M. W. Kunst, H. Mattie
Cefazolin and Cephradine: Relationship between Serum Concentrations and Tissue Contents in Mice Summary: The relationship between serum concentrations and tissue levels of various doses of cefazolin and cephradine was determined in experimentally infected mice. An infection was induced by injection of 5 x 10 ~ Escherichia coli into the fight hind leg, antibiotics were administered 1 h later. At 15-minute intervals mice were killed by exsanguination after a blood sample was taken, and the infected thigh was taken out and homogenized. The total amount of antibiotic per gram thigh muscle tissue was calculated on the basis of the concentration in the supernatant of the homogenate. From the parallel course between blood concentrations and total tissue contents it may be concluded that the thigh was easily accessible for both cephalosporins. The ratio between the total tissue content and the free serum concentrations was the same for both antibiotics despite the difference in protein binding between cefazolin and cephradine in mouse serum. This implies that the discrepancy between the relative antibacterial activity of the cephalosporins in vitro and in vivo found in earlier experiments cannot be explained by differences in accessibility of the tissue. Zusammenfassung: Cefazolin und Cephradin: Verhiiltnis zwisehen der Serumkonzentration und dem Gewebegehalt bei Miiusen. Das Verh~Itnis zwischen der Serumkonzentration und dem Gewebegehalt von verschiedenen Dosen Cefazolin und Cephradin wurde bei experimentell infizierten Miiusen bestimmt. Die Infek~ion wurde dutch Injektion yon 5 x 106 Escherichia coli in das rechte Hinterbein erzeugt; Antibiotika wurden eine Stunde sp~iter gegeben. In Absdinden yon 15 Minuten wurden die M~iuse, nachdem eine Blutprobe entnommen worden war, durch Ausbluten getftet, und der infizierte Oberschenkelmuskel wurde abgenommen und homogenisiert. Die Gesamtmenge an Antibiotika pro Gramm Oberschenkelmuskelgewebe wurde aus der Konzentration des Oberstandes yon Homogenisat berechnet. Aus dem parallelen Verlauf zwischen Blutkonzentrationen und Gesamtgewebespiegel daft man schlie6en, dab das Muskelgewebe fiir beide Cephalosporine leicht zug~inglich war. Das Verh~iltnis zwischen dem gesamten Gewebegehalt und der freien Serumkonzentration war fiir beide Antibiotika gleich, obwohl die EiweiBbindung von Cefazolin und Cephradin unterschiedlich ist. Das bedeutet, dat3 die Diskrepanz zwischen der relativen antibakteriellen Wirksamkeit der Cephalosporine in vitro und in vivo, die in frfiheren Experimenten gefunden wurde, nicht durch die unterschiedliche Zug~nglichkeit des Gewebes erkI~rt werden kann.
Introduction I n a previous study the relative antibacterial activity of eefazolin and cephradine in vitro was c o m p a r e d with that in experimentally infected mice (1). W h e n the area u n d e r the concentration-time curve ( A U C ) of the non-proteinb o u n d drug in individual mice was analyzed in relation to the effect of the antibiotic in vivo, a discrepancy was f o u n d between the relative efficacy of the cephalosporins in v i v o and in vitro, cefazolin being 6.1 times m o r e
166
Infection 6 (1978) Nr, 4
potent than cephradine in vitro, while in vivo it was only 3.2 times m o r e potent. It was therefore concluded that the antibacterial activity of antibiotics in vivo cannot be predicted solely f r o m the activity in vitro and the free serum concentrations. O n e possible explanation of this p h e n o m e n o n is that free serum concentrations do not reflect concentrations in the interstitial fluid, and consequently differences in accessibility would account for the a b o v e - m e n t i o n e d discrepancy. T h e purpose of the present investigation was to elucidate further the relationship between free serum concentrations and tissue contents of the antibiotics under study.
Materials and Methods Antibiotics: Cephradine (966 #g/mg, Mycofarm, Delft, The Netherlands) was dissolved in phosphate buffer (pH 6.0) to obtain a concentration of 2 mg/ml; cefazolin (1000 #g/ml, Fujisawa Pharmaceutical Co., Ltd., Japan) was prepared in the same way. Mice: Specific pathogen-free (SPF) male mice, Swiss type, weighing 20-25 g (Central Institute for the Breeding of Laboratory Animals, TNO, Zeist, The Netherlands) were used. Experimental injection and determination of thigh-tissue contents: The mice were infected by intramuscular injection of Eseherichia coli 054 into the posterior muscle of the right hind leg, as described elsewhere (1). Antibiotics were administered subcutaneously as a single dose one h after the inoculation, at dosages of 10, 20, 40 mg/kg body weight for cefazolin and 20, 40, 80 mg/kg for cephradine. At intervals of 15 or 30 min, blood was taken from the tail vein for the determination of blood concentrations, as described in detail elsewhere (1). The sampling period was taken long enough to allow the blood and tissue levels to approach zero or at least very low values. Since in the earlier studies no binding of these cephalosporins to mouse erythrocytes could be demonstrated in vivo (1) the total serum concentrations were calculated from the blood concentrations after correction for hematocrit. Free serum concentrations were calculated from the total serum concentrations by correction for protein binding, amounting to 50% for cefazolin and 11.3% for eephradine (1). The technical procedure was as follows. Immediately after a blood sample has been taken, the animal was killed by exsanguination via heart puncture. Then the infected thigh was removed, dissected from the bone, weighed, and homogenized with teflon pestles in 5 ml phosphate-buffered saline (pH 7.4) in Potter-Elvejhem tubes cooled in ice, After centrifugation of the homogenate for 10 min at 1000 g, the concenReceived: 19 December 1977 Dr. M. W. Kunst, Dr. H. lVlattie, Departments of Infectious Diseases and Clinical Pharmacology, University Hospital, Rijnsburgerweg, Leiden, The Netherlands. Reprints: Dr. M. W, Kunst
M. W. Kunst, H. Mattie: Tissue Levels of Cephalosporins
tration of the antibiotic in the supernatant was determined. For this assay, the agar diffusion method of Grove and Randall as modified by Mattie et aI. (2) was used, with Bacillus calidolactis as test organism. The assay with B. caIidolactis is performed at 56 °C, at which temperature E. coli does not grow. Because it could not be ruled out that there would remain some fl-lactamase activity at this temperature, standards were prepared with infected thigh homogenate, held at room temperature for i h, and similarly centrifuged for 10 rain at 1000 g. However, there turned out to be no systemic difference between the antibiotic contents of the infected and the uninfected thigh muscles of the same animal (n =. 5; 0.80 < P < 0.90). Although the antibiotics are not very stable at 56 °C, there is no reason to expect a difference between standard and sample. The total amount of antibiotic per thigh and the amount of antibiotic per gram thigh tissue (tissue content) were calculated from the concentration of antibiotic/ml in the supernatant. For each dose of both antibiotics the ratio (R) between A U C of the total thigh tissue content and A U C of the free serum concen~trations-both determined by the trapezoid m e t h o d was calculated. Pharmacokinetic model: A model was assumed in which free antibiotic can diffuse passively from the plasma to the interstitial fluid. Both the volume of the interstitial fluid (as a fraction of the total tissue volume) and the binding to other tissue constituents are unknown. In this model, the following equations hold: dCi d--T= DaCp - DaCi, (t)
in which Ci Cp D a
= = = =
aqueous concentration in interstitial fluid aqueous concentration in plasma ( = non-protein-bound) diffusion coefficient area of diffusion boundary
Integration leads to t
t
Ci = Da ( f Cpdt - f Cidt), o
(2)
o
Results F o r both cephalosporins at all dosage levels the blood concentrations and total tissue contents followed a fairly parallel course, as is shown in F i g u r e 1. These curves, which are based on the m e a n s of the results of two mice at each time point, provide an indication of the accessibility of the thigh muscle, the elimination of the drug f r o m the muscle, and the relationship between the blood and tissue levels. A f t e r correction for h e m a t o c r i t and protein binding, the free serum concentrations were calculated. A n e x a m p l e is given in Figure 2 (left), which shows the curves of the free serum concentrations and the thigh tissue contents after 40 m g / k g cefazolin. T h e ratio (R) between the A U C of the total thigh tissue content and the A U C of the free s e r u m concentrations for each dose of both cephatosporins is shown in T a b l e 1. The difference between the antibiotics is not statistically significant (p > 0.50). The concentrations in the interstitial fluid at individual time points w e r e calculated by dividing t h r o u g h R total tissue contents. F i g u r e 2 (right) shows the curves of the free serum concentrations and the calculated antibiotic concentrations in the interstitial fluid after 40 m g / k g cefazolin. Table 1: Ratio (R) between the area under the curve (AUC) o[ the total thigh tissue content and the A U C of the [ree serum concentrations a/ter various doses cefazolin and cephradine. Ratio for Cefazolin Cephradine l0 20 40 80
mg/kg mg/kg mg/kg mg/kg
0.19 0.23 0.23 --
-0.23 0.27 0.20
0.22* 0.02
0.23* 0.02
in which Mean SEM
t Cdt = area under the concentration-time curve (AUC) o
When, after a single dose, Ci returns to zero, Equation (1) leads to J" Cidt = J" Cpdt O
(3)
O
The relationship between the tissue content and the concentrations in the interstitial fluid and other tissue components is expressed in the following equation CT = fiCi + (I - fi) Cr,
(4)
in which CT = total tissue content fi == volume fraction of interstitial fluid Cr = mean concentration in other tissue components Combination of Equations (3) and (4) leads to AUCr AUCp
R - fi 1- fi
R--
AUC:r AUCp
in which.
(5)
* This difference is not statistically significant (p > 0.50).
Discussion The relationship between free serum concentrations of cefazolin and cephradine and thigh muscle tissue levels was studied in experimentally infected mice, using an experimental thigh infection m o d e l described in detail elsewhere (1). T h e results show that the accessibility of the thigh tissue for b o t h cefazolin and cephradine is good; the calculated antibiotic concentration in the interstitial fluid follows the free serum levels v e r y closely (Figure 2, right). This rapid equilibration is in a g r e e m e n t with data obtained f r o m l y m p h draining dog legs (3). Despite a m a r k e d difference in protein binding between these cephalosporins in m o u s e serum, the ratio between total tissue, content and free s e r u m levels was the same for both. This indicates that the discrepancy between the relative antibacterial activity of cefazolin and cephradine in vitro and in vivo found in earlier experiments (1) cannot be explained by a difference in the accessibility
Infection 6 (1978) Nr. 4
167
M. W. Kunst, H. Mattie: Tissue Levels of Cephalosporins
CEPHRADINE
CEFAZOLIN
og/mt{g)
ug/rnt (g)
BLOOD CONCENTRATIONS
(~ug/mt) THIGH TISSUE CONTENT (,ug/g)
10-
10
20 mg/kg 5-
5
15.
10"
/
0.5
1
~~20
1.5
15-
n~/kg
10-
0.5
1
:?.
1.5
mg/kg
5-
5.
(,,,
-
0
0.5
1
'E5'
1'.5
.-.....,, ;
115 i
~
1'.s
20.
20.
i
15
/,0 mg/kg
15
10
10
5-
/
/
I
|
i
' 0.5
,
'
i
1:5
i hours
"
o.5 i
'
T
i hours
Figure 1: Concentration-time curves after various doses o/ ce/azolin and cephradine, administered subcutaneously to experimentally infected mice. Blood concentrations and total thigh muscle tissue content are shown. (Each point represents the mean value of 2 mice.)
168
Infection 6 (1978) Nr. 4
M. W. Kunst, H. Mattie: Tissne Levels of Cephalosporins
,ug/m~
,ug/mt (g)
20-
20-
CEFAZOLIN
CEFAZOLIN o--o lS-
free serum concentrations e---e
~to.---o
total thigh tissue content
10-
free serum concentrations
e---e
15-
%orrectedNthigh tissue content
10"
5
o /
02i
1
1.5
2
hours
i
i
i
i
0.5
1
1.5
2
hours
Figure 2: Concentration-time curves after 40 mg/kg cefazolin administered subcutaneously to experimentally infected mice, showing free serum concentrations and total thigh muscle tissue content (left), and free serum concentrations and calculated interstitial fluid concentrations in thigh muscle tissue (right). (Each point represents the mean value of 2 mice.)
of the tissue. Therefore, determination of levels of these two antibiotics in homogenized tissue does not provide any extra information about the free serum levels or the potency of the antibiotics in vivo. In general, in vivo levels in homogenized tissue have a limited value for the prediction of antibiotic activity, because in all probability neither antibiotics nor bacteria are homogeneously distributed in the infected tissue. The amount of antibiotic per gram tissue is not equal to the concentration of free, potentially active antibiotic. This is contrary to what is suggested by many authors who predict the activity of antibiotics in vivo on the basis of a comparison between total tissue contents and minimal inhibition concentrations of bacterial growth in vitro. The total tissue content is determined by the free aqueous antibiotic concentration, the tissue-bound fraction of the antibiotic, and the tissue fraction that is impermeable for the antibiotic. Although the studies of K u n i n (4) showed no tissue binding of penicillins and cephalexin in 250/0 homogenates of rabbit mnscte tissue, it is not excluded that a certain amount of tissue binding occurs in the mouse thigh tissue in our study. Since the amount of thigh tissue that is impermeable for antibiotic is unknown, the tissue binding cannot be calculated. However, because the ratio (R) between the tissue content and the free serum levels is the same for both cephalosporins, it may be concluded that if tissue binding occurs it must be the same for both antibiotics despite the difference in protein binding. Substitution in Equation 5 of the value of 0.22 found for R indicates that the volume of the interstitial fluid is maximally 220/0 of the total muscle tissue volume. In that .zase, 78o/0 of the volume of the
thigh muscle tissue would be impermeable for cefazolin and cephradine. On the basis of the assumptions described for the pharmacokinetic model, a free tissue level curve at the site of infection was constructed (Figure 2, right). With the time intervals used in our study, no delay could be demonstrated between the peak tissue level and the peak of the free serum concentrations, which means that equilibration between the blood and tissue levels of the cephalosporins in these mice must be very rapid. Several experimental models have been developed in attempts to evade the problem of tissue binding and the impenetrability of part of the tissue for antibiotics. The most important of these models concern tissue cages (5, 6, 7), skin windows (8, 9), fibrin clots (10), skin blisters (11), and subcutaneous pouches (12). All these models have different drawbacks. In the first place, the problem remains whether the fluid within these artificial spaces is really comparable to normal interstitial fluid: for example, the protein content of the fluid within the tissue cages is about 40°/0 and in the granuloma pouches as much as 90°/0 of the serum protein content. F o r proper pharmacokinetic assessment protein binding of the antibiotics under investigation should be known at the actual protein concentrations, and total concentrations should be corrected accordingly. More important is that the equilibration between free serum concentrations of the antibiotic and interstitial fluid in these models probably does not occur as rapidly as is suggested (5). The dimensions of these artificial compartments are large if compared with the average intercapillary distance in normal or inflamed tissue. Therefore, slow diffusion in the fluid that is already present in these artificial spaces
Infection 6 (1978) Nr. 4
169
M. W. Kunst, H. Mattie: Tissue Levels of Cephalosporins might explain the relatively low concentration of antibiotic in the "interstitial fluid", including antibiotics with a low degree of protein binding; this might also explain the prolonged presence of the antibiotic, long after it has disappeared from the blood. In other words, the concentrations in the artificial fluid of these models are probably not really homogeneous, because the concentration may well decline toward the centre of the fluid mass or fibrin clot. On the basis of all this, we think that our model reliably reflects not only the potentially active concentration of these two cephalosporins in interstitial fluid, at least in the type of tissue we used, but also the time course of the free antibiotic concentrations in tissues in relation to the free serum levels.
Acknowledgements This investigation was supported by a grant from Beecham B. V., The Netherlands and furthermore financial support was given by Gist-Brocades B. V., Delft, The Netherlands. The authors are greatly indebted to Ria Binnendi]k-van Wiik, Gerda Wensveen and Winy Los for their skilled technical assistance, to Ralph van Furth for his critical remarks, to Juul Noomen for typing the manuscript, and Mechtilde Kever for the translation of the summary.
Literature 1. Kunst, M. W., Mattie, H.: Cefazolin and cephradine: Relationship between antibacterial activity in vitro and in experimentally infected mice. J. Infect. Dis. 137 (1978) 391-402. 2. Mattie, H., Goslings, W. R. 0., Noach, E. L.: Cloxacillin and nafcillin: Serum binding and its relationship to antibacterial effect in mice. J. Infect. Dis. 128 (1973) 170-177.
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Infection 6 (1978) Nr. 4
3. Acred, P., Brown, D. M., Clark, B. F., Mizen, L.: The distribution of antibacterial agents between plasma and lymph in the dog. Br. J. Pharmaeol. 39 (1970) 439-446. 4. Kunin, C. M.: Binding of antibiotics to tissue homogenates. J. Infect. Dis. 12i (1970) 55-64. 5. Chisholm, G. D., Waterworth, P. M., CaInan. J. S., Garrod, L. P.: Concentration of antibacterial agents in interstitial tissue fluid. Br. Med. J. t (1973) 569-573. 6. Eiekenberg, H.-U., Scharfenberger, L., Waterman, N. G,: Concentration of antibiotics in renal interstitial fluid, soft tissue interstitial fluid, urine and serum. Infection 4 Suppl. 2 (1976) 97-102. 7. Waterman, N. G., RaN, M. l., SchatJenberget, L., Barnwell, P. A.: Protein binding and concentrations of eephaloridine and cefazolin in serum and interstitial fluid of dogs. J. Infect. Dis. 133 (1976) 642-647. 8. Tan, I. S., Trott, A., Phair, ). P., Watanakunakorn, C.: A method for measurement of antibiotics in human interstitial fluid. J. Infect. Dis. 126 (1972) 492-497. 9. Raeburn, or. A.: A method for studying antibiotic concentrations in inflammatory exudate. J. Clin. Pathol. 24 (1971) 633-635. 10. Barza, M., Samuelson, T. Weinstein, L.: Penetration of antibiotics into fibrin loci in vivo IL Comparison of nine antibiotics: Effect of dose and degree of protein binding. J. Infect. Dis. 129 (1974) 66-72. 11, Simon, C., Materczyk, V., Brahmstedt, E., Toetler, W.: Cefazolin, ein neues Breitspektrum-Antibiotikum. Deutsch. Med. Wschr. 98 (1973) 2448-2450. 12. Nishida, M., Murakawa, T.: Exudate levels and bactericidal activity of cefazolin in a new local infection system using rat granuloma pouches. Antimicrob. Ag. Chemother. 11 (i977) 1042-1048.
Cefazolin and Cephradine: Relationship between Serum Concentrations and Tissue Contents in Mice Summary: The relationship between serum concentrations and tissue levels of various doses of cefazolin and cephradine was determined in experimentally infected mice. An infection was induced by injection of 5 x 10 ~ Escherichia coli into the fight hind leg, antibiotics were administered 1 h later. At 15-minute intervals mice were killed by exsanguination after a blood sample was taken, and the infected thigh was taken out and homogenized. The total amount of antibiotic per gram thigh muscle tissue was calculated on the basis of the concentration in the supernatant of the homogenate. From the parallel course between blood concentrations and total tissue contents it may be concluded that the thigh was easily accessible for both cephalosporins. The ratio between the total tissue content and the free serum concentrations was the same for both antibiotics despite the difference in protein binding between cefazolin and cephradine in mouse serum. This implies that the discrepancy between the relative antibacterial activity of the cephalosporins in vitro and in vivo found in earlier experiments cannot be explained by differences in accessibility of the tissue. Zusammenfassung: Cefazolin und Cephradin: Verhiiltnis zwisehen der Serumkonzentration und dem Gewebegehalt bei Miiusen. Das Verh~Itnis zwischen der Serumkonzentration und dem Gewebegehalt von verschiedenen Dosen Cefazolin und Cephradin wurde bei experimentell infizierten Miiusen bestimmt. Die Infek~ion wurde dutch Injektion yon 5 x 106 Escherichia coli in das rechte Hinterbein erzeugt; Antibiotika wurden eine Stunde sp~iter gegeben. In Absdinden yon 15 Minuten wurden die M~iuse, nachdem eine Blutprobe entnommen worden war, durch Ausbluten getftet, und der infizierte Oberschenkelmuskel wurde abgenommen und homogenisiert. Die Gesamtmenge an Antibiotika pro Gramm Oberschenkelmuskelgewebe wurde aus der Konzentration des Oberstandes yon Homogenisat berechnet. Aus dem parallelen Verlauf zwischen Blutkonzentrationen und Gesamtgewebespiegel daft man schlie6en, dab das Muskelgewebe fiir beide Cephalosporine leicht zug~inglich war. Das Verh~iltnis zwischen dem gesamten Gewebegehalt und der freien Serumkonzentration war fiir beide Antibiotika gleich, obwohl die EiweiBbindung von Cefazolin und Cephradin unterschiedlich ist. Das bedeutet, dat3 die Diskrepanz zwischen der relativen antibakteriellen Wirksamkeit der Cephalosporine in vitro und in vivo, die in frfiheren Experimenten gefunden wurde, nicht durch die unterschiedliche Zug~nglichkeit des Gewebes erkI~rt werden kann.
Introduction I n a previous study the relative antibacterial activity of eefazolin and cephradine in vitro was c o m p a r e d with that in experimentally infected mice (1). W h e n the area u n d e r the concentration-time curve ( A U C ) of the non-proteinb o u n d drug in individual mice was analyzed in relation to the effect of the antibiotic in vivo, a discrepancy was f o u n d between the relative efficacy of the cephalosporins in v i v o and in vitro, cefazolin being 6.1 times m o r e
166
Infection 6 (1978) Nr, 4
potent than cephradine in vitro, while in vivo it was only 3.2 times m o r e potent. It was therefore concluded that the antibacterial activity of antibiotics in vivo cannot be predicted solely f r o m the activity in vitro and the free serum concentrations. O n e possible explanation of this p h e n o m e n o n is that free serum concentrations do not reflect concentrations in the interstitial fluid, and consequently differences in accessibility would account for the a b o v e - m e n t i o n e d discrepancy. T h e purpose of the present investigation was to elucidate further the relationship between free serum concentrations and tissue contents of the antibiotics under study.
Materials and Methods Antibiotics: Cephradine (966 #g/mg, Mycofarm, Delft, The Netherlands) was dissolved in phosphate buffer (pH 6.0) to obtain a concentration of 2 mg/ml; cefazolin (1000 #g/ml, Fujisawa Pharmaceutical Co., Ltd., Japan) was prepared in the same way. Mice: Specific pathogen-free (SPF) male mice, Swiss type, weighing 20-25 g (Central Institute for the Breeding of Laboratory Animals, TNO, Zeist, The Netherlands) were used. Experimental injection and determination of thigh-tissue contents: The mice were infected by intramuscular injection of Eseherichia coli 054 into the posterior muscle of the right hind leg, as described elsewhere (1). Antibiotics were administered subcutaneously as a single dose one h after the inoculation, at dosages of 10, 20, 40 mg/kg body weight for cefazolin and 20, 40, 80 mg/kg for cephradine. At intervals of 15 or 30 min, blood was taken from the tail vein for the determination of blood concentrations, as described in detail elsewhere (1). The sampling period was taken long enough to allow the blood and tissue levels to approach zero or at least very low values. Since in the earlier studies no binding of these cephalosporins to mouse erythrocytes could be demonstrated in vivo (1) the total serum concentrations were calculated from the blood concentrations after correction for hematocrit. Free serum concentrations were calculated from the total serum concentrations by correction for protein binding, amounting to 50% for cefazolin and 11.3% for eephradine (1). The technical procedure was as follows. Immediately after a blood sample has been taken, the animal was killed by exsanguination via heart puncture. Then the infected thigh was removed, dissected from the bone, weighed, and homogenized with teflon pestles in 5 ml phosphate-buffered saline (pH 7.4) in Potter-Elvejhem tubes cooled in ice, After centrifugation of the homogenate for 10 min at 1000 g, the concenReceived: 19 December 1977 Dr. M. W. Kunst, Dr. H. lVlattie, Departments of Infectious Diseases and Clinical Pharmacology, University Hospital, Rijnsburgerweg, Leiden, The Netherlands. Reprints: Dr. M. W, Kunst
M. W. Kunst, H. Mattie: Tissue Levels of Cephalosporins
tration of the antibiotic in the supernatant was determined. For this assay, the agar diffusion method of Grove and Randall as modified by Mattie et aI. (2) was used, with Bacillus calidolactis as test organism. The assay with B. caIidolactis is performed at 56 °C, at which temperature E. coli does not grow. Because it could not be ruled out that there would remain some fl-lactamase activity at this temperature, standards were prepared with infected thigh homogenate, held at room temperature for i h, and similarly centrifuged for 10 rain at 1000 g. However, there turned out to be no systemic difference between the antibiotic contents of the infected and the uninfected thigh muscles of the same animal (n =. 5; 0.80 < P < 0.90). Although the antibiotics are not very stable at 56 °C, there is no reason to expect a difference between standard and sample. The total amount of antibiotic per thigh and the amount of antibiotic per gram thigh tissue (tissue content) were calculated from the concentration of antibiotic/ml in the supernatant. For each dose of both antibiotics the ratio (R) between A U C of the total thigh tissue content and A U C of the free serum concen~trations-both determined by the trapezoid m e t h o d was calculated. Pharmacokinetic model: A model was assumed in which free antibiotic can diffuse passively from the plasma to the interstitial fluid. Both the volume of the interstitial fluid (as a fraction of the total tissue volume) and the binding to other tissue constituents are unknown. In this model, the following equations hold: dCi d--T= DaCp - DaCi, (t)
in which Ci Cp D a
= = = =
aqueous concentration in interstitial fluid aqueous concentration in plasma ( = non-protein-bound) diffusion coefficient area of diffusion boundary
Integration leads to t
t
Ci = Da ( f Cpdt - f Cidt), o
(2)
o
Results F o r both cephalosporins at all dosage levels the blood concentrations and total tissue contents followed a fairly parallel course, as is shown in F i g u r e 1. These curves, which are based on the m e a n s of the results of two mice at each time point, provide an indication of the accessibility of the thigh muscle, the elimination of the drug f r o m the muscle, and the relationship between the blood and tissue levels. A f t e r correction for h e m a t o c r i t and protein binding, the free serum concentrations were calculated. A n e x a m p l e is given in Figure 2 (left), which shows the curves of the free serum concentrations and the thigh tissue contents after 40 m g / k g cefazolin. T h e ratio (R) between the A U C of the total thigh tissue content and the A U C of the free s e r u m concentrations for each dose of both cephatosporins is shown in T a b l e 1. The difference between the antibiotics is not statistically significant (p > 0.50). The concentrations in the interstitial fluid at individual time points w e r e calculated by dividing t h r o u g h R total tissue contents. F i g u r e 2 (right) shows the curves of the free serum concentrations and the calculated antibiotic concentrations in the interstitial fluid after 40 m g / k g cefazolin. Table 1: Ratio (R) between the area under the curve (AUC) o[ the total thigh tissue content and the A U C of the [ree serum concentrations a/ter various doses cefazolin and cephradine. Ratio for Cefazolin Cephradine l0 20 40 80
mg/kg mg/kg mg/kg mg/kg
0.19 0.23 0.23 --
-0.23 0.27 0.20
0.22* 0.02
0.23* 0.02
in which Mean SEM
t Cdt = area under the concentration-time curve (AUC) o
When, after a single dose, Ci returns to zero, Equation (1) leads to J" Cidt = J" Cpdt O
(3)
O
The relationship between the tissue content and the concentrations in the interstitial fluid and other tissue components is expressed in the following equation CT = fiCi + (I - fi) Cr,
(4)
in which CT = total tissue content fi == volume fraction of interstitial fluid Cr = mean concentration in other tissue components Combination of Equations (3) and (4) leads to AUCr AUCp
R - fi 1- fi
R--
AUC:r AUCp
in which.
(5)
* This difference is not statistically significant (p > 0.50).
Discussion The relationship between free serum concentrations of cefazolin and cephradine and thigh muscle tissue levels was studied in experimentally infected mice, using an experimental thigh infection m o d e l described in detail elsewhere (1). T h e results show that the accessibility of the thigh tissue for b o t h cefazolin and cephradine is good; the calculated antibiotic concentration in the interstitial fluid follows the free serum levels v e r y closely (Figure 2, right). This rapid equilibration is in a g r e e m e n t with data obtained f r o m l y m p h draining dog legs (3). Despite a m a r k e d difference in protein binding between these cephalosporins in m o u s e serum, the ratio between total tissue, content and free s e r u m levels was the same for both. This indicates that the discrepancy between the relative antibacterial activity of cefazolin and cephradine in vitro and in vivo found in earlier experiments (1) cannot be explained by a difference in the accessibility
Infection 6 (1978) Nr. 4
167
M. W. Kunst, H. Mattie: Tissue Levels of Cephalosporins
CEPHRADINE
CEFAZOLIN
og/mt{g)
ug/rnt (g)
BLOOD CONCENTRATIONS
(~ug/mt) THIGH TISSUE CONTENT (,ug/g)
10-
10
20 mg/kg 5-
5
15.
10"
/
0.5
1
~~20
1.5
15-
n~/kg
10-
0.5
1
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5.
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-
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i
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15
10
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/
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|
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'
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T
i hours
Figure 1: Concentration-time curves after various doses o/ ce/azolin and cephradine, administered subcutaneously to experimentally infected mice. Blood concentrations and total thigh muscle tissue content are shown. (Each point represents the mean value of 2 mice.)
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M. W. Kunst, H. Mattie: Tissne Levels of Cephalosporins
,ug/m~
,ug/mt (g)
20-
20-
CEFAZOLIN
CEFAZOLIN o--o lS-
free serum concentrations e---e
~to.---o
total thigh tissue content
10-
free serum concentrations
e---e
15-
%orrectedNthigh tissue content
10"
5
o /
02i
1
1.5
2
hours
i
i
i
i
0.5
1
1.5
2
hours
Figure 2: Concentration-time curves after 40 mg/kg cefazolin administered subcutaneously to experimentally infected mice, showing free serum concentrations and total thigh muscle tissue content (left), and free serum concentrations and calculated interstitial fluid concentrations in thigh muscle tissue (right). (Each point represents the mean value of 2 mice.)
of the tissue. Therefore, determination of levels of these two antibiotics in homogenized tissue does not provide any extra information about the free serum levels or the potency of the antibiotics in vivo. In general, in vivo levels in homogenized tissue have a limited value for the prediction of antibiotic activity, because in all probability neither antibiotics nor bacteria are homogeneously distributed in the infected tissue. The amount of antibiotic per gram tissue is not equal to the concentration of free, potentially active antibiotic. This is contrary to what is suggested by many authors who predict the activity of antibiotics in vivo on the basis of a comparison between total tissue contents and minimal inhibition concentrations of bacterial growth in vitro. The total tissue content is determined by the free aqueous antibiotic concentration, the tissue-bound fraction of the antibiotic, and the tissue fraction that is impermeable for the antibiotic. Although the studies of K u n i n (4) showed no tissue binding of penicillins and cephalexin in 250/0 homogenates of rabbit mnscte tissue, it is not excluded that a certain amount of tissue binding occurs in the mouse thigh tissue in our study. Since the amount of thigh tissue that is impermeable for antibiotic is unknown, the tissue binding cannot be calculated. However, because the ratio (R) between the tissue content and the free serum levels is the same for both cephalosporins, it may be concluded that if tissue binding occurs it must be the same for both antibiotics despite the difference in protein binding. Substitution in Equation 5 of the value of 0.22 found for R indicates that the volume of the interstitial fluid is maximally 220/0 of the total muscle tissue volume. In that .zase, 78o/0 of the volume of the
thigh muscle tissue would be impermeable for cefazolin and cephradine. On the basis of the assumptions described for the pharmacokinetic model, a free tissue level curve at the site of infection was constructed (Figure 2, right). With the time intervals used in our study, no delay could be demonstrated between the peak tissue level and the peak of the free serum concentrations, which means that equilibration between the blood and tissue levels of the cephalosporins in these mice must be very rapid. Several experimental models have been developed in attempts to evade the problem of tissue binding and the impenetrability of part of the tissue for antibiotics. The most important of these models concern tissue cages (5, 6, 7), skin windows (8, 9), fibrin clots (10), skin blisters (11), and subcutaneous pouches (12). All these models have different drawbacks. In the first place, the problem remains whether the fluid within these artificial spaces is really comparable to normal interstitial fluid: for example, the protein content of the fluid within the tissue cages is about 40°/0 and in the granuloma pouches as much as 90°/0 of the serum protein content. F o r proper pharmacokinetic assessment protein binding of the antibiotics under investigation should be known at the actual protein concentrations, and total concentrations should be corrected accordingly. More important is that the equilibration between free serum concentrations of the antibiotic and interstitial fluid in these models probably does not occur as rapidly as is suggested (5). The dimensions of these artificial compartments are large if compared with the average intercapillary distance in normal or inflamed tissue. Therefore, slow diffusion in the fluid that is already present in these artificial spaces
Infection 6 (1978) Nr. 4
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M. W. Kunst, H. Mattie: Tissue Levels of Cephalosporins might explain the relatively low concentration of antibiotic in the "interstitial fluid", including antibiotics with a low degree of protein binding; this might also explain the prolonged presence of the antibiotic, long after it has disappeared from the blood. In other words, the concentrations in the artificial fluid of these models are probably not really homogeneous, because the concentration may well decline toward the centre of the fluid mass or fibrin clot. On the basis of all this, we think that our model reliably reflects not only the potentially active concentration of these two cephalosporins in interstitial fluid, at least in the type of tissue we used, but also the time course of the free antibiotic concentrations in tissues in relation to the free serum levels.
Acknowledgements This investigation was supported by a grant from Beecham B. V., The Netherlands and furthermore financial support was given by Gist-Brocades B. V., Delft, The Netherlands. The authors are greatly indebted to Ria Binnendi]k-van Wiik, Gerda Wensveen and Winy Los for their skilled technical assistance, to Ralph van Furth for his critical remarks, to Juul Noomen for typing the manuscript, and Mechtilde Kever for the translation of the summary.
Literature 1. Kunst, M. W., Mattie, H.: Cefazolin and cephradine: Relationship between antibacterial activity in vitro and in experimentally infected mice. J. Infect. Dis. 137 (1978) 391-402. 2. Mattie, H., Goslings, W. R. 0., Noach, E. L.: Cloxacillin and nafcillin: Serum binding and its relationship to antibacterial effect in mice. J. Infect. Dis. 128 (1973) 170-177.
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3. Acred, P., Brown, D. M., Clark, B. F., Mizen, L.: The distribution of antibacterial agents between plasma and lymph in the dog. Br. J. Pharmaeol. 39 (1970) 439-446. 4. Kunin, C. M.: Binding of antibiotics to tissue homogenates. J. Infect. Dis. 12i (1970) 55-64. 5. Chisholm, G. D., Waterworth, P. M., CaInan. J. S., Garrod, L. P.: Concentration of antibacterial agents in interstitial tissue fluid. Br. Med. J. t (1973) 569-573. 6. Eiekenberg, H.-U., Scharfenberger, L., Waterman, N. G,: Concentration of antibiotics in renal interstitial fluid, soft tissue interstitial fluid, urine and serum. Infection 4 Suppl. 2 (1976) 97-102. 7. Waterman, N. G., RaN, M. l., SchatJenberget, L., Barnwell, P. A.: Protein binding and concentrations of eephaloridine and cefazolin in serum and interstitial fluid of dogs. J. Infect. Dis. 133 (1976) 642-647. 8. Tan, I. S., Trott, A., Phair, ). P., Watanakunakorn, C.: A method for measurement of antibiotics in human interstitial fluid. J. Infect. Dis. 126 (1972) 492-497. 9. Raeburn, or. A.: A method for studying antibiotic concentrations in inflammatory exudate. J. Clin. Pathol. 24 (1971) 633-635. 10. Barza, M., Samuelson, T. Weinstein, L.: Penetration of antibiotics into fibrin loci in vivo IL Comparison of nine antibiotics: Effect of dose and degree of protein binding. J. Infect. Dis. 129 (1974) 66-72. 11, Simon, C., Materczyk, V., Brahmstedt, E., Toetler, W.: Cefazolin, ein neues Breitspektrum-Antibiotikum. Deutsch. Med. Wschr. 98 (1973) 2448-2450. 12. Nishida, M., Murakawa, T.: Exudate levels and bactericidal activity of cefazolin in a new local infection system using rat granuloma pouches. Antimicrob. Ag. Chemother. 11 (i977) 1042-1048.
