Journal of
Neurology
J. Neurol. 218, 137--144 (1978)
© by Springer-Verlag 1978
In vivo Interaction of Anticonvulsant Drugs The Mathematical Correlation of Plasma Levels of Anticonvulsant Drugs in Epileptic Patients
J. Abarbanel, Y. Herishanu*, P. Rosenberg, and U. Eylath Neurology Unit, Neurochemistry and Clinical Laboratory, Shaare Zedek Hospital, Jerusalem, Israel
Summary. The phenytoin plasma levels were measured in 45 epileptic patients whose only treatment was phenytoin. The plasma of 20 other patients receiving both phenytoin and phenobarbital was also tested for the concentration of these two drugs and 18 patients treated with phenytoin, phenobarbital and primidone were investigated in the same way. The results were used to calculate the plasma levels of phenytoin in relation to dosage and to measure the effect of the simultaneous use of phenobarbital on the phenytoin plasma levels and of primidone together with phenobarbital on phenytoin concentration. The results led to the following conclusions: The population of epileptic patients can be divided into 2 groups. In the first group the patients reach equilibrium at the relatively high phenytoin plasma level for a given dose of phenytoin, and in the second group the phenytoin plasma level tends to be significantly lower for parallel dosages. Both groups, in their behavior, obey mathematically an exponential graph specific for each group. Phenobarbital tends to lower the plasma phenytoin level when the two drugs are used simultaneously. It is also possible, by the graphs produced, to calculate the expected phenytoin plasma levels when using the drugs together. Primidone and phenobarbital together decrease the phenytoin level much more than expected from the effect of phenobarbital alone. Key words: Diphenylhydantoin - Primidone - Phenobarbital - Plasma level Epilepsy.
Zusammenfassung. Die Plasmakonzentration von Phenytoin wurde bei 45 Epileptikern, die nur dieses Medikament erhielten, bestimmt. Bei 20 weiteren Patienten, die auch Phenobarbital erhielten, wurde im Serum Dekonzentra*
Address for offprint requests: Dr. Y. Herishanu, Neurology Unit, Shaare Zedek Hospital,
P.O.B. 293, Jerusalem, Israel
0340-5354/78/0218/0137/$01.60
138
J. Abarbanel et al. tion der beiden Antiepileptika, bei 18 Patienten, die auBerdem auch Primidon einnahmen, Dekonzentration der drei Medikamente bestimmt. Es wurde die Plasmakonzentration von Phenytoin auf die eingenommene Medikamentendosis bezogen und der EinfluB der gleichzeitigen Einnahme von Phenobarbital bzw. sowohl von Phenobarbital wie auch von Primidon auf die Phenytoinkonzentration analysiert. Aufgrund der eigenen Untersuchungsergebnisse kSnnen folgende SchluBfolgerungen gezogen werden: 1. Die Epileptiker k6nnen mit Bezug auf die Phenytoinkonzentration im Serum in zwei Gruppen unterteitt werden. In einer ersten Gruppe wird ein Gleichgewicht bei einem relativ hohen Phenytoinspiegel im Serum, bezogen auf eine bestimmte Medikamentendosierung, erreicht, in einer zweiten Gruppe besteht die Tendenz zu einer deutlich niedrigeren Plasmakonzentration bei gleicher Dosis. Beide Gruppen entsprechen ihrem Verhalten mathematisch einer exponentiellen Kurve, die fiir jede Gruppe spezifisch ist. 2. Bei gleichzeitiger Einnahme mit Phenytoin senkt Phenobarbital tendenzm~iBig den Phenytoin-Plasmaspiegel. Aufgrund der vorgelegten Kurvenbilder kann man den zu erwartenden Phenytoinspiegel bei gleichzeitiger Verwendung beider Medikamente errechnen. 3. Wenn zus~itzlich zum Phenytoin sowohl Primidone als auch Phenobarbital gegeben werden, senkt dies den Phenytoinspiegel weit mehr, als aus der atleinigen Gabe von Phenobarbital zu erwarten w~ire.
Introduction
Since the development of methods for the determination of anticonvulsant plasma concentration it has been shown that there is no clear-cut relationship between the dose and plasma concentration or between plasma concentration and the control of seizures. In spite of this Richens and Dunlop (1975) have built a n o m o g r a m for adjusting phenytoin dosage and prediction of the serum phenytoin level. Lund and Atvan (1975) emphasized the importance of monitoring the plasma level of phenytoin and that it is necessary to relate its level to seizure control and drug-induced side-effects. Phenytoin (Dilantin®) is often given in association with other major anticonvulsants and a variety of interactions may take place between them. These are discovered by unexpected changes in the clinical condition of patients when new drugs are added to previous medication. Phenobarbital, one of the major anticonvulsants given in association with phenytoin, can change the phenytoin plasma level in two directions: decrease it when stimulation of the phenytoin metabolizing enzyme is more prominent or increase it when the role of phenobarbital as a competitive inhibitor of the enzyme is more prominent. Primidone (Mysolin®) is converted in vivo to phenobarbital and to PEMA (phenyl ethyl malonamide) (Samuel et at., 1971) and the ratio of phenobarbital/ P E M A plasma level was reported to be increased with the addition of phenytoin. The purpose of this study is to tabulate the dose/serum concentration relationship in treatment with phenytoin and to find the mathematical correlation
Anticonvulsant Drug Interaction
139
between the plasma concentration of the three major anticonvulsant drugs, phenytoin, phenobarbital and primidone, while being administered simultaneously.
Patients and Methods During the last three years 300 epileptic patients were monitored by determination of their
plasma anticonvulsant concentration. Of these, 45 patients were on phenytoin, 20 patients on phenytoin and phenobarbital and 18 on phenytoin, phenobarbital and primidone treatment. All patients included in this study were adults. The plasma concentration of these anticonvulsants was determined by gas-liquid chromatography, as previously reported (Herishanu and Eylath, 1974). The coefficient of correlation between phenytoin dosage and plasma level, between phenobarbital and phenytoin dosages and their concentrations, as well as between the dosages ofphenytoin, phenobarbital and primidone and their plasma concentration, were evaluated by Pearson's formula.
Results
The Relation between Phenytoin Plasma Concentration and Its Dosage The mathematical evaluations showed that the population of our 45 patients treated with phenytoin alone consisted of two groups. The first group (20 patients) had a relatively higher phenytoin plasma concentration and behaved in conformity with the following logarithmic equation (1), or exponential function (2): (1) In [DPH] = 0.254 DPH+ 0.933, [DPH] = e 0.254 DPH + 0.933,
(2)
[DPH] = plasma concentration of phenytoin in gg/ml,
DPH= dosage of phenytoin in m g / k g body weight.
7
5
_
~. . ..
. ." in iDPH3:.096DPH.1.115
2£ o
_=
0
5DPH~q--g 10
15
2(DPH*e"TSDPH~'933 t 1!
Fig. 1. The logarithmic relation between phenytoin
plasma level and daily dose Fig. 2. The exponential relation between phenytoin plasma level and daily dose
s D~.~
lo
~s
2
140
J. Abarbanel et al.
"o!"o ~1~ "1~o
~,o .~o
,17o
15
~-o
IPJ~, . 2 1 P b -4:7 DPH!" DPH
T o
10
i 0
3
5
Pb
10
2
i
i
4
DPH
6
i Pbmg~ Kg
, 10
, 12
i 14
i-16 4
Fig. 3. The relation between the ratio of phenobarbital and phenytoin plasma concentration and the ratio of phenobarbital/phenytoin daily dosage Fig.4. The relation between the ratio of phenytoin/phenobarbital plasma concentration and phenobarbital daily dose
The coefficient of regression of this function is r =-0.78. The second g r o u p (25 patients) presented a lower blood level of phenytoin and behaved in c o n f o r m i t y with equations (3) and (4). (3) l n [ D P H ] = O.096DPH+ 1.115615, (4)
[ D P H ] = e O . O 9 6 D P H + 1.115615.
The latter g r o u p had a lower regression coefficient than the first group: r = 0.306. The graphic illustration o f (1) (2) and (3) (4) are presented by Figures 1 and 2 respectively. The first g r o u p which has a significant regression coefficient is more h o m o genous than the second.
The Relationship between Phenytoin and Phenobarbital Using two parameters: x function: (5)
Pb DPH
' .
y =
[ D[Pb] PH]
we deduced the following linear
y = 2 1 . 3 x - 4.7.
The coefficient o f regression was f o u n d to be highly significant: r = 0.91. Figure 3 shows the graphic representation of the function (5).
141
Anticonvulsant Drug Interaction Table 1 Phenytoin dosage 100 mg Asymptotic value
200 mg
300 mg
400 mg
x = 22.3
44.7
67.1
89.1
43.9
75.5
104.8
132.7
Point of symmetry
d[DPH] DPH d[Pb] = 21.3Pb-4.7DPH"
(6)
For various phenytoin dosages (200,300 and 400 mg) the graphic presentation of (6) is shown in Figure 4. The mathematical form of function (6) points to the hyperbolic character of this function. This function lies between two asymptotic lines: X axis and the second one depends on phenytoin dosage. Table 1 presents the four asymptotic values in relation to four commonly used phenytoin dosages (100, 200, 300, 400 mg). From function (6) the point of symmetry which depends on phenytoin dosage might be deduced, too. Up to the point of symmetry the function descends rapidly and later on much slower. The R e l a t i o n s h i p b e t w e e n P h e n y t o i n , P h e n o b a r b i t a l a n d P r i m i d o n e
Two parameters were used: y =
[Pb] + [M] . In [DPH] '
x-
Pb + M DPH "
M = Primidone plasma concentration.
18 .18
12 .12
:S Q.
dl,n[D P H~ ~_6-3{Pb+M) -D P H
+5'9
DPH
~+ 06
r:0"85844923 ~ - - - - - - ~
o 5
::
:~ eu,-M DPH
Pb+M
..
300
looo
Fig. 5. The relation between the ratio of the phenobarbital and primidone plasma concentration/ Ln of phenytoin plasma concentration and the ratio of phenobarbital and primidone/phenytoin dosages Fig. 6. The relation between the derivate of In phenytoin plasma concentration/phenobarbital primidone concentrations and phenobarbital + primidone dosage
6
142
J. Abarbanel et al. A following linear function was obtained:
(7)
y=6.34x+5.9.
A significant coefficient of regression was obtained: r = 0.85. Figure 5 presents the graphic representation of function (7). Another equation (8) (Fig. 6) was deduced from the function (7). DPH d (In [DPH]) (8) d--~-b]+ [--~) = 6.34(Pb + M) + 5.9 DPH"
In Figure 6 the phenytoin dosage was constant (100,200,300 and 400 mg) and the function is also hyperbolic but the asymptotic value of Pb + M has no importance being negative for all four values of phenytoin. The other asymptotic line is always y = 0.
Discussion The Relationship between Phenytoin Dose and Its Plasma Concentration Level
The plasma level of phenytoin was found to increase linearly with increasing dosage expressed as dose on body weight (Stensrud and Palmer, 1964) but scattered levels were obtained in different people for doses expressed as total daily dosage (Svensmark, Schiller and Buchthal, 1960; Triedman, Fishman and Yahr, 1960). Eadie, Tyrer and Hooper (1973) showed that children under 11 years behave as a homogenous group which differed from adults requiring higher phenytoin/body weight to get the same plasma level. In individual patients Bochner et al. (1972) found that the plasma level increases with increasing dose not linearly when the plasma level is greater than 6--9 lag/ml. The phase of rapid rise in plasma level of phenytoin with metabolism approaching saturation occurs through the therapeutic range of 10--20tag/ml. This study demonstrates that the population of our patients is divisible into two groups. The members of the first group (45%) are those who behave in accord with the mathematical prevision and achieve relatively higher plasma concentration of phenytoin. The prevision of their plasma level is made considering a good absorption of the drug and a normal enzymatic system for its catabolism. The significant regression coefficient indicates the uniformity of this group. The second group (55%) is more problematical. All its members have a lower plasma level of the drug, therefore they do not confirm the previous prevision. The heterogenicity of the second group could be due to a malabsorption of the drug or to an accelerated catabolism of the drug, or both. The malabsorption of the drug a n d / o r accelerated catabolism depend on multifactorial systems which cause the wide distribution of the data. Determinations of the major phenytoin catabolite, HPPH, in the urine showed that the majority of a group of 25 epileptic patients (partially included in this study) have a low H P P H urinary concentration and subtherapeutic phenytoin plasma concentration which point to malabsorption of the drug at the level of the intestine (Herishanu et al., 1977).
Anticonvulsant Drug Interaction
143
The exponential behavior of both groups is in accord with Michaelis law on the equilibrium between enzyme and substrate. Saturation of the enzyme (parahydroxylase) has the consequence that some supplement of substrate (phenytoin) will increase the plasma concentration up to a toxic level. In the first group the discrepancy between the dosages giving a therapeutic plasma concentration and a toxic concentration (above 20 pg/ml) is 2.7 mg/kg. In the second group we found a much larger discrepancy with a larger security range which depends on malabsorption a n d / o r accelerated phenytoin catabolism in the liver. About the interaction between phenytoin and phenobarbital, there are controversial data in the literature. Cucinell et al. (1963) found that chronic administration of phenobarbital shortened the half-life of phenytoin from 7.3 h to 2.1 h in animals. Pretreatment of rats with phenobarbital prior to sacrifice resulted in a moderate increase in the activity of the microsomal enzyme studied in vitro. Lower plasma levels were found by Cucinell et al. (1965) in adult patients treated with phenytoin and phenobarbital than in those treated with phenytoin alone. Buchanan et al. (1969) found the same in a study made on five nonepileptic institutionalized patients. Kristensen et al. (1969) demonstrated in adults that previous treatment with phenobarbital for 10 days decreased the half-life of a single dose of 14C-phenytoin from 12.5 h to 8.5h. A longitudinal crossover study failed to show any stimulation of phenytoin metabolism by phenobarbital over a 2 month period (Booker et al., 1971). Various changes of the phenytoin plasma level were obtained by Kutt et al. (1969) on combined treatment with phenobarbital. Izumi (1970) and Booker et al. (1971) failed to find any significant effect of phenobarbital on the phenytoin level, but Sotaniemi et al. (1970) showed that epileptic patients on long term phenobarbital and phenytoin treatment have lower phenytoin plasma levels than on phenytoin alone. In this study the hyperbolic graphic representation of function (6) shows the correlation between phenobarbital and phenytoin. Any value of phenobarbital dosage which is lower than the asymptotic value is not relevant to the function (6) i.e. has no influence on the phenytoin plasma level. This asymptotic value seems to be the threshold of enzyme induction by phenobarbital. The higher the phenytoin dosage the higher the threshold of phenobarbital induction of the enzyme. The zone between the asymptote and symmetry point is probably the zone which has the optimal parahydroxylase-phenobarbital proportion for more enzyme induction.
The Interactions between Phenytoin, Phenobarbital and Primidone Primidone was reported to decrease phenytoin plasma concentration (Toseland, 1973). In this study the function (8) is also hyperbolic. There is no asymptotic importance in this function because the asymptotic line has all the values negative. Phenytoin plasma concentration is an indirect functional value and its parameters are primidone and phenobarbital dosages and their plasma concentrations. Function (7) shows the importance of primidone in the enzymatic induction of parahydroxylase. But one can not deduce from it which proportion of this
144
J. Abarbanel et al.
i n d u c t i o n is due to the conversion of p r i m i d o n e to p h e n o b a r b i t a l a n d which to P E M A metabolite. The data show that p r i m i d o n e is lower in all cases than p h e n o b a r b i t a l a n d indicate a m a j o r p h e n o b a r b i t a l role. The difference between f u n c t i o n (8) a n d (6) indicates the role of P E M A in this process.
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