A of an orally administered drug that

A Project Proposal:
Design of semisimultaneous oral/intravenous studies for complex absorption
IntroductionPage 2
Literature ReviewPage 3
Semisimultaneous methodPage 3
Absorption modelsPage 10
Proposed WorkPage 17
ReferencesPage 21

Introduction
Oral bioavailability (F%) is the fraction of an orally administered drug that reaches systemic circulation from site of administration 9. Oral bioavailability is an important drug properties in pre-clinical and clinical trial.

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Bioavailability is usually determined by measuring the area under the plasma concentration-time curve (AUC). 10 Bioavailability of a drug administered orally is the ratio of the area calculated for oral administration compared with the area calculated for intravenous administration. Bioavailability = AUCoralAUCintravenousx 100. Absolute bioavailability requires intravenous administration. Ratio of the oral:intravenous AUC values normalized for dose. Fabs=(AUCoral/AUCiv)*(Dose iv/Dose oral). Oral bioavailability depends on amount absorbed and amount metabolized before reaching systemic circulation (first pass metabolism). In order to determine the oral bioavailability, intravenous study have to be carried out and AUC are obtained from both oral and intravenous study separately.

However, some drugs do not exhibit the absorption profile like the usual common concentration-time profile with only one peak (Cmax) or only one absorption rate constant in the profile. These drugs display complex absorption.
Nonlinear mixed-effects models are frequently used for population pharmacokinetic data analysis, and they account for intersubject variability in pharmacokinetic parameters by incorporating subject-specific random effects into the model. Models are built using a range of software such as NONMEM, Phoenix, Matlab, R and Winonlin. This nonlinear mixed-effects model is used to understand the relationship between patient characteristics and pharmacokinetic (PK) behaviour and then design recommended dose. In this PK model, oral drug always enters depot then absorbed into central compartment in an absorption rate unlike intravenous drug directly enter the central compartment.
There are approaches for population pharmacokinetic analysis which are the two-stage approach and the nonlinear mixed effects modelling approach. Nonlinear mixed-effects modelling provides population characteristics estimates that describe the population distribution of the PK (and/or pharmacodynamic) parameter. This modelling approach is always used to estimate the parameters of the population directly from the full set of individual concentration values. Even when PK data are sparse, the ‘uniqueness’ of each subject can still be maintained and accounted for.
15 Karlsson and Bredberg (1989) mentioned that for some conditions the use of an inappropriate absorption model draw slightly reduced accuracy with poor fitting to the data. Fitting of a simpler or a more complex disposition model can produce accurate and precise estimates which are similar to those from the true model. If a proper design was used, the absorption characteristics of the simulated drugs could be adequately established in experiments lasting for 12hr or less.

Literature Review
Semisimultaneous study
In a traditional approach to determine drug bioavailability, reference dose(intravenously) and test dose(extravascularly) are usually separated into two studies. Instead of traditional method (oral and intravenous study separated into a few days or weeks), Gabrielsson and Weiner developed a conventional way to estimate the oral drug bioavailability 1. In their method, intravenous,iv and extravascular(oral) doses are administered in a sequential way with a dose interval of one day or a week. It is always assumed that clearance is constant between two occasion for the estimation of bioavailability. If the two different regimens are administered in a much shorter dosing interval (a few hours), instability or change in clearance parameter over time is mostly avoided. This method has been widely used to estimate the oral bioavailability as this method not only shorten the study duration but also reduce the demand for subjects. However, Garielsson and Weiner also stated a short yet sufficient time period should be applied between the first and second doses in this semisimultaneous study. This is to avoid the incomplete elimination of drug from the organism. The benefit of the semi-simultaneous study over the traditional method is the reduction in the influence of intraindividual variability. In the traditional method, intraindividual variability remains the main problem in bioavailability assessment.
Figure 1.

Figure 1 is adapted from 1. Reference dose and test dose studies are separated into one or several days. Blood samples of the organisms are obtained at the designated different time point and a graph of concentration versus time is plotted. Bioavailability (F) of the drug from different route of administration is determined from the area under curve (AUC) of the plotted graph Concentration versus Time.
Figure 2.

Figure 2. is adapted from 1. Reference dose and extravascular dose are carried out on the same day with two doses separated for a few hours. Gabrielsson and Weiner also stated that the difference in clearance of drug should be very little between two occasions.
Due to the convenience and short duration of this semisimultaneous method, there is an increasing number of studies carried out using this method. In semisimultaneous method, dose order is arranged according to the design of the study. As the number of studies involving this approach increased, some issues have been noticed in semisimultaneous method with oral given before intravenous dose(oral/iv).

In Karlsson and Bredberg studies from 1989, bioavailability and rate of absorption, ka of lithium were evaluated in the traditional and semisimultaneous method 17. The first dose of 1.33mmol/kg, given either intraperitoneal (ip) or intravenously (iv), with a time interval, 2 hours between doses given by the other route of administration. The following dose is 2-fold higher than the first dose. The two doses were administered in the order iv-ip (N=5) or ip-iv (N=6). In their study, the concentration-time lithium profiles were adequately described by a biexponential disposition model with first-order absorption. In their results, they found that the precision in the bioavailability estimation was good and accurate but it was independent of both dose order (ip-iv/iv-ip). In conclusion, their study results showed that bioavailability and ka of lithium can be determined by the semisimultaneous method more precisely, compared to the traditional method. This semisimultaneous approach was also developed to reduce the impact of changes in elimination with time.
Table 1. Bioavailability of Lithium in the Rat
Model Method
Semisimultaneous Traditionala
(N = 7)
iv-ip
(N = 5) ip-iv
(N = 6) Disposition Absorption Biexponential First order 0.990b (6.4) 0.974 (4.2) 1.031 (13.3)
0.959c (6.0) 0.994c (4.1) –
Biexponential Zero order 0.964 (6.5) 0.962 (4.5) –
Triexponential First order 1.035 (9.0) 0.989 (4.7) –
Model independent – – 1.035 (10.9)
a correction according to Eq.(5).

b Results are given as the mean coefficient of interindividual variation (%).

C Models fitted to reduced data sets (0- to 4-hr samples only).

Table 1. is adapted from 17. The interindividual variability in the bioavailability estimates was greater with the traditional method than with the semisimultaneous method.

Table 2. Pharmacokinetic Parameters of Lithium in the Rat
Parameter Semi-simultaneous method,
model dependenta Traditional method
(iv, 1st dosing occasion)
iv-ip ip-iv (N=5)
(N=5) (N=6) Model dependent Model independent
V1 (ml/kg) 363b (11.1) 365 (10.3) 312 (4.5) –
1 (hr -1) 3.06 (17.1) 2.58 (22.6) 3.17 (13.2) –
2 (hr -1) 0.132 (11.5) 0.144 (16.6) 0.138 (9.9) 0.108 (11.5)
C’1 0.726 (2.9) 0.710 (3.3) 0.786 (2.0) –
ka (hr -1) 27.5 (89.4) 38.8 (28.1) 176c (139) –
AUC12hr- (%)d 21 (27) 20 (39) 19 (15) 24 (13)
CL (ml/hr/kg) 157 (19.1) 158 (18.5) 169 (8.7) 162 (5.3)
a A biexponential disposition model with first-order absorption of the ip dose.

b Results are given as the mean coefficient of interindividual variation (%).

c Determined from all separate ip doses (N=7).

d Ratio of the extrapolated AUC to the total AUC.

Table 2. is adapted from 17. The ka estimation of lithium from Table 1 highly suggest the advantage of the semisimultaneous method over the fitting of a single extravascular concentration profile as the coefficient of interindividual variation (CV) of ka is significantly lower than CV of ka obtained from traditional method . They concluded that semisimultaneous study has a few advantages in bioavailability studies which are decreased intraindividual variability, potential to detect nonlinear kinetics with administration of different dose orders, a good precision and convenience of the study schedule.
From Karlsson and Bredberg’s another study 20, they investigated the possibility of determining absorption characteristics by the semi-simultaneous method. In this study, they have found that the estimations of the extent and rate of absorption were greatly dependent on the interval between the doses () and on their relative size (RD). The precision of the parameters increased only slightly when the dose interval ()was increased beyond 2hr (Figure 3.).
Figure 3.

In figure 3, it is clearly stated that dose interval () plays a vital role in estimating the accurate bioavailability (F) and absorption rate (ka). In all experiments, precision in F significantly increased when dose interval increased. In experiment A (po-iv), dose interval 2h is insufficient for the accurate estimate of bioavailability. A longer dose interval, 4h in figure 3 is much more adequate to estimate the accurate oral bioavailability. Therefore, accurate dose interval is important for semisimultaneous study, especially po-iv study.
Karlsson and Bredberg also mentioned that it is essential to ensure the concentrations following the oral dose has reached declining phase before the iv dose was administered in order to obtain high precision with a dose order of po-iv.

Table 3. Influence of the kinetic rate constants on the precision of absorption parametersa.

-762001615440-63500148844001336040
Poor design of semisimultaneous study may lead to poor parameter estimates which are shown in Table 3. Experiment 2 and 3 showed poor F and ka estimates as some amounts remained to be absorbed at the time of the iv administration with higher ka t1/2. In addition, t1/2,1 (i = disposition rate constant of the ith exponential phase) in experiment 4 and 5 are 1 and 2 hr respectively (Blue arrow). These t1/2,1 are higher than those in experiment 1,2 and 3. The peak of the oral curve nearly coincided with the time of the iv administration (=2hr). Poor F and ka are obtained with short in this case. Table 3, Experiments 6-10 showed that increasing the interval between doses led to substantial improvement in precision. In experiment 6, good F and ka estimates are obtained (Yellow arrow). With t1/2,ka=1hr, t1/2,1=0.25hr, t1/2,2=4hr, =8hr, CV obtained for F= 5.7% and 9.6% for ka.
Table 4. Parameter Estimates of Nonlinear Regressiona
Mean estimates CV (% of true values)
Method
Semi-simultaneous Traditional
Parameter po-iv iv-po iv and/ or po
F 10110 1007.4 1016.6
ka 10422 10419 10657
V1 1015.9 997.7 1007.3
1 9913 10113 10416
2 1027.6 10310 1008.5
Tlag 1017.9 999.2 1005.2
C’1 992.8 992.6 1002.5
aFor the semisimultaneous experiments the default model was used, with RD=2, T=12hr and =2hr. For the traditional method, the disposition parameters and ka were obtained by separately fitting the iv and oral data, respectively, and F was obtained as the ratio of the AUC’s predicted from the two fits.

The parameter estimates between three study designs (po-iv, iv-po and traditional) are similar. Still, the rate of absorption was found to be better estimated with better precision in semisimultaneous study than traditional method. This result is shown similar to the previous work which was also done by them 17.
Furthermore, Karlsson and Bredberg concluded that the rate of absorption is the key drug characteristics in the choice of dose interval. The slower the absorption, the longer the is required. Of the two dose orders, po-iv requires the longest interval. For this order of doses, the absorption should be almost complete and the concentration-time curve already decreasing before the iv administration.
Correct parameter estimates may be difficult to obtain from a very complex concentration-time relationship, especially for the complex absorption. A correct absorption model is essential for the modelling of the absorption process of a drug in order to obtain more precise and accurate parameter estimates.
By using this semisimultaneous study, the advantage is the feasibility of determining bioavailability on a single occasion. The reduction in intrasubject variability thus obtained varies between drugs and individuals. This semisimultaneous method is also favourable in clinical settings because of the intraindividual changes in patients and drug administration on a second occasion is often not feasible. This single occasion experiment not only reduces subject discomfort but also the subject dropout. In traditional method, the extrapolated fraction of the AUC is low, which may be problematic for a drug with a long terminal half-life. The determination of absorption parameters and bioavailability by the semisimultaneous method may be accurate and precise despite the large extrapolated areas and long terminal half-lives. This method is beneficial for drugs with large intraindividual variability or long terminal half-lives and also when a determination on a single occasion is desirable.
As mentioned above, semisimultaneous study is ideal for clinical study as a clinical study such as intensive pretransplant pharmacokinetic test design by Fanta et al. (2007) as semisimultaneous study simplified this time-consuming clinical design. In Fanta et al. (2007), pharmacokinetics of ciclosporin in paediatric renal transplant patients were studied by using 12 blood samples taken within 0 to 28 hours after intravenous dose (3 mg kg-1) and 10 blood samples taken within 0 to 24 hours after oral dose (10mg kg -1). This clinical study design is time-consuming, expensive and also highly demanding on the candidates. Therefore, semisimultaneous method was used by Hennig et al. (2012) 21, which reduced 22 samples to 6 samples and carried out iv/oral study within 8 hours. With this simplified study design, fewer samples are needed to relieve the patient burden and also reduced patients dropout as they are able to follow the entire procedure during a single visit to the clinical and there is no need for staying overnight. Clearly, semisimultaneous study displays superiority for some complicated clinical study design.
Two papers about using semisimultaneous method to study pharmacokinetics of midazolam from Brill et al. (2015) and Lee et al. (2002) were published. Semisimultaneous method is indeed a good method for clinical studies. Brill et al. (2015) compared the hepatic and intestinal extraction ratios (ERH and ERG, respectively) of the CYP3A probe drug midazolam in semisimultaneous and traditional method. They also evaluate the hepatic and intestinal metabolism of midazolam with and without ketoconazole by the semisimultaneous method. In both traditional and semisimultaneous method, a 2-compartmental model with zero-order absorption was used. On the semisimultaneous method, each subject received oral midazolam, 5.0mg. With 6-hour dose interval, the subject is given an intravenous midazolam infusion (2mg) over 30 minutes.

Figure 4.

Figure 4. Midazolam concentration versus time (upper panel) and nurse-related sedation score versus time (NRSS) (lower panel) after semisimultaneous midazolam administration (mean and standard error of the mean).

Figure 4. adapted from 28 showed midazolam concentration versus time profiles were well described by the integrated oral-iv model with zero-order absorption. In figure 4, the oral study profile seems very good as it showed a good profile for accurate oral bioavailability estimation before intravenous administration at 6 hours.
In this study, they also demonstrated that semisimultaneous is a suitable approach can for the assessment of drug interaction as this method also yielded expected remarkable changes in the parameters as a result of ketoconazole inhibition. In this study, special study design considerations for phenotyping with the semisimultaneous midazolam method included the doses used and the timing of intravenous midazolam administration. The 6-hour interval was fixed to ensure complete absorption and distribution of midazolam after the oral dose before the start of the intravenous infusion. This interval was appropriate as no subject was in the absorption or distribution phase when the intravenous infusion was commenced (longest absorption time, 65minutes; longest distribution half-life, 73.4 minutes).
Although midazolam PK parameter estimates and the liver- and intestine-specific measures of CYP3A activity determined by semisimultaneous study showed no difference from those determined by the traditional method, this semisimultaneous study is ideal for complex clinical study design which involved a lot of candidates and time.
In a study by Brill et al. (2015)2, semisimultaneous method was also used to study the PK of CYP3A probe substrate midazolam in a cohort of morbidly obese patients that were studied before and 1 year post bariatric surgery. Patients were given a 7.5mg midazolam tablet (orally) and after 16048min an iv dose of 5mg was administered. For the population PK analysis, a three-compartment model best described the data. Midazolam oral absorption was best described using five transit compartments.
Figure 5.

126527598258100
Figure 5 is adapted from 2. Midazolam concentration versus time after oral dose profiles upon a 7.5mg oral midazolam dose and a 5mg intravenous dose separated by 160 ± 48 min in 20 morbidly obese patients before (black lines) and 1 year after surgery(grey dotted lines).
As Brill et al. (2015) mentioned, before bariatric surgery, the peak concentrations after the iv dose were found to vary largely and this was due to the differences in time of intravenous midazolam administration. Due to this large differences in time of iv administration (even one patient was dosed intravenously at about 300minutes, indicated arrow in figure 5), this causes different oral profile of midazolam in this cohort of patients. As Karlsson and Bredberg mentioned, dose interval is a factor of precision of parameter estimates 20. In this case 2, the large difference in oral and intravenous doses interval in these 20 morbidly obese patients may lead to less accurate and precise estimation of parameters such as bioavailability. Also, a dose interval of 160 ± 48 min seems to be generous as pharmacokinetic of midazolam could alter in a period of 48 minutes.
Semisimultaneous method has been shown to be a good method for precise estimation of oral bioavailability and other parameters such as absorption rate. However, for oral/ intravenous study, it is essential to have a precise and accurate time for the intravenous administration after oral administration (Lag time). A short lag time may not provide a precise and accurate oral bioavailability estimation as the oral drug may not be absorbed and distributed completely at the start of the intravenous administration. Moreover, some drugs exhibit complex absorption, for example, sequential first-order and zero-order absorption. For this complex absorption characteristic, a longer lag time may be needed as drug takes a longer duration to enter the systemic circulation from the site of administration. A more complex absorption model is also needed for drugs with complex absorption. For pharmacokinetic modelling, additional parameters from more complex absorption models benefit the drugs with complex absorption. Additional parameters and longer lag time could capture the complex absorption phase of drugs more precisely and accurately which could then provide a more accurate and precise bioavailability estimation when compared to observed data.
Absorption models
In pharmacokinetic modelling, most of the oral drugs are assumed to display a first-order absorption. In NONMEM, subroutines like ADVAN2 TRANS2 and ADVAN4 TRANS3 are commonly used with the first-order absorption parameterized in ka.

For oral administration, drug is mostly absorbed in the gastrointestinal tract (GI) and then enters the systemic circulation 24.
1424482110342DB VD
DB VD
Absorption Elimination
27747739076140403790761DGI DE
The rate of change in the amount of drug in the body, dDB/dt, is dependent on the relative rates of drug absorption and drug elimination.
dDBdt= dDGIdt- dDEdt
Where DGI is amount of drug in the GI and DE is amount of drug eliminated. During the absorption phase, elimination occurs as long as drug is present in the plasma.
Zero-order absorption model is used for drug which is absorbed by a saturable process or in controlled-release formulation 24. Drug is being absorbed in zero-order absorption, k0 from the site of administration into the plasma.
1222597147158DB VD
DB VD
k0 k
2594344106946276446106946DGI
One-compartment pharmacokinetic model for zero-order drug absorption, k0 and first-order drug elimination.
The net change per unit time in the body is expressed as:
dDBdt=k0 -kDB
Integration of this equation with the substitution of VD Cp for DB produces:
Cp=k0VDk (1- e-kt)
First-order absorption model is mostly used in drug in immediate release form.
1190847120960DB VD
DB VD
ka k
2392267807480025518180748DGI
dDBdt=FkaD0e-kat-kDB
ka is the first-order absorption rate constant form the GI tract, F is the fraction of drug absorbed systematically, D0 is the dose of the drug. The drug in the GI follows a first-order decline, thus the amount of drug in the GI at any time t is equal to D0e-kat.

Cp= FkaD0VDka-k e-kt-e-kat
Besides these two typical absorptions, some drugs exhibit mixed-order absorption.
Figure 6.
2455811323717Zero-order
0Zero-order
662305975360First-order
00First-order

Figure 6. is an absorption profile of drug with sequential first-order and zero-order absorption.
In 18, five absorption rate models have been compared for describing cefetamet data in 34 adults after given cefetamet pivoxil orally. In their results, the most consistent estimates of the disposition parameters and the extent of bioavailability were achieved with the sequential zero- and first-order model. Different absorption models have a different number of parameters and the population parameter estimation was performed using a nonlinear mixed effect model NONMEM. In their study, a time delay, Tlag in absorption is implemented in each absorption model.

The 5 absorption rate models tested are shown below:
First-order Model (KA)
Absorption occurs by a first-order kinetic. F is the extent of bioavailability. The absorption rate is proportional to the amount of drug remaining in the gut and an absorption rate constant ka.
Cp = KA(F Dose, ka , T – Tlag)
Zero-order Model (K0)
The absorption rate remains for a period of time, Tk0, the apparent input duration.

Cp = K0(F Dose, TK0 , T – Tlag)
Sequential Independent Zero- and First-order Model (K0KA)
A fraction of the Dose, FKO, is absorbed by a zero-order process whereas the remaining fraction is then absorbed by a first-order process. The first-order absorption process follows the zero-order process, otherwise they are independent of each other.

Cp= K0( F Dose FK0, TK0 , T – Tlag) + KA(F Dose (1- FK0), ka , T – Tlag – TK0)
Sequential Linked Zero- and First-Order Model (K0KA*)
ka is defined by the parameters FK0 and TK0. The absorption of cefetamil pivoxil is constant (zero-order) until the solubility product is achieved. For the zero-order period, the absorption rate Ratesol will be
Ratesol= FK0?DoseTK0FK0 is the fraction of dose absorbed while solubility is limiting the amount of cefetamet pivoxil in solution and TK0 is the time duration when this fraction of dose is absorbed.
Zero-order absorption period terminates when the solubility product is reached and then first-order absorption begins, the amount remaining in the gut is (1-FK0) ?Dose, therefore the absorption rate by each of the two processes will be the same
Rate= FK0?DoseTK0=ka?1-FK0?DoseFrom this equation, ka* can be determined where
ka*=FK01-FK0?TK0The absorption time course is defined by
Cp = K0 (F Dose FK0, TK0 , T – Tlag) + KA (F Dose (1- FK0), ka , T – Tlag – TK0)
Saturable Adsorption Model (MM)
In this model, a saturable mechanism with a maximum absorption rate, Vmax is used to describe absorption phase. The absorption rate of 50% of Vmax when the amount in the gut is Km.

dCpdt=F? Vmax?GutKm+Gut- Cp?CLVssAll of the five absorption models mentioned above are the absorption models tested in Holford et al. study (1992) 18.
Transit compartment model is a commonly used absorption model which can describe the delay in drug absorption. This model was shown to be an appealing alternative for modelling drug absorption delay, particularly in a case when a LAG model poorly describes the drug absorption phase 27.
Figure 7. Schematic view and mathematical description of the drug flow through the chain of transit compartments.

Figure 7. is adapted from 27. This model described the absorption delay by the progress of drug through a series of transit compartments with a single transfer rate constant, ktr. The rate of change of the amount of drug in the nth compartment is given by:
dandt=ktr? an-1-ktr? an (1)
In Eq(1), dan/dt is the rate of change of substance a in compartment n at time, t, an is the drug amount in the nth compartment at time t, ktr is a transit rate constant from nth -1 compartment to the nth compartment and n is the number of transit compartments.
An optimal number of transit compartments is also estimated. To find the optimal number of transit compartment, the analytical solution for an is:
ant=F?Dose ? ktr ?tnn! ? e-ktr?t(2)
In Eq. 2, F is drug bioavailability and n! is the n factorial function with argument n. The approximation of Stirling to n! was then used to compute Eq. 2 numerically. (Eq. 3):
n! ? 2? ? nn+0.5? e-n (3)
An approximation error of the Stirling formula is less than 1% for n > 2. If n is a small value (< 2), an improved version of the approximation need to used.

The disappearance of drug in this absorption model was described with the rate constant ka. The rate of change of drug amount in the absorption compartment (dAa/dt) is given by:
dAadt=Dose ?F ? ktr ? ktr?tn? e-ktr?t2? ? nn+0.5?e-n-ka? Aa (4)
Stirling’s approximation to n! is a continuous function of n, which allowed implementation of Eq. 4 in NONMEM using subroutines for general non-linear models and to estimate the number of transit compartments n.
To prevent numerical difficulties when n was large, Eq. 5 was needed.

dAadt=eln?(Dose ?F ? ktr ? ktr?tn? e-ktr?t2? ? nn+0.5?e-n)-ka? Aa (5)
Mean transit time (MTT) is a useful parameter in the TRANSIT model. This parameter represents the average time spent by drug molecules travelling from the first transit compartment to the absorption compartment. The relationship between MTT, n and ktr is shown in Eq. 6:
ktr= n+1 MTT (6)
In Brill et al. (2016), a transit compartment model was implemented to describe the absorption of midazolam in the midazolam semi-PBPK model. In the transit compartment model, the oral absorption rate was equalized to the transit compartment rate (Ktr) was used.
In Lee et al. (2015), more complex absorption was implemented into a population pharmacokinetic (PK) model of sumatriptan which shows atypical absorption profile with multiple peaks. In their results, they found the PK of sumatriptan is best described by a one-compartment model with first-order elimination, and a combined transit compartment model and first-order absorption with lag time (Figure 8).
Figure 8.

Figure 8. is adapted from 16. It shows the scheme of the final PK model of sumatriptan. ka1, absorption rate constant from the depot; ka2, absorption rate constant from the final transit compartment to the central compartment; ktr, identical transfer rate constant of the transit compartment model; f, fraction of the dose absorbed through the absorption compartment; n, number of transit compartments placed before the central compartment; an, the drug amount in the nth compartment; CL, clearance.
This absorption model contains more parameters than the first-order and zero-order absorption model. Parameters are ka1, ka2, MTT(mean transit time), n: number of transit compartments, f: fraction of the dose absorbed by transit compartment model.
In 6, the complex, multiple peaks, absorption kinetics of simvastatin was best described by a pharmacokinetic model using three parallel, mixed zero and first-order absorptions (Figure 9).
Figure 9.

Figure 9 is adapted from 6. This is a model with three parallel, mixed zero- and first-order absorption models. The dose of the drug is distributed to three depot compartments, with the absorption of drug following mixed zero- and first-order kinetics with lag times in each absorption process. In this model, there are 35 parameters.
In 6, the relative bioavailability from each of the three depot compartments are described by the following equations:
F1 = 1(1+BA1+BA2)F2 = BA1(1+BA1+BA2) F3 = BA2(1+BA1+BA2)F1, F2 and F3 here are the bioavailabilities from each depot compartment.
BA1 and BA2 are parameters in the absorption model that describe the relative bioavailabilites. The population averages of BA1 and BA2 are estimated respectively. F1, F2 and F3 are the total amounts of bioavailable drug is absorbed through all the absorption peaks sequentially.
An accurate absorption model is vital to describe the absorption phase of drug precisely and thus estimation of the parameters will be improved. All of the studies mentioned earlier have shown the good precision of parameter estimates by using semisimultaneous study. However, none of the studies indicated the reason of choosing the particular time for intravenous dose after oral dose (lag time) in their semisimultaneous oral/intravenous study although the estimation of parameters such as bioavailability is good with low standard error (SE). Furthermore, there is no guidance established about the method to be used to choose the optimal, accurate lag time in a semisimultaneous oral/iv study. It is important that a precise lag time is chosen in an oral/iv study in order to provide an accurate estimation of bioavailability of a drug.
The aim of this study is to identify the impact of lag time on the parameters estimates in an oral/iv study using different absorption models. Different absorption models are investigated as a more complex absorption model such as sequential first- and zero-order absorption may need a longer lag time in an oral/iv study as the drug takes a longer time to reach the systemic circulation (central compartment in population pharmacokinetic model) from the site of administration. In contrast, first- and zero-order absorption model are simple with fewer parameters. A more complex absorption model also has more parameters than first- and zero-order absorption. With more parameters, the complex absorption model can capture the absorption phases of drugs with complex absorption better and more precisely. Therefore, the relationship between different lag time, different absorption models and estimation of parameters will be determined in this study.
Proposed Work
Objective: To investigate the impact of lag time (Tlag) on the estimation of parameters in an oral/intravenous study using different absorption models. Tlag is the time interval between oral dose and intravenous dose in this oral/iv study.

Population parameter estimation is performed using a nonlinear mixed effect model NONMEM. Simulation is carried out based on realistic parameters on clearance (CL), volume of distribution (V), bioavailability (F) and absorption rate constant (ka). The input of ?, and ? for CL, V, F and ka is obtained from previous literature for simulation. Bioavailability, F is varied in a range of 0-1 in order to investigate if bioavailability would affect the parameters estimates. A range of lag time tested is 30-720minutes.
Precision of parameter estimates in different absorption models with different lag time is investigated by comparison of the coefficient of variation (CV%) generated in NONMEM simulation. Parameter estimates interested in is CL, V, F and ka. Absorption models used are shown in Table 5. Graph of Tlag versus CV% of F and ka is plotted after simulation.
For statistical model, the individual parameter estimate (Empirical Bayes Estimate or post hoc value) of the ith individual was modelled using Eq(1):
?i=?mean×exp?i (1)
Where ?mean is the population mean parameter value, i is the deviation from the population value for the ith individual with a mean of zero and variance of 2, assuming log-normal distribution in the population. The residual unexplained variability is described with a combined proportional and additive error model. The jth observed midazolam concentration of the ith patient(Yij) in Eq.2:
?ij= Cpred,ij×(1+ ?ij) (2)
Where Cpred,ij is the population predicted midazolam concentration of the ith individual at the jth time, and ij is a random variable with a mean of zero and variance of 2.
Table 5.

Model Absorption model
M1 First-order
M2 Zero-order
M3 Sequential zero-order then first-order absorption
M4 Sequential first-order then zero-order absorption
M5 Single mixed, zero- and first-order absorption
M6 Two parallel, mixed zero- and first-order absorption
M7 Transit-compartment model
M8 Transit-compartment model and first-order absorption
Table 6. Parameter estimates of different absorption models with different lag time in an oral/iv study.

Absorption model Transit-compartment model and first-order absorption Transit-compartment model Two parallel, mixed zero- and first-order absorption Single mixed, zero- and first-order absorption Sequential first-order then zero-order absorption Sequential zero-order then first-order absorption Zero-order First-order Parameter CL (L/h) V (L) Ka (hr-1) ka2 (hr-1) F Interindividual variability (%) CL V Ka F Proportional residual error (%) Additive residual error (%) OFV
References
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