Simple Methodology to Estimate Bioavailability in Early Clinical Studies: Theory and Reality

Abstract

Aim: We propose a simple methodology to estimate oral bioavailability from Phase I clinical trials, which can be broadly phrased as ‘calculated bioavailability’ (F_CAL). Materials & methods: F_CAL is estimated by obtaining the product of circulating maximal observed drug concentration (C_max’) and the estimated volume of distribution at steady state (V_SS’) followed by dividing this product by the administered dose (d). V_SS’ is estimated by allometric scaling based on the preclinical intravenous data. Results & conclusion: Overall, these analyses indicate that when the absorption is faster than elimination process and the V_SS’ allometry exponent is between 0.9 and 1.1, the Fcal is a good estimate of the F.

Keywords::

• absorption
• allometric scaling
• C_max
• drug development
• formulation
• human
• oral bioavailability
• pharmacokinetics
• Phase I
• Vd

Understanding of oral bioavailability is a key consideration in drug development. Oral bioavailability, commonly referred to as bioavailability (F), is defined as an estimate of the relative fraction of the orally administered dose that enters into the systemic circulation [1]. The regulatory requirements state that the absolute oral bioavailability for a New Chemical Entity is not needed unless there is a particular reason to require such data [2]. Such a study is typically conducted once the New Chemical Entity is furthered along in clinical development (Phases II and III) and there is confidence in its clinical safety and efficacy. The requirements of absolute oral bioavailability studies are slightly different in different regulatory environments [3]. Due to the cost and resources required to perform intravenous (iv.) pharmacokinetic (PK) studies, iv. data are not available in almost all early stages of clinical development and in most New Drug Applications and marketed oral drugs [4].

Bioavailability (F) is obtained by complementing oral (PO) dosing with iv. dosing and using Equation (1) [3]:

where AUC_po and AUC_iv. are areas under the curves of concentration-time plots obtained after PO and iv. administration, respectively, and D_iv. and D_po are the iv. and PO doses, respectively. It is known that F is a product of the fraction absorbed (F_a) and the fraction that escapes intestinal (F_I) and hepatic (F_H) elimination (Equation (2)) [5].

For a given drug, F_I and F_H are physiologically dependent parameters, which typically cannot be readily modulated. But F_a may be manipulated by optimization of the formulation or drug form. Thus, if exposure limitation was mainly due to low F_a, then it may be feasible to optimize the formulation to enhance the drug exposure. For example, if F is less than 10–20% when the hepatic first pass effect is estimated to be low to moderate, one may be able to improve it by formulation or by form and size control. In this current study, we introduce a simple methodology termed ‘calculated bioavailability’ (F_cal) for the purpose of estimating bioavailability (F) prospectively, providing data that could be used in early clinical development in the absence of human iv. data to identify absorption issues that can benefit from formulation work. In this study, we examined a theoretical basis of F_cal along with its limitations, and finally assessed its utilities using multiple clinical examples.

Theory & methods

Theory & simulations

The oral F_cal was estimated using Equation (3):

where C_max’ is the maximal observed drug concentration in systemic circulation after PO dosing, D is the administered oral dose and V_ss’ is the apparent volume of distribution at the steady state. V_ss’ can be estimated by either allometric scaling based on preclinical iv. data as a prospective method or human iv. data [6] as a retrospective analysis.

For simplicity, we used a one-compartment model with first order absorption and elimination to build a theoretical relationship between F_cal and F. Under this one-compartment assumption, the concentration (C) in circulation after PO dosing was expressed as Equation (4) [5]:

where k_a and k are the absorption rate constant and elimination rate constant, respectively, F is the bioavailability, D is the administered oral dose, V is the volume of distribution and, t is the time after dosing. At the corresponding time of C_max, namely t_max, the theoretical C_max could be calculated as Equation (5):

Since the rate of change of concentration is 0 at t_max, the following equation holds true:

Then,

Therefore, the theoretical t_max could be calculated as Equation (8) in the one-compartment model as follows:

Based on Equation (7),

Accordingly, the theoretical C_max could be further rearranged as Equation (10) after Equation (9) was incorporated into Equation (5) and expressed as follows:

When the observed C_max [C_max’ in Equation (3)] is the same as or close to the theoretical C_max, we can replace C_max’ in Equation (3) with C_max in Equation (10),

Similarly, when the predicted or measured V_ss [V_ss’ in Equations (3) and (11)] is the same as or close to the theoretical V,

Since e^−ktmax < 1, therefore F_cal < F when V_ss’/V = 1. For the prediction of PK parameters in human, besides the in vitro in vivo correlation, the allometric scaling also has been widely used with the assumption that there are anatomical, physiological and biochemical similarities between animals and human. In general, comparing with the prediction of the clearance, the allometric scaling has been reasonably accurate on the prediction of volume of distribution with or without the correction of the protein binding [7].

Based on Equations (8) and (12), Equation (13) can be derived as follows:

Equation (13) was used to examine the relationship between F_cal/F versus k_a and k, and their ratio k_a/k.

Clinical examples

Marketed drugs

The PK parameters, including preclinical and clinical V_ss, human bioavailability (F), observed C_max’, together with the doses (D) for the marketed, orally dosed drugs (total of 35 drugs) were obtained from two independent sources reported in 2005 and 2011 [8,9]. All drugs with the available PK parameters were included in the analysis without preselection. C_max’ is the reported observed maximal drug concentration after PO dosing expressed in units of μM and the administered dose is expressed in mg/kg. V_ss’ was determined by either preclinical simple allometric scaling methodology in units of L/kg or the measured values from published studies in 2011 for comparison [8]. Based on the definition, the F_cal was estimated using Equation (3). Correlations were evaluated between F_cal and measured F and visualized using the Vortex program (Dotmatics, Bishops Stortford, UK).

Vismodegib

F and other PK parameters for vismodegib in healthy female subjects were obtained from the existing literature [10].

GDC-0834

A PO suspension dose of 105 mg of GDC-0834 was administered to healthy volunteers and the PK parameters were reported in previous studies [11].

Human subjects & clinical trials

The studies were reviewed and approved from the formally constituted review board (institutional review board or ethics committee).

Preclinical examples

The PK parameters of mouse, rat, dog were examined. These were PK studies that both iv. (1 mg/kg) and oral (2 or 5 mg/kg) administration of the drugs were conducted. All compounds with the available PK parameters were included in the analysis without preselection. The numbers of studies were 519 for mouse, 986 for rat and 44 or 85 for dog. C_max’ was the reported observed maximal drug concentration after PO dosing expressed in units of micrometers and the administered dose was expressed in milligrams per kilogram. Measured V_ss was used for mouse and rat. For dog V_ss, both the measured and estimated from mouse and rat based on simple allometric scaling were used. Based on the definition, the F_cal was estimated using Equation (3). Correlations were evaluated between F_cal and measured F and visualized using the Vortex program (Dotmatics).

Results

Simulations

The theoretical relationships between F_cal/F versus k_a and k are presented in Figure 1. The plot demonstrated that for the purpose of using F_cal to predict F (assuming a one-compartment model), a high k_a (fast absorption) and a low k (slow elimination) would be required. To state this more simply, the proposed F_cal method will provide a more accurate estimate of F for those compounds with relatively fast absorption and slow elimination. The relatively fast absorption may depend on several factors including rates of dissolution, food and stomach emptying. Furthermore, in quantitative terms, it is the ratio k_a/k that determines the accuracy of this proposed method based on Equation (13). The relationship between F_cal/F versus k_a/k is shown in Figure 2. It is clear that a high ratio of k_a/k results in a high ratio of F_cal/F (approaching 100% with more accurate prediction). Our simulations indicated that when k_a/k = 30, then F_cal was calculated to be 90% of F; when k_a/k = 12 and 6, then F_cal was found to be 80 and 70% of F, respectively.

Figure 1. The effect of k_a and k on F_cal/F.

When k is small (the half-life is long) and k_a is large (the absorption is fast), F_cal is fairly close to the measured F (left upper corner). However, as k grows larger and/or k_a becomes smaller, F_cal becomes a smaller fraction of F (right lower corner).

Figure 2. The theoretical relationship between F_cal/F and k_a/k.

A high ratio of k_a/k will result in a high ratio of F_cal/F (approaching 100% with more accurate prediction). Our simulations indicate when k_a/k = 30, then F_cal = 90% of F; when k_a/k = 12, then F_cal = 80% of F; and when k_a/k = 6, then F_cal = 70% of F.

Clinical examples

Marketed drugs

When the F_cal method was used and V_ss’ was determined by allometric scaling, good correlation was observed between measured F and calculated F_cal provided that the allometric exponents were between 0.9 and 1.1 (Figure 3A, green dots). The improvement of V_ss’ prediction with other methods could further improve the usefulness of the F_cal method as demonstrated in Figure 3B under the ideal condition by using the measured V_ss’.

Figure 3. The F_cal method for marketed drugs.

(A) When the F_cal method was used with V_ss’ determined by simple allometric scaling, there was a good correlation between measured F and calculated F_cal provided the exponents were between 0.9 and 1.1 (Figure 3A, green dots). (B) The estimate of F_cal could be further improved under ideal condition by using the measured V_ss’.

Vismodegib

When dosed orally at 150 mg, the average C_max calculated was 5.95 μM (n = 6)

GDC-0834

GDC-0834 was dosed PO at 105 mg to healthy volunteers. After dosing, the drug was not found in the circulation, except for the major circulating metabolite or hydrolyzed product (referred to as M1) as reported previously [11]. The average C_max’ of M1 was 9 μM or 390 ng/ml. In a separate study, the metabolite M1 was dosed intravenously in rats and the V_ss’ was determined to be 1.94 l/kg. If we assume the same volume of distribution normalized by the body weight between rat and human (allometric exponent, b = 1), the total amount of metabolite M1 at t_max is 53 mg (calculated as V_ss’ × C_max’, assuming that the average human body weight is 70 kg). This resulted in F_cal value of 70% (absorption of GDC-0834 into portal circulation) compared with the parent dose after the conversion of the molecular weight from M1 to parent (Figure 4).

Figure 4. Estimation of absorption of GDC-0834 into portal circulation in human using data from M1 metabolite.

GDC-0834 was dosed PO at 105 mg to control volunteers. No drug was detected in the circulation except for the major circulating metabolite M1 (hydrolyzed product). The average C_max’ of M1 was 9 μM or 390 ng/ml. In a separate study, the metabolite M1 was dosed intravenously in rats and the V_ss’ was determined to be 1.94 l/kg. If we assume the same volume distribution normalized by the body weight between rats and humans (allometric exponent, b = 1), the total amount of metabolite M1 at t_max is 53 mg (calculated as V_ss’ × C_max’ assuming that the average weight of human body is 70 kg). This resulted in F_cal about 70% compared with the parent dose after the conversion of the molecular weight from metabolize (M1) to the parent GDC-0834. The molecular weights of GDC-0834 and M1 are 597 and 433 Da, respectively.

Preclinical assessment

Robust correlations were observed between log measured %F and %F_cal for the data from all three species tested (Supplementary Figure 1). Linear regression was performed for each set. The largest dataset, from rat, included 898 compounds and the measured %F spanned four orders of magnitude (from 0.03 to 300). For over 90% of the set, the measured %F was greater than %F_cal. Log measured %F showed a good linear fit by log %F_cal, with a slope of 0.77 and an intercept of 0.64; the R² of the correlation was 0.75.

Discussion

F_cal is a simple, mathematical term used for representation of bioavailability of orally administered drugs. It is derived as a product of C_max’ and V_ss’ divided by the total administered dose. F_cal can be calculated after First in Human studies and the potential absorption issues can be identified and could be potentially addressed by formulation work. Using conditions of a one-compartment model, we elaborated the theoretical aspects of this concept in the current study. We also demonstrated the circumstances where F_cal closely matches F and finally were able to explore the practical usage of this method. Compared to one-compartment model, the two-compartment model was examined for the proposed method and the results were not conclusive since more PK parameters were involved. For two-compartment model, more uncertainties occur as at t_max the central compartment and peripheral compartment may have different concentrations. Therefore, here we used the one-compartment model for the purpose of determination of F_cal in terms of C_max’ and V_ss’ and the total administered dose.

The core feature of this concept is based on the amount of drug remaining in the body at t_max after the oral dose. This parameter is dependent on both k_a and k as described in Equations (8) and (12). There are two factors that cause F_cal to underestimate the measured F. The first factor is theoretical and based on Equation (12). Theoretically, F_cal is always less than F as it is well established that F_cal is the remaining fraction of F at t_max. The parameter that is not accounted for in the F_cal (compared with F) is the fraction of the bioavailable dose (F) eliminated from time zero to t_max, namely 1- e^−ktmax. Therefore, the relationship between F_cal and F could be understood from the mass balance point of view, in other words, the more of the drug remaining at t_max (larger e^−ktmax), the closer F_cal is to F. With this knowledge, based on Equation (13), it seems possible to improve the accuracy of F_cal, at least theoretically, by dividing the F_cal by the expression e^−ktmax, where k can be estimated from the slope of the PK curve, assuming a one-compartment model. The effects of k_a and k on the F_cal method or F_cal/F are apparent in Figure 1. When k is small (the half-life is long) and k_a is large (the absorption is rapid), F_cal is fairly close to measured F (left upper corner of Figure 1). However, as k grows larger and/or k_a gets smaller, F_cal becomes a smaller fraction of F (right lower corner of Figure 1). Considering a drug with a reasonable half-life and a short t_max, F_cal should provide a reasonable assessment of F, especially for the drugs intended for immediate release with once a day dosing. Another way to visualize this relationship is by comparing the ratios of k_a/k to F_cal/F (Figure 2). When k_a/k > 6, F_cal/F is about 70% of true oral bioavailability, which is a reasonable estimation considering the normal data variability is around 30% (internal communication). This means that the calculations using F_cal account for the majority of the absorbed dose in the body. There is a second factor that makes F_cal lower than measured F. Specifically, the maximal observed concentration (C_max’) usually is considered to be lower than the theoretical C_max due to the limited number of sampling time points. This issue can be addressed by increasing the frequency of PK sampling around the t_max, if feasible.

In addition, there is an important factor influencing the application of the F_cal method to the prediction of F, which is the value of V_ss’ as used in the calculation (Equation 11). This factor is usually not a serious concern based on the assumption of scalability of V_ss except the case when free fraction (f_u) is highly variable across species. However, by comparing (A) and (B) in Figure 3 with the marketed drugs, it was clearly demonstrated that the accuracy of V_ss’ played a critical role in the accuracy of the F_cal method. The V_ss’/V in Equation 11 should be close to 1 if the measured values were used and the compound follows one-compartmental model kinetics. Therefore, there is a probability that F_cal/F would in fact be > 1 as shown in Figure 3 because of the overprediction of V_ss’. In Figure 3A, the allometric scaling method was used and the prediction confidence of F_cal could be stratified based on the value of the exponent from V_ss’ allometry. The improvement of the V_ss’ prediction with other methods could significantly improve the usefulness of the F_cal method as demonstrated in Figure 3B under ideal conditions by using the measured V_ss’. There are several methods for the prediction of V_ss’ [13] however they are beyond the scope of this work. Generally, allometric scaling and in vitro methods are considered relatively reliable and accurate to predict human volume of distribution within twofold of error for most of compounds [7]. Since V_ss’ plays a critical role in the F_cal method, we propose that the F_cal method should be used cautiously when the exponent value is far outside the range of 0.9–1.1 based on allometric scaling of V_ss’, or ‘free’ allometry should be considered for the V_ss’ prediction when the plasma protein binding was significantly different from each species.

To further explore this methodology, we used two in-house clinical examples to demonstrate the concept with available clinical data. These examples allowed for the assessment of F_cal methodology and decide on the next steps. Vismodegib had a very long half-life plus the micromolar sustained concentrations. For GDC-0834, only a cleaved product was observed in circulation and the question was related to the absorption of the drug-related material.

The first example involved vismodegib, a drug that has an extremely low k with a terminal half-life of several weeks [10]. The low rate of elimination of the drug is mainly due to the very low hepatic metabolic clearance. Vismodegib has unusual ADME (absorption, distribution, metabolism and excretion) properties, but one aspect of it that could be useful for our examples is the determination of bioavailability of this drug using a conventional method versus the proposed method. Based on an absolute bioavailability studies in humans, F is 31.8% for vismodegib. By using the measured V_ss’, F_cal was 27.4%, which was comparable to the measured F. However, the F_cal was calculated as 77.2% when the predicted V_ss’ was used based on the allometric scaling. It was not clear what the reason(s) were behind the difference between measured and predicted V_ss’. This example further demonstrated the important role of V_ss’ in the estimation of F_cal.

The second clinical example involved GDC-0834, a clinical candidate used for inhibiting Bruton’s tyrosine kinase [11]. Preliminary metabolite identification studies of GDC-0834 suggested significant species differences in the extent and type of metabolism [11]. In vitro studies showed evidence for amide hydrolysis observed mainly in human liver fractions. This hydrolysis rate was observed as a high risk for this program but expedited clinical studies were necessary to confirm this. In the clinical studies, GDC-0834 (105 mg) was dosed orally and plasma samples at various time points were collected to quantitate GDC-0834 and its hydrolyzed metabolite M1 [11]. No detectable level of GDC-0834 was observed, however the major metabolite M1 was detected. Here, we applied the F_cal concept to determine the exposure of GDC-0834 based on the M1 PK data (Figure 4). Based on these calculations, F_cal was approximately 70% (absorption of GDC-0834 into portal circulation). This estimate was used to demonstrate that metabolism but not absorption was the reason behind the lack of exposure to GDC-0834.

Though the focus here has been the clinical utility of this methodology in early clinical studies, the preclinical studies also confirmed its usefulness. This correlation between measured F and F_cal was robust using measured V_ss (Table 1). When the dog volume of distribution was calculated by allometric scaling from the V_ss’s of mouse and rat, the correlation was weaker (R² = 0.44) than that using the measured V_ss, nonetheless it is still significant (n = 44 and p < 0.001).

Table 1. Significant correlations between the logarithm (base 10) of %F_cal with the logarithm (base 10) of measured %F in mouse, rat and dog.

Species		Number of data points	Correlation coefficient R^2	F statistic (Probability for the F value if not correlated)	Linear regression fit
					Slope	Intercept
Rat		896	0.75	2672 (p < 0.001)	0.77	0.64
Mouse		519	0.66	1018 (p < 0.001)	0.64	0.80
Dog	Vss by measurement	85	0.73	227 (p < 0.001)	0.68	0.62
	Vss by allometric scaling from mouse & rat	44	0.44	33 (p < 0.001)	0.78	0.29

Conclusion

In summary, this work demonstrates an easy method to calculate the oral bioavailability when iv. data are not available. As such the usefulness of this method is valuable for getting a quick read on oral bioavailability once C_max’ for a given dose is obtained from Phase I study. Based on the theoretical and clinical studies, two conditions are prerequisites when using the F_cal method to estimate F for compounds. These prerequisite conditions can be listed as follows: fast absorption and slow elimination as shown in the simulations (k_a/k > 6); accurate prediction of V_ss’ as demonstrated in the marketed drugs. Based on these, F_cal is derived as a product of C_max’ and V_ss’ divided by the total administered dose. The degree of success of the F_cal method is dependent on the effectiveness of the prerequisite conditions. As a result, it can help to identify the need or not (like GDC-0834) for formulation fixes to improve oral exposure. The intent is to apply this concept to estimate oral bioavailability in early drug development to decide if we can optimize the formulation to improve the drug exposure. We do not advocate using the proposed method to replace iv. study for determination of absolute oral bioavailability.

Summary points

• A simple methodology to estimate oral bioavailability from Phase I clinical trials, which can be broadly phrased as ‘calculated bioavailability’ (F_cal).

• F_cal is estimated by obtaining the product of circulating maximal observed drug concentration (C_max’) and the estimated volume of distribution at steady state (V_ss’) followed by dividing this product by the administered dose (d).

• This methodology is very sensitive to the measured C_max’ and estimated V_ss’.

• This methodology was examined in 35 marketed drugs. When the F_cal method was used and V_ss’ was determined by allometric scaling, good correlation was observed between measured F and F_cal provided that the allometric exponents were between 0.9 and 1.1.

• When examined in preclinical species (mouse (n = 519), rat (n = 986) and dog (n = 85)), robust correlations were observed from all the three species tested.

• For best prediction, two prerequisite conditions can be listed as follows: fast absorption and slow elimination as shown in the simulations (k_a/k > 6); accurate prediction of V_ss’ as demonstrated in the marketed drugs.

• The intent of F_cal is to apply this concept to estimate oral bioavailability in early drug development to decide if we can optimize the formulation to improve the drug exposure.

• We do not advocate using the proposed method to replace intravenous study for determination of absolute oral bioavailability.

Acknowledgements

We would like to thank the staff in the Departments of Drug Metabolism and Pharmacokinetics and Clinical Pharmacology for their contributions in generating data for this study. The clinical trials of vismodegib and GDC-0834 were funded by Genentech, Inc.

Financial & competing interests disclosure

All the authors are employees of Genentech, Inc. The clinical trials of vismodegib and GDC-0834 were funded by Genentech, Inc. The authors have no other relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript apart from those disclosed.

No writing assistance was utilized in the production of this manuscript.

Additional information

Funding

All the authors are employees of Genentech, Inc. The clinical trials of vismodegib and GDC-0834 were funded by Genentech, Inc. The authors have no other relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript apart from those disclosed. No writing assistance was utilized in the production of this manuscript.