusion.  Based  on  the  general  equation  for  PHC curves,  the  PHC  curve  of  each  preparation  was  fitted  from the observed values, from which the pH of the mixed infusion could be estimated.

pH Titration  Various commercial  injections were diluted  to 500 mL with 

distilled water and titrated against 0.5 M hydrochloric acid and sodium hydroxide. Similarly, 500 mL aliquots of various com-mercial infusions were titrated against 0.5 M hydrochloric acid and sodium hydroxide.Fitting the PHC Curve of the Injection Preparation  Injectable  drugs  are  generally  classified  as  weak  acids, 

weak bases or salts. Taking a preparation of weak acid, with a total concentration of Ca1,  the ionization of the weak acid may be represented as: HA→H++A−, where HA  is  the non-ionized acid, A−  is  the ionized acid and H+ is hydrogen ion. Applying the law of mass action, material balance and charge balance to the equilibrium of this weak acid, the general equation of the PHC curve for a preparation can be expressed as in Eq. 1. Similarly, taking a preparation containing two kinds of weak acids of which the total concentrations are Ca1 and Ca2, the general equation for the preparation can be expressed as in Eq. 2. If a preparation contains n kinds of weak acids, the general equation of the PHC curve for the preparation can be expressed as in Eq. 3.

a1 1 wt

1[H ]

[H ] [H ]C K K

C CK

⋅++ += + + ++

(Eq. 1)

a1 1 a2 2 wt

1 2[H ]

[H ] [H ] [H ]C K C K K

C CK K

⋅ ⋅++ + += + + + ++ +

(Eq. 2)

a wt

1

[H ][H ] [H ]

ni i

ii

C K KC C

K⋅

++ +

=

= + + ++

(Eq. 3)

In order to improve solubility, preparations of weak bases often contain a strong acid as an excipient. The preparation of the weak base can therefore be assumed to be a preparation of  a  conjugated weak  acid. Accordingly,  the  general  equation of the PHC curve for a preparation of a weak base can be ex-pressed as in Eq. 1, and the PHC curve of the preparation of n kinds of weak bases can be represented as in Eq. 3.The general equation of the PHC curve for injectable prepa-

rations can therefore, for practical purposes, be represented as Eqs.  1  to  3,  and  the  influence  of  dilution with  titrants  can  be corrected by Eqs. 4 to 6.

a 0a

0 t

nn

C VC

V V′ ⋅

=+

(Eq. 4)

0

0 t

C VC

V V′ ⋅

=+

(Eq. 5)

t tt

0 t

C VC

V V′ ⋅

=+

(Eq. 6)

where Ca1, Ca2, Ca3, . . ., Can are the concentrations of weak acids 1, 2, 3, . . ., n in the sample solution; K1, K2, K3, . . ., Kn are the dissociation constants of the weak acids 1, 2, 3, . . ., n, respectively; C is the concentration of the strong acid (repre-sented as a positive value) or the base (negative value) present as an excipient in the sample solution; Ct is the concentration of HCl (represented as a positive value) or NaOH (negative value), added as the titrant to the sample solution; C′an is the initial concentration of the acid (positive value) or base (nega-tive value) in the sample solution, respectively; C′t is the con-centration of HCl or NaOH added to the sample solution as titrant; V0 is the initial volume of the titration sample (500 mL) and Vt is the volume of the titrant added to the sample. [H+] is the hydrogen ion concentration and Kw is the ion product of water. For practical purposes, [H+] and Kw at 25°C were regarded as 10−pH obs and 1.0×10−14, respectively.

The parameters of the general equations for the PHC curve (i.e., concentrations and pKs of weak acids and concentra-tions  of  strong  acids  or  bases)  were  fitted  with  some  of  the observed values. The parameters of the PHC curve were then obtained by solving the simultaneous equation Eq. 2. Next, the parameters other than pK  were  fitted  by  the  nonlinear  least-squares method (simplex method). The PHC curves simulated by these parameters and the observed titration values were drawn  graphically.  If  the  PHC  curve  only  partially  fitted,  the parameters of the PHC curve were modified by the simultane-ous equation Eq. 1 and the simplex methods.

Simulation of the PHC Curve of Mixed Infusions The effect of dilution was an important factor when the

parameters  of  the  PHC  curve were  fitted  to  the  titration  data. Nevertheless, once these parameters had been obtained, the PHC curves of the preparations could be treated simply ac-cording to Eqs. 1 to 3, without Eqs. 4 to 6. Therefore, assum-ing  the  general  equations  of  the  PHC  curves  for  an  injection, an infusion, a mixed infusion of these preparations and water, to  be  Eqs.  7  to  10,  respectively,  the  relationship  Eq.  9=Eq. 7+Eq. 8−Eq. 10 held at a constant ion concentration. Each of the terms except CtA, CtB, CtW and CtM could then be eliminat-ed from Eqs. 7 to 10 at a constant hydrogen ion concentration, to obtain Eq. 11. Since each PHC curve represents the relation between the pH and the volume of the titrants (i.e., CtM), the PHC curves of mixed infusions could be simulated by apply-ing Eq. 11 at all pHs. If n kinds of preparations were mixed, the PHC curve of the mixed infusion could be simulated from the PHC curves of n−1 kinds of preparations and another ad-ditive injection. 

aA A wA tA

A[H ]

[H ] [H ]C K K

C CK

⋅++ += + + ++

(Eq. 7)

aB B wB tB

B[H ]

[H ] [H ]C K K

C CK

⋅++ += + + ++

(Eq. 8)

250 Vol. 63, No. 4 (2015)Chem. Pharm. Bull.

aA A aB B wA B tM

A B[H ]

[H ] [H ] [H ]⋅ ⋅C K C K K

C C CK K

++ + += + + + + ++ +

 (Eq. 9)

wtW[H ]

[H ]K

C++= + (Eq. 10)

tM tA tB tWC C C C−= + (Eq. 11)

Revision of the PHC Curve for Increased Infusion Volumes The  influence  of  dilution with  additive  injections  is  not  in-

cluded in Eq. 11. If the infusion volume is increased with ad-ditive  injections,  the  PHC  curves  of  the mixed  infusion must be corrected by Eq. 12. This equation was obtained following the same process as for Eq. 11.

tC t tW( 1)C r C r C⋅ − − ⋅= (Eq. 12)

where r is the concentration ratio (initial infusion volume (500 mL)/increased  infusion volume with additives), CtC is the corrected concentration of HCl or NaOH (added as the titrant) in the mixed infusion at a constant pH, Ct is the concentration of HCl or NaOH in a 500 mL aliquot of the mixed infusion at the same pH, and CtW is the concentration of HCl or NaOH in a 500 mL aliquot of distilled water at the same pH. At Ct and CtW,  the  influence of dilution with additive  injections was omitted.

Simulation of the PHC Curve of a Mixed Infusion According to Eqs. 11 and 12, the PHC curve of the mixed

infusion can be simulated from the PHC curves of each con-stituent preparation.

Estimated pH of a Mixed Infusion  The  pHs  of  the  injections  (diluted  to  500 mL with  distilled 

water) or infusions are represented by the pHs at the origin of the PHC curve of the preparations. The estimated pH of the mixed infusion was thus obtained as the pH at the origin of the simulated PHC curve.

Kinetic Procedures The stability of the meropenem solu-tion (500 µg/mL)  buffered  at  pH  4.0–10.0  in  the  presence  of SBS  (0,  0.1,  0.5  and  1.0 mM) or L-cysteine (0, 0.25, 0.5, 1.0 and  2.0 mg/mL)  was  examined  at  4,  25  and  40°C.  The  sta-bility of Meropen®  in  AMINOLEBAN®  Injection,  Fructlact Injection,  AMINOFLUID®  Injection,  FULCALIQ® 2 and AMIGRAND® was examined at 4, 25 or 40°C.

Results and DiscussionFactors Affecting the Stability of Meropenem Degradation of Meropenem at pH 4.0–10.0 The degradation of mepenem, 500 µg/mL,  was  studied  at 

25°C. The pH-profile of mepenem degradation in the pH range 4.0–10.0 is shown in Fig. 1, where the rate constants are ex-pressed  on  a  logarithmic  scale.  It was  concluded  that  specific hydrogen-ion-catalyzed  degradation  occurred  at  pH  4.0–5.0, water-catalyzed degradation at pH 5.0–8.0, and hydroxide-ion-catalyzed degradation at pH 8.0–10.0.As  the  data  plot  in  Fig.  1  seemed  to  display  specific  acid–

base catalysis kinetics, Eq. 13 was used as the model kinetic equation for the effect of pH on k0.

20 H O OH H[OH ] [H ]k k k k−−⋅ ⋅+

+= + + (Eq. 13)

where kH+ and kOH− are the second-order rate constants for the

hydrogen-ion-catalyzed  degradation  and  the  hydroxide-ion-catalyzed  degradation  reaction,  respectively,  and  kH2O is the first-order  rate  constant  for  the  spontaneous  water-catalyzed degradation reaction.

At 25°C, the residual meropenem concentration as de-termined by HPLC, and [H+], [OH−] calculated from pH, were assigned to Eq. 13. The fractional rate constants, kH2O, kOH−, and kH+ were estimated by the nonlinear least-squares method (quasi-Newton method using the solver in Micro-soft Excel) and determined to be: kH2O, 1.15×10−3 h−1; kOH−, 3.00×103 M−1 h−1 and kH+, 1.36×102 M−1 h−1.The influence of temperature was also investigated. The Ar-

rhenius equation (Eq. 14) shows the relationship between the degradation rate constant and the absolute temperature.

aobs

1log log

2.303E

k AR T− ⋅= + (Eq. 14)

where kobs is the degradation rate constant, Ea is the activation energy, R  is  the  gas  constant  (1.987 cal mol−1), T is absolute

Fig.  1.  pH  Profile  of  the  Degradation  of  Meropenem  at  25°C  and μ=0.15

Initial concentration of meropenem 500 µg/mL.

Fig. 2. Arrhenius-Type Relationship between the Degradation Rate Constant of Meropenem and the Temperature (4, 25 and 40°C) at pH 4.0–10.0 and μ=0.15

Initial concentration of meropenem 500 µg/mL. ◇ pH 4.0, * pH 5.0, ◆ pH 6.0, × pH 7.0, ▲ pH 8.0, ○ pH 9.0, ■ pH 10.0.

Vol. 63, No. 4 (2015) 251Chem. Pharm. Bull.

temperature (K), and A is the frequency factor. As shown in Fig. 2, Arrhenius plots revealed good linearity in the range pH 4.0–10.0, with Ea values for mepenem of 10.7 kcal/mol (pH 4.0),  16.1 kcal/mol  (pH  5.0),  15.9 kcal/mol  (pH  6.0),  12.9 kcal/mol  (pH  7.0),  14.8 kcal/mol  (pH  8.0),  20.6 kcal/mol  (pH  9.0) and 16.7 kcal/mol (pH 10.0).Degradation Rate of Meropenem in the Presence of SBS   SBS,  present  as  a  stabilizer  in  injectable  preparations,  is 

known to degrade β-lactam antibiotics.13) However, the mecha-nism by which the SBS concentration affects meropenem deg-radation has not yet been elucidated. Therefore, kinetic experi-ments were performed, and the residual meropenem concen-tration measured by HPLC. The degradation of meropenem, at an initial concentration of 500 µg/mL,  by  SBS  at  various concentrations was evaluated at 25°C and pH 4.0–10.0. The degradation rate constant of meropenem in the presence of SBS  (kobs) was measured at 25°C. A linear relationship was observed between time and log residual ratio (%) at pH 6.0 (Fig. 3), indicating that the degradation of meropenem fol-lowed  pseudo-first-order  kinetics.  This  was  also  the  case  at other  pHs.  The  apparent  first-order  rate  constants  were  ob-tained from the slopes of the semi-log plots. The slope of the line increased with increasing SBS concentration.

The rate constant for the catalytic hydrolysis of meropenem by SBS (kSBS) is obtained from Eq. 15.

obs2.303

log100r

k t − ⋅

= (Eq. 15)

where kobs  is  the  pseudo-first-order  reaction  rate  constant,  t is time after mixing, and r is the residual ratio (%). Typical plots for  SBS  concentration  versus degradation rate constants of meropenem (pH 6.0, 25°C) yielded a straight line as shown in Fig. 4. The degradation rate of meropenem was proportional to  the  total  concentration  of  SBS  ([SBS]total). Therefore, the rate  constant  of meropenem  in  the  presence  of SBS  (kobs) can be represented by Eq. 16.

obs 0 SBS total[SBS]k k k= + × (Eq. 16)

where SBS concentration ([SBS]total) is represented by Eq. 17.4)

2total 2 3 3 3[SBS] [H SO ] HSO ] [SO ]− −= +[ + (Eq. 17)

Based  on  the  dissociation  constant  of  SBS  at  25°C (100 kPa), kSBS1=1.72×10−2 (pKSBS1=1.8) and kSBS2=6.24×10−8 (pKSBS2=7.2).14)  SBS  in  this  pH  range  (pH 4.0–10.0) was  con-sidered to be present as bisulfate ions (HSO3

−) and sulfite  ions (SO3

2−), kSBS×[SBS]total can therefore be represented as Eq. 18:

23 3

2SBS total 3 3SO HSO[SBS] [SO ] [HSO ]k k k− −

− −× = × + × (Eq. 18)

and  the  dissociation  constants  of  SBS  (KSBS1, KSBS2) can be represented by Eqs. 19 and 20. 

3SBS1

2 3

[H ] [HSO ][H SO ]

K−+ ×

=   (Eq. 19)

23

SBS23

[H ] [SO ][HSO ]

K−

−

+ ×= (Eq. 20)

From Eqs. 16 to 20, kSBS can be represented as shown in Eq. 21.

2

3 3SBS1 SBS1 SBS2HSO SOSBS 2

SBS1 SBS1 SBS2

[H ][H ] [H ]

k K k K Kk

K K K− −⋅ ⋅ ⋅ ⋅

⋅ ⋅

+

+ +

+=

+ + (Eq. 21)

where kHSO3− is the second order degradation constant of

HSO3−, and kSO3

2− is the second order degradation constant of SO3

2−. The fractional rate constants, kHSO3− and kSO3

2− were estimated by nonlinear least-squares method (quasi-Newton method using the solver in Microsoft Excel), and values of kHSO3

− (2.78 M−1 h−1) and kSO32− (2.75 M−1 h−1) were obtained.

These  results  show  that  the  accelerating  effect  of  sulfite  ions on the hydrolysis of meropenem was the same as that of bisul-fate ions at pH 4.0–10.0 and 25°C.The influence of temperature on the degradation of merope-

nem by SBS was also investigated. As shown in Fig. 5, Arrhe-nius plots revealed good linearity between SBS concentrations of 0, 0.1, 0.5 and 1.0 mM at pH 6.0, and the values obtained for the Ea  of  meropenem,15.9 kcal/mol,  15.7 kcal/mol,  16.5 kcal/

Fig. 3. Pseudo-First-Order Plot for Degradation of Meropenem in the Presence of SBS  (0,  0.1,  0.5  and 1.0 mM) in 0.05 M Phosphate Buffer  (pH 6.0, μ=0.15) at 25°C

Initial concentration of meropenem 500 µg/mL. ◇  SBS  0 mM, ○  SBS  0.1 mM, △ SBS 0.5 mM, □ SBS 1.0 mM.

Fig.  4.  Relationship  between  the  Total  Concentration  of  SBS  and  the Degradation Rate Constant (kobs) of Meropenem in 0.05 M Phosphate Buffer (pH 6.0, μ=0.15) at 25°C

Initial concentration of meropenem 500 µg/mL.

252 Vol. 63, No. 4 (2015)Chem. Pharm. Bull.

mol, and 14.7 kcal/mol, respectively.Degradation Rate of Meropenem in the Presence of L-

Cysteine L-Cysteine is often added to infusions for purposes of

nutrition. It may be present as the free amino acid or as N-acetylcysteine, which can be degraded by hydrolysis in the body. L-Cysteine is known to degrade carbapenem antibiotics, but the effect of the L-cysteine concentration on the rate of degradation has not been elucidated. Kinetic experiments were therefore carried out, with the residual meropenem concentra-tions measured by HPLC. The degradation of meropenem at an initial concentration of 500 µg/mL  by  various  concentra-tions of L-cysteine or N-acetylcysteine was evaluated at 25°C and pH 4.0, 6.0 and 8.0. The degradation rate constant of meropenem in the presence of L-cysteine (kcys) was measured at 25°C. Typical plots for L-cysteine concentration versus deg-radation rate constants of meropenem yielded a straight line as shown in Fig. 6. N-Acetylcysteine concentrations were con-verted to L-cysteine concentrations. N-Acetylcysteine itself ap-peared to have little effect on the degradation rate constants of meropenem. The degradation rate of meropenem was directly proportional to the total concentration of L-cysteine ([cys]total). Based  on  the  dissociation  constant  of  L-cysteine at 25°C, kcys1=1.20×10−2 (pKcys1=1.92),  kcys2=4.68×10−9 (pKcys2=8.33) and kcys3=1.66×10−11 (pKcys3=10.78),15) the degradation con-stant of meropenem in the presence of cysteine (kobs) can be represented as Eq. 22, [cys]total as Eq. 23 and kcys×[cys]total as Eq. 24.

obs 0 cys total[cys]k k k= + × (Eq. 22)

total 3 3

3 2

[cys] [COOH NH SH] [COO NH SH][COO NH S ] [COO NH S ]

−

− − − −

⋅ ⋅ ⋅ ⋅⋅ ⋅ ⋅ ⋅

+ +

+

= +

+ + (Eq. 23)

3

3

2

cys total

2cys1COO NH SH

cys1 cys2COO NH S

cys1 cys2 cys3COO NH Stotal3 2

cys1 cys1 cys2

cys1 cys2 cys3

[cys]

( [H ][H ]

)[cys]

[H ] [H ] [H ]

−

− −

− −

⋅ ⋅

⋅ ⋅

⋅ ⋅

⋅ ⋅⋅ ⋅ ⋅

⋅ ⋅ ⋅⋅ ⋅ ⋅

⋅ ⋅

k

k Kk K K

k K K KK K KK K K

+

+

+

+

+ + +

×

++

= ×+ ++

(Eq. 24)

The fractional rate constants, kHSO3− and kSO3

2− were esti-mated by the nonlinear least-squares method (quasi-Newton method using the solver in Microsoft Excel) to obtain the following values: kCOO−·NH3

+·SH (2.48×10 M−1 h−1), kCOO−·NH3+·S−

(1.20×104 M−1 h−1) and kCOO−·NH2·SH+ (3.31 M−1 h−1). The value of kCOOH·NH3

+·SH was much smaller than the other fractional rate constants, so kCOOH·NH3

+·SH was omitted from the calculations, as it seems to have little effect on the degradation rate con-stants of meropenem.The  influence  of  temperature  on  the  degradation  of  me-

ropenem by L-cysteine was also investigated. As shown in Fig. 7, Arrhenius plots revealed good linearity at L-cysteine concentrations  of  0,  0.25,  0.5,  1.0  and  2.0 mg/mL  at  pH  6.0. The values obtained for the Ea  of meropenem were  11.7 kcal/mol  (0.25 mg/mL),  11.0 kcal/mol  (0.5 mg/mL),  10.4 kcal/mol (1.0 mg/mL)  and  10.6 kcal/mol  (2.0 mg/mL),  while  the  value obtained for the Ea  of  meropenem  was  16.0 kcal/mol  in  the absence of L-cysteine  (0 mg/mL).  There  were  no  differences between the values of Ea in presence of L-cysteine (0.25, 0.5, 1.0,  2.0 mg/mL).  However,  there  was  difference  between  the values of Ea in the presence of L-cysteine and the value of Ea in the absence of L-cysteine. The dose-dependent effect of L-cysteine on the Ea of meropenem in this reaction is suggested to be small. The log kobs of meropenem showed a temperature-dependent increase at any concentration of L-cysteine. From these results, the degradation of meropenem is suggested to increase in a temperature-dependent manner.

Fig. 5. Arrhenius-Type Relationship between the Degradation Rate Constant of Meropenem and Temperature (4, 25 and 40°C) in the Pres-ence  of  SBS  (0,  0.1,  0.5,  1.0 mM) in 0.05 M  Phosphate  Buffer  (pH  6.0, μ=0.15)

Initial concentration of meropenem 500 µg/mL. ◇  SBS  0 mM, ○  SBS  0.1 mM, △ SBS 0.5 mM, □ SBS 1.0 mM.

Fig. 6. Relationship between the Total Concentrations of L-Cysteine (0,  0.25,  0.5,  1.0,  2.0 mg/mL)  and  N-Acetylcysteine (0, 0.25, 0.5, 1.0, 2.0 mg/mL; Converted  to L-Cysteine Concentration) and the Degradation Rate Constant (kobs) of Meropenem in 0.05 M  Phosphate  Buffer  (pH  6.0, μ=0.15) at 25°C

Initial concentration of meropenem 500 µg/mL.  ○ N-acetylcysteine, ● L-cysteine.

Vol. 63, No. 4 (2015) 253Chem. Pharm. Bull.

pH Estimation Method for a Mixed Infusion After mixing Meropen®  with  AMINOLEBAN®  Injection,  Fructlact Injection,  AMINOFLUID®  Injection  or  FULCALIQ® 2 or AMIGRAND®, pH was estimated at 25°C using the PHC curve. Figure 8 shows the correlation between the estimated and determined pH values in the mixed infusion (y=1.00x, r2=0.98).  The  pH  of  each mixed  infusion  could  be  estimated correctly using the PHC curve.

Stability Prediction of Meropenem in Practical Mixed Infusions From the above results, the degradation rate con-stant of meropenem after mixture with an infusion contained SBS and L-cysteine at pH 4.0–10.0, can be represented by Eq. 25.

1

23 3

2

3

3

obs 2

1 20 1 a

1 2

SBS1 SBS1 SBS2HSO SOtotal 2

SBS1 SBS1 SBS2

1 2a

1 2

total

2cys1COO NH SH

cys1 cCOO NH S

( )

( ) exp( / )

( [H ] )[SBS]

[H ] [H ]

exp( / )

[cys]

( [H ]

− −

−

− −

⋅ ⋅

⋅ ⋅

−⋅ − ⋅

⋅

⋅ ⋅ ⋅ ⋅⋅

⋅ ⋅

−− ⋅

⋅

⋅ ⋅⋅ ⋅

+

+

+

+ +

+

=

++

+ +

×

+

+

×

k T

T Tk T E R

T T

k K k K KK K K

T TE R

T T

k Kk K K

2

3

ys2

cys1 cys2 cys3COO NH S3 2

cys1 cys1 cys2

cys1 cys2 cys3

1 2a

1 2

[H ])

[H ] [H ] [H ]

exp( / )

− −⋅ ⋅

⋅⋅ ⋅ ⋅

⋅ ⋅ ⋅⋅ ⋅

−− ⋅

⋅

+

+ + +

++ ++

×

k K K KK K KK K K

T TE R

T T

(Eq. 25)

where Ea1 is the activation energy in the presence of the

acid–base catalytic effect, Ea2 is the activation energy in the

presence  of  SBS, Ea3 is the activation energy in the presence

of L-cysteine; kobs at any temperature (T2) can be calculated if 298 K  (25°C)  is  assigned  to T1 and the derived concentrations and  constants  at  298 K  (25°C)  and  activation  energy  values 

(Ea1 to Ea3

) are assigned to Eq. 25. The meropenem residual ratio (%) is represented by Eq. 26:

obs{ ( /2.303)}10 100k tr ⋅ −= × (Eq. 26)

Fig. 8. Correlation between pH Estimated Using PHC Curve and the pH Values Determined after Mixing Meropen®  with  AMINOLEBAN® Injection  ( ),  Fructlact  Injection  (×), AMINOFLUID®  Injection  ( ), FULCALIQ® 2 ( ) or AMIGRAND® ( ) at 25°C

y=1.00x, r2=0.98.

Fig.  9.  Correlation  between  Estimated  and  Observed  Residual  Ratio (%) after Mixing Meropen®  with  AMINOLEBAN®  Injection,  Fructlact Injection, AMINOFLUID® Injection, FULCALIQ® 2 and AMIGRAND®, at 4, 25 and 40°C

Initial concentration of meropenem 500 µg/mL.  y=1.00x, r2=0.98.  ○  AMINOLEBAN®  Injection  at  4°C,  —  Fructlact  Injection  at  4°C,  □ AMINOFLUID®  Injection  at  4°C, ◇ FULCALIQ® 2 at 4°C, △ AMIGRAND® at 4°C.   AMINOLEBAN®  Injection  at  25°C,  ×  Fructlact  Injection  at  25°C, 

AMINOFLUID®  Injection  at  25°C,  FULCALIQ® 2 at 25°C, AMIGRAND® at 25°C. ● AMINOLEBAN®  Injection at 40°C, + Fructlact In-

jection  at  40°C, ■ AMINOFLUID®  Injection  at  40°C, ◆ FULCALIQ® 2 at 40°C, ▲ AMIGRAND® at 40°C.

Fig. 7. Arrhenius-Type Relationship between the Degradation Rate Constant of Meropenem and Temperature (4, 25 and 40°C) in the Pres-ence of L-Cysteine  (0,  0.25,  0.5,  1.0,  2.0 mg/mL)  in  0.05 M Phosphate Buffer (pH 6.0, μ=0.15)

Initial concentration of meropenem 500 µg/mL. ◇ L-cysteine 0 mg/mL, ○ L-cys-teine 0.25 mg/mL, △ L-cysteine 0.5 mg/mL, □ L-cysteine 1.0 mg/mL, × L-cysteine 2.0 mg/mL.

254 Vol. 63, No. 4 (2015)Chem. Pharm. Bull.

From Eqs. 25 and 26, the meropenem residual ratio (%) can be predicted at any time after mixing into an infusion containing SBS and L-cysteine at pH 4.0–10.0.

The correlation between the estimated and determined residual ratio (%) of meropenem in Meropen® at 0, 1, 2, 3 and  4 h  after  mixing  with  AMINOLEBAN®  Injection,  Fruct-lact  Injection,  AMINOFLUID®  Injection,  FULCALIQ® 2 or AMIGRAND® at 4, 25 and 40°C (y=1.00x, r2=0.98) is shown in Fig. 9. The  initial concentration of meropenem was 500 µg/mL.  The  high  correlation  coefficient  q2  (0.99),  shows  a  high correlation between the estimated and determined residual ratios (%) of meropenem obtained in this study, which is rel-evant for the drug combinations used in the clinical field.These  results  confirm  that  an  equation  predicting  the  sta-

bility of meropenem, at any time and any temperature, after mixing with an  infusion containing SBS and L-cysteine at pH 4.0–10.0 has been derived in this study.

We have previously derived an equation predicting the stability of imipenem, at any time and any temperature, after mixing with an  infusion containing SBS and L-cysteine at pH 4.0–10.0.16) Both  the kSBS and kcys of meropenem were smaller than those of imipenem. This means that meropenem is more stable than imipenem after mixing with an infusion contain-ing  SBS  and  L-cysteine, probably because hydrolysis of the β-lactam ring of imipenem occurs more easily than that of meropenem, due to its chemical structure.

Itagaki et al.17)  reported  on  the  influence  of  L-cysteine on the degradation of meropenem after mixing with an amino acid infusion. In their report, N-acetyl cysteine had no effect on the degradation of meropenem after mixing with an amino acid infusion, thus supporting the result in the present paper. It is assumed that N-acetyl cysteine is unable to mount a nu-cleophilic attack on the β-lactam structure of meropenem be-cause the electron density on the S atom of N-acetyl cysteine is  significantly  lower  than  that  of  L-cysteine, due to the pres-ence of the acetyl group, an electron-accepting substituent.SBS  is  included  in  amino  acid  infusions  as  a  stabilizer.  In 

the present study, it is suggested that SBS affects the degrada-tion of meropenem after mixing with the amino acid infusion. Thus  the  influence  of  not  only  L-cysteine  but  also  SBS must be considered when attempting to improve the precision of prediction of the stability of meropenem in mixed infusions.

Our results indicate that, if antibiotics are administered as an infusion using a bypass line, they may become unstable if mixed  with  an  infusion  in  the  infusion  line  or  by  back-flow from the bypass line to the main line. Yoshioka et al. reported that the effectiveness of doripenem was decreased by a bypass administration from amino acid infusion line.18) We suggest that the effectiveness of meropenem may also be decreased by a bypass administration from an amino acid infusion line. The required minimum dosage and length of treatment should therefore take account of this interaction between carbapenem antibiotics and amino acid infusions, in order to maximise the effectiveness of the antibiotics and avoid the appearance of resistant bacteria. The equation derived in this study will

enable prediction of the required concentration of meropenem in mixed infusions and will therefore be useful for drawing up an administration plan for this drug.

ConclusionThe  key  factors  influencing  the  stability  of  meropenem  in 

a  mixed  infusion  were  found  to  be  pH,  SBS  concentration, and L-cysteine concentration. Equations describing the deg-radation rate constants (kobs)  for pH, SBS and L-cysteine have been derived, and the activation energy (Ea) and frequency factor (A) calculated using the Arrhenius equation. The pH of the mixed infusion could be estimated using the PHC curve. Finally, an equation has been derived giving the residual ratio (%) of meropenem at any time after mixing any infusion at any temperature at pH 4.0–10.0. A high correlation was shown between the estimated and the determined values for residual ratio (%). The equation derived in this study will enable us to predict the concentration of meropenem in mixed infusions and will therefore improve the correct use of this drug.

Conflict of Interest The  authors  declare  no  conflict  of interest.

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